Safety of Chemical Batch Reactors and Storage Tanks

7/23/2019 Safety of Chemical Batch Reactors and Storage Tanks

http://slidepdf.com/reader/full/safety-of-chemical-batch-reactors-and-storage-tanks 1/455

EURO

courses

RELIABILITY AND RISK ANALYSIS

VOLUME 1

Safety of

Chemical Batch Reactors

and Storage Tanks

edited by

A. Benuzzi a n d J. M . Za ldiva r

Kluwer Academic Publishers

for the Comm ission of the European Comm unities









Safety of Chemical Batch Reactors and Storage Tanks



EURO

C O U R S E S

A series devoted to the publication of courses and educational seminars

organized by the Joint Research Centre Ispra, as part of its education and

training program .

Published for the Commission of the European Communities, Directorate-

General Telecommunications, Information Industries and Innovation,

Scientific and Technical C omm unications Service.

The EUROCOURSES consist of the following subseries:

- Advanced Scientific Techniques

- Chem ical and Environmental Science

- Energy Systems and Technology

- Environmental Impact Assessment

- Health Physics and Radiation Protection

- Com puter and Information Science

- Mechanical and Materials Science

- Nuclear Science and Technology

- Reliability and Risk Analysis

- Remote Sensing

- Technological Innovation

RELIABILITY AND RISK ANALYSIS

Volume 1

The publisher will accept continuation orders for this series which may be cancelled at any

time and which provide for automatic billing and shipping of each title in the series upon

publication. Please w rite for d etails.



Safety of Chemical

Batch Reactors

and Storage Tanks

Edited by

A. Benuzzi

and

J. M. Zaldivar

Commission of

th e

European Communit ies,

Joint Re search Ce ntre ,

Inst itute for Safety R e search , Ispra, I taly

PARI EURCP B'.bi.V.H.

L J

f f

KLUWER ACADEMIC PUBLISHERS

DORDRECHT / BOSTON / LONDON



Based on the lectures given during the Eurocourse on

'Safety of Chemical Batch Reactors and Storage Tanks '

held at the Joint Research Centre Ispra, Italy, April 1 5-1 9,1 99 1

ISBN 0-7923-1233-3

Publication arrangements by

Commission of the European Communities

Directorate-General Telecom mun ications, Information Industries and Innova tion,

Scientific and Technical Communications Service, Luxembourg

EUR 13457

©1 99 1 ECSC, EEC, EAEC, Brussels and Luxembourg

LEGAL NOTICE

Neither the Com mission of the European Com munities nor any person acting on behalf of the

Com mission is responsible for the use which m ight be made of the following information.

Published by Kluwer Academic Publishers,

P.O. Box 17, 3300 AA Dordrecht, The Netherlands.

Kluwer Academic Publishers incorporates the publishing programm es of

D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press.

Sold and distributed in the

U.S.A.

and Canada

by Kluwer Academic Publishers,

101 Philip Drive, Norwell, MA 02061, U.S.A.

In all other cou ntries, sold and distributed

by Kluwer Academic Publishers Group,

P.O. Box 32 2, 3300 AH D ordrecht, The Netherlands.

Printe d on acid-free paper

All Rights Reserved

No part of the material protected by this copyright notice may be reproduced or

utilized in any form or by any mean s, electronic or mech anical,

Including photoc opying, recording or by any information storage and

retrieval system , without written permission from the copyright ow ner.

Printed in the Netherlands



C O N T E N T S

1. Incidents in the chem ical industry due to therma l-runaw ay chemica l reactions

J. A. Barton and P. F. Nolan 1

2.

Fundam entals on Runaw ay Reactions: prevention and protection measures

J.M.ZaldivarComenges 19

3 .

Controlling Run-away Reaction hazards within the framework of the "SE VE SO -

Directive"

G. Drogaris

49

4. Labo ratory testing proced ures

P. Cardillo 79

5. Equ ipmen t characterisation

C. Barcons I Rises 99

6. M odelling and simulation for safety analysis of batch reactors and storage tanks

H. J. Hernandez 125

7. Risk assessment methodologies

N. Labath

147

8. Control technique s

C. Moussas

161

9. Early on-line detection of Runaw ay initiation

J. M. Zaldivar Comenges 201

10. Emergency relief system sizing: in-vessel fluid flows

J. Duffield 227

11. Emergency relief system sizing: vent line fluid flows

A.

Benuzzi 255

12 . Vent sizing for tempered vapor systems

J. C. Leung

285

13 .

Vent sizing for gassy and hybrid systems

J. C. Leung 299

14.

Calorimetry for Emergency Relief Systems design

J.L.Gustin 311

15 .

Treatment of relieved fluids

J. Singh 355

16. Runaway Reactions: a case study

T.J.Snee 371

17.

Reaction hazard evaluation

P.F.Nolan 391

18.

Outline of the modelling activities in venting

A.

N. Skouloudis 409





INCIDENTS IN THE CHEMICAL INDUSTRY DUE TO THERMAL-RUNAWAY CHEMICAL

REACT

,

I«jNS

BARTON, J.A. (1) and NOLAN, P.F. (2)

1) Health and Safety Executive, Research and laboratory Services

Division, Harpur

Hill,

Buxton, SKL7 9JN

2) Department of Chemical Engineering, South Bank Polytechnic, London,

SE1 OAA

Introduction

Thermal-"runaway" is characterised by progressive increases in rate of

heat generation, temperature and pressure (the latter generally caused by

components in the reaction mass vapourising and/or decomposing to yield

gaseous products at the elevated temperatures involved).

Thermal-runaway begins when the heat generated by a reaction exceeds the

heat removal capabilities of the hardware in which the reaction is being

carried out. At first the accumulated heat produces a gradual temperature

rise in the reaction mass which causes an increase in the reaction rate.

This self-accelerating process may finally lead to an explosion. The

problem is that an increase in temperature has a linear effect upon the

rate of heat transfer but has an exponential effect on the rate of

reaction and subsequently on the rate of heat generation.

Runaway is a major problem in unsteady-state batch reactors, since the

task of specifying the design, operation and control of an apparently

simple kettle reactor with stirrer, heating/cooling coils, possibly reflux

facilities,

and emergency relief venting can be difficult, if all the

time-dependent parameters are considered. It is a task which requires a

systematic approach. The problem is often compounded because batch

reactors are frequently multi-purpose rather than dedicated to one

process. Due to economic factors a batch reactor may be used to carry out

many different chemical processes, and it is necessary to ensure that the

heat of reaction does not exceed the existing cooling capacity of the

vessel for each reaction.

A.

Benuzzi and

J.

M. Zaldivar (eds.). Safety of Chemical Batch Reactors a nd Storage Tanks, 1—17.

© 1991

ECSC.

EEC. EAEC.

Brussels

and

Luxembourg. Printed in the

Netherlands.



Barton and Nolan (1,2) have previously examined case histories of

industrial incidents in batch reactors involving thermal-runaway chemical

reactions of the type A + B — > products (incidents involving thermal

stability problems with single components are not included) to determine

any apparent trends with a view to drawing general lessons from previous

mistakes,

having regard in particular to lack of knowledge of the process

chemistry, faulty design, e.g. scale-up procedures, and deviations from

operating procedures. This present paper updates the information from

that previously given and now covers the period 1962-1987.

The present analysis classifies the incidents in terms of:

(a) chemical processes;

(b) prime causes;

(c) industries involved.

Analysis of Incidents

Between 1962 and 1987, 189 incidents which occurred in industrial batch

reactors were reported to HM Factory Inspectorate (Health and Safety

Executive).

The information available on many of the incidents was not as

full as might have been wished. Even had the information on each incident

been complete the data presented below would have no statistical

significance because of the uncertainties of under reporting. Furthermore

it is not possible to say, for instance, that a particular process has a

poor record in comparison with others, because to be able to do so it

would be necessary to place the figures in context taking into account

such factors as numbers of reactors, production tonnages, unreported near

miss data, operating standards etc.

THE CHEMICAL PROCESSES

Eleven principal chemical processes were involved in the incidents as

shown in Table 1.

It was not possible to identify the chemical processes being carried out

in all of the 189 incidents, due to lack of information. However, 134

incidents could be classified.

From Table 1 it is apparent that polymerisation reactions featured in by

far the most incidents, followed by nitration, sulphonation and hydrolysis

reactions. Of the polymerisation reactions 20% (13) involved phenol-

formaldehyde condensations. In view of the number of incidents with

phenol-formaldehyde resin production the British Plastics Federation (BPF)

came forward with an exemplary approach to the problem in its publication

"Guidance for the safe production of phenolic resins" (3 ). Although the



3

BPF document is specific to phenolic resins the general approach adopted

could be used elsewhere. It is perhaps significant that no phenol-

formaldehyde polymerisation incidents have been reported over the last few

years.

THE PRIME CAUSES

The prime causes which led to overheating and eventual thermal-runaway for

169 of the incidents (20 were without sufficient details for the

assignment of a prime cause) are classified below under the main

headings:

(a) process chemistry;

(b) plant design and operation.

(a) PROCESS CHEMISTRY

(i)

Reaction Chemistry/thermochemistry

Thirty-four of the incidents

are attributable to little or no study or research or development work

being done beforehand, with the result:

no appreciation of the heat of reaction on which

to base cooling requirements for the reactor

(scale-up) 8

- the product mixture decomposed 7

unstable and shock sensitive by-products

were produced 6

- the reaction was carried out en-masse (i.e. all

reagents added simultaneously at start) whereas

staged addition would have been appropriate 4

unintended oxidation occurred (instead of

nitration) 3

the reaction was carried out with reactants at

too high a concentration 2

the reaction was carried out at too low a

temperature resulting in accumulation of reactants

and subsequent en-masse reaction 1

the reaction accelerated due to:



- catalysis by materials of construction of

the reactor 1

- unsuspected autocatalysis 1

a phase change of the product (to the vapour

state) occurred 1

34 (20%)

(ii)

Raw Material Quality Control

Fifteen of the incidents are

attributable to the use of out of specification materials:

- water contamination 9

other impurities 5

changed specification; a moderator should

have been used on start of new supply but this

change was not recorded in instructions 1

15 (9%)

(b) FIANT DESIGJ AND OPERATION

(i) Temperature Control

failure to control steam pressure or time of

application (includes one case of improper use

of steam to unblock vessel out-let, causing

decomposition of product) 6

- probe wrongly positioned to monitor reaction

temperature 6

failure of temperature control system (leading

for example, to cooling water being automatically

shut off; heating oil overheating; steam valve

remaining open) 7

loss of cooling water (not monitored)

(reactor 3 ; condenser 2) 5

error in manual reading of thermometer or

chart recorder 4



failure

to

provide sufficient separation

distance between reactor

and

adjacent

hot

plant

2

too rapid heating

at

reaction initiation

1

thermocouples coated with polymer giving

slow response

1

32

(19%)

(ii)

Agitation

inadequate stirrer specification

-

mechanical failure,

for

example, stirrer

blades sheared

off due to

solidification

of

the "heel"

from previous batch;

although

an

overload switch

was

fitted

the

motor

was too

powerful

for the

paddle

securing bolts

operator either failed

to

switch

on

agitator

or switched

it on too

late,

the

nett result

was en-masse reaction

6

loss

of

power supply

2

agitator stopped

by

operator

to

make

an

addition (localised high concentration

caused liquor

to

boil

and

erupt)

2

17

(10%)

(iii) Mischarging of Reactants

overcharging (includes

2

cases

of

overcharging

a

catalyst

and one

where

the

metering device

was

faulty.

In 5 cases, the

total volume

of the

reaction mixture

was

incorrect

and the

cooling capacity

of the

reactor

was

inadequate.

In the

other

6

cases

the

reaction mixture contained

the

wrong proportions

of

reactants)

12



too rapid addition (including

a

catalyst)

8

wrong sequence

of

addition

4

wrong material

5

vindercharging

3

improper control (use

of

hose-pipe)

2

addition

too

slow

1

(v)

Human

Factors

-

operator failed

to

follow written instructions

35

(21%)

(iv)

Maintenance

-

equipment leaks (scrubber

1;

valves

3 ;

cooling pipes/jacket

3 ) 7

blockages (vent pipes

2;

transfer pipes

3 ;

separator 1)

6

condenser solvent locked

due to

valve

in

reflux return line being closed following

shut-down

for

maintenance

3

residues from previous batch

2

water

in

transfer lines (including

one

case

of water siphoning from quench tank)

3

in situ replacement

of

closures (cracked

sight-glass

1;

cover plate 1) during

course

of

reaction

2

unauthorised modifications

1

-

loss

of

instrument

air

supply

1

25

(15%)



- product run off before completion 3

deviations caused by poor communications at

times of staff changeover (change of shift,

holiday, sickness) 3

pTwûct filtered at wrong stage of process 1

11 (6%)

INDUSTRIES INVOLVED

Batch reactors are ubiquitous in the chemical industry due to their

convenience and flexibility. The pattern of incidents, however, shows, as

might be expected, a preponderance to certain specific industries (Table

2 ) .

RECENT INCIDENTS

The analysis of Barton and Nolan (2) covered the period 1962-1984. The

data covering 1985, 1986 and 1987 can be summarised:-

A total of 47 incidents were reported, 3 in 1985, 16 in 1986 and 28 in

1987. Either there was a real upsurge in incidents in 1986 and 1987,

which seems unlikely, or, which seems more probable, the impact of the new

reporting regulations (Reporting of Injuries, Diseases and Dangerous

Occurrences Regulations 1985 [RIDDOR]) has resulted in improved

reporting.

The prime causes (3 incidents in 1987 were without sufficient information

for the assignment of a cause) of the incidents follow the familiar

pattern:

8 (18%) (ca. average) were due to little or no study or research or

development work being done before scaling up and going into production.

14 (32%) (well above the average) were due to mischarging of reactants of

which 4 were due to overcharging (1 catalyst); 4 were due to addition of

the wrong material, e.g. drums of wrong material were stored with drums of

one of the reactants and were charged in error; 3 to too rapid addition; 1

to wrong sequence of addition; 1 to undercharging of a reactant and 1 to

improper control (use of a hosepipe).

4 (9%) were due to temperature control failures.



5 (11%) were due to the presence of impurities, particularly water

3 ) ,

in

raw materials.

5 (11%) were due to problems with agitation, 2 because the agitator had

not been switched on; 2 because the agitator was switched on late once the

error was realised and 1 because of mechanical failure.

6 (14%) were maintenance related; 1 was due to a blocked transfer pipe; 1

to a blocked separator; 1 to unauthorised plant modification; 1 to loss of

instrument air supply; 1 to a leaking cooling jacket and 1 to an

improperly secured cover plate; and

in 2 (5%) the operators failed to follow written instructions; in 1 they

failed to separate an aqueous phase from an organic phase before

proceeding and in the other, filtration was carried out at the wrong stage

of the process.

13 of the incidents occurred in the fine and intermediate organics

industry; 7 in the plastics, rubber and resin industry; 13 in the heavy

organics industry; 4 in the pharmaceuticals industry; 2 in the dyestuffs

industry and 1 in the metal processing indusry.

Of the chemical processes involved polymerisations accounted for 17

incidents. The polymerisations involved vinyl acetate; vinyl chloride

9 ) ;

polyester resins (2); butadiene/acrylonitrile; hydroxyethyl

methacrylate; and urea-formaldehyde (due to contamination of the urea with

ammonium

nitrate).

Other chemical processes involved were sulphonation (4 ); amination (3 );

nitration (2); halogenation (2); diazotisation (2); alkylation (1);

esterification (1) and hydrolysis (1).

9 persons were injured (8 operators and 1 fireman). In one incident

(runaway nitration) 20 people off-site were affected by acid-spray.

INJURIES AND DAMAGE

The result of the runaway incidents ranged from a simple foam-over of the

reaction mass to a substantial increase in temperature and pressure

leading to violent loss of containment, with in some instances the release

of large quantities (up to several tonnes) of flammable and/or toxic

materials into the environment. In a few cases where flammable materials

were released a fire and/or a secondary explosion followed. As a result 4

fatalities and 82 injuries (as defined in relevant health and safety

legislation (4)) occurred in the period 1962-1987.



The injuries to operators were due, for example, to splashing by hot

liquors or the effects of blast, missiles or toxic fumes. They generally

occurred when the operators were attempting to regain control of a

reaction. Eleven injuries, one of which was fatal, occurred when manual

additions of ingredients were being made to the reactor and the reaction

mixture then erupted over the operator.

Plaiic usually suffered down-time at least and/or it was more or less

seriously damaged as also, in some cases, was the building housing the

plant.

In a small

number of cases, surrounding areas both on- and off-site were put at risk.

In one incident 20 people off-site were affected by acid spray.

General Lessons

The analysis indicates that incidents occur due to: -

(i) a basic lack of proper understanding of the process chemistry and

thermochemistry;

(ii) inadequate engineering design for heat transfer;

(iii) inadequate control systems and safety back-up systems (including

venting);

and

(iv) inadequate operational procedures, including training.

In order to deal with hazards it is first necessary to identify them, then

decide how likely they are to occur, and how serious the consequences

would be. A formal system should be used to study the plant, and identify

and record process hazards (see Appendix 1 ) . This area is further

developed by other speakers at the symposium. It is apparent from the

analysis of incidents that this is still not common practice for batch

reactors.

It is axiomatic that in order to avoid conditions for runaway arising it

is necessary to have knowledge of the chemistry and associated

thermochemistry of the desired reaction and potential side reactions and

also of the thermal stability and physical properties of reactants,

intermediates and products.

Some of this necessary information can be obtained from the literature or

from computer-based modelling of reactions. The thermal behaviour

characteristics of reactants, products and occasionally reaction



10

intermediates/mixtures can be found using laboratory techniques. A

variety of laboratory techniques are available for use to acquire this

knowledge. The Association of the British RTarmaceutical Industry

developed a laboratory scheme (5) for screening new products and

processes. More sophisticated techniques include use of accelerating rate

calorimetry (6) or other adiabatic calorimetry systems. The study of

reaction mixtures is ideally carried out by using a heat flow calorimeter

7 ) . These techniques will be described in more detail by other speakers

at the Symposium. A thermal hazards assessment strategy is discussed

below.

It is also possible to obtain information relating to changes in heat

transfer coefficients and control parameters, due to changes in properties

such as viscosity and specific heat as the reaction proceeds, using heat

flow calorimetry (8 ).

The laboratory studies can provide data on the onset temperature of and

magnitude of exotherms. The detected onset of an exotherm is scale

dependent i.e. the larger the reaction

mass,

the lower the onset

temperature. From such information and a thorough examination of previous

plant operating experience, it is possible to set safety margins and hence

select the operating temperature for the given reactor charge size.

The ensured quality of the raw materials is vital to safe operation. The

analysis shows that the presence of impurities, water in particular,

appears to present a problem. The presence of water can cause additional

heat evolution, raising the total heat output above the reactor cooling

capacity, leading to temperature rise and increased rate of reaction

causing subsequent further increases in heat generation.

With reference to the prime causes relating to plant design and operation,

it is obvious that heat removal rate is an important criterion for batch

reactor design, to which adequate agitation, eg stirrer speed, is related,

particularly with regard to scale-up from laboratory data. Numerous

correlations exist for heat transfer in agitated, jacketed vessels (9,10)

and it is possible to scale-up data on inside film heat transfer

coefficients from heat flow reaction calorimeters to industrial size batch

reactor plant (8 ). It is imperative that the cooling capacity of the

designed plant can cope with the heat generation from all the chemical

processes envisaged.

It is unusual for batch reactor plant to be designed to resist any

calculated pressure rise resulting from a runaway reaction. Ideally, of

course, the objective should be for process control to eliminate any

runaway potential. However, pressure relieving of the reactor or dumping

the contents or quenching the reaction should be considered in case of

emergency. If pressure relief venting is considered, attention must be



paid to the nature of the material likely to be released, e.g. its

toxicity and/or flammability, and it may be necessary to install catchpots

or other means of containment or entrainment to capture the released

material (11). The vent sizing of reactors has been advanced recently by

the work of the AIChE's Design Institute for Emergency Relief Systems

(DIERS) (12). This work has included the development of two-phase flow

equations: and the 'Satire' computer code for vent sizing of realistic

releases. For reactions not previously investigated or adequately covered

in the literature, the DIERS programme also produced a laboratory-scale

apparatus to provide the necessary information for input into the

developed models. Vent sizing for reactors is covered by other speakers

at the Symposium.

Many of the incidents resulted from the mischarging of reactants,

inadequate temperature control and poorly defined operating procedures and

operator training. The safe operation of plant can be aided by the use of

computer or other automatic control techniques; however, two of the

incidents in this analysis occurred due to the operator over-riding the

alarm signals.

Assessment Strategy

Runaway inside a batch reactor is characterised by the loss of thermal

control.

The purpose of a thermal hazards assessment strategy is to:

(a) identify materials and unit processes which are potentially

hazardous;

(b) quantify the hazards which arise from these with a rujiimum of

testing.

It involves a sequential approach, which cavers thermochemical evaluation,

reaction calorimetry and the effects caused by scale, accumulation and

cooling/agitator failure.

A typical strategy is shown in Figure 1 (13,14). This is discussed more

fully in the references given.

The thermochemical evaluation consists of data on the thermal stability,

heat of reaction and total heat capacity of reactants of the desired

reaction, the expected adiabatic temperature rise and any general process

hazards, e.g. flammability and toxicity of reactants.



12

Reaction calorimetry, either in the form of heat flow or adiabatic Dewar-

based calorimeters allows the measurement of many process variables

(agitation, heating, and cooling requirements) and reaction

characteristics (kinetics, reaction enthalpy, heat release rates and

reactants

1

heat capacity) under known environmental heat loss conditions.

The reaction calorimetry stage of the assessment also allows for the

determination of adiabatic temperature rise and gas generation potential.

The heat release per unit mass or unit volume of reactants can be used

with the previously established plant cooling capacity to ascertain safety

margins for safe operation. It is also usually necessary to consider the

potential results following the failure of agitator and cooling systems,

along with the results from heat accumulation storage tests.

Conclusions

Despite the apparent knowledge which exists, the techniques which are

available and the commercial instruments on the market for the assessment

of potential runaway reactions, to aid process and plant design, control

and operation, incidents continue to occur due, in the main, to common

errors.

The hope is that more chemical manufacturers will introduce systematic

assessment procedures. A systematic approach should reduce the types of

common errors exemplified in the analysis. It is essential to have a

thorough understanding of the process chemistry and thermochemistry and

then to ensure adequate engineering design for heat transfer, adequate

control systems and safety back-up systems and adequate operational

procedures, including training.

An assessment strategy for chemical reaction hazards, has been outlined.

A need is perceived for coherent and concise guidance to be produced,

particularly for small and medium-sized companies, covering the areas of

thermal haz ards assessment, venting, and a formalised approach to process

control. HSE has now initiated, and in part, sponsored, the production of

a User Guide on safety in exothermic reactions by I Chem E. Other

sponsors have come from industry. The publication is being written by an

Industrial Fellow reporting to a Steering Committee. It will seek to

bring together information produced in the last few years on all aspects

of the subject, including thermal hazards assessment, process design, heat

transfer problems, process control, vent sizing and operator training. It

will not be a full text-book but should alert smaller to medium sized

companies to the problems in these areas and point out where to go for

further help and advice.



REFERENCES

1 Barton, J.A., and Nolan, P.F., April 198 4. Runaway reactions in

batch reactors, in: The protection of exothermic reactors and

pressurised storage vessels, I.Chem.E. Symp. Ser. 8 5, Chester.

2 Vclon, P.F., and Barton, J.A., 1987. Some lessons from thermal-

runaway incidents. Journal of Hazardous Materials 1 4 , 233 -239.

3 British Plastics Federation; 1980. Guidelines for the safe

production of phenolic resins. BPF Thermosetting Materials Group,

London.

4 Factories Act, 196 1; Notification of Accidents and Dangerous

Occurrences Regulations, 1980; Reporting of Injuries, Diseases and

Dangerous Occurrences Regulations, 1985.

5 Association of the British Pharmaceutical Industry; 198 2. Guidance

notes on chemical reaction hazards analysis. ABPI London.

6 Townsend, D.I., March 1981. Accelerating rate calorimetry, in:

Runaway reactions unstable products and combustible powders,

I.Chem.E. Symp. Ser. 6 8 , Chester.

7 Brogli, F., Giger, G., Randegger, H., and Regenass, W., March 1981.

Assessment of reaction hazards by means of a bench scale heat flow

calorimeter in: Runaway reactions, unstable products and combustible

powders, I.Chem.E. Symp. Ser. 6 8 , Chester.

8 Steele, C.H., Ph.D. thesis, Heat transfer characteristics and scale-

up under isothermal and reflux conditions in batch reactors (in

preparation).

South Bank Polytechnic.

9 Chapman, F.S., and Holland, F.A., 196 5. Heat transfer correlations

in jacketed vessels. Chem. Eng. Feb 15 175.

10 Chilton, C.H., Drew, T.B., and Jebens, R.H., 1944 . Heat transfer

coefficients in agitated vessels, Ind. Eng. Chem. 3 6 , 510 .

11 Burgoyne, J.H., June 198 7. Safe disposal of relief discharges.

I.Chem.E. Symp. Ser. 10 2, 201-213, UMIST, Manchester.

12 Fauske, H.K., 1985. Emergency relief system design. Chem. Eng.

Prog. 8 1, 8,

53-56.



14

13 Cronin, J.L., Nolan, P.F., and Barton, J.A., June 1987. A strategy

for thermal hazards assessment in batch chemical manufacturing.

I.Chem.E. Symp. Ser. 102, UMIST, Manchester.

14 Cronin, J.L., January 1987. A strategy for thermal hazard

assessment in batch chemical manufacture, Ph.D. thesis, CNAA (South

Bank Polytechnic).

15 KLetz, T.A., 1986. HAZOP & HAZAN - Notes on the identification and

assessment of hazards, I.Chem.E (Loss Prevention), Rugby.

16 The Chemicals Industries Associated Limited (Chemical Industry

Safety and Health Council of), 1977. A guide to hazard and

operability studies. CIA London.

17 Lees, F.P., 1980. Loss prevention in the process industries,

Butterworths.



FIGURE I ASSESSMENT STRATEGY

CHEMICAL REACTION HAZARDS

THERMOCHEMICAL

EVALUATION

magni tude & rate of

hea t r e l ease

DESIRED PROCESS

reac t ion temperature

addi t ion t imes

ma x imum ho ldu p t ime

operating procedures

REDEFINE

CONDITIO

MODEL PROCESS :

REACTION

CALORIMETRY

kinetics, heat release

gas generat ion

N

PROCESS DEVIATION

REACTION

CALORIMETRY

magn i tude o f e xo the rm ,

adiabat ic temperature

increase,

gas genera t ion

secondary reactions

produc t s tab i l i ty

residual cool ing

r e q u i r e m e n t

THERMAL

STABILITY OF

REACTION

GOMPONENTS

PLANT

(OPERATIONAL

DATA

cool ing capaci ty

cont ro l parameters

PLANT FAILURES

&MALOPERATIONS

IDENTIFIED DURING

PROCESS ANALYSIS

PROCEED TO

PILOT PLANT



16

Table 1

Number of incidents per specified chemical process

Chemical Process

Polymerisation

(including condensations)

Nitration

Sulphonation

Hydrolysis

Salt formation

Halogenation

(Chlorination and Bromination)

Alkylation using

Friedel and Crafts Synthesis

Amination

Diazotisation

Oxidation

Esterification

Number of Incidents

64

15

13

10

8

8

5

4

4

2

1

134

Table 2

Specific manufacturing industries, in which reported batch reactor

runaway incidents have occurred during the period 1962-1987

Manufacturing Industry

Fine and intermediate organics

Plastics, rubbers and resins

Heavy organics

Metallurgy and metal processing

Dyestuffs

Pharmaceuticals

Number of incidents

- including animal health products

Agricultural chemicals

Food and flavourings

Paint and varnish

Miscellaneous

51

41

20

13

13

13

5

5

5

23

189



17

APPENDIX 1

IDENTIFYING HAZARDS

Among the better known formal systems are 'Hazard and Operability Study

1

(HAZOP), used to identify hazards, and Hazard Analysis (HAZAN), used to

quantiry hazards (15,16).

Having identified a hazard it is still necessary to decide what to do

about it. Ways must be found to reduce the probability of a runaway

occurring.

Where consequences are judged to be severe, or where the causes giving

rise to the hazard are many or interrelated, it is recommended that a

'fault-tree' (17) is constructed, showing the way in which various events

or faults can give rise to a hazard. When constructed the tree can be

used to see where the most likely causes of an incident lie, and where

additional precautions can be introduced to minimise the risks.

For the most rigorous examination it is necessary to allocate

probabilities to each event in the fault tree, allowing the total

probability of the final event to be calculated (HAZAN).

Where companies are not able to carry out such examinations of their batch

processes alone, they can call on the services of consultant practitioners

to assist them.





FUNDAMENTALS ON RUNAWAY REACTIONS:

PREVENTION AND PROTECTION MEASURES

J .M . Z A L D I V A R C O M E N G E S

Com mission of the European Com munities

Joint Research Centre

Safety Technology Institute, Process Engineering Division

1-21020 Ispra(VA), Italy

ABSTRACT. The circumstances leading to accidents are often very complex but most of them

could have been foreseen by the use of laboratory tests, hazard analysis and chemical reaction

engineering technique s. In this paper, different approaches to imp rove the safety of chemical batch

processes and storage tanks will be studied, as well as emergency procedures to minimize the

effects of a thermal excursion of the reaction mixture. The objective is give a global vision of the

diversity of aspects that must be covered and the basic concepts to deal with them.

1.

Introduct ion

The rapid development of the Chemical Industry in the past decades has increased the complexity

of chemical plants, and the diversity of products. In parallel, there has been a corresponding

increase in the number of accidents and therefore, the quantity of human losses, material damages

and environment impact has augmented.

The study of accident case histories [1, 2] shows that the circumstances leading to accidents are

often very complex, involving human error, insufficient knowledge about the chemistry of the

process, poor training of the operator, inadequate instrumentation, etc. but it also shows, that the

accident probably could have been foreseen in a high percentage of the cases, by means of

laboratory tests, hazard analysis, and chemical reaction engineering techniques.

Loss of thermal control due to undesired or poorly controlled desired reactions, which can lead

to destruction and release of toxic materials, is a Chemical Engineering area, in which the main

contributions are to develop p rocess concep ts which prevent the loss of control of the reactions and

countermeasures to protect against runaway events. In any case, prevention and protection against

chemical reaction hazards is based on the understanding of the basic phenomena involved. In order

to achieve safety, the study of four different aspects is vital: the thermo-kinetic phenomena, the

physical and chemical properties of reagents and products, the equipment characteristics, and the

operating conditions.

In recent years, the search for inherent safety has been widely recommended [3]. A process is

inherently safe, in a rigurous sense, when no disturbance whatsover can cause an accident. In

practice, this is impossible to achieve. However, this concept should be an objective in process

design, since considerable reduction in the potential hazard can be reached at this stage, and even

19

A. Benuizi and J. M. Zaldivar (eds.). Safety of Chemical Batch Reactors a nd Storage Tanks,

19-47.

© 1991

ECSC.

EEC,

EAEC,

Brussels a nd Luxembourg. Printed in the Netherlands.



20

the effects of disturbed operating conditions such as cooling system malfunction or agitator

stoppage can be assessed.

A detailed analysis on the probability of an incident and its severity cannot be effected in the

absence of data with regard to the phenomena involved. Then, this is an important condition that

should be fulfilled.

In this paper different approaches to improve the safety of chemical processes will be studied,

as well as emergency procedures to minimize the effects of a thermal excursion. The objective is

give a global vision of the diversity of aspects that must be covered and the basic concepts to deal

with them.

2. Runaway React ions and Thermal Explosion Theory

Reaction systems in which the heat removed from the reaction mass to the surroundings becomes

less than the heat generated by chemical reaction, will increase their temperature, and due to the

exponential dependence of the reaction rate on it, will self-accelerate and "runaway".

That means, they will produce a large amount of heat in a very short time, developing

temperature and pressure excursions of the reacting mass with the consequent danger for people,

installations and environment.

In order to gain basic understanding of runaway reactions it is convenient to study the theory of

thermal explosion. This theory stems from ideas of van't Hoff (1884), but the first mathematical

formulation of conditions for ignition, or explosion, in a gaseous self-heating system was given by

Semenov [4] during the 1930s. Its most extensive development - theoretically and experimentally -

with the application to runaway reactions in solids and liquids has taken place during the past 50

years [5-8].

Thermal

f l o w

Heat generation

rate

©

Tempera tu re

Figure 1. Therm al diagram

Thermal explosion theory is concerned with the competition between heat generation by

exothermic reaction and heat removal by conduction, convection and/or radiation from the reaction

mass to the surroundings. The heat generation depends exponentially on temperature while the heat

loss depend s linearly (see figure 1). W hen the heat generation ex ceeds the heat remov al capacity,

runaway will occur. Intersections of the two curves represent steady states in which the rate of heat



21

loss equals the rate of heat generation in unit volume. The upper and lower steady states, of the

intersection between the sigmoid function of heat generation rate and heat removal rate in figure 1,

are stable to temperature perturbations while the intermediate one is not.

Acco rding to figure 1, in a thermal explosion it is possible to distinguish the following phases:

1/ Auto-thermal behaviour : Initially, the exothermic reaction is stable and under control. If for

some re°.iîi iiie reaction becomes unstable, that is, it can no longer be held in check by normal

process control, then the temperature will gradually begin to rise.

2/

Initiation: The reacting mass reaches a temperature in which the heat generated is higher than the

heat disipated by the cooling system. Hence, there is a self-heating behaviour with an acceleration

due to the exponential depend ence on temperature of the reaction rate.

3 /

A cc ele rat ion : The reacting mass rises until it reaches a temp erature that triggers off the

deco mp osition reactions , characterised by their high exoterm icity and gas produ ction. The

pressure of the system increases suddenly due to gas production and/or vigorous evaporation of

the liquid phase.

4/ Explosion or reaction auto-controlled: If the reactions continue to accelerate, the pressure

reaches the limit of wall resistance of reactor and an explosion occurs. Otherwise, the reaction rate

sometimes can be controlled by reactants consumption or by diffusion rates if the mass transfer

phenomena plays an important role (e.g. oxygen diffusion for combustion reactions).

Representing the evolution of temperature versus time (see figure 2), it is possible to define

different parts. At the first stage the system is stable and completely defined by the initial

cond itions. The second and third stages are the early stages of an instability and it may be possible

to restabilize the reaction by taking unusual actions such as emergency cooling, addition of a

supressant, and quenching. At some point in time, no such restabilization method can bring the

reaction back under control. The reaction is said to runaway. The only recourse to avoid pressure

buildu p and possible explosion is venting.

Temperature

PREVENTION PROTECTION

Figure 2. Temperature-time history of a runaway reaction.

t ime

Depen ding o n the type of reaction involved in the runaway initiation, it is possible to distinguish

between two different cases; the former is a production process which becames unstable, while the

later is an unw anted reaction that goes out of control:

a/ Loss of control of the desired reaction. The behaviour of the wanted reaction may become

unstable by different causes: high reactant accumulat ion, high sensi t ivi ty to impuri t ies,



22

degenerat ing operat ional condit ions (i .e . poor mixing, too high feed rates, wrong ini t ial

temp erature), failure of the cooling sy stem, etc.

b/

U ndesired reactions, fundamentally decomp osition and oxidation reactions that are unwanted.

The main possible causes are: reactive compounds mixed accidentally (e.g. cooling water that

penetrates into the reactor), the temperature of the reaction mass increases until decompositions are

triggered off, low heat dissipation capacity that even in very weakly active undesired reaction

systems -in the long term- runaway can be produced (i.e. storage tanks).

An other clasiffication on types of thermal explosion w as given by Bow es [9] in function of how

the unstable steady state point is reached. The first kind occurs at the point where the stable and

unstable steady states converge (see figures 4 and 5) and beyond which only high-temperatue

diffusion-co ntrolled steady states can exist, and the seco nd kind requires the self-heating system to

be forced through an unstable steady state with the aid of some other heat source for thermal

explosion to occur.

3 .

Safety measures against a runaway react ion

There are essentially two different types of measures and countermeasures that can be taken in

order to avoid runaway reactions depending on the region of the temperature-time history which

has been reached by the system (figure 3):

- Prevention mea sures: oriented to avoid situations that can lead to a runaway scenario.

- Protection measures: oriented to stop or to minimize the consequences of a thermal excursion

(region of abnormal behaviour).

/

O f f - l i n e ^

PREVENTION

On- l lne<

\

Calorimetric studies

Improving plant design

Analyt ical cr i ter ia

Simulat ion

New synthetic routes

- Instrumentation

- Improving control techniques

- Detection of initiation of runaway

s^ Simulation

-Full cooling

Stopping the '

r u n a w a y

P R O T E C T I O N

P r e s s u r e

^ Quenching'

rel ief

Add an inhibitor

Add cold liquid

Dump

C o n t a i n m e n t

Figure 3. List of the prevention and protection measures.



23

Clearly, the prevention measures are the most desirable ones because they do not affect the

integrity of desired products. These measures can be divided into off-line and on-line. The former

is part of the systematic process analysis before carrying out the process in the plant and aiming at

the obtention of basic data as a prerequisite for understanding the process behaviour and the risk

associated. The later tends to avoid the loss of control of the process when operating and to detect

possible deviations from the safe operation at an early stage.

The p

r

oicîion measures have as an objective to restabilize the control of the reactor, by means

of active emergency actions such as full cooling, fast injection of a supressant or dumping the

reactor contents; or at least to reduce the damage for people, installation and environment, by

means of passive measures such as containment. These measures are taken when the process is

outside of desired conditions, that means when the rate of heat generation has surpassed the rate of

heat remo val and the process is getting to a dangerou s state.

4. Prevent ion mea sures

4.1 . OFF-LINE AND ON-LINE TECHNIQUES

The logical way of obtaining knowledge about the process in order to prevent the potential hazard

of thermal explosion, begins with safety tests performed under laboratory conditions, using small

samples. Apart from basic data, such as physical properties and data related to process equipment,

the type of experimental information necessary for the evaluation of the thermal safety of a

chemical process, can be divided into different types [10].

The first type of tests to be performed concern the evaluation of the thermal stability of

substances and mixtures of substances. Typically, the mixed starting materials and samples from

intermediate process phases are investigated using mg. quantities (eg. DTA, Differential Thermal

Analysis).

For information on the desired reaction, heat flow reaction calorimetry has proved to be an

appropriate tool. The method provides information measured under conditions very similar to

industrial situations wh ich permits the gaining of know ledge about the process and the influence of

the operating conditions on its behaviour [11].

Other required experimental data concerns the heat evolution dynamics of secondary reactions.

Unwanted exothermic reactions can be characterised [12] by a small-scale thermal stability test

(e.g. DTA or DSC) using mg. quantities; adiabatic test (e.g. Dewar, ARC, PHI-TEC); isothermal

test; and test for deflagration. Exothermic secondary reactions are a particularly difficult safety

problem. When a reaction of this type has been established, it is important to determine the

temperature at which this reaction can be observed [10]. When this temperature is more or less the

same or lower than the desired reaction temperature, then it is practically impossible to run the

reaction safely and new operating conditions or synthetic routes must be studied.

The experimental data, obtained by the procedures described above, can be used to apply the

criteria and rules for the safe design of the process (see chapter 4.2) and/or to feed numerical

simulators. The advantage of the former is that it is easy and quick to apply but the information

obtained is relatively reduced when compared to numerical simulation. The advantages of using

mathematical modelling in hazard analysis evaluation are: to interpret the experimental data, to

reduce the num ber of expe rime nts need ed to establish an acceptable deg ree of und erstand ing , to

predict the dynamic behaviour of the reactor under conditions which are not easily achieved with

laboratory equipment and to perform the scale-up procedure [13].



24

Complementary to off-line techniques there are other types of procedures to prevent the potential

hazard. These are called on-line supervision techniques because they are carried out in real time.

Furthermore to improve instrumentation devices (ie. double sensors for important measures like

reaction mass temperature) and/or to improve control procedures (i.e. introduction of adaptive

strategic); an important on-line prevention measure consists on the detection of potential hazardous

situations with sufficient time in advance to take necessary countermeasures to avoid the thermal

excursion. This can also be done by means of some rule or criteria, or by means of model-based

techniques involving on-line numerical simulation.

4.2.

ANALYTICAL CRITERIA

The mathematical modelling of the behaviour of compounds or mixtures that can lead to runaway

reactions has followed two different approaches. On one side, the theory of thermal explosion

which have been applied in the fields of combustion and explosion. On the other side and in

parallel, the concepts developed by this theory has been used in Chemical Reaction Engineering in

orde r to assess potentially dangerou s situations and to design chemical reactors for safe o peration.

In this chapter several main points of the thermal explosion theory will be presented. From the

simplest approach (Semenov Theory) that treats a system with uniform reaction mass temperature

and without reactant consumption, to more advanced theories that describe the effects of non

uniform reactant distribution temperature. A more detailed treatment of this theory is available

elsewhere [6,9].

4.2 .1 .

Semenov Model. The Semenov model [4] assumes an uniform temperature distribution

within the reacting system. This is more or less the case of homogeneous systems in stirred tank

reactors.

The theory considers a pseudo zero order exothermic reaction (A —> R) with an Arrhenius type

rate equation given by

-E.

d C .

RT

— A = -r . = - k - C . = - A e

m

C

A

dt A A A

(1)

It is assumed that the effect of decreasing concentration is negligible, compared to that of

increasing temp erature (which is the case for highly energetic reactants), that implies, C

A

=

C

A Q

.

In this case, the heat generated by chemical reaction is given by the following expression,

-E,

RT

^Generated =

V

^

H

R '

r

A

=

V

m - A H

R

- A - e

m

-C

( 2 )

o

The rate of heat production is mainly governed by the exponential term: exp(-E,/RTj.

Semenov further supposed an uniform temperature of the surrounding T

e

, which is smaller than

the temp erature of the reacting m ass. Assum ing that there is a cooling jacket, the heat transfer to it -

in accordance with Newton's rule- is given by



25

^Removed

U-S (T

m

- T

e

)

(3)

Hen ce, the heat dissipated is a linear function of the temperature of the reacting m ass.

It is pos sible to repres ent the equ ation s in the so-ca lled therm al diagram and obtain three

different states, which are graphically show n in figure 4. They are subcritical, critical and

hypercritical states. In the straight line 1, there are two stationary states in which the heat

generation equals the heat removal rate, the points A and B. The operating point in the low

temp erature region is called stable and the other at higher tempe rature metas table. Any point

beyond the point B intersection represents a runaway condition. At any point below point B the

condition is stable.

There are two ways to affect the equilibrium:

a/ The coolant temperature can increase while the heat removed slope remains practically parallel.

If this occurs, the heat removed line moves parallel to itself until it becomes tangential to heat

generated line in the critical state and until there are no intersection points between both lines

(hypercritical states).

Therma

f low

Tempera tu re

c r c r ^

Figure 4. Semenov plot traces relationship for heat generation and removal. Influence of the

cooling temperature.

b/

The loss of heat transfer capacity, such as by the loss of cooling, or loss of mixing, will lower

the slope of the heat removed line, although the stationary cooling temperature remains the same

(see figure 5 ).

Thermal

f l ow

( U A ) > ( U A )

c r

(UA)< (UA)

c r

Tempera tu re



26

Figure 5. Semenov plot traces relationship for heat generation and removal. Influence of the heat

transfer parameter.

The situation for the critical state can be described mathematically by equations (4) and (5):

q

G

= % (4)

d(

h _

d

q

R

dT

m

d T

m

(5)

At Tm,.,. the heat generation rate equals to heat removal rate, eq. (6), and also, the slope of the

heat gen erated line equals to the slope of the heat removal rate, eq. (7).

RT

m

V

m

A H

R

A e "

b

C

A

= U - S ( T

m c r

- T

e

)

(6)

^ ^ V ^ -

6 =US

R T

m

C

r

(7)

Substituting equation (7) into equation (6) and rearranging:

T - a

m c r -

2

R

1±

1

_ 4 R T

e

(8)

Eq. (8) shows that an exothermic reaction can lead to a runaway condition only if E

a

> 4 R T

e

, and

also, that ignition phenomena may occur only as long as T

e

lies in the range 0<T

e

S E

a

/4R. Thus

the maximum value of

Tmc,.

occurs when T

e

=E

a

/4R and is given by Tmc

r

=E

a

/2R which implies at

very high temperatures (i.e. 10

3

to 10

4

K). Hence, it is necessary consider only the lower of the

two critical temperatures given by equation (8). Expanding the square root of eq. (8) in a binomial

T

A

m

(9)

with b„=2,2,4,10,28,. .



27

■ cr

RT?

T„+-—^

+

2

f 2 3\

v

E

> ;

' R T

+

5

F

V

a

J

(10)

and truncating the series after the second term [13]:

RT?

(11)

The Semenov number <> can be formulated:

rate of heat generation in a certain volume at T

e

(p=

rate of heat loss at a steady-state temperature excess AT=(T

m

-T

e

) by Newtonian cooling

< is a dimensionless heat flow number and can be defined in terms of the chemical and physical

properties

of

the

system.

For

a

zero-order

reaction

is:

AH„ A E . e

R T t

C ,

R

a

A .

US

RT?

(12)

It is possible to define

<J)

cr

by substituting th e critical condit ion, eq. (6), into eq. (12) and

rearranging as,

* « = ■

E

a

(Tn^- T

e

)

R

1 J_

T n w T ,

RT?

(13)

Developing

E

a

/RT

m

in

Taylor

series

for

T

m

=T

e

,

=

- ^ . _ ^ ( T

m

- T

e

)

+

^ i . ( T

m

- T

e

) . .. .

R T

m

R T

e RT?

(14)

RT:

truncating

the

series

after

the

second

term

(only

valid

if

E

a

>>RT

e

)

and

introducing

the

dimensionless

temperature

rise:



28

Q

_ E

a

( T

m

- T

e

)

RT?

(15)

it is possible to define

but substituting Tm,.

r

by the aproximate equation (11):

0

c r

= 1 and (|>

cr

= e"

1

(16)

(17)

that means,

a

steady state exists

if

<t><<t>cr and

a

thermal exp losion will occur

if

<|>><t>

cr

. The

conditions at criticality can b e en capsulated into the values of two d imensio nless groups : the

dimensionless Semenov number which equals to e

1

and the dimensionless temperature excess 0„

which is unity.

The advantage of the Semenov model is its simplicity. It gives a clear picture of the occurrence

of a critical state and of the influence of several parameters and variables such as activation energy,

heat of reaction, heat transfer coefficient and temperature. However, in order to describe other

important cases, i.e. unstirred self-heated reactants (for instance, storage tanks), the assumptions

of the Semenov model are not valid and other approaches must be employed.

4.2.2.

Frank-Kamenestkii Model.

The Frank-Kam enetski i model assumes

a

non-uniform

temperature (T

m

) distribution as a function of an spatial variable [15] and it is based upon the

Fourier heat transfer equ ation for the conduction of heat in an isotropic me dium :

5T„

5 t C

Pn

1

f 2

5T,

n

r

5x

2

m G " T

m

5x

5>

ÂH,r

:

i= l

(18)

where the geometric symetry is defined by o as , a = 0,1,2 for infinite slab, infinite cylinder and

sphere, respectively.

Then , for a zero-order reaction:

8T„

5t

C

Pn

1

r

5

2

T

m

+ c

5T

m

^

8x

2

x

5x

- A H

D

A e

R T m

C

A

R A„

(19)

with boundary conditions:

T

m

= T„ at x=x

n



29

and

'm

d x

= 0 at x= 0

If dimensionless quantities and approximation given by equation (14) are introduced, eq. (19)

may K transformed into:

, 2 ,

'

9

5 9

=

j 5 _ e

+

J l 5 e

+

5 e l

1 + E e

; (20)

5x 6z

2 z

5z

with boundaiy conditions:

0=0 a t z= l

and

4^-=0 at z=0

dz

wh ere e is the dim ension less amb ient tem perature, x is the dimensio nless time, and z is the

dimensionless d istance from the centre :

e = ^ (21)

1 =

Xm t

(22)

Pm Cp

m

X

Q

z f (23)

x

o

Frank-Kamenetskii was the first to solve a simplified form of equation (20) for stationary state

(d9/dt = 0) and assuming that e< <l and 0 is not large:

d e

+

j r j d i

=

_ 5 e

9

( 2 4 )

d z

2 z

dz

where 5 is the dimensionless heat flow, called Frank-Kamenestkii number, that can be formulated

as,



30

ra te of heat genera t ion in a given vo lume at T

e

5

=

rate of conduc t ive hea t loss at a steady-sta te t empera tu re excess (T -T

e

)

where Tm,, refers to th e temperature in th e centre. For a zero-order reaction this number can be

defined as ,

-E

a

A H

R

E

a

x

2

0

A e

R T

' C

A

5 =

_ _

\

(25)

^ .

m

R T

e

As opposed to the Semenov model where the heat resistance only occurs within the substance,

which

means

that

this

model

results

in

a

temperature

gradient

in

th e

substance

without

a

temperature difference across th e surface of th e reactant. For a symetrically heated system th e

temperature gradient in the centre of reacting mass is assumed to be zero, which also means that

the maximum temperature occurs in the centre.

4.2.3.

Thomas Model. The Frank-Kamenetskii model assumes that the reactant temperature equals

to the surroundings at the wall. Apart from the thermal resistance to heat flow due to finite thermal

conductivity,

Thomas

(16)

considered

the

case

where

there

is

heat

exchange

with

the

surroundings

following Newton's law. In fact, th e Thomas model is th e more general and it is possible to derive

the Semenov and Frank-Kamenetskii models as extreme cases.

The

Thomas

model

is

described

by

eq .

(18)

with

boundary

conditions:

■ ^ m l

' d T

m

dx

= U (T -T

e

)

X=X

^ 5 1 = 0 at x= 0

dx

where Tm,, refers to the temperature of the reacting mass at the surface.

Introducing

th e

dimensionless

numbers ,

it

is

possible

to

obtain

eq.

(20)

with

boundary

conditions:

_ d 0

=

B i e „ atz=±l whena = 0

dz °

at z= 1 when a = 1 or 2

^ i = 0 whenz=0

dz



31

where 9

0

is the dimensionless tem perature rise at the surface and Bi is the Biot num ber, that can be

formulated as,

heat t ransfer reasistance of react ing mass

Bi =

heat t ransfer resistance at the surface (boundary)

and hence,

B i = ^-± (26)

The relationship between the theories of Semen ov, Frank-Kamen etskii and Thom as can be shown

by function of the Biot number. The Semenov and Frank-Kamenetskii models are two extreme

cases of Thom as theory [5].

a) Bi « 1 b) Bi => 1 c) Bi » 1

Figure 6. Temperature profile in staedy-state at critical conditions as a function of Biot number.

Thomas solved eq. (23) with the boundary conditions gived in (26). The results for

critical values of 5 and 6 as a function of the Biot number are given in figure 7.

When Bi

—*

0 (Semenov Model) then,

( o + l ^Bi

c r

e

If

Bi—>

<*> (Frank-Kamenetskii model) the critical conditions are:



32

{

.8S

2.0

3.3

and 0„

■{

.19

1.39

1.61

for

o=

0 =

G =

0

1

2

(28)

2.5

0.5

pr

s

sphe re

s ^

cyl inder

slab

1

Bi

->

°o

5 ^ 3 . 3 2

Bi

- > ~

Bi

- >

M

6

->

0.88

1

e„

-

Bi

15

2.0

C

1.0

0

9

C

- > 1 . 6 1

_ ^ I 7 r , 3 9

■ 9 ^ 1 . 1 9

1

r 1

1 1 1

sphe re

cyl inder

slab

i

sphere

s lab

Bi

a)

The

critical

Frank-Kamenetskii

number

b)

The

critical

dimensionless

temperatures

9

c

(centre)

and

5

C

as function of the Biot number e

0

(surface) as functions of the Biot number.

Figure 7. Critical conditions as a function of Biot number [4].

4.3.

THE CHEMICAL REACTION ENGINEERING APPROACH

In th e last years batch and semibatch operations have become more popular due to their versatility

which

allows

the

obtention

of

special

chemicals

-

with

very

good

yields

-

in

small

amounts

(when

compared to those of continuous processes), and permits a rapid change from one process to other

with minor modifications.

However , th e study of accident case histories [1 ] shows that batch units are usually more

frequently involved in accidents (57% of cases) than continuous process plants (about 11% of

accidents).

These

results

ar e

not

surprising

because

batch

processes

are

usually

very

complex,

with

strongly nonlinear dynamics and with time-varying parameters. In a batch cycle there is no steady

state and therefore, batch operation requires continuous corrections and decisions to be made by

th e operator. Moreover , due to th e small production levels and th e variety of processes, the

understanding of reactor dynamic behaviour is usually not economically justified.

Consequent ly , th e optimization of such processes should take into account tw o different

aspects: performance and safety. From the performance point of view, the optimal process design

must allow the manufacture of products with the desired specifications in the minimum amount of

time and with low operating costs. From the safety point of view, optimum process desing must

significantly reduce the risk of thermal runaway, avoiding intermediate accumulation of hazardous

compounds ,

and

reducing

th e

effects

of

cooling

system

malfunction

or

agitation

stoppage.



33

Obviously, the ideal situations would be those in which the process is inherently safe [3], that

means, w here no disturbances, whatsoever, can cause an incident.

Hugo, and Steinbach have determined some safety rules for assessing conditions under which

batch or semibatch processes cannot be carried out, and for selecting safe operating conditions,

that have been accepted as practical guidelines by Westerterp and co-workers [26]. In the next

chapter some of these criteria will be reviewed, but a more detailed treatment can be found

elsewhere [17,19-23,26] .

4.3.1.

Batch and Semi-Batch Processes. Two different discontinuous operating modes are usually

carried o ut: batch and sem ibatch. In the first case, the reactor is charged with all reagents, solvents

and catalyst. In the second case, only a part of the reagents is present from the beginning, and the

other part (a reagent or a catalyst) is added.

Reaction vessels for batch operation are normally provided w ith standard cooling/heating jackets

and/or internal coils, a stirrer, a condenser and, for semibatch operation, a feeding system. The

temperature development is controlled by means of removing the heat generated by exothermic

chemical reactions through a cooled heat transfer fluid that circulates in the jacket or in the case of

working at the boiling point through the removal of heat by evaporation by means of a condenser.

For strongly exotherm ic reactions, the heat removed capacity may be too small to keep the reacting

mass at the required reaction temperature, in the case of batch operation, and then the heat

generated by chemical reaction has to be reduced. This can be accomplished by adding one of the

reagents during a certain period of time (semibatch). That means, some additional control of the

reacting mas s behaviou r can be obtained regulating the metering rate.

Different phases [17] can be differentiated in a batch process:

- Phase of heating: The reactor is charged at the starting temperature Tm„ and the reaction starts. If

the reaction rate is suficiently high, this phase is performed in nearly adiabatic conditions (with the

heating/cooling system switched off),while if the reaction rate is not considerable at the starting

temperature, the content of the reactor is heating following a temperature ramp.

Temperature Temperature

Phase of

cooling

/

T i m e

u /

a/ b /

Figure 8. Exam ple of different tactics for cooled batch or semibatch processes, a/ Isothermal

operating mode (T con stan t), b/ Isoperibolic operating mode (T

c

^constant).

Time

- Phase of cooling: When the reacting mass reaches a pre-selected temperature, T„ cooling is

started. After a certain period of time the maximum temperature , T m „ „ is attained. There are

mainly two different operating modes: isothermal or isoperibolic. In the first case, the temperature



34

of the reaction medium is kept constant by regulating the jacket temperature; in the second case, the

cooling temperature is constant (see figure 8).

It is evident that the mo me nt to start the cooling is critical. If it is started too soon (small T,), the

reaction time will be long and the performance will be reduced; moreover, low temperature can

produce accumulation of one of the reagents and consequently the formation of undesirable by

products (low yield or unstable compounds that can trigger off decomposition reactions). If the

starting is produced too late (high T,) the high temperature obtained can reduce safe operability

margins by triggering off secondary unwanted reactions with the risk of a thermal excursion.

Assuming the uniformity of concentration and temperature in the entire reactor and ideal

disolution [18], the mass and energy balance equations for batch and semibatch processes can be

written as

d t

dC.

2 ,

Q

S

B

S

k=l

n

r

r^ i F.

C

j d V

m

V

m

d t

; j = i . .» ,n

c

(29)

(30)

i=l

d T m _

i

d t r „

r n

r

^ i-1 J k=l

(31)

An important parameter for safety analysis is the adiabatic temperature rise, AT

a

d, which

indicates how much the temperature of the reaction mixture would rise if the reaction were to

proceed adiabatically (q=0) to completion. Replacing eq. (30) into eq. (31), rearranging and

integrating for the specie A with the initial conditions Tn^Tnjg and XA=0

a t t=

0> where % A *

S

^

relative conv ersion of A , defined by XA

=

1"

CA</CA>

it is possible to find that for batch

processes:

ad

C

A

Q

AH

R

p C p

(32)

and then, the relation between the temperature and the conversion in an adiabatic reactor is:

T

m

= T

m

+ A T . Y

ad

A

A

(33)



35

4.3.2. Criteria for safe operation of a Batch process . Hugo [17] has determined some rules in

order to decide if a process could be carried out in batch, or semibatch should be chosen because

the heat removal capacity was too small to keep the reaction mixture at the required temperature.

The analysis was applied to a batch process in which the reaction starts adiabatically at the

temperature TmQ and when the reaction mixture has heated itself to the preselected temperature T„

the cooling is started. After a certain period of time the maximum allowable temperature Tm™, is

reachpj (.see figure 9).

From the safety point of view, it is only necessary to limit the study at the point at which the

system reaches the maximum temperature, Tm

m

„,and suppose that at this point the rate of heat

generation and removal are equal, then

U S ( T

m

- T

c

) :

ffl

R

V

D

r ( T

m

_

)

(34)

Temperature

Temperature

o L L l

Time ^ a * ^

n a x

Conversion

Figure 9. Temperature history and temperature-conversion trajectory in a batch reactor [17].

The problem for solving eq.(34) is that the conversion at the maximum temperature, XA

m a

, . '

s

unknown. An approximate value can be found by extrapolating the adiabatic line of conversion

given by eq. (33) to Tm™

x

(see figure 9), so

nimax

J

\nax

A T

(35)

ad

This value of conversion represents the fraction of the chemical heat production required to heat

the reaction mixture from T

m o

to Tm

m

„. The advantage of this formu lation is that XA

m a x

is

independen t of the switch-on point, but at the same time is a too conservative value of XA

max

-

Considering the following formal kinetic formulation:

r

A = -

k C

A

1

.

C

B (

1

- X A )

n

(36)



36

it is possible to develop th e energy and mass balances corresponding to th e different operating

phases of the batch process.

For the adiabatic period (Tm<T,):

dt

■=-AT

a d

C

A

(37)

and

X

A

T - T

AT

(38)

ad

with the initial conditions Tm ^ u Q ,

XA=0

at t=0 .

During the heat removal period:

d T

m -U S

( T

m

- T

c

) - A T

dt r

m c

^ C

(39)

d

A

-

f

A

dt C

A

(40)

dividing eq . (39) by eq . (40) , it is possible to find the temperature-conversion trajectory:

U S C

A

(T

m

-T

e

)

d I

m ^ o

+ A T

r

m

r

A

(41)

but, at T

m

= T

m m a x

dT

m

/d t = 0 and dÂ/dt * 0 then,

U S _ ~

A T

a d

r

A (

T

n w )

(42)

replacing eq . (42) in eq . (41),

— A T ,

dX

A

a d

r A ^ m ^ ) (T

m

-T

e

)

A ( ^ n v ^ ' ^ e )

(43)

,and introducing the reaction rate expression, eq . (36),



37

d T

m

d%

A

AT

ad

T -T

T -T

1-%

A

rt

rr

i -x

A

' E

a

(

T n w

- T

m )

^

•exp

RT

m

T,

X a i

(44)

Hugo and co-workers [19] integrated numerically eq. (44) satisfying the condition given by eq.

(33 ; , for many different initial conditions of T

m

and %A and for many different combinations of

T

m

-T

e

and A . and they found the following em piric correlation:

r i - x

A

. >

K =

l

- x

A

a - V * )

n

V

where

<)

is a dimensionless parameter given by

T -T

( - X

A

) A T

ad

(45)

(46)

and with the correlation parameters m and K, where

m = 0.6 n + 0.8

and

K(3 = P + 0 .114

E a ( T

" ; "

T

l

s

)

( p

2

- l . 2 5

2

)

R T i

(47)

(48)

where p is the dimensionless temperature difference between reaction mass and heat transfer fluid:

E

a

Inserting this approximation in eq. (34), it is possible to obtain the following expression,

x)/

m ax

K p = ( l - x

A

)

n

( l - ^ )

m

(49)

(50)

with the two dimensionless variables P and y

m

ax given by,



38

RTûs

¥ m a

* E

a

( - A H

R

) k

m a x

C

A

C

B

V

m

( 5 1 )

0 0

By applying eq . (50), the temperature set-point in order to ensure the control of the reaction can be

set. Once, the data set T

e

, T

m 0

, and T

s

has been established for a specific process, there are some

rules and criteria to be observed. The most imp ortant param eter is the temperature sensitivity of the

reactor, S, defined [17] as,

S = - ^ (52)

d T

e

S takes into account the variation of the maximum temperature respect to any change in the heat

transfer fluid tem perature as the critical param eter. This p aram eter gives a value of the influence in

the reactor temperature of changes in the operating conditions. For example, if S=3 a change of 4

°C in the heat transfer fluid temperature would produce 12 °C of increase in the maximum reactor

temperature that in some circumstances can be dangerous (i.e. triggering off secondary reactions).

Replacing eq. (36) in eq. (34), derivating in function of T

e

, and using the approximative

solution, eq. (50 ), to calculate the derivative of the con version,

S

=WHM)

( 53 )

with,

n m

2B(l-x

A i

)V* (1-V*)

(54)

where

B =

a a d

(55)

R T „

B is the thermal reaction num ber that gives information about the exothermicity and dynam ic of the

reaction. Hugo [17] defined two possible cases: if fx>

1,

S is always smaller than 1, and it

decreases when the temperature difference p increases, then, this is the stable cooling range; if

however

|0.<1,

then S will increase with (J, which means it is possible to go to critical regions

(S>1).

Since generally [3>1, the only requirement for maintaining control of the reaction is |J.>1.

From eq. (54) it is possible to define a B

c r

;

t

when u=l and then using the unfavorable case of

^'

A

max pl

o t the

divisory bo rder line betw een critical and non -critical region (see figure 10).



39

0 .0 0 .2 0 .4 0 .6 0 .8 1.0

Figure 10 . Critical limits of B

cr

jt in function of A

m ax

[17].

4.3.3.

Criteria for safe operation of a SemiBatch Process. Steinbach [20-22] followed the same

type of procedure for semibatch processes and developed an empirical correlation based on

computer simulat ion results in order to discriminate between safe and dangerous operating

conditions,

- v

A

- k - C

B o

- t

V

add.

\

y

U - S - t

>

1

V

m

- C p - p

(56)

where V ^ is the volume feeded.

In this case, th e accumulation of unreacted reagents must be avoided, and for this reason, the

semibatch reactor should be operated in an ignited condition (opposite to batch reactor); that

means,

trying

to

maintain

the

reaction

rate

equal

to

the

feed

rate

as

in

an

infinitely

fast

reaction.

For these type of processes a very important point to be considered in the design phase is the

development of some type of interlock that switches off the feeding of reagent automatically in case

of

incident

(i.e.

breakdown

of

cooling,

stirrer

stoppage,

etc.)

Hugo,

Steinbach

and

Stoessel

[22]

showed that it is possible to find an opt imum temperature in order to guarantee th e lowest

temperature increase in case of breakdown of cooling (adiabatic reactor).

4.3.4. Application example. A simple reaction system has been chosen in order to illustrate by

means of an example the design principles explained before.

A

+

B

- > S

+

P



40

The system investigated was

a 1:1

molar mixture

of

A and B. Th e objective

is to

assess

if

such

a

process can be carried out batchwise with

CA„=C

B( )

=

4.56 KmoL'm

3

.

The heat

of

reaction

(AHR)

was obtained from adiabatic tests

and is

equal

to

-64.9 kj/mol,

the

specific heat capacity

of

the

reaction mixture

(Cp)

is

2512. J/Kg-K,

and the

density

is

937.

Kg/m

3

, hence pCp=2354 kJ/m

3

K. From the same

set of

experiments

a

simple reac tion rate w as

fitted:

' A - * c

A o

- c

B o

. ( i -

3

t

A

) ( i - c

A o

^ . )

B

o

where k = 2 .446604-10

7

exp(-8348.7/T) m

3

K m o l Is.

The adiabatic temperature rise can be calculated from eq. (31):

A T

H

=

4

-

56

; 6

4

-

9

-

l o3

= 125.7 °C

a d

2 3 5 4 .

From DSC studies

it

was sho wn that an unw anted reaction

(C

—> products) can take place,

and

,

m a x

should

be

established 100 °C.

With this data B

c r

i

t

, eq. (54), can be calculated,

R

8348.7-125.7

7

<

A

From

the

diagram

of

figure

4.7 [17] it is

possible

to

read

A

m a x

that should

be at

least 0.68.

Hence, using eq. (34), the Tm,, can

be

obtained as Tm,, =T

mma x

-%'A

max

-ATad=14.0 °C.

Another important aspect

is

the ratio between the surface area and the volume

of

the reactor

at

the critical conditions, eq. (33).

P - c p . A T

a d

- k - c

B

( i - x ; ) d - c |^-)

S_

=

° _2l (57)

V

= U

(

T

n w -

T

e )

Assuming U=350 W/m

2

K, S/V= 21.4 m

2

/m

3

in

this examp le,

For an

small reaction calorimeter

(11) this ratio is higher, approximately S/V=3 1.4 , but for an standard installation it is too high

(S/V between

3-5

m

2

/m

3

). Th is indicates that this reaction may

be

carried

out in the

laboratory

with

a

small reactor (2

1) but if

it

is

transferred

to an

standard installation

a

runaway will occur.

In the case of semibatch processes, the control of the heat generated

can be

done

by

means

of

the cooling circuit

or by

regulating

the

metering rate.

If the

metering rate

is too

strong,

the

maximum allowable temperature can be overshot, but if it is too low, the reaction rate can be low

and the total reaction time

too

long, with the problem of accumulation

of

unreacted reagents into



41

the reactor. Figure 11 shows an example of this situation. Normally, the optimum dossing time

can be calculated once the working temperature h as been selected by m eans of,

A H C

A

V

m

A

o

d° s U S ( T

m

- T

e

)

393

(58)

n 1 1 1 1 r

1320 1650 1980 23t) 2540 2970 3300

Time (s)

Figure 11 . Temperature-time profiles of a semibatch processes, modifying the metering rate.

4.3.4. Extension to heterogeneous systems. A great number of industrial processes involve

systems in which two partially miscible phases coexist, which are in general, organic and aqueous.

However, a considerable amount of incidents, concerning runaway reactions occur in this type of

system [2].

The analysis of reactions taking place between partially miscible liquids is further complicated

due to the mass transfer phenomena between the phases. The reaction usually takes place in one

single phase, which means one compound present in the non-reactive phase diffuses to the

interface, and then into the bulk reactive p hase; w hile diffusing into the reactive ph ase, it reacts to

form the product. Examples of this type of systems are nitrations, sulphonations, polymerisations,

hydrolisis, esterifications, alkylations, etc.

The formulation described above for homogeneous systems has been extended by Steensma and

W estertep [23,24] for liquid-liquid reactions.

In order to study these type of reactions the following simple reaction w as con sidered:

A + B

—>

products

According to the general theory of mass transfer combined with a chemical reaction [26], it is

possible to define the following two typical situations:



42

Figure 12. Example of semibatch process with two liquid phases.

a/ B is present in the continuous phase (subscript c) and A is present in the dispersed phase

(subscript d) in form of droplets of different size.

Cont inuous

B

Dis p e r s e d

\ A+B — ► products

Figure 13. B is transfered into the dipersed phase where it diffuses and reacts with A. The reaction

occurs only in the dispersed phase.

b/ B is present in the dispersed phase and A is present in the continuous phase (see figure 14).

For these cases expressions for the overall reaction rate can be developed [26], depending on

th e

controlling

phenomena

(mass

transfer

or

chemical

kinetics)

and

consequently,

some

new

variables that did not exist in homogeneous systems have an important influence making the

develoment of the criteria more complex:

- The droplet size, which will determine th e interfacial area and thus affecting the overall reaction

rate in case of mass transfer control.

- The distribution coefficient between th e phases , which will determine th e maximum

concentration of the reactant in the reaction phase.



43

- The phase inversion phenomena which is capable of producing abrupt changes in the reaction rate

during a semi-batch process [25].

C o n t i n u o u s

A+B products

D i s p e r s e d

B

Fig ure 14. B is transfered into the con tinuo us ph ase w here it diffuses and reacts with A. The

reaction occurs only in the continuous phase.

5 .

Protect ion m easures against runaway react ions

As previously stated, the protection measures are taken when the process is outside of desired

conditions and normally it is going to a dangerous state. The objective of these measures is to

restabilize the control of the reactor or at least reduce the danger for people, and the damage to both

the installation and the environment. The type of action required is highly dependent on the nature

of the reaction which must be kept under control and also on the reason for the potentially

dangerous situation.

5.1. STOPPING THE RUNAWAY

5.1.1.

Full cooling. In cases where the temperature of the reacting mass is high but the rate of heat

generated is still w ithin the heat remov al capacity of the reactor (see figure 15), then switching to

full cooling will suffice. Interlocking systems of this type must be implemented on reactors in

which potentially dangerous reactions are carried out.

Thermal

f l o w

Tempera ture

Figure 15. Effect of emergency full cooling in stopping the loss of control. The heat removal flow

capacity is increased from 1 to 2.



44

5.1.2. Quenching, a/ Fast addition of a supressant: The method is based on the inerting in situ of

the reactive mixture through the injection of a calculated amount of inert diluent which reduces

reaction rate by cooling the mix ture and also by dilution, or a chem ical inhibitor which modifies

the reaction rate expression. The application of such a procedure requires that a number of

previous considerations and preparation be made:

- Choice of an appropriate liquid which does not react too exothermally with the reaction mixture.

The addition of an inhibitor requires also intimate knowledge of how the reaction rate can be

influenced

- Sufficient free volume in the reactor

- Technical installations which provide the addition of the liquid in due time.

b/

Dumping of the reactor contents: The reaction mixture is dumped into a vessel which contains

cold diluent with or without an inhibitor. This method requires again good knowledge of the

reacting m edium and technical installation to perform the dump ing procedu re.

5.2. PRESSURE RELIEF

The venting of the reaction mass is the most used safety measure. The main effect of pressure

relief is temperature stabilisation, due to the heat removed by evaporation. However, this system

has three main problems:

- the design of the relief system (vent area sizing and starting pressure)

- the containm ent of the ejected material

- its ineffectiveness for low vapor pressure systems

Th e sizing of the vent line is one of the most imp ortant aspects in safety of chemical reactors or

storage tanks, since a faulty design could lead to a catastrophic vessel failure with very serious

consequences. The adequacy of a particular relief vent depends on three factors:

- the accuracy in the determination of the "worst case" initial conditions,

- the accuracy with which the thermo-kinetics and physical properties of the reacting mass are

known,

- the accuracy with which the effects of the emergency device can be calculated.

5.3 .

CONTAINMENT

The objective of a containment system is to keep toxic chemical substances away from people

and environment, to protect the surroundings from missile generation, fires and pressure wave

effects, and to avoid chain incidents (domino effect).

F i n a l r e m a r k s

Due to the limited space available, this paper has only presented the main points. Some of the

aspects mentioned here will be covered in more detail by other contributions, however, the cited

literature is strongly recommended.



N o t a t i o n

45

C

Cp

CPL

D

Ea

F

H

K

K

L

k

N

n

E

n

R

n

Q

q

R

R

r

S

T

U

US

V

Set of chemical species

orpre-exponential factor,

Molar concentration,

Specific heat capacity,

M olar heat capacity of a chemical species,

Diffusivity,

or diameter,

Activation energy,

Molar flow,

Molar enthaply (liquid),

constant,

Overall mass transfer coefficient,

Reaction velocity constant,

Number of species

Number of reactant feed streams

Number of independent reactions

Molar Hold-up,

Volumetric flow,

Thermal flow,

Rate of chemical production,

Radius,

or Gas constant,

Rate of reaction,

Surface,

or Sensitivity

Temperature,

Heat transfer coefficient,

Effective heat transfer coefficient,

Volume,

Molar volume,

Molar fraction

or distance from the center

depends on kinetics

mol -n r

3

J K g - ^ K "

1

J-mol-^K"

1

7

-1

m

z

-s '

m

J-mol-

1

mol-s"

1

J-mol-

1

n v s

- 1

depends on kinetics

mol

-,3.,

m

J

-s

_ I

W

mol-m

_3

-s

_1

m

J-mol"

1

-K"

1

m o l m "

3

-s

_ 1

m

2

K

W-m-2-K-

1

W-K"

1

m

3

m

3

-mol

_ 1

Greek symbols

X

r

y

Conversion

Thermal capacity,

toichiometric coefficient, reactant(-), product(+)

Thermal conductivity,

Dynamic viscosity,

partial order of reaction

J-K-l

W-nH-K"

1

k g - i r r ^ s "

1



46

e

p

a

T

Parameter of a heat transfer correlation

Density,

Geometric simetry factor

Time constant,

k g m

m3

Subscripts

0

cr

e

i

L

R

s

w

Supersc

initial con dition

Critical

Heat transfer fluid

Reaction or Input

Liquid

Rem ove d, reaction

Set-point

Wall or Wetted part

riptS

ad

E

h

J

m

r

T

z

Adiabatic

Feed of reactants

Heating

Species

Reaction mixture

radial

Total

Axial

continuous phase

dispersed phase

reaction phase

R e f e r e n c e s

1.

Ras mu ssen, B. (1988) 'Occurrence and imp act of unw anted chemical reactions', J. Loss

Prev. Process Ind. 1, 92 .

2 .

Barton, J.A. and Nolan, P.F. (1984) 'Runaw ay reactions in batch reactors', The Protection

of Exhotermic Reactors and Pressurised Storage Vessels, IChemE Symposium Series, 85, 13.

3 .

Reg enass , W. (1984) 'The control of exotherm ic reactors', The Protection of Exhotermic

Reactors and Pressurised Storage Vessels, IChemE Symposium Series, 85, 1.

4 . Semenov , N.N . (1928), Z. Phys. Chem. 48, 571 .

5 .

Fran k-K am enets kii, D.A. (1969) 'Diffusion and heat transfer in chem ical kinetics', 2nd ed,

Translated by J.P. Appleton, Plenum Press, New York .

6. Gray , P. and Lee , P.R. (1967), 'Thermal Explosion theory', Ox idation and Com bustion

Reviews, vol. 2, Elsevier, New York .

7. M erzh ano v, A.G. and Du bov itskii, F.I. (1966 ) 'Present state of the theory of thermal

explosion' , Russ. Chem. Revs., 35 (4), 278.

8. Sem enov , N.N . (1959) 'Som e problem s of chem ical kinet ics and react ivi ty ' vol 2,

Translated by J.E.S. Bradley, Pergamon Press, London.

9. Bo we s, P.C . (1984) Self-heating: evaluating and controlling the hazard s, Dep artment of the

Environement, B uilding Research E stablishment, London .

10. Grew er, T., Klusacek , Loffler, H.U., Rog ers, R.L. .Steinbach, J. (1989) 'D etermination

and assessement of the characteristic values for the evaluation of the thermal safety', J. Loss Prev.

Process Ind., 2, 215.



47

11 .

Riesen ,R. and Grob , B. (1985) 'Reaction Calorimetry in Chem ical Process D evelopment',

Swiss Chem., 7, 39.

12 . Grew er.T. (1975), Chem .-Ing.-Tech.

,51,231.

13 .

Go rdon ,M .D., O'Brien, G.J., Hensler , C.J., Marcali , K. (1982), 'Mathem atical M odeling

in Therm al Hazards Evaluation', Plant/Operation P rogress, 1, 27 .

14. Gra y, P. , Harp er, M.J. (1960 ) Reactivity of solids , Pro c. of the 4th Symp . on the

ReacH', iiy or Solids, Elsevier, Amsterdam, 283.

15.

Frank-Kam enetskii, D.A. (1939), Zuhr. Fiz. Khim., 13, 73 8.

16. Tho mas , P.H. (1958), Trans. Faraday Soc.,54, 60.

17.

Hu go, P. (1980) 'Start-Up and Operat ion of Exotherm ic Batch Processes' , Chem. Ing.

Tech., 52, 712.

18 . Fro me nt , G.F. and Bischoff, K.B. (1990) Chemical Reactor Analysis and Design, 2nd ed.,

J. Wiley & Sons, Singapore.

19.

Hu go, P., Konczella , M. and Mau ser, H. (1980) 'App roximation solutions for the design

of exothermic batch processes with indirect cooling', Chem. Ing. Tech., 52, 761 .

20. Hu go, P. and Steinbach , J. (1986) 'A Comp arison of The Limits of Safe Operation of a

SBR and CSTR', Chem. Eng. Sci . 41,4,1081-1087.

21. Hu go, P., Steinbach , J. and Stoessel, F. (1988) 'Calculation of the M aximum Temperature

in Stirred Tank Reactors in Case of a Breakdown of Cooling', Chem. Eng. Sci. 43, 8, 2147-

2152.

22. Steinbach, J. (1989) 'Fundam entals/Theory of Run away Chem ical Reactions', Conference

on Techniques for Assessment of Chemical Reaction Hazards, London 5/6 December.

23 .

Steens ma, M. and W esterterp, K.R. (1988) 'Therm ally safe Op eration of a cooled semibatch

reactor. Slow liquid-liquid reactions', Chem. Eng. Sci. 43, 8, 2125-2132.

24.

Steensm a M. (1990) ' Run away and Therm ally safe Op eration of batch and semi-batch

reactors', Ph.D. Thesis, Deventer.

25.

Al-Khud hairy, D., Barcons, C , Hernandez, H, and Zaldivar, J.M. (1989), 'Modell ing of

Two Liquid Phases with Chemical Reactions Applied to Toluene Mononitration', Technical Note

N° 1.89.57, Comm ission of The European C omm unities, Joint Reasearch Centre, Ispra (Italy).

26. Westerterp, K.R., Van Swaaij , W.P.M. and Beenackers, A.A.C.M. (1987), Chemical

Reactor Design and Operation, Student ed., J. Wiley & So ns, M anchester.





CONTROLLING RUN-AWAY REACTION HAZARDS WITHIN THS FRAMEWORK OF THE

SEVESO-DIRECTIVE

Dr. G. DROGARIS

Institute for Systems Engineering and Informatics

CEC - JRC - Ispra Site

ABSTRACT. The requirements imposed by the Council Directive 82/501/CEC

on the major-accident hazards of certain industrial activities (SEVESO-

Directive) both on manufacturers and the national Competent Authorities

are briefly presented followed by a short reference to other relevant

EEC Directives, international conventions and other related activities

as well as various guidelines codes of practise etc. for accident pre

vention. Safety related standards are also discussed. A general

overview of the national approaches in the implementations of the

SEVESO-Directive with emphasis in tackling run-away reaction hazards in

the safety report (notification) is given. Major Commission activities

such as the Major Accident Reporting System (M.A.R.S.) and the Commu

nity Documentation Centre on Industrial Risk (C.D.C.I.R.) are described

and some lessons learned from accidents involving run-away and other

unexpected reactions and/or electrostatic loads are also presented.

1. Introduction

The EEC Council Directive 8 2/501/EEC [ 1] , or the so-called "SEVESO-

Directive" provides an effective tool for an enhanced accident and loss

prevention policy. This Directive was the response to a series of major

accidents occurred in the last few decades and which attracted the

interest of the public to the hazards presented by industrial installa

tions and highlighted the need for an improved European policy to con

trol potentially dangerous activities.

The accident of 1976 in Seveso, North Italy is mainly considered

as the initiating event for this directive. However it should be

reminded that the disaster of 1974 in Flixborough, U.K. had already

initiated reactions to this same end. Actually the legal frame for the

implementation of this directive in U.K. is based on acts and actions

49

A. B enuzzi and J. M. Zaldivar (eds.). Safely of Chemical Batch Reactors and Storage Tanks,

4 9 - 7 7 .

© 1991 ECSC, E EC, EAEC, Brussels and Luxembourg. Printed in the Netherlands.



50

taken according to the recommendations of the Flixborough accident

investigations.

Up to now this SEVESO-Directive has been amended twice. The first

amendment was adopted in March 1987 as a response to the 1984 disasters

in Bhopal and Mexico City and mainly aimed to tightening up the provi

sions for certain very dangerous chemicals, including chlorine, MIC,

phosgene and sulphur trioxide.

In 1986 the accident in Basel demonstrated the need to strengthen

the requirements of the Directive for isolated storage installations.

The second amendment that was adopted in November 1988 extended sub

stantially the scope of the Directive to storage of dangerous sub

stances and/or preparations at any place. This amendment also attempted

to clarify requirements for risk communication to the public.

The publication cited here [1] contains the consolidated text of

the SEVESO-Directive after the first two amendments.

A fundamental revision of this Directive has been already initi

ated. It will be based on the experience gained after over five years

of application of the SEVESO-Directive, which came in force in July

1984. Requirements for controls on land-use planning both for new

installations and new urban developments around existing installations

will be included following a council resolution [2] .

Here below the objectives and the requirements of the SEVESO-

Directive are presented. Further the two main activities of the Insti

tute for Systems Engineering and Informatics of the CEC Joint Research

Centre at Ispra as part of its support to the Commission for the imple

mentation of this Directive, namely the:

- Major Accident Reporting System (M.A.R.S.), and

- Community Documentation Centre on Industrial Risk (C.D.C.I.R.),

will be discussed.

There are also other EEC Directives related to safety issues as

for example the Directive on health and safety at work and the classi

fication, packaging and labelling of dangerous substances. They will be

presented together with other similar international regulations as well

as rules and guides on the same subject recently developed in the USA.

The role of standards on industrial safety will be also discussed.

SEVESO-Directive as all Council Directives are addressed to the

Member States. This means that they are not automatically imposed to

the national legislation; on the contrary each Member State has to

develop a legislative framework in which the requirements of the Direc

tive will be implemented. A general overview on the national approaches

for the implementation of this Directive with emphasis on the safety

reports of installations is therefore necessary for getting an insight

in the practices for controlling major industrial hazards. Methods of

tackling run away reaction hazards in the safety reports will be dis-



51

cussed separately.

Up to the end of 1990 almost 100 accidents have been registered in

M.A.R.S.

Run-away or other unexpected reactions have been identified

among the causes in 17 incidents or accidents. Their characteristics

and the lessons learned from these 17 accidents as well as from 7

acci

dents involving electrostatic loads conclude this presentation.

2. The SEVESO-Directive

2.1. Objectives

The objectives of the SEVESO-Directive, which are mainly based on the

objectives and principles of the Community's Environmental policy, can

be summarized as follows:

a) The protection of the public and the environment as well as of work

ers from the hazards connected with industrial activities involving

dangerous chemicals.

b) Convergence of legislative and practical national approaches to

industrial safety towards an enhanced level within the frame of a

free market.

c) Accident and Loss Prevention, mitigation of consequences of major

accidents.

2.2. Content of the SEVESO -Directive

2.2.1. Definitions-Application of this Directive.

This Directive covers

industrial activities

where

dangerous substances

are processed or

stored. Both terms are defined in Article 1 of the Directive. In gen

eral toxic, flammable, explosive and oxidizing substances are consid

ered as dangerous substances. Annex IV the Directive contains indica

tive criteria for characterizing substances as toxic, flammable, explo

sive or oxidizing according to their physicochemical properties. In

addition 180 dangerous substances are listed in Annex III with inven

tory threshold values. Annex II refers to storage of dangerous sub

stances (either isolated or associated to a process plant) and contains

a list of 28 dangerous substances (26 out of these are listed also in

Annex III) with respective inventory threshold values as well as inven

tory threshold values for the various categories of dangerous sub

stances .

Industrial activities for the purpose of this Directive is consid

ered any industrial installation involving, or possibly involving, one

or more dangerous substances. This implies that

manufacturers

(defined

as any person in charge of an industrial activity) should also consider



52

the potential generation of a dangerous substance (e.g. generation of

nitrogen oxides as a result of uncontrolled and/or unintended decompo

sition of an even not dangerous substance).

Annex I contains also an indicative list of processes and unit

operations that are covered by this Directive (practically all widely

applied processes of organic and inorganic chemicals). This Directive

is not applied to nuclear and military installations, manufacturing and

separate storage of explosives, gunpowder and munition and mines.

Installations for the disposal of toxic and dangerous waste are also

excluded provided that are covered by other Community

Acts.

Since for

the time being no such Acts exist this exclusion is considered inac

tive.

The concept of

major accident

is rather fuzzy despite its defini

tion in the Directive as: "an occurrence such as a major emission, fire

or explosion resulting from uncontrolled developments in the course of

an industrial activity, leading to a serious danger to man, immediate

or delayed, inside or outside the establishment, and/or to the environ

ment,

and involving one or more dangerous substances".

Therefore a scale of "gravity indices" has been adopted for a two-

year trial period [2] . Three gravity indices, ranging in a scale from 1

(worth noting) up to 5 (catastrophic), describe:

- the actual or potential danger (based on the amount of dangerous sub-

stance(s)

involved);

- the extent of the consequences of the accident;

- the extent of intervention or safety measures external to the indus

trial activity.

But the scale has not yet been used to define a "threshold" of

gravity for notification purposes.

2.2.2. Notifications-Safety Repo rts.

The manufacturers of installations

are obliged to take all measures necessary to prevent major accidents

and to limit their consequences for man and environment. The manufac

tures have to prove to the Competent Authorities (see point 2.2.3.

below) that they have identified the major hazards and have taken all

proper safety measures and precautions. These obligations (defined in

Articles 3 and 4 of the Directive) are valid if the inventory of dan

gerous substances in an installation exceed the lower inventory thresh

old values specified in Annex II and III. Should the inventories exceed

the higher threshold values then manufacturers have to submit a notifi

cation containing information on dangerous substances, the installa

tion, major hazards and safety precautions (safety report). Annex V of

the Directive contains the minimum content requirements for this safety

report.

These installations covered by the requirements of the

Arti

cle 5 of the Directive are the so-called top tear sites.



53

These requirements apply

to

both

new and

existing facilities.

Major modifications of existing installations are treated as new

installations.

2.2.3. Com petent Authorities. The

Member States have

to set up or

appoint the Competent Authority (or Authorities) responsible for

the

implementation of the Directive. The complete list of all Competent

Authorities has been given in [ 4 ] . Almost half of the Member Countries

have appointed more than one Competent Authority. Environmental Min

istries are the most common Competent Authorities (9 Member

Countries),

while the Ministry of Labour has been also appointed as one of the Com

petent Authorities in four Member Countries. In Ireland and U.K.

autonomous bodies (Health and Safety Executive

in

U.K., Occupational

Safety and Health in Ireland) are the Competent Authorities.

The Committee

of

the Competent Authorities (CCA) chaired

by the

Commission (DG XI/A/2) and composed of the national Competent Authori

ties meets regularly every four months and provides a wide forum for

exchange of experience and review of the progress in the implementation

of the Directive.

2.2.4. Information to the Public.

The Directive required that "persons

liable to be affected by a major accident originating in a notified

industrial activity within the meaning

of

Article

5

are informed

in an

appropriate manner of the safety measures and of the correct behaviour

to adopt

in

the event

of an

accident". Further all this information

disseminated to the public should be made available to the other Member

States concerned.

The second amendment of the Directive underlined the importance

of

this information flow to the public requiring that such information has

to be communicated to all persons liable to be affected in case of an

accident

without these persons

to

request

it and adding that this

information has to be repeated and updated at appropriate intervals and

shall also

be

made publicly available. Annex VII states

the

minimum

requirements for the information to be communicated to the public.

2.2.5.

Major Accidents.

Experience gained from accidents is precious

for

an

active prevention policy. Hence the Directive requires that

as

soon as

a

major accident occurs the manufacturer notifies the Competent

Authority providing adequate information for assessing the effects of

the accident on man and the environment and measures to prevent recur

rence of such an accident.

The Competent Authority

in

turn has to notify the accident

to

the

Commission. Minimum requirements to be supplied to the Commission for

major accidents are given in Annex V I.



54

This notification procedure is the basis of the M.A.R.S. see

point 2.3. herebelow).

2.2.6.

Emergency Planning.

The

Competent Authorities examining

the

notification of installations submitted pursuant to Article 5 shall

ensure that internal emergency plans sufficient to cope with potential

major accidents have been drawn by the manufacturer.

Further they shall ensure that

an

emergency plan

is

drawn

up

for

action outside the establishment in respect of the information col

lected from safety reports.

It shall be clarified that the Competent Authority shall not nec

essarily draw up emergency plans but shall mainly ensure adequate

information flow to the emergency planning authority(ies).

2.2.7.

Exchange

of

Information

and

Experience.

Article 12 requires that

"the Commission shall set up and keep at the disposal of the Member

States a register containing a summary of the major accidents which

have occurred within the territory

of

the Member States, including

an

analysis of the causes of such accidents, experience gained and mea

sures taken, to enable the Member States to use this information for

prevention purposes".

Information obtained by the Competent Authorities and/or the Com

mission within the framework of this Directive are considered confiden

tial.

This confidentiality requirement, however, "shall not preclude

the publication by the Commission of general statistical data or infor

mation on matters of safety containing no specific details regarding

particular undertakings or groups of undertakings and not jeopardizing

industrial secrecy" (Article 13 ).

2.2.8.

Application Schedule.

The Council Directive 82/501/EEC required

Member States to take the measures to comply with it at the latest on

January 8

t h

, 1984. Submission of safety reports of existing installa

tions was to be due

by

latest July 8

t h

, 1989. In the mean time instal

lations covered by the requirements of Article 5 should submit a decla

ration (name, address, location, type of activity, dangerous sub

stances) latest by January 8

t h

, 1985.

Amendment 1 came in force 18 months after its publication (i.e.

September 19

t h

, 1988 ) but safety reports for existing installation sub

jected to the provisions of this Directive for the first time following

adoption of this amendment were to be submitted not later than

March 1 9

t h

, 1989.

The second amendment applies

to new

installations latest from

June

l

c

,

1990 and will become effective for existing installations

by

'latest June 1

s t

, 1991.



55

Existing installati ons covered by the requireme nts of Article 5

for the first time following adoption of this second amendment have to

submit safety reports by latest June 1

s t

, 1994.

This directive can be amended by a majority of 45 vot es, the votes

of the Member States being weighted as provided for in Article 148(2)

of the Treaty.

2.3.

Ma jor Accident Reporting System (M.A.R.S.)

To store and retrieve the accident reports notified by the Member

States under a rticl es 10 and 11 of the SEVES O Directiv e (see point

2.2.5. above), the M.A .R. S. (Major Accident Reportin g System) data bank

has been established at the JRC/I SEI. The content of the information to

be supplied has been defined in consultation with the Committee of Com

petent Authorities (CCA), so that:

- all countries can use a uniform reporting procedure;

- the inform ation supplied is consist ent with the requiremen ts of the

Directive;

- the informatio n is adequate to under stand the primar y as well as the

underlying causes and circumstances of the accidents;

- information can be easily processed and stored in the M.A .R. S. infor

mations structure.

Special accident reporting forms , designed to meet the above

requirem ents, have been adopted and are now in use. Details of this

reporting form have been presented elsewhere [ 3 , 5 ] . The main topics

covered by it are:

1) general data of the accident;

2) type of accident and substances involved;

3) circumstances of the accident;

4) emergency measures taken;

5) analysis of causes;

6) nature and extent of damage;

7) preventive measures.

Accident notifications are , upon rec eipt, loaded into the M.A .R. S.

(working language of M.A.R.S. is English) and analysed in order to:

a) Classify the notified accidents according to var ious parameters

(country, year of occurrence, type of activity, type of accident,

consequences, substances involved).

b) Calc ulat e gravity indices (see also point 2. 2.1. above).

c) Identify the c ausat ive f act ors . This is a very import ant step

because it enables one to extract lessons to be learned from each

notified accident.

Finally, a feedback by the notifying Competent Authorities ensures

that essential features of the notified accidents are correctly inter-



56

preted and that all important lessons to be learned from each notified

accident are identified.

Up to the end of 1990 , 98 accident notifications had been received

and loaded into M.A.R.S. Though the Directive requires notification of

major accidents only, in practice the tendency is, whenever important

lessons are to be learned from such events, to report also near misses

and incidents that had the potential to lead to serious consequences.

M.A.R.S.

enables the Commission to fulfil the requirements of

arti

cle 12 of the Directive by the preparation of the following documents

at regular intervals:

a) At each CCA meeting, a summary of major accidents notified, indicat

ing causes, consequences and measures to prevent recurrence of

simi

lar accidents and/or mitigate the consequences. This report as well

as the content of M.A.R.S. are confidential (see also point 2.2.7.

above).

b) A report on lessons learned from notified accidents containing also

some general statistical data. This report is purged from all confi

dential information so that it can be made periodically available to

the public. The first version of it has been recently published as

an EUR-report [3 ].

2.4. Com munity Docum entation Centre on Industrial Risk (CDC IR)

In addition to M.A.R.S., the CDCIR is a Commission activity aiming to

diffuse safety-related knowledge and experience to the public. The

objectives and tasks of the CDCIR have been defined as follows [ 6 ] :

"One of the most essential areas for action identified was the need for

a systematic diffusion of information concerning the practical imple

mentation of the Directive in the Member States, including the techni

cal rules and guidelines applied, the safety practices and the lessons

learned from major accidents. Therefore, the Commission decided to set

up a Community Documentation Centre on Industrial Risks (CDCIR). This

Documentation Centre is run by the European Commission, Joint Research

Centre,

Institute for Systems Engineering, at Ispra, Italy. Through the

Documentation Centre the Commission plays a very significant role as a

central point for the collection and classification of technical rules

and documents issued by national governments or produced by national or

international organizations, industrial and professional associations

and so on. Furthermore, the Centre also actively looks for any other

relevant issues in the field of industrial risks. The Documentation

Centre collects, classifies and reviews technical rules, guidelines and

documents concerning the requirements of the Directive 82/501/EEC, as

well as the safety of industrial installations run by governments,

administrative, scientific or technical bodies, national or interna-



57

tional organizati ons and industrial or professional associa tions. Docu

mentation on major accidents in the form of reports and videotapes are

also collected and reviewed".

The documents collected in the CDCIR are classified as follows:

i) the SEVESO Directive requirements and related issues ;

ii) techni cal guid elin es or safety asses sment s specific to non pro

cess/facilities;

iii) technica l guide lines or safety as sessme nts spe cific to a process

or a facility;

iv) accident document ation;

v) other relevant issues.

This list contains only the five major categories. Details on sub

categories and on the CDCIR organization are available elsewhere [ 7] .

Up to now the number of documents collected by the CDCIR

approaches 10 0 0 . Four volumes of the inventory have been published (the

third one is a consolidated version containing the first two and the

fourth one is dedic ated to acciden t case historie s availab le in the

literatures.

Upon request the CDCIR may provide to any interest party:

a) a list of documents or other issues available for a specific subject

relevant to the CDCIR scope. In case of a general inquiry the pub

lished CDCIR catalogues will be forwarded to the party making the

inquiry, if these are not already in its possession;

b) copies of docume nts conta ined in it when these are not covered by

copyright or are not restricted in distribution. For documents cov

ered by copyright or which are restricted in distribution, the CDCIR

will advise on the proper contact address.

The CDCIR is also available for on site consultation upon request.

Inquiries of any type should be addressed to the attention of

Mr.

Wiederstein,

C.C.R.,

T.P. 6 32 ,

1-21020

Ispra (VA) , Italy.

3. Other Related Directi ves, Regulations and Standards

3.1. Other EEC Council Directives

One of the major issues in the SEVESO-Di rective is the characteriz ation

and identification of dangerous substances (see also point 2.2.1.

above). This same problem is also tackled by the so-called CPL

(Classification, Packaging and Labelling) Dire ctive [ 8 ] , where explo

sive, oxidising, easily flammable, flammab le, very to xic, toxic , harm

ful,

corrosive and irritant substances and preparations are defined.

Annexes of the CPL-Directive as well as its amendments contain list of

substances and preparations classified to one of the categories men-



58

tioned above.

Another Council Directive related to prevention of major hazards

and amelioration of their consequences is the 89/391/EEC Directive [ 9] .

Though the objective of this Directive is limited to occupational

safety and health issues there are quif.e a few common issues with the

SEVESO-Directive (accident prevention, hazard identification, personnel

training,

etc.);

risk communication and consultation issues are however

limited to the labour force of the establishment concerned. Within the

framework of the Directive 89/391/EEC, another Directive [10] contain

ing the minimum safety and health requirements for workplaces has been

already issued and further actions are expected.

Different, minimum requirements are set for new and existing

installations; a 3 years period is given to existing installations for

conforming with the respective minimum requirements.

3.2. Regulations in USA

The OSHA is also preparing a new rule with reference to safety manage

ment of highly hazardous chemicals [11] . This proposed rule, which

makes reference to the SEVESO-Directive, mainly refers to a process

hazard analysis and gives emphasis to managerial issues (procedures,

personnel training, safety reviews, safety audits, incident investiga

tions, emergency planning and

response).

The primary requirement for on-site emergency response in USA is

the OSHA regulation 29 CFR 1910.120 "Hazardous waste operations and

emergency response", while the framework for off-site emergency plan

ning is the Title III SARA (the Superfund Amendments and Reauthoriza

tion Act) also known as the Emergency Planning and Community Right-to-

Know Act.

On an international level there are a lot of initiatives on Major

Accident prevention or related issues.

3.3 . International Gu idelines, Conventions, etc.

The OECD is very active on this area and work is carried out from an ad

hoc group of experts and in a series of workshops. Recent relevant OECD

publications include decision-recommendations on provision of informa

tion to the public and public participation in decision-making

pro

cesses,

exchange of information on accidents [12], good practices for

accident prevention [13 ], risk communication to the public and the role

of operators in accident prevention and emergency response [14] and

land-use planning under consideration of major accident hazards [15] .

The World Bank has also developed guidelines for identifying, ana

lyzing and controlling major hazard installations in developing coun-



59

tries [16] and has developed a hazard assessment manual which provides

measures to control major hazard accidents affecting people and the

environment. A list of dangerous substances is included [17].

United Nations Environment Programme has also prepared a handbook

on the APELL Process [18] (Awareness and Preparedness for Emergencies

at Local Level). This process is designed to assist decision makers and

technical personnel in developing countries to identify hazards and

prepare emergency response taking into account local conditions.

International conventions for major accident prevention are under

preparation in the following forum:

- United Nations Economic Commission for Europe;

- Council of Europe (compensation for damage resulting from dangerous

activities);

- Nordic Council;

- International Labour Office (Code of Practice on the Prevention of

Major Industrial Accidents).

Codes,

guidelines or technical documentation under preparation at

international level include:

- code of conduct to promote economic developments focus on accident

prevention and on emergency response (United Nations Centre for

Transnational

Corporations);

- guidelines for disaster prevention including land use and prepared

ness (United Nations Disaster Relief Coordination);

- technical documentation on chemical spills at sea (International Mar

itime

Organisation);

- a PC-Safety Audit System for identifying, analysing and controlling

major hazard installations (World Bank);

- guidelines on external hazard, human error and common cause failure

(International Atomic Energy Authority);

Other relevant activities at international level worth mentioned:

- study on circumstances and causes of accidents associated with the

release of chemicals (World Health

Organisation);

- international programme for the promotion of working conditions and

the Environment-PIACT (International Labour Conference);

- preparation of Environmental Health criteria documents (International

Programme on Chemical Safety);

- studies on lessons learned from emergencies after accidents involving

dangerous substances (EEC-CDCIR);

- studies on environmental accidents (EEC-CDCIR);

- studies on effective provision of public information on major indus

trial accident hazards (EEC-JRC).



60

3.4. Literature on Major Accident Hazards

Consequently there is also a very extensive literature on major

acci

dents hazards. The CDCIR inventory publications [19] give a good

overview of the available material. With reference to guidelines on

hazard and risk evaluations and on safe handling of dangerous sub

stances very active are the H.S.E. [20 ]. The Institution of Chemical

Engineers,

the American Institute of Chemical Engineers, which has also

created a "Center for Process Safety", U.S. EPA and OSHA. It is also

worth noted that manufacturers are giving an increased attention to

safety issues [3,21-25].

3.5. Safety Related Standards

There are standards specifically related to safety. However standards

covering various areas such as indicated herebelow are also related to

safety issues:

- fabrication of various equipment (pumps,

etc.),

- pressure vessel fabrication,

- steam boiler fabrication,

- construction,

- civil works,

- testing and inspection of equipment/installations,

- electrical apparatus/area classification,

- safety devices,

- fire protection,

- fire detection,

- fixed fire extinguishing systems,

- fire extinguishers,

- personnel protection equipment,

- safety at work places.

Each country has its own standardization organization (e.g. DIN -

F.R.G., AFNOR - France, BSI - U.K.,

etc.).

In some countries not all

subjects are covered by standards; for certain issues codes of prac

tices are issued instead (e.g.

U.K.).

Specific areas may be covered by

other organizations (e.g. in France the standardization organization is

AFNOR but electrotechnical standards are covered by UTE). Finally in

the U.S.A. standards are issued by various organizations (ASTM, API,

NFPA,

etc.).

Due to the historical development of the various standardization

organization various standards on the same subject may differ substan

tially. In areas that have been recently developed (e.g. instrumenta

tion and control systems) there exist ISO standards that have been also

adopted by most countries. This is not however easy for all areas. In



61

the European level at least an harmonization of standards is needed to

remove trade barriers in view of an open European market. For this pur

pose the European Committee for Standardization (CEN - Comite Europeen

de Normalisation) has been created. CEN is an association of the

national standards organizations of 18 countries of the European

Eco

nomic Communities (EEC) and the European Free Trade Association (EFTA).

CENELEC (European Committee for Electrotechnical Standardization)

deals specifically with electrotechnical standards.

CEN and CENELEC member countries are Belgium, Denmark, F.R.G.,

France, Greece, Ireland, Italy, Luxemburg, Netherlands, Portugal, Spain

and U.K. (EEC), Austria, Finland, Island, Norway, Sweden, Switzerland

(EFTA).

Their official languages are English, French and German. Member

ship is open to the national standards organization of any European

country which is, or is capable of becoming, a member of EEC or EFTA.

The principle task of CEN and CENELEC is to prepare European Stan

dards (EN) . Other documents published may be Harmonization Documents

(HD) or European prestandard (ENV).

- An European Standard (EN) is a set of technical specifications estab

lished, in collaboration with and with the approval of the parties

concerned in the various member countries. It is established on the

principle of consensus and adopted by the votes of a weighted major

ity. Adopted standards must be implemented in their entirety as

national standards, regardless of the way in which the member voted

and any conflicting standards must be withdrawn latest by the date

fixed by the Technical Board.

- A Harmonization Document (HD) is drawn up and adopted in the same way

as an European Standard but its application is more flexible so that

the technical, historical or legal circumstances pertaining to each

country can be taken into account.

- An European Prestandard (ENV) can be prepared as a prospective stan

dard for provisional application in areas of technology where there

is a high level of innovation or where an urgent need for guidance is

felt,

and where the safety of persons or goods is not involved. The

time required for its preparation is therefore reduced; once adopted,

ENVs are subjected to an experimental period of up to three years.

Members have to announce their existence at national level in the

same way as for EN/HD. However, any conflicting national standards

may be kept in force.

CEN and CENELEC have also a certification task for either the

issuing of an European mark of conformity to standards, or the mutual

recognition of test results and inspection. The CEN framework European

Certification scheme is known as CENCER.

CENELEC has a Marks Committee dealing mainly with the certifica-



62

tion scheme within the framework of the Low Voltage Directive (LVD),

within the CENELEC Certification Agreement (CCA) on the mutual recogni

tion of test results for approval of electrical equipment and household

appliances and the scheme for the marking of harmonized low voltage

cables and cords (HAR agreement).

CEN and CENELEC work on a contractual basis (General Guidelines,

Framework Contract) signed with the Commission of the European Communi

ties;

specific mandates for new standards may be also received in the

form of "Order Vouchers" for areas of concern where the Commission

wishes to resolve trade barrier situations which have been notified to

it by the Member States.

A review of the 1989 CEN catalogue [26] showed that only following

specifically safety related European Standards exist:

- EN2 : classification of fires,

- EN3 : portable fire extinguishers (5 standards),

- EN54 : components of automatic fire detection systems

(10 standards),

- EN-132 up to EN-149 : respiratory protective devices and Personnel

eye protection.

4.

Practical Application of the SEVESO-Directive

A detailed comparison of all aspects of the implementation of the

SEVESO-Directive in the Member Countries is hardly possible, since

there various framework for the application of this Directive. Some

countries (e.g. F.R.G., France) operated a full licencing scheme for

industrial installations while in some others (e.g. Ireland, U.K.) no

industrial installation licencing is required. The background from

which the implementation of the Directive started varied from one coun

try to another.

Furthermore in almost half of the countries there is only one Com

petent Authority charged with the task to implement the Directive

(F.R.G., Greece, Spain, France, Ireland, Portugal and U.K.), in the

others there two (Belgium, Italy, Luxemburg, Netherlands) or even three

(Denmark). Cooperation and coordination among the various Competent

Authorities is not always an easy task. In addition some countries

(e.g. F.R.G., Spain) have to face the problem of coordination of the

work of the local authorities operating in the federal regions.

A comparison of the national approaches to the safety report

(notification as per Article 5 of the Directive) performed by the JRC

[27] gives an opportunity for an in depth review of the application of

the SEVESO-Directive in the Member States since the safety report is

tiot a stand alone object. Safety is controlled by inspections, safety



63

audits,

standards, etc.

The main differences observed in this comparison [27] are related

to the control/acceptance approaches applied.

The Netherlands has made probably the most extensive use of quan

titative risk studies of any of the EC countries. There are quantita

tive ri

<;k

acceptance criteria approved by the parliament and define

maximum permissible risk (action required of situation unacceptable)

and for negligible risk (no action required)

.

However, it should be

noted that these acceptability criteria are related to the "external"

safety report which is submitted to the Environmental Ministry and is

available to the public while there is also an "internal" confidential

safety report examined by the Ministry of Labour.

In Ireland and U.K. there is neither a specific requirement for

Quantitative Risk Assessment (Q.R.A.) nor a set of acceptability crite

ria.

Use of Q.R.A. is however not discouraged and is accepted as a sup

port evidence of qualitative conclusions and decisions taken by the

manufacturer. Further H.S.E. in U.K. itself uses Q.R.A. for land use

planning decisions.

In France the laws and regulations themselves are prescriptive and

do not give any quantitative acceptability criteria. No Q.R.A. is

required and the safety analysis has to follow the deterministic

approach. Results of probabilistic analysis, if submitted, are also

judged for the final decision.

F.R.G. represents the other extreme case in comparison to Nether

lands.

Safety analysis has to use a deterministic approach. The safety

report has to show that safety measures taken correspond to the "State-

of-the-art of safety technology" and has to prove that there is no dan

ger for men outside the plant. Even operators of nearby process

units/facilities of the same establishment are considered as "men

out

side the plant". However, Q.R.A. is accepted as a support for selecting

among various alternative safety solutions but is never used for a

whole plant or installations.

Contrary to these differences there are also some important points

of convergence such as:

- Though the limitations due to lack of data of a Q.R.A. analysis, this

method is useful for selecting among various alternatives or for

stating priorities.

- Compilation of the safety report by the operator of the plant is very

useful, since substantially contributes to the awareness of the

hazards inherent in the process.

- The safety report is not a stand alone object that is once compiled

and examined. It should be a part of a dynamic process of continuous

inspections from the authorities in order an ever improving level of

safety to be achieved.



64

- Evaluation of safety reports is a multidisciplinary task. This

requires either the assistance of various specialized experts or at

least as an aid very detailed checklist containing the concentrated

experience of various experts.

- Human factors are very important and have to be addressed appropri

ately in the safety report, evaluation of human factor issues is not

an easy task [ 3 3 ].

4.1. Run-away/'Side/Decomposition Reaction Hazards

Generally batch processes are considered as more problematic in compar

ison with continuous operation processes since they involve much often

transient operations (start-up, shut-down, loading-unloading, transient

conditions, etc.). It should be noted that in all countries (with the

exception of Spain) hazard identification is required to be performed

for every plant state [27].

With reference to run-away/side/decomposition, etc. reaction haz

ards the answers of the Competent Authorities can be grouped together

in three categories:

a) No specific requirements because either such a hazard is not present

in any of the installations (Luxembourg) or the Competent Authori

ties have not yet been confronted with this problem.

b) general requirements such as that the manufacturer has to identify

conditions that may lead to a hazardous incident and hence identify

any risk of run-away reactions. If data are not available in the

literature experimental campaigns should be performed.

c) More specific requirements such as:

- Should a major accident hazard can be perceived to result from an

unwanted or uncovenanted reaction the implications of that sce

nario are to be investigated and the relevant safeguards de

scribed.

This also requires experienced inspectors who can be assisted by

referring to either general rules (e.g. attention to exothermic

steps such as polymerisations, nitrations, Grignards, etc.) or to

data from sources like:

. Brethick (1975) in

Lees'

Loss Prevention, p. 1080 [3 2] ,

. data bank DIMDI in FRG,

. NFPA guide,

. International Process Safety Analysis guidelines (if an y).

- Data to be supplied in this case may include:

. Process chemistry, thermochemistry rates of reaction, laboratory

techniques to determine reaction rates DSC, DTA, Dewer Calorime-

try, ARC tests,

. details of research work performed (if an y),



65

impurity controls,

vessel design,

measures to prevent releases (justification of venting or not,

DIERS sys tems, venting and scrubbing/blowdown/flaves

systems),

other precautions to reduce such risks,

==sessment of consequen ces of a reactor ex plosio n including ri sk

to operator/other persons in nearest building/public.

5. Lessons Learned from Accidents Notified

By the end of 1990 a total of nine tyeig ht (98) accidents had been reg

istered in M.A .R. S. Competent Autho rities , having recognized the impor

tance of an exchange of experience for an active accident prevention

policy, notify also some not major accidents whenever this enables

extraction of important lesso ns. Accidents notified can be broken down

as follows:

Major accidents 69

Other accidents 20

Accidents occurred before 198 4 9

Total 98

The numbe r of accident noti ficat ion from each country largely

depends both on the efficiency of national control organizations, which

in turn is related to the background from which the implementation of

the Dire ctiv e sta rted, and on the interpre tation of the rather fuz zy

defini tion of "major acci dent " (see also point 2 .2.1. above).

As a result the accid ents included in M. A. R. S. do not represent an

uniform sample of process accidents and can hardly be used for statis

tical purposes. However, the characterization of the accidents by

vari

ous parameters *) leads to some useful remarks [3 ] that can be summa

rized as follows:

a) almost 2/3 of the accide nts involved the releas e of dange rous sub

stances;

b) main process u nits are more often involved in accid ents wherea s the

number of accidents in isolated storages is also significant;

c) almost 1/3 of the accidents occurred during maintenance, loading/un

loading, transfer, start-up, shut-down and other non-standard opera-

(*) Type of act ivit y, type of acc iden t, conseq uen ces, subst ances in

volved, gravity indices and causative facto rs, see also point 2.3 .

above.



66

tions;

d) substances very commonly used (e.g. flammable gases and liquids,

chlorine, hydrogen) are most often involved in the accidents;

e) the vast majority of the accidents notified could have been

pre

vented by proper application of existing experience and diffused

knowledge;

f) managerial/organizational omissions could be identified among the

causative factors in about 90% of the accidents of which the causes

are known;

g) design modifications/improvements were suggested after the accident

in almost 70 % of the accidents of which the causes are known.

6. Accidents Involving Unexpected Reactions

6.1. Gen eral Characteristics

In 17 out of the 98 accidents unexpected reactions were identified

among the primary causes of the accidents. This is a significant

portions of the total number of accidents notified; furthermore it

should be noted that unexpected reactions are ranked as the third in

frequency primary cause of accidents after component failures (in 45

out of the 98 cases) and operator errors (in 25 out of the 98 cases) .

These accidents can be broken down according to their notification as

follows:

Major accidents 11

Other accidents 3

Accidents occurred before 1984 3

Total 17

Type of these accidents:

Explosion 2

Fire 1

Release 1

Explosion and fire 2

Explosion and release 3

Fire and release 1

Explosion, fire and release 7

Total 17

These tables show that in almost all cases (14 out of 17)



67

explosion occurred while frequency of explosion occurrence is less than

45%

in the total 98 accidents.

The breakdown of the accidents according to the type of industrial

installation is as follows:

Type of Activity Accidents

Run-away All

Other industries

Refinery, petrochemical

Pharmaceutical

Halogen, alkali, etc.

Isolated storage

9

2

4

1

1

3 9

4 0

1 5

7

1 3

17 98

This breakdown shows that unexpected reaction hazards are higher

in pharmaceutical activities and rather low in storage activities in

comparison to the total number of accidents registered in M.A.R.S. Ten

of the accidents occurred in batch processes, five in continuous

pro

cesses and one during unloading operation in a storage installation.

6.1.1. Consequences of the accidents.

The consequences of th-°se 17

accidents are given herebelow together with the consequences of all 98

accidents included in M.A.R.S.

Such a comparison suggests that accidents involving unexpected

reactions show a higher tendency to inflict losses (fatalities,

injuries - especially operator injuries - and material damage) in com

parison to the average accidents in process industries. This should be

attributed to the higher frequency of explosions observed in this type

of accidents.

6.1.2.

Accident causes.

There hardly exist accidents with a single

causative factor. Causes of accidents can be further subdivided in

pri

mary and underlying causes. Identification of all causative factors for

extracting experience useful for a preventive policy. The classifica

tion of causative factors for accidents currently used is given in [ 3 ] .

The most dominant other primary causes that have been identified

in the 17 accident involving unexpected reactions are:

- component failures : 6 accidents (in 3 out of these 6 instrumenta

tion/control

failures);

- operator errors : 6 accidents (all 6 operations related errors).



68

Consequences

None or negligible

Fatalities

on-site

off-premises

Injuries

on-site

off-premises

Material damage

within the establishment

off-premises

Environmental damage

Traffic interruption

Public evacuation

Plant evacuation

Public annoyance

Public deprived from potable water

Accidents

involving

reactions

2

4

4

12

12

3

15

15

6

1

2

2

1

1

(11.8%)

(23.6%)

(23.6%)

-

(70.6%)

(70.6%)

(17.7%)

(88.2%)

(88.2%)

(35.4%)

(5.9%)

(11.8%)

(11.8%)

-

(5.9%)

(5.9%)

Tot

ace

21

20

19

2

43

40

8

64

61

13

11

10

7

5

3

2

al

idents

(21.4%)

(20.4%)

(19.0%)

(2.0%)

(43.9%)

(40.8%)

(8.2%)

(65.3%)

(62.2%)

(13.3%)

(11.2%)

(10.2%)

(7.1%)

(5.1%)

(3.1%)

(2.0%)

15 (88.2%)

14 (82.3%)

14 (82.3%)

11 (64.7%)

3 (17.7%)

(17.7%)

(23.6%)

The most dominant underlying causes are:

a) Managerial/organiz ational omissions

- insufficient or unclear procedures

- design inadequa cy

. process inadequately analyzed

. design error

. codes applied provided for

limited prote ction only : 3

b) Appro priat e proc edure s not followed (short-cuts) : 4

The study of the causative factors of these accidents reveals the

conclusions drawn in [3] (see also point 5. above) and is in agreement

with other accident reviews [28 -30 ] underlying the importance of human

factors for accide nt prev enti on. A proper s afety manag ement system is

indispensable for an effective accident prevention policy. If a safety

culture exists then early identification of hazards with the help of a

structured hazard as sessm ent techniq ue (e.g. combina tion of a technique

mainly aiming to hardware such as HAZ OP, HAZ AN, FMEA with techniques

focussing mainly on manag erial and organ isatio nal aspects such as MOR T

[31]) is more effective.

It is worth noted that the recently published Cullen report "The

Public Inquiry into the Piper Alpha disaster" suggests that also off-



69

shore installati ons to be covered by the requiremen ts of the SEVE SO-

Directive since a formal safety assessment is expected to enhance the

safety of such installations [30].

6.2. Lessons Learned from Accidents Involving Unexpected Reactions

The lessons learned extract ed from the acciden ts in M. A. R. S. are pre

sented in [3 ] grouped t ogether in the following categ orie s:

1) design/construction-related,

2) operation/maintenance-related,

3) emergency handling,

4) mobiliz ation after and emergency,

5) substance specific,

The lessons extracted from the 17 accidents involving unexpected

reactions are given herebelow; lessons of categories 3 and 4 are pre

sented together.

6.2.1. Design/construction-related.

a) Contro l rooms in plants whic h handle flammab le and/or explosive sub

stances should be able to withst and ex pected bla st (blast-proof

design) so that control room operato rs can take the prope r act ions

in the case of an emergency.

b) To a maximum p ossib le extent an inherent ly safe design must be

adopted whenever possib le. The application of this rule is illus

trated in the case where for vinyl chloride polymerization to PVC:

- a plasti ciz ing agent was used requiring heati ng by steam at 16 5"C-

175°C,

while latex starts to decompose at 14 0 °C;

- there was no means for the detec tion of the failure of the agita

tor and, consequently, it was not possible to automatically cut

off the steam supply when the agitator failed in order to avoid

the development of hot spots.

The same principle is also highlighted in another accident where a

by-pass on a control valve was installed without any possibility to

safely interlock this by-pass manually so that no dangerous situa

tion would arise in case of maloperation.

Accident investigation in a third case indicated that process modi

fication in the direction of an inherently safe design could prevent

similar accidents to occur (substitution of the wast e wate r trea t

ment method

employed).

c) The creation of explosive mixtures when handling flammable materials

must be avoided using inert substan ces (e.g. nitrogen). This very

well-known practice could have prevented a series of the reported

accidents (10 out the 98 reported accidents among which one involv

ing an unexpected reaction)

.

If for a certain case inert ing is not



70

considered feasible, technical measures have to be taken to avoid

the presence of ignition sources (e.g. installation of flame

arrestors in piping connecting a system with a potential explosive

mixture to an environment where ignition sources can not be elimi

nated) .

d) Proper th ermoche mical data and ass ociated conditi ons mu st be

obtained for possible run-away reactions before any substance, sus

pected to cause or undergo such a run-away reaction, is used in a

substant ial quantity (e.g. even in pilot -plant scale trials).

e) Provi sions for safe disposa l or con tainme nt of the maximum fire

water flowrate, that could be used in the case of emergency, are

necessar y to avoid damage to the envir onment (this has been demo n

strated in at least 3 of the 98 acc idents one of which involving

unexpected reaction; this later case caused the cut-off drinking

water to 200,000 persons). Attempts to provisionally contain the

fire water led to flooding of the establishment and damage to

machin ery and electrical equipment in another cas e. On the other

hand, there are indications that this particular lesson has been

learned, since in five other recent a cci den ts, the containmen t and

the safe disposal of used fire-water has been reported.

f) Fire water supply faci lities m ust be designed in such a way that

adequate fire water supply is ensured in the case that even a single

failure occurs in the system.

6.2.2. Operation/Maintenance related

a) Extrem e care mu st be taken and pro cedur es must be accurately fol

lowed in order to avoid mixing of incompatible chemicals or invert

ing the order of introduction of chemicals in a reactor. There are 3

among the 17 acciden ts initi ated in such a way ; their caus alitie s

were personnel injuries and material damage and in one case one

fatality.

b) Proce dures for performing v ariou s analytical tests must alway s be

strictly followed; in one case deviation from the specified proce

dures masked the identification of a run-away reaction in operating

conditions.

c) Inadequat e perso nnel training has been identified among the cause s

of 9 out of 98 accide nts notified (2 of them involving also run

away reactions). Ho wever, even experienced operators may make errors

under condit ions of excessive w ork load or due to unclea r pr ocedur es

as is indicated in other 3 of the notified accidents.

6.2.3. Lessons Learned from Emergencies

a) The location of a release to the environment must also be identified

and monitored. Reference is made to an accident , where chloride and



71

hydrochloric acid c oncentr ations, measured at the plant's fence,

were very low , but the location of emission of thes e gases to the

atmosphere was close to the air intake of the ventilation system of

an adjacent building. Due to the low levels measured, it was not

considered necessary to alert the population, but concentrated

fumes, sucked in by the venti latio n s ystem , affected 29 per so ns, 11

of whom needed to be taken into the hospital for observation.

b) The effective action of spray/deludge systems, automatically or man

ually operated, has been experienced in several cases both for

assisting in dispersing the emission of toxic substances (two acci

dent s both involving run-away exother mic reactions) or fi ghting

fires (three cas es one of whic h involving unexpec ted reaction) .

There is also a reported case where the activation of a sprinkler

system by the release of hot liquid hexane was not adequate to pre

vent the explosion of its vapours, since the ignition point was

obviously qu ite far from the release sou rce . The instal lation of a

water drench syst em was decided up on in at least one case aft er

accident investigation.

c) The appl icatio n of cooling w ate r, at an adequat e ra te , to storag e

tanks adjacent to a fire can effectively prevent the spreading of

the fire to the content of the tank as has been experienced in two

accidents one of which involving an unexpected reaction.

d) Following an explosion and fire in a chemical factory situated close

to the to wn (about 2 km away), a blast and smok e caused public c on

cern.

The manufa cture r soothed people' s fear by stating on national

radio and TV that the smoke was not toxic.

e) Delay s in getting skilled deci sion- maker s and neces sary fire fight

ing equipment and material at the scene of the accident may con

tribute to an unnecessary escalation of the accident. Therefore,

they must be accounted for in the emergency planning.

f) Fire fighting intervent ion teams must be in the posit ion to acti vate

quickly alter native external fire water sources since the good func

tioning of the fire water supply systems of the establishment cannot

always be guaranteed.

6.2.4.

Substance Specific Lessons Learned

a) Chlorin e: the use of hydrochloric acid , contaminated by traces of

methanol in chlorine/alkali electro lysis, may lead to methylnit rate

formation and, consequently, to danger of explosion. Hence, careful

analytical monitoring of raw materials is recommended. Reference is

made to an accident where an explosion attributed to this reason

caused injuries to 6 persons and material damag e.

b) Hydrogen peroxide: rapid exothermic decomposition of hydrogen perox

ide may occur in the presence of sulphur components and at pH higher



72

than 7.5. Hence, the use of hydrogen peroxide for waste-water treat

ment in the presence of volatile flammable substances may be danger

ous.

Referen ce is made to an acc ide nt, wher e 1 person was killed and

large material damage was caused by an explosion and fire.

c) Hydro gen peroxide and pyri dine : a rapid exoth ermic reactio n may be

caused by excessive hydrogen peroxide addition rate to pyridine.

d) Nitro -orga nic com poun ds: this type of compounds is well known as

unstable and subject to run-away reactions. In four of the reported

accidents, nitro-organic compounds were involved.

Inversion of the order of introduction of sulphuric and nitric acid

in the synthesis of 3-methylthioa niline caused the formation of

methy lnitr ate which , in turn , initiated a run-away reaction leading

to an expl osio n, which caused injuri es to one person and large mat e

rial damage.

Still unknown catalytic effects (inorganic salts) caused an unex

pected run-away reaction in a nitroanthraquinone production plant

leading to an explosion, which caused the death of one person,

injuries to 5 perso ns and large materi al dam age .

The distillation of a crude product containing also orthonitroben-

zaldehyde (which had been formed by the oxidation of this product by

nitric acid) led to a run-away explosion which caused injuries to 2

persons and large material damage.

The run-away explosion during distillation of l-methyl-2-formyl-l-

nitro -imida z ole caused injuries to 2 pers ons and large materi al dam

age.

e) PV C: A run-away explosion in a polymerization reaction which caused

large mate rial d ama ge, was attri buted to the combina tion of the fol

lowing parameters:

- inadequat e ammoni a a ddit ion, which could not compe nsate the hy

drogen chloride produced;

- latex coagulation due to an excess of hydrogen chloride;

- mixer failure due to latex coagulation;

- no device had been installed to indicate mixer failure;

- local overheating due to no mixing;

- decom positi on of latex due to local over heating (steam at 165°C-

175°C was used due to the plasticizing agen t, while latex decompo

sition starts at 1 4 0 ° C ) ;

- attack of reactor material by an excess of hydrogen chloride.

The reactor burst although the steam supply had been interrupted and

external cooling started due to overpressure and the reduction of

wall thickness from 9.8 to 2 mm.

After this accident, the following was decided:

- the substitution of the plasticizing agent so that steam at maxi

mum 127°C can be used;



73

- the installation of warning signals and a steam supply cut-out

system;

- batch analytical controls of the latex pH and its persulphate con

tent are required

f) Raney nickel: pyrophoric nickel material may ignite vapours from

flammable material. Reference is made to an accident where ignition

causing a flash-fire was attributed to this reason.

7. Accidents due to Electrostatic Hazards

7.1. General Characteristics

There are 7 out of 98 accidents for which electrostatic loads have been

identified among their primary causes. Only 1 out of these 7 is a major

accident according to the interpretation of the relevant notifying Com

petent Authority.

In all seven accidents an explosion occurred; in four of them a

fire was also broken thereafter.

Five out of the seven occurred in pharmaceutical industries, the

other two in installations specified as general chemical industry. All

seven occurred in batch processes.

Review of these accident characteristics suggests similarities

with the conclusion drawn for accidents involving unexpected reactions

(see point 6.1.

above).

In 3 out of these 7 cases persons were injured, in 2 of them the

plant was damaged and in one case plant evacuation was necessary. In 3

out of these 7 accidents consequences were negligible. However 6 out of

these 7 cases were incidents that have not been considered as major

accidents.

Only in three cases another primary cause has been identified, too

(component failure in all 3 ) .

With reference to underlying causes following was observed:

- Managerial/organisational omissions : 7 (100%)

- Lack of safety culture : 6 (85.7%)

- Insufficient/unclear operating procedures : 6 (85.7%)

- Design inadequacy : 1 (14.3%)

It should be noted that design inadequacy has been identified for

the only one major accident falling in this category.

Hence these 7 accidents suggest also the same conclusions with

reference to an active accident prevention policy as the ones drawn

from the whole of notified accidents (see point 6.1.

above).



74

7.2. Lessons Learned from Acciden ts Caused by Electrostatic Loads

7.2.1. Design/Construction-related

a) The creation of explosive mixtures when handling flammable materials

must be avoided using inert substances (e.g.

nitrogen).

This very

well-known practice could have prevented could have prevented 6 out

of these 7 accidents as well as a series of others (see also point

6.2.1.C

above).

b) In the case of the operation of a vacuum drier with a flammable sol

vent,

the monitoring of its pressure is recommended. When the vacuum

falls to a pre-set value, the automatic stop of the rotation and the

start of the nitrogen purge are recommended.

c) Earthing of metal components is necessary to avoid electrostatic

charges in areas where flammable materials are handled. The failure

to comply with this well-known rule was identified among the causes

of four reported accidents.

7.2.2. Operation/Maintenance-related

a) Non-standard operations must be avoided. Whenever their execution is

inevitable, a careful review from a safety point of view should take

place before they start in order to assure that all the operators

involved are fully aware of the inherent potential danger. Reference

is made to an accident, where an explosion followed by fire occurred

when dry powder instead of the usual wet cake was added to a

flammable solvent for recrystallization.

b) Nitrogen purging is mandatory before starting to charge material to

vessels/equipment containing flammable solvents or whenever such

equipment are opened for sampling or similar operations. This

requirement was not fulfilled in four of the reported accidents, as

post-accident investigations showed.

c) Frequent inspections of equipment with rotating elements containing

flammable material (e.g. batch centrifuges) are recommended to

assure that there is no spark danger due to tear of the coating of

the metal parts. Reference is made to an accident where a friction

spark was among the possible explanations of the ignition sources of

the isopropanol vapours.

7.2.3.

Substance Specific Lessons Learned

a) Powders and flammable solvents: Handling powders in the presence of

flammable solvents must be performed with extreme care and with all

necessary precautions such as:

- inert (e.g. nitrogen) purging to avoid explosive mixtures;

- earthing of metal components to avoid static electricity build

up;



75

- exclusion of other ignition sources (e.g. sparks).

Reference is made to five incidents where explosions and fires were

caused by not respecting these rules,

b) Styrene:

- all metal components in contact with styrene must be earthed;

- it is recommended for vessels containing gelcoat (polyester in 4 0 %

styrene) to locate safety valves on the pressurized air supply

pipe and not on the pressure vessel itself (reference is made to

an explosion and fire accident that caused large material damage).

5. References

[1] Commission of the European Communities (1990) "Council Directive

82/501/EEC on the major accident hazards of certain industrial

activities", EUR 12705, Luxembourg: Office for Official Publica

tions of the European Communities.

[2] Council resolution 8 9/C273/01, Official Journal of the European

Communities, No.

C273/1.

[3] Drogaris, G. (1990) "M.A.R.S.-Lessons Learned from Accidents

Noti

fied", EUR-(in press), Luxembourg: Office for Official Publica

tions of the European Communities.

[4] Otway, H. and Amendola, A. (1989) "Major Hazard Information Policy

in the European Community: Implications for Risk Analysis" 9. (4) 505.

[5] Amendola, A., Contini, S. and Nichele, P. (1988)

"M.A.R.S.:

The

Major Accident Reporting System" in "Preventing Major Chemical and

Related Process Accidents", I. Chem. E. Symposium Series No. 110 ,

EFCE Publication Series No. 7 0 , p. 455.

[6] Testori-Goggi, P. (1989) in the Preface of CDCIR, Vol. 1, Report

S.P./1.89.12 (JRC-Ispra).

[7] Rasmussen, K. (1990) "European Community Documentation Centre on

Industrial Risk", Toxicological and Environmental Chemistry 25 213.

[8] Commission of European Communities (1967) "Council Directive on

the approximation of

laws,

regulations and administrative provi

sions relating to the classification, packaging and labelling of

dangerous substances - 67/548/EEC", Official Journal of the Euro

pean Communities L 196/1, 16.08.67.


on the introduction of measures to encourage improvements in the

safety and health of workers at work - 89/391/EEC", Official Jour

nal of the European Communities L

183 /1,

29.06.89.



76


concerning the minimum safety and health requirements for the

workplace - 89/654/EEC", Official Journal of the European Communi

ties L

393/1,

30.12.89.

[11] U.S. Department of Labour - OSHA (1990) "29 CFR Part 1910 -

Pro

cess Safety Management of Highly Hazardous Chemicals" Notice of

Proposed Rulemaking, Federal Register 5_5_, No. 13 7, July 17, 1990.

[12] OECD (1989) "Accidents Involving Hazardous Substances" Environmen

tal Monographs No. 24.

[13] OECD (1990) "Atelier sur la prevention des accidents lies aux sub

stances dangereuses. Bonnes pratiques de gestion" Environmental

Monographs No. 28.

[14] OECD (1990) "Atelier sur la communication d'informations au public

et le role des travailleurs dans la prevention des accidents et

1'intervention", Environmental Monographs No. 29.

[15] OECD (1990) "Workshop on the Role of Public Authorities in Pre

venting Major Accidents and in Major Accidents Land-Use Planning",

Environmental Monographs No. 3 0.

[16] Batstone, R.J. and Lepkowski, W. (1986) "World Bank Acts to Pre

vent Chemical Disaster", Technology Review.

[17] The World Bank (1985) "Manual of Industrial Hazard Assessment

Techniques", London.

[18] United Nations (1988) "Awareness and Preparedness for Emergencies

at Local Level. The APEL Process" United Nations Environment

Pro

gramme.

Industry and Environment Office.

[19] CEC-JRC-ISEI (1990) "Community Documentation Centre on Industrial

Risk", ISEI/SER-1899, S.P./I.90.18.

[20] H.S.E. (1990) "Library Information Service - Publication in Series

List"

H.S.E. Library and Information Services.

[21] CONCAWE (1989) "Methodologies for Hazard Analysis and Risk Assess

ment in the Petroleum Refining Industry".

[22] CEFIC (1987) "A Guide to Safe Warehousing for the European Chemi

cal Industry".

[23] LPGITA (1988) "Guide to the Writing of L?G Safety Reports".

[24] Chemical Manufacturers Association "Evaluating Process Safety in

the Chemical Industry".

[25] Chemical Manufacturers Association "Safe Warehousing of Chemicals".

[26] CEN (1989) "Catalogue" Ed. 2.

[27] Amendola, A. and Contini, S. (1990) "National Approaches to the

Safety Report. A Comparison" CEC-JRC-ISEI/SER, S.P. ISEI/SER 1761.

[28] H.S.E. (1987) "Dangerous Maintenance" ISBN 0 11 8 839578, London.

[29] Shortreed, J. (1990) "Recent Advances in Research and Future

Requirement", Plant/Operation Progress, 9_ (3 ), 198 .



77

[30] Boniface, A. (1990) "Piper report set to reform", The Chemical

Engineer, No. 485

(15.11.90),

15.

[31] Smokas, J. (1988) "The Role of Safety Analysis in Accident Preven

tion", Accid. Anal. & Prev., 1Q (1), 6 7.

[32] Lees, F.P., (1983) "Loss Prevention in the Process Industries",

Vol. I and II, Butterwort, London.

[33J Amendola, A. (1990) "Human Reliability Models" CEC-JRC-ISEI, Tech

nical Note No. 1.90.23, PER 184 0/90.





LABORATORY TESTING PROCEDURES

Paolo CARDILLO

Stazione sperimentale per i Com bustibili

V.le A. De Gasperi 3

20097 San Donato Milanese

Italy

ABSTRACT. In order to avoid conditions for thermic hazards it is neces

sary to have knowledge of the chemistry and associated thermochemistry

(kinetic and thermodynamic data) of the desired reaction and potential

side reactions and also of the thermal stability and physical properties

of reactants, intermediates and products. The various instruments and

testing methods currently used provide a means of assessing thermal ha

zard. Over recent years great progress has been made. New methods have

been developed and many new instruments have been offered to the market.

In addition, many institutions have codified the procedural aspects of

safety investigation.

1.Introduction

In any chemical process there is always the danger that the rate of heat

generation will be greater than the rate of heat removal so that the ma

terials will undergo an undesired temperature increase. At this higher

temperature, it will produce even more heat, and the temperature will

increase exponentially in the direction of a thermal explosion.

Essentially chemical reaction hazards are associated with loss of

control of exothermic reactions, gas evolution and/or decomposition phe

nomena.

Hazardous runaway reactions may occur in all operations in which

chemicals are involved including t

1

) :

- conversion of chemicals (desired reaction)

- unit operations (drying, grinding, distillation, etc.)

- storage and transportation of bulk chemicals.

Potentially dangerous heat formation can occur in the desired

pro

cess as well as in undesired consecutive and decomposition reactions

[2,3] .

The accumulation of starting materials or intermediate products

is, in many cases, the initial step of a runaway reaction: common causes

of reactant accumulation are wrong kinetic assumption, too high feed ra

te,

too low temperature, incorrect initiation, or insufficient mixing

and impurities that can affect the kinetics. Under disturbed operating

conditions (for example, loss of cooling), the energy release associated

79

A.

Benuzzi and J. M . Zaldivar (eds.). Safety of Chemical Batch Reactors and Storage Tanks, 79-97.

© 1991 ECSC. EEC. EAEC, Brussels and Luxembourg. Printed in the Netherlands.



80

with the reactant accumulation can cause the batch temperature to rise

to a critical level where secondary, unwanted reactions are triggered.

In order to avoid conditions for thermic hazards it is necessary

to have knowledge of the chemistry and associated thermochemistry (kine

tic and thermodynamic data) of the desired reaction and potential side

reactions and also of the thermal stability and physical properties of

reactants, intermediates and products. Only a detailed analysis can

pro

vide quantitative, reliable data on the probability of an incident and

its severity. The key to success here is initiating a comprehensive ana

lysis at an early stage in project development.

It is not enough that the process steps have been carried out on

laboratory scale without incident, for plant conditions are different.

For example, metals are used in place of glass for the construction of

equipment, pressures and temperatures may be higher, residence times may

be longer, by-products may accumulate in recycle streams, or impurities

may be introduced by substituting commercial for reagent chemicals.

The scale of operation may also be an important factor, particularly in

batch operations.

The assessment strategy is to evaluate two types of hazard. In the

first case, one or more of the reactants, intermediates or products is

inherently unstable and limits have to be determined for the safe opera

tion of the process so the lowest possible temperature at which the on

set of decomposition can be detected is not reached. In the second case,

we must consider that any reaction which is exothermic is potentially

hazardous unless the plant used is capable of handling the heat load.

2.

Testing procedures

A testing sequence is required that screens processes for potential ha

zard, defines process conditions under which uncontrolled reactions

could be initiated, quantifies the consequences of such reactions, and

monitors the margin of safety between the normal operating conditions

and the onset of dangerous exothermic activity.

The questions that should be answered by a test program are:

. which process data do we have to know?

. by which methods can we determine the necessary data?

. what can we conclude from the test results?

In order to specify the safe operating conditions, the primary da

ta required are:

1. the rate of heat evolution

2. the cooling capacity of the plant

In order to determine the consequences of a runaway reaction, it

is necessary to determine:

1. the total heat of reaction

2. the specific heat

3. the adiabatic A T

4.

the boiling point of the mass

5. the temperature range in which secondary or decomposition reactions

can be expected and the heat of decomposition of such reactions

6. the amount and rate of gas or vapor evolution (pressure developed and

'rate of pressure increase)



81

7.

effects of mischarging, impurities and errors.

If the intended reaction is exothermic, heat production is unavoi

dable and the corresponding cooling has to be provided.

Heats of reaction can be roughly assessed by calculation using

heats of formation, and for well-known reactions published data are so

metimes available f

4

-9]. For the majority of the processes under deve-

lopme^

1

", the reaction heat and the time profile of the heat evolution

rale has to be measured experimentally.

The instantaneous heat evolution rate of chemical process proves

to be an ideal property to measure. Not only it is indicative of whether

and how fast reactions are actually occurring but it is also directly

the risk-related quantity which can be easily transformed into a tempe

rature increase rate for the case of emergency loss of cooling.

An essential quantity for the estimation of the severity of a gi

ven chemical process will be the maximum temperature increase to be ex

pected under adiabatic conditions (adiabatic

/ \ T ) .

It allows us to

cal

culate the maximum final temperature in case of a runaway situation.

Comparing this final temperature to the temperature range of se

condary reactions and to the physical properties of the reaction mixture

under investigation such as melting point, vapor pressure and boiling

point, yield direct information about the consequences of a runaway

(Fig. 1).

Until a few years ago experimental determinations were all aimed

at establishing the temperature range in which decomposition occurs I

10

-

15] .

decomp. reac t ion

A H • 8 0 0 J / g

des i red reac t ion

A H - 170 J /g

50 C

90 C

A

Tad - 45 C

T e m p e r a t u r e

Figure 1. Simplified scenario of a thermal runaway.



82

In reality, only very few substances have a clearly defined decom

position temperature. Exothermic decomposition starts at the temperature

at which heat generated exceeds the lower detection limit of the measu

ring instrument. Thus instruments with high sensitivity will indicate a

lower starting temperature for the same decomposition reaction than in

struments with a lower sensitivity [16-19]

#

When the decomposition temperature is given, it is essential to

describe the instrument used and the experimental conditions employed

(sample size, heating rate, sample holder, e c c ) .

The temperature at which the initiation of exothermic decomposi

tion is detected during thermal stability tests depends on several fac

tors.

These do not only concern the materials properties and the speci

fic decomposition reaction but can include the experimental systems'

characteristics and experimental parameters.

A good example of this is the thermal stability study of the "Se-

veso mixture". The Seveso accident (1976) has met with great interest in

the scientific world; it has probably never happened in the past that

such an effort was made to understand, from a physico-chemical point of

view, an accident occurring in a chemical plant.

Several authors studied the thermal stability of the mixture and

its components supposed present in the reactor. All available methods of

thermal analysis (1976-1983) were used: simultaneous thermogravimetry

and differential scanning calorimetry (TG/DSC) [20,2i]

j

differential

thermal analysis (DTA) [ 22] , miniautoclave, Sikarex, Dewar flask [23 ],

accelerating rate calorimeter (ARC) [24] under different experimental

conditions (dynamic, isothermal, adiabatic, isochoric, and

isobaric);

in

open platinum sample holder, in air or nitrogen; in closed crucibles of

nimonic, glass or gold.

The most significant results of these studies can be summarized as

follows:

. the atmosphere surrounding the sample and the material of the contai

ner does not affect the observed exothermic behaviour;

. the Seveso mixture kept at 160 °C does not show appreciable exother

mic reactions;

. the experiments in miniautoclave do not show exothermic reactions be

low 200 °C; self-heating of the mixture proceeds at an appreciable rate

only above this temperature t

23

l;

. DSC measurements with an instrument made in 1970 did not show any e-

xothermic behaviour below 230 °C t

2

° ] ;

. DSC/DTA measurements with more recent instruments show - both under

dynamic and isothermal conditions - slow and week (about 105 - 125 J/g)

exothermic behaviour starting a 180 °C; these phenomena were previously

unknown. These measurements also show other, known and more intense, e-

xothermic reactions above 230 °C [20-22].

. in the Sikarex calorimeter, under isothermal conditions and with open

sample holder, the self-heating proceeds at an appreciable rate only a-

bove 200 °C; under adiabatic conditions, with open sample holder at 160

°C, the temperature of the mixture increases by about 10 °C in four

days; at 180 °C only a small temperature gradient can be observed, which

gets exhausted after 24 hours t

2 3

) ;

'. under heat-accumulating conditions (Dewar flask) at 180 °C the tempe-



83

rature increases

by 1-2 °C

only,

and the

rate

of

pressure rise

is 10

mbar/h I

23

l ;

.

the

adiabatic calorimeter

ARC

confirmed existence

of a

first exother

mic effect

at 180 °C (/\H 122 J/g) ,

strong enough

to

increase

the

tem

perature

by

about

60 °C

(under strictly adiabatic conditions)

and to

start

a

second, more violent, runaway reaction.

The ARC

test also showed

that.

° ove 180 °C, the mixture gets self-heated, always in adiabatic

conditions,

causing

a

pressure increase

of 4 bar (the

safety disk

at IC-

MESA was set at this value) in 8 hours I

24

l.

The ability to detect very low rates of self heating is of great

importance. This

is

illustrated

in Fig. 2.

j

O)

c

C O

C D

C O

B

Temperature T1

T2 T3

Figure 2. Simple exothermic reaction.

A relatively insensitive test method

(A)

will detect exotherm

at

temperature above T3. As the sensitivity of the method increases (B,C)

the detection temperatures drops (T2,Ti).

As can be

seen,

no

matter

how

sensitive the test method is, there will always be a reaction occurring

below

Ti.

It

is

important

to

note that

the

difference between

Ti and T3 is

typically 50-100 °C.

Under temperature control (cooling

and agitation), the low

rates

of heat evolution may be insignificant but under heat accumulation con

ditions,

then very

low

rates

of

heat evolution

may

give rise

to a ha

zard.

The example shown

in Fig. 2 was of a

simple exothermic reaction.

If the chemistry is more complex, then the need for high sensitivity can

be even greater

as

shown

in

Figures

3 and 4.



84

Fig. 3 shows a typical system of two overlapping reactions. The

main thermal hazard is caused by the major peak. However, the hazard

from this major exotherm is triggered by a very small reaction at lower

temperature. Recognition of the small reaction is of absolutely crucial

importance in understanding and hence controlling the thermal hazard.

However, low sensitivity techniques will fail to recognize its existen

ce.

c

CO

0)

CO

B

r ^

I

Temperature

Figure 3. Two overlapping reactions.

T1 T2 T3

Fig. 4 shows another example where good sensitivity is of para

mount importance. In this case, the main exotherm is autocatalytically

induced. The instrument C is sensitive enough for this to be recognised

instantly (the steep initial slope is a sure indicator of autocataly-

sis),

but the others are not.

This is a serious defect of less sensitive techniques since the

recognition of autocatalysis is crucially important in thermal hazard e-

valuation.

When assessing the consequences of a runaway reaction, it is im

portant to remember that the real damage is caused by the effects of ex

cessive rate of gas and vapor evolution and that the exothermic events

only act as the driving force.

The pressure produced during decomposition is in turn determined

by the quantity of gas liberated and the decomposition energy, which is

decisive for the attainable final temperature. In addition, the decompo

sition rate, which itself is very much dependent on the temperature at

tainable during decomposition, is decisive for the rate of the pressure

'increase.



85

c

'+*

0

.c

I

5 3

C O

B

Temperature

Figure 4. Autocatalytic reaction.

T1 T2 T3

Some modern instruments can now measure the temperature-pressure

curve under different conditions t

2 5

.

2 6

3 . Fig. 5 shows the ARC self heat

curve of a liquid monomer A. At least three reactions can be seen, the

initial exotherm being detected at 180 °C with a mechanism change about

6 or 7 °C later. The initial mechanism may be deduced to be autocataly

tic from the shape of the first part of the curve. The third reaction,

the decomposition of the polymer, is seen as the shoulder on the right

of the curve.

Fig. 5 also shows the pressure versus temperature curve making ap

parent that the last reaction, the small shoulder on the right is the

real danger.

3.INSTRUMENTS AND METHODS

The various instruments and testing methods currently used provide a

means of assessing thermal hazard. Over recent years great progress has

been made [27-36]

t

New methods have been developed and many new instru

ments have been offered to the market. In addition, many institutions

have codified the procedural aspects of safety investigation and come up

with more sophisticated testing systems. Progress continues, and new in

strumentation is expected. Also the methods already used for decades are

being improved. Also worthy of mention, are new interpretation methods

that enable us to make better use of the same readings; modern data

pro

cessing, in particular, offers possibilities by which data can be trea

ted mathematically and various extrapolations carried out. The number of

measurement being made is rising rapidly, partly as a result of growing



86

safety consciousness and partly because of the aforementioned automa

tion, which is cutting the cost of such studies.

The test methods included here do not represent a complete "state-

of-the-art" but are those of which the author has practical experience.

+

e l f -heat ing

Pressure

_C

'+*

C O

C D

sz

I

C D

C O

T

- P

4 -

1

C D

W

C O

C

i

CD

F

11 i l l I I I I

Temperature

Figure 5. ARC self-heating and pressure curves of a liquid monomer.

3.1. Screening tests

Where a large number of samples has to be tested, a fast screening

met

hod is necessary. G enerally, screening tests determine only the rough i-

nitial temperatures for the exothermic decomposition reaction. In order

to fix a safe working temperature from these initial temperatures, safe

ty margins are necessary.

The first step in the identification of reactive chemicals hazards

is the evaluation of the thermodynamic potential of the system. This

will tell first, whether a reaction is thermodynamically possible and

second, how much thermal energy can be released by the reaction. The po

tential quantity of thermal energy released by the system can then be

related to increases in temperature and pressure within the system being

considered.

One can write balanced chemical equations for the reactions to gi

ve "maximum energy release" for which the heats of decomposition can be

estimated [

3 7

] . The heat of reaction/decomposition can be estimated by

computer programs and used to predict the possibility of explosion or

decomposition.

Yoshida [

3 8

] , for example, has studied different combinations of



87

typical chemicals by carrying out computations with the program REITP2

(Revised Program for Evaluation of Incompatibility).

The use of computers as a prediction tool in chemical process ha

zard evaluation began in 1974 with the introduction of the CHETAH (Che

mical Thermodynamic and Energy Release) program '

3 9

1 . Since then, the

CHETAH program has been widely used in the chemical industry for hazard

evaluation.

Although its chief aim is to predict deflagration/detonation po

tential from molecular structure, it can be used to estimate heats of

reaction, heat capacities, and entropies of a pure chemical, a chemical

mixture,

or a chemical reaction.

Four criteria of energy hazard potential, based on classical ther

modynamics, have been developed and are included in the program.

For the first criterion of energy hazard potential, CHETAH uses

the amount of each element present and thermodynamic data in conjunction

with a linear programming technique to define those products which could

be formed from the reaction mixture and which would release the maximum

amount of energy. The program obeys the laws of thermodynamics and the

principles of stechiometry. For this criterion, the program lists the e-

nergy hazard potential as low if the maximum heat of reaction is more

positive than -0.3 kcal/g, as medium if the maximum heat of reaction is

between -0.3 and -0.7 kcal/g, and as high if it is equal to or more ne

gative than -0 .7 kcal/g.

The second criterion compares the difference between the heat of

combustion of the compounds in an excess of oxygen and the maximum heat

of decomposition to the maximum heat of decomposition.

The third criterion is based on the "oxygen balance" concept of

Lathrop and Handrix l*°i

.

If the oxygen balance is more positive than -24 0 or more negative

than -160, the energy hazard potential is rated as low. If the oxygen

balance is between + 240 and + 120 or -160 and -8 0 , the energy hazard po

tential is rated as medium. If the oxygen balance is between -8 0 and

+120, the energy hazard potential is rated as high.

The fourth criterion is represented by the following equation:

y = 10 A H

2

n

ax W/n

where /\Hmax maximum energy of decomposition

W = weight of compound in grams

n = number of moles

If y is greater than 110, the energy hazard potential is rated as

high.

If y is between 30 and 110, the energy hazard potential is rated

as medium. If y is below 3 0 , the energy hazard potential is rated as

low.

The program uses pattern recognition to classify the compound as

sensitive or insensitive. The program gives a sensitivity rating of

high,

medium or low each of four criteria, and then it gives one overall

rating (Energy Release Potential, ERP) for the compound or mixtures.

The exact details of operation of CHETAH can be found in the lite

rature [39,41-43] .

Because of its ability to predict the potential hazards of a mate

rial or mixture solely from a knowledge of chemical structure, CHETAH is

ideal for preliminary hazard evaluation (Table 1).



TABLE 1. Examples of CHETAH application

c r i t e r i o n

1

k c a l / g

acetonitrile C2H3N = 1.25 C + 0.5 N2 + 0.75 CH4

-0.88 H -6.37 L -214.36 M 52.96 M HIGH

acrylonitrile C3H3N = 2.25 C + 0.5 N2 + 0.75 CH4

-1.09 H -6.70 L -226.14 M 89.37 M HIGH

p-benzoquinone C6H4O2 = 6.0 C + 2.0 H2O

-0.81 H -5.22 L -177.62 M 58.75 M HIGH

chlorotrifluoroethylene C2CIF3 = C + 0.25 CCI4 + 0.75 CF4

-0.42 M -0.87 M -34.34 H 34.43 M HIGH

diazomethane CH2N2 = 0.5 C + N2 + CH4

-1.90 H -3.40 M -114.17 H 304.05 H HIGH

e t h y l e n e

o x i d e

C2H4O

=

1 .5

C

+

H2O

+ 0 . 5

CH4

- 1 . 2 3 H - 5 . 3 8 L - 1 8 1 . 6 0 M 9 5 . 1 4 M HIGH

nitrobenzene C6H5NO2 = 5.75 C + 0.5 N2 + 2.0 H2O + 0.25 CH4

-1.11 H -4.78 M -162.46 M 108.22 M HIGH

phenyl isocyanate C7H5NO = 6.25 C + 0.5 N2 + H2O + 0.75 CH4

-0.62 M -6.14 L -208.19 M 33.03 M HIGH

styrene CsHs = 6.0 C + 2.0 CH4

-0.68 M -9.10 L -307.24 L 30.25 M HIGH

3.2.Thermal analytical ■ethods (DSC/DTA)

The theory and practice of DSC/DTA are well known and available from

many sources t

4 4

-

4 6

. These methods require small sample sizes, tipical-

ly, a few mg, and short analysis times (an hour or two at

most).

Thus, DSC/DTA are advantageous for first examinations of even the

most explosive unknown products or reaction mixtures.



89

For a more detailed examination, these advantages often became di

sadvantages:

- the small sample size employed make accurate mixing difficult and the

composition of a sample of a few mg taken from a grossly heterogeneous

sospension, is not necessarily representative of the whole mass;

- the observed beginning of an exothermic reaction, i.e. the first de

flection from the zero line, is a function of the heating rate, shifting

tov'j.rd lower temperatures at lower heating rates;

- no additions can be made during a run;

- no agitation is possible;

- no measure of pressures generated in sealed pans is possible;

- only a limited range of sealable pans are available.

Recently, a special designed capillary tube and tube holder have

been developed for thermal hazard evaluation using DSC I

4 7

J. This capil

lary tube container has several important advantages compared to other

common sample encapsulation approaches. The glass container is inert to

most materials and is capable of withstanding pressures in excess of 200

bar and temperatures up to 500 °C. The vaporization effect, often pre

sent in DSC of liquids to high temperatures, is negligible because high

sample volume to total volume ratios are possible.

In spite of the difficulties in transfering the DSC results to

plant condition, we think DSC to be a very useful method to in many ca

ses get a quick view of the thermal stability of a substance I

4 8

"

5 0

.

The rate at which the energy is released is very important: thus a

sharp rise in the rate indicated by a steep slope of the exothermic

shows that the reaction may be haz ardous; a broad exotherm peak is

indi

cative of a slower reaction. The area of the peak is proportional to the

energy of the exotherm.

In the dynamic mode (temperature programmed experiment) f

51

l, one

obtains a quick overview of the entire temperature range of interest.

The observed initial temperature of the exothermic response permits a

first estimation of the temperature region in which the undesired reac

tion must be taken into consideration.

Isothermal measurements t

52

l in the region of the onset temperatu

re of the exothermic peak usually clarify, in a short time, wheter or

not a decomposition occurs by an autocatalytic mechanism. Key results

from isothermal experiments are heat evolution rates. Since heat evolu

tion rates vary with time, one may simple refer to their maxima, which

occur either at the beginning or, in the quite frequent cases with for

mally autocatalytic mechanism, after a time delay. Plotting the log of

the maximal heat evolution rates of a number of isothermal experiments

in an Arrhenius plot provides information on the temperature dependence.

The slope of the line is referred to as activation energy (Ea) t

50

.

3.3.Isoperibolic (quasi-isotheraal) Methods

The sample temperature is increased in pre-defined steps and is allowed

to equilibrate before being monitored for exothermic sel-heating.

The isoperibolic methods (Dewar flask, Sikarex, etc.) [23,32,33]

are generally more sensitive than micromethods and, therefore, make it

possible to determine if exotherms occur at correspondingly lower tempe-



90

ratures. Also, they make it easy to recognize autocatalytic processes.

Large sample sizes are sometimes necessary, which is most disadvanta

geous when dealing with expensive or toxic substances.

3.4.Adiabatic calorinetry

The Accelerating Rate Calorimeter (ARC) is a commercially available

thermoanalytical instrument in which it is possible to examine the ther

mal characteristics of a material in a closed environment and in near

perfect adiabatic conditions. The ARC was initially designed by members

of the Dow Chemical Company and was first described by Townsend

t

28

J

in

1977. A considerable number of publications have appeared in the scien

tific literature: the design concept and thermochemical performance have

been described and a number of papers have outlined the basic ARC system

and its operation

[24,53-70]_

The adiabatic calorimetry is almost the ideal method for thermal

hazard investigations because the adiabatic course of a reaction pre

sents the thermal behavior under the most unfavorable conditions as far

as the safety is concerned.

There are two main modes of operation of the ARC. The most common

is known as the heat/wait/search mode. A sample is heated to a preset

start temperature. A wait period follows and, once equilibrium has been

established, a search period is initiated. During this time the sample

is held adiabatically. If the increase in the system temperature is be

low the preset value (0.02 °C/min) then the system is heated stepwise to

the next set point. The heat, wait, search cycle is repeated until the

temperature rise during the search period exceeds the preset value.

The ARC can also be used in isothermal mode and this method of o-

peration should be employed where unstable materials are likely to be

held for long periods of time at elevated temperatures.

In the recorded temperature/time and pressure/temperature curves,

all the thermal, kinetic, and physical property data of the reaction

mass are implicitly contained.

The risk of processes with normal residence time of the substances

can easily be evaluated with the helps of experimentally determined a-

diabatic time to maximum rate of the thermal decomposition.

The list below gives the data which can be obtained from an ARC

experiment:

. adiabatic rate of selfheating vs. temperature

. adiabatic time to maximum rate vs. temperature

. pressure rise or rate of pressure rise vs. temperature

. maximum rate of reaction and heat of reaction (or decomposition)

. activation energy

. pseudo rate constant

If the logP vs. 1/T graph is a straight line, this is likely to be

vapor pressure. If the graph is curved or there are variations then ot

her reactions can be implied. If a pressure is still left in the bomb at

the end of the experiment non condensable gas must have been formed. A-

fter suitable correction for the fill ratio (ratio of reaction volume to

freeboard volume), solubility, compressibility and vapor pressures are

made,

the quantity of gas generated can be established.



91

3.5. Reaction calorinetry

At all stages in the development of a chemical manufacturing process,

thermodynamic and kinetic data pertaining to each of the process steps

are required. Early in the development process, before a synthetic pat

hway has been chosen, a reaction step that is obviously highly exother

mic may be encountered. A determination of the total amount of heat

dis

sipated in the step would enable a judgement to be made on the thermal

hazard posed by the step. Development work on the step could more easily

be halted at this early stage, before a significant investment is made

in the reaction. A pathway having been chosen, conditions must be iden

tified. Profiles of the instantaneous rates at which heat is dissipated

or absorbed throughout the course of each process step would indicate

the temperature range in which reaction runs to completion fastest, or

in which a runaway is a problem.

The desired reaction can generally be carried out only in a very

definite temperature range. At too low a temperature, the reaction is

either too slow or doesn't occur at all. At too high a temperature, the

formation of undesired by-products often occurs or a region of undesired

consecutive or decomposition reactions is eventually reached.

Many processes providing a high exothermicity of the reaction are

hence designed with a large safety margin (e.g. low reaction temperature

to be far away from the start point of dangerous decomposition). And a-

gain very often these preventive measures work against yield.

At the optimal reaction conditions, the maximum rates of heat dis

sipation and absorption for each step are required to determine the re

frigeration and/or heating capacity needed for plant reactors.

Reaction calorimetry allows to simulate plant conditions and to

simultaneously determine actual heat generation data.

A prerequisite for determination of the heat effects is equipment

suitable for dealing with the many varied problems which arise. In par

ticular the reaction enthalpies of chemical reactions should be measured

as stated in the operating conditions. Enthalpies of solution, dilution

and mixing also pose various safety related problems which must be sol

ved.

Reaction calorimetry is not a simple task, since it has to fulfill

a number of sometimes demanding requirements:

- for measuring of the heat of reaction, the investigated chemical syn

thesis has to be carried-out. Modern organic chemical processes demand

often precise maintanence of the reaction conditions, such as temperatu

res, dosing rates, pressures, reaction times, weights of added or di

stilled products, etc. Also the handling of the reaction mixtures is o-

ften specifically prescribed and basic unit operations are required,

i.g. stirring, distillation, boiling under reflux, etc.

- as a result of the measurement not only the net reaction enthalpy is

required, but sometimes also various other heat sources have to be con

sidered, i.g. dissipative energy of the stirrer, endothermic process in

the condenser, etc.

- besides heat of the reaction measurement, other information about im

portant engineering parameters are often requested, especially if their

changes influence the interpretation of the calorimetric measurements,



92

i.g. values and changes of the heat transfer coefficient through the

wall of the reactor.

- during a reaction, a number of physical properties of the reaction

mixture can drastically change. A typical example is the change of vi

scosity due to forming and precipitation of unsoluble product and the

resultanting deterioration of the heat transfer on the inner

wall.

Many examples of applications of reaction calorimeters can be

found in the literature [29,30,71-81].

Now we can see some of the most frequent problems in routine expe

rimentation.

4.Selection of the substances or processes to be tested

It is not possible to test every substance for every possible type of

hazard. Obviously, there are intrinsic factors controlling the systema

tic procedure for thermic safety testing, such as:

- the type of problem/process to be evaluated, i.g. is it a matter of

assessing the hazards of a complete process; is it a matter of determi

ning the permissible storage conditions for a specific product or is it

a simple distillation to be evaluated, etc.

- the structure of the compounds involved in a process

- the instruments available.

A decision as to whether a material should be submitted for test

can be made by consideration of its chemical constitution, the oxygen

balance of the molecule £

40

J and its behavior in small scale heat tests.

For a molecule containing x carbon atoms, y hydrogen atoms and z oxygen

atoms the oxygen balance Bo is:

Bo = -1600 (2x + y/2 -z)/mol.wt

Oxygen balance for some compounds are reported in Table 2. DSC/ARC

tests have confirmed their instability.

Table 2. Examples of oxygen balance

o.nitro benzyl bromide -111.09

o.nitro benzyl chloride -139.87

o.nitro benzyl alcohol -151.50

o.nitro benzaldehyde -142.93

isoxazole -150.72

3-amino-5-methyl isoxazole -163.26

dimethyl sulfoxide -122.87

5-nitro imidazole -53.92

1,3-dibromo-5,5-dimethylhydantoin -61.55

N-bromosuccinimide -71.91

It is recommended that materials with an oxygen balance more po

sitive than

(-200)

should be tested for explosibility. This is an arbi

trary choice but is not unreasonable; it is recognized that it errs on

the side of safety

(82,83].



93

The presence of certain chemical groups may indicate thermal in

stability. For example, groups such as nitrate ester, aromatic nitro and

nitramine are closely linked with explosibility; azo, azide, nitroso,

peroxide and acetylene are groups that can form part of explosive struc

tures t

1

J .

5.Selpf.tion of test method

If the nature of the hazard is not know, it is impossible to decide in

advance which test method wuold be most appropriate. The situation beco

mes critical when a chosen method would not show up the specific hazard

at all. The choice of method may often be governed by the availability

of the apparatus, by tradition or habit rather than by it's suitability.

The most powerful use of the instruments can be achieved, when

their limitations are known and when the plant conditions to be judged

are borne in mind during interpretation of results. This knowledge al

lows to apply simple procedures where these are adequate and to use more

extended tests where critical conditions in the plant are relatively

close to the expected real conditions.

Generally, results of safety measurements reflect only the beha

vior of the material under conditions of the experimental setup and te

sting procedure used in the instrument. Any other interpretations of the

results, or conclusions made for the manufacturing process, is an extra

polation. Unfortunatly, conditions in production plants are often signi

ficantly different from those used in testing instruments. Consequently,

there is a danger from thermal hazards which can remain undetected l

8 4

l.

Typical examples are: exothermicities masked through endothermic evapo

ration of solvent remainders, if tested in an open container; or oxida

tive reactions which cannot be properly detected by tests in closed

ves

sels.

Other parameters can effect the detection of the onset temperatu

re:

1. sample size (which affects the extent of heat accumulation within the

sample)

2. thermal inertia (which will cause heat to be absorbed limiting self

heating. The level of thermal inertia is dependent on sample size rela

tive to sample container size and material)

3. vessel material (which can either catalyse or inhibit the reaction)

4. heating rate (which can have an effect on the detection sensitivity,

with higher heating rates raising the detectable onset

temperature).

An often-used rule in thermal hazard evaluation which has been

perpetuated throughout the chemical industry is the "100 Degree Rule".

This rule states that if the operating temperature of a process is 100

°C away from the nearest detectable exotherm observed in a DSC experi

ment,

the operation will not "experience" this thermal event, and it is

not necessary to obtain more detailed information via a technique such a

ARC.

The "100 Degree Rule" failed for a large number of reactions which

commonly occur in the chemical industry [85,86]

_

6.Selection of samples for testing

Most safety testing is carried out prior to the start of large-scale



94

production. The problem is to find a sample that will be representative

of the ultimate production material. This often proves difficult, becau

se:

- the material produced in a laboratory may have different impurities

than the production material. And even after production has been star

ted, apparently trivial changes, i.g. in a raw material, can produce a

significant modification of the thermal behaviour.

- some instruments are designed to handle such small amounts that the

sample cannot be considered representative.

- substance properties depend on the process itself. In other words, the

thermal behaviour of the substance changes depending on the treatment

undergone. Substantial differences in properties may be found if the

process conditions vary.

For example, recently in a fine chemicals factory a drum contai

ning about 100 kg of 3-amino-5-methyl isoxazole exploded I

8 7

. Samples

from the batch involved in the accident (A) showed a DSC purity of 96

X,

and samples from previous batches (B) gave a purity of 98 %. TLC analy

sis showed the presence of the isomer 5-amino-3-methyl isoxazole as main

impurity. From DSC and ARC tests, sample A appeared to be much more un

stable than the others (ToA = 62 °C, ToB = 106 °C).

7.Process and plant operation variables

The following indicate some of the variables which must be considered in

a testing sequence l

8 3

3 :

. effects of adding incorret quantities of starting materials, solvents

or catalysts;

. recycle and recovery streams;

. nature of by-products, still residues, waste and effluent streams;

. quality of raw materials, catalysts, solvents and reaction intermedia

tes;

. effect of scale of operation;

. catalytic action by materials of construction of the plant or products

of corrosion;

. ingress of heat transfer fluids in the reactor;

. extended heating times of reactants due to unforeseen circumstances.



95

REFERENCES

[1] Bretherick, L. (1990) Handbook of Reactive Chemical Hazards, But-

terworths, London

[2] Nolan, P.F. and Barton, J.A. (1987)

J. Haz. Materials

14, 233-239

[3] Cardillo, P. (1988) Incidenti in ambiente chimico: discussione di

7

n

0 casi, CINEAS, Milan

[4]

Janz,

G.J. (1967) Thermodynamic Properties of Organic Compounds,

Academic Press, New York

[5] Stull, D.R., Westrum, E.F. and Sinke, G.C. (1969) The Chemical

Thermodynamics of Organic Compounds, Wiley &

Sons,

New York

[6] Cox, J.D. and Pilcher, G. (1970) Thermochemistry of Organic and

Organometallic Compounds, Academic Press, London

[7] Pedley, J.B., Naylor, R.D. and Kirby, S.P. (1986) Thermochemical

Data of Organic Compounds, 2nd Ed., Chapman and Hall, London

[8] Daubert, T.E. and Danner, R.P. (1989) Physical and Thermodynamic

Properties of Pure Chemicals, Hemisphere Publishing Co., New York

[9] Barin, I. (1989) Thermochemical Data of Pure Substances, VCH,

Weinheim

[10] Duswalt, A.A. (1968)

Analysis of highly exothermic reactions by

DSC

in R.S. Porter and J.F. Johnson (eds.) Analytical Calorimetry,

Plenum Press, New York, p. 313

[11] Lutolf, J. (1971)

Staub/Reinhalt Luft

31, 9

[12] G roothuizen, Th.M., V erhoeff, J. and De G root, J.J. (1977)

J.Hazard.Materials

2, 11

[13] Zatka, A.V. (1979)

Thermochim. Acta

28, 7

[14] Seyler, R.J. (1980) Thermochim. Acta 4 1, 55

[15] Bersier, P., Valpiana, L. and Zubler, H. (1971)

Chem. Ing. Tech.

24 , 1311

[16] Brogli, F. and Eigenmann (1978)

Me thods of investigation of ther

mal hazards potential in the chemical industry

in Colloque sur la

scurit dans l'industrie chimique, Mulhouse

[17] Cardillo, P. (1982)

Cronache di Chimica

69, 19

[18] Cronin, J.L. and Nolan, P.F. (1987)

J.Hazard. Materials

14, 293

[19] Cronin, J.L. and Nolan, P.F. (1987)

Plant/Operat. Progress

6, 89

[20] Cardillo, P. and Girelli, A. (1980)

Chimica e Industria

62,651


I.Chem.E. Symp. Series

68 , 3N-

1

[22] Salomon, Ch.M., (1982)

Chimia

36 , 133

[23] Kunzi, H., (1982)

Chimia

36 , 162


Chimica e Industria

65,611

[25] Grewer, Th. and Klais, 0. (1980 )

Pressure increase in exhothermic

decomposition reactions

in 3rd Internat. Symp. Loss Prevention and

Safety Promotion in the Process Industries, Basilea


J. Chem. Eng. Data

29, 348

[27] Hub, L. (1977) J.

Chem . E. Symp. Series

49, 39

[28] Townsend, D.I. (1977)

Chem. Eng. Prog.

73, 80

[29] Regenass, W. (1977)

Thermochim. Acta

20, 65

[30] Regenass, W. (1978)

ACS Symp. Ser.

65, 37

[31]

Hakl,

J. (1980)

Thermochim. Acta

38 , 253

[32] Grewer, Th. (1981) /.

Chem. E. Symp. Series

6 8 , 2E 1



96

[33] Rogers, R.L. (1989) in Internat. Synp. on Runaway Reactions,

CCPS,

Boston, p. 281

[34] Sing, J. (1989) in Internat. Symp. on Runaway Reactions,

CCPS,

Boston, p. 313

[35] Fauske, H.K., Clare, G.H. and Creed, M.J. (1989) in Internat.

Synp. on Runaway Reactions,

CCPS,

Boston, p. 364

[36] Laye, P.G. and Nelson,D.C. (1989)

Thermochim. Acta

153, 221

[37] Stull, D.R. (1977) Fundamentals of Fire and Explosion, AIChE Mono

graph Series n. 10

[38] Yoshida, T. (1980) Handbook of Hazardous Reactions with Chemicals,

Tokyo Fire Department, Tokyo

[39] Seaton, W.H., Freedman, E. and Treweek, D.N. (1974) CHETAH: The

ASTM Chemical Thermodynamic and Energy Release Potential Evalua

tion Program. ASTM Data Series Publication DS 51, Philadelphia

[4 0] Lathrop, W.C. and Handrix, C.R. (1949)

Chem. Rev.

44, 419

[41] Laforest, J.C.,and Leleu, J.(1981)

Cahiers de Notes Docum entaires

105, 405

[42] Davies, C.A., Kipnis, I.M., Chase, M.W. and Treweek, D.N. (1985)

The thermochemical and hazard data of chemicals. Estimation using

the ASTM CHETAH program,

In J.M. Hoffmann and D.C. Maser

(eds),

Chemical Process Hazard Review, ACS Symp. Series 274, 81

[43] Fruip, D.J., Freedman, E. and Hertel, G.R. (1989)

Plant/Operat.

Progress

8, 100

[44 ] Wendland, W.Wm. (1986) Thermal Methods of Analysis, Wiley &

Sons,

New York

[45] Garn, P.D. (1965) Thermoanalytical Methods of Investigation, Aca

demic Press, London

[46] Mackenzie, R.C. (1970,1972) Differential Thermal Analysis, Vol.1

and II, Academic Press, London

[47] Whiting,L.F., Labean, M.S. and Eadie, S.S. (1988 )

Thermochim. Acta

136, 231

[48 ] Gygax, R., Meyer, M.W. and Brogli, F. (1980 ) in Proc. of the 6th

Internat. Conf. on Thermal Analysis, Bayreuth, p. 541,549

[49] Barton, J.M. (1983 )

Thermochim. Acta

71, 337

[50] Gygax, R. (1990)

Chem. Eng. Prog.

86 [2] 53

[51] ASTM, (1976) Assessing the thermal stability of chem icals by met

hod of differential thermal analysis,

ASTM E 537

[52] ASTM, (1974)

Constant tempera ture stability of chem ical ma terials,

ASTM E 48 7

[53] Townsend, D.I. and Tou, J.C. (1980)

Thermochim. Acta

37 , 1

[54] Tou, J.C. and Waiting, L.F. (1981)

Thermochim. Acta

4 8, 21


Chimica e Industria

64, 231

[56] Waiting, L.F. and Tou, J.C. (1982)

J. Thermal Analisis

24, 111

[57] Duch, M.W., Marcali, K., Gordon, C.J., Hensler, C.J. and O'Brien,

G.J. (1982)

Plant/Operat.Progress

1, 19

[58] Waiting, L.F..Raykovitz, H.F.andTou, J.C. (1983 )

Thermochim. Acta

62, 65


Chimica e Industria

65, 611

[60] Huff, J.E. (1982)


1, 211

[61] De Haven, E. (1983 )


2, 21


Annali di Chimica

74, 129



97

[63] Fenlon, W.J. (1984)


3, 197


Chimica e Industria

67, 403

[65] Coates, C.F. (1985)

Thermochim. Acta

8 5, 369

[66] Cardillo, P. and Girelli, A. (1986 )

Thermochim. Acta

85, 339


Chimica e Industria

68, 68

[68 ] Cardillo, P. (1988)

Chimica e Industria

70, 90

[691 Cardillo, P., Quattrini, A. and Vajna de Pava, E. (1989)

Chimica

e Industria

71, 38

[70] Kohllbrand, H.T. (1989) in Internat. Symp. on Runaway Reactions,

CCPS,

Boston, p.86

[71] Beyrich, J., Regenass, W. and Richarz , W. (1980 )

Chimin

34 , 244

[72] Schildknecht, J. (1981)

Thermochim. Acta

49, 87

[73] Hoppe, T.F. and Weir, E.D. (1981) in Proc. 13th NATAS Conf., Phi

ladelphia,

p.

193

[74] Schulz.N.,

Pilz,

V. and Schacke H. (1983)

I.Chem.E.Symp.Series

82,

Bl

[75] Regenass, W. (1983)

Chimia

37, 430

[76] Riesen, R. and Grob, B. (1985)

Swiss Chem.

7,39

[77] Weir, E.D., Gravenstine, E.D. and Hoppe,T.F. (1986)

Plant/Operat.

Progress

5,142

[78] Riesen, R., Grob, B. and Vogel, K. (1987)

Thermochim. Acta

114,83

[79] Hoffmann, W. (1989)

Chimia

43,62

[80 ] Hoppe,T. and Grob, B. (1989) in Internat. Syap. on Runaway Reac

tions,

CCPS, Boston,

p.

132

[81] Steele, C.H. and Nolan, P.F. (1989) in Internat. Symp. on Runaway

Reactions, CCPS, Boston, p.198

[82] Gibson, N., Harper, D.J. and Roger, R.L. (1985)

Plant/Operat. Pro

gress

4, 181

[83] The Association of the British Pharmaceutical Industry, (1990)

Guidelines for Chemical Reaction Hazard Evaluation

[84] Hub, L.(1980 )

Can thermic hazards remain undetected?

in 3rd Inter

nat. Symp. Loss Prevention and Safety Promotion in the Process In

dustries, Basilea

[85] Hofelich, T.C. and Thomas, R.C. (1989) in Internat. Symp. on Ru

naway Reactions, CCPS, Boston, p. 74

[86] Health and Safety Executive (1977)

The explosion at the Dow Facto

ry, Kings'Lynn,

Her Majesty's Stationery Office, London

[87] Cardillo, P.(1988)

J. Loss Prevention

1, 46





EQUIPMENT CHARACTERISATION

C. BARCONS I RIBES

Chemical engineering department

Institut Quimic de Sarrid, Barcelona, Spain

Present address: JRCIspra Site

Safety Technology Institute

1-21020 Ispra(VA)

ABSTRACT. The manufacture of chemical products by means of batch processes has recendy become

very important due to the flexibility offered by this type of equipment in w hich they are carried out. The

proper characterisation of this equipment will allow die performance of a wide variety of chemical

reactions with a minimum risk. The response of the system depends basically on the heat capacity of the

vessel, heat losses, heat transfer availability and other sources of input/output heat. An approach for

determining them either theoretically or experimentally is described in this paper. The procedure to

determine the safe operating conditions is basically the same for every different process. A basic method

for scaling-up a chemical process is described as a result of the proper equipment characterisation. This

paper has been written with the purpose of helping engineers on the characterisation of their batch

chemical plants, in order to avoid accidents when there is a need to scale-up a laboratory process.

1 .-

I n t r o d u c t i o n .

The chemical Industry has become important in recent years due to the large number and variety of

chemical processes which have been developed. Human needs and the important evolution of

technology have encouraged the development many chemical processes without a basic knowledge

of the potential risk involved, thus leading to a large number of accidents.

Accidents in the chemical industry are often due to unexpected and/or undesired reactions,

resulting from an over-heating of the reacting mixture and leading to a thermal-runaway. This

happens when the heat generated by the reaction exceeds the heat removal capabilities of the

equipment in which the process is carried out. According to Rasmmusen [1], the largest number

of accidents within the chemical industry occur in batch and semi-batch processes, involving 57%

of cases against 11% in continuous processes.

A significant number of chemical processes, particularly where large scale production is not a

major req uiremen t, are carried out in batch chemical reactors becaus e of their versatility. This type

of equipment often allows the performance of many different processes with minor modifications.

For this reason, batch reactors have become very common in the Fine Chemicals sector.

The standard equipment for this type of processes consists of a vessel, which can be heated or

cooled by means of an external jacket and/or internal coils. An agitator is frequently axially

centered in the vessel and its paddles are placed close to the bottom of the vessel to provide good

agitation of the reacting mixture. External condensers are often available for processes involving

reflux or distillation. Th e temp erature evolution of the reactor contents depend s on the heat transfer

fluid temperature, circulation speed and properties. The heat transfer fluid can be temperature

99

A.

Benuzzi and J . M. Zaldivar (eds.). Safety of Chemical Batch Reactors and Storage Tanks,

9 9 - 1 2 3 .

© 1991

ECSC, EE C, EAEC, Brussels and Luxembourg. Printed in the Netherlands.



100

controlled for isothermal processes or may have a constant inlet temperature for isoperibolic ones.

In semi-batch processes, the temperature control can be aided by the rate of addition of reagents

(and their temperature) in order to avoid a large quantity of heat accum ulated in the reaction mass.

This equipment is normally designed to work under small pressure. Many different probes and

devices for control and measurem ent purposes can easily be installed (temperatu re, pH , redox and

so on) according to the particular process requirements.

Barton and Nolan [2], analysed the incidents which occured in batch reactors due to

overheating of the reacting mass and concluded that these were due to:

- basic lack of knowledge of the process chemistry and thermochemistry

- inadequate en gineering for heat transfer

- inadequate control systems and safety back-up systems

- inadequate operational procedures

From this study, it is possible to conclude that a proper equipment characterisation and scale-up

procedure are important aspects in the design of these installations. This paper will cover these

subjects and special emphasis will be given to experimental and theoretical determination of the

heat removal capabilities of a process vessel. Further, the power input due to stirring, the heat

losses to the surrounding s and the influence of the addition of reactants will be considered, as well

as the heat capacity of the vessel and internal devices, in order to know how the characteristics of

the vessel can affect the process under dynamic conditions.

2 .-

Eva lua t ion o f t he rma l capac i t i e s and hea t l osse s .

An important parameter relating to a vessel in which a chemical process will be carried out is its

thermal capacity. Normally, thermal capacities of laboratory vessels have an important thermal

effect when a reaction is studied. In process vessels this thermal effect is less important because

the ratio between the thermal capacity of the vessel and the mixture is proportionally much small.

It is relatively simple to determine thermal capacities of vessels. Theoretical prediction is

accurate as they are built-up with well known materials and geometry. There are also easy

methods to perform experiments to determine thermal capacities.

It is more difficult to use available data to find out the value of heat losses as a function of

ambient temperature. It is also problematic to evaluate them experimentally, because of their small

value, how ever, they can be neglected if the reactor is properly insu lated.

2.1.

THEORETICAL PREDICTION OF THERMAL CAPACITIES AND HEAT LOSSES .

Chemical reactors are usually made of well known materials. Data describing the physical

properties of such materials is easy to find elsewhere [3].

Theore tical calculation of the thermal capacity of the vessel is made throug h adding together all

the thermal capacities of the different parts of the vessel in contact with the reaction mixture, which

means the reactor wall and all the probes and devices, such as stirrer, temperature, pH and so on.

n

r

t

= £ m,C

i =1

wh ere: i refers to every individual part in contact with the reaction mix ture.

t = ^ W " Y ° P ; (2-1)

i=1



101

The prediction of the heat losses to the surroundings is more difficult to calculate than the

thermal capacity of the vessel. It will mainly depend on reaction mixture properties (vaporisation

and condensation of the mixture on the reactor walls), air circulation around the vessel (natural

convection) and on solid parts in contact with it (conduction). The importance of heat losses

should be checked and the possibility of a thermal insulation considered. If the reactor is insulated

and working conditions are not drastically far from ambient temperature, heat losses can be

ne ^c cte a, otherwise complex methods to evaluate them are described by Ku mana/Kothari [4] and

different approaches can be found in many heat transfer handbooks [5], [6].

2.2.

EXPERIMENTAL EVALUATION OF THERMAL CAPACITIES AND H EAT LOSSES.

Experimental evaluation of the whole thermal capacity and heat losses of a process vessel can be

done in several different ways using the energy balance for a closed system.

2.2.1.-

Electrical Heating

+

free cooling. Heat a know n am ount of pure liquid w hich has a very

constant (or very well known) specific heat capacity in the temperature range in which is going to

be used, i.e. water, with a constant power input and no cooling services.

Allowing a free cooling after the heating operation, time constant for heat losses can be

determined. Heat losses can easily be influenced if the mixture is stirred. For an approximative

calculation, free cooling without stirring can be allowed.

A combination of both effects using a non steady state temperature evolution analysis allows to

calculate both values accurately at the same time if accurate data of temperature evolution is

available. Using the energy balance of the system and assuming that the whole system is in

thermal equilibrium, the equation involved for this calculations is the following one:

dT

m

q

m

"i j _

(

r. + r

+

x . ' I

t r, + r

T

T

-1 a

t m

T„ - T

m

(2.2)

wh ere: Tt is the vessel thermal capacity

r

m

is the mixture thermal capacity

\ is the time cons tant for heat losses

qj is the power input

Du ring the free coo ling in w hich the electrical heating is off, the po we r input is restricted to the

one that is introduced by means of the agitation. Depending on the heat losses value, this can be

considered or neglected. If heat losses are important, they can be easily evaluated by means of a

very simple computer program using temperature evolution data without taking into account any

small pow er input. The v alue found can then be used to ma ke a precise calculation of the thermal

capacity of the system, and better results may be found if iterative procedures are used when other

small heat contributions as the stirrer effects are considered.

2.2.2.- Fast injection. A rapid addition of a cold/hot liquid to a hot/cold one (normally the same),

will produce a fast temperature change of the whole system, involving the liquid, the vessel and all

the inserts in contact with the liquid. Wa ter is also suitable in this cas e. The difference between the

theoretical final temperature if no thermal capacities other than liquid were involved and the one



102

measured experimentally, is due to the thermal capacity of the whole equipment in direct contact

with the liquid. The first temperature inflexion is reached in a short time depending on the time

constant for the response of the system. At this moment, the vessel wall and the fittings in contact

with the liquid have reached the thermal equilibrium. The value of this temperature difference

allows the calculation of the thermal capacity of the reactor wall and inserts, which can be called

heat transfer barrier. This evaluation needs also no heat transfer fluid present inside the reactor

jacket.

n

i

= 1

r r

V

C „ - | T

i

- T ) =

P: ^ i

) ~

u

(2.3)

wh ere: i is refered to each amoun t of liquid.

T is the theoretical final temperature.

Th e am ount of liquid used should be enou gh to be in contact with the who le heat transfer area at

the end, and the temperature difference between both amounts before the injection should be as

large as possible. This method is reliable if heat losses are neglectible compared with the amount

of heat involved in the thermal changes of the system, and if thermal equilibrium is reached in a

short period.

2.3. APPLICATION EXAMPLE [8].

For a 100 L Pfaudler standard glass lined batch reactor [7], insulated from the surroundings, the

theoretical thermal capacity using material properties available data can be calculated as follows:

glass => m

g

- C p

g

= 3.6-800 (Kg-J/K g/K) = 2.9(kJ/K )

metal => m

m

- C

p m

= 471.4-500 (Kg-J/Kg/K) = 23 5.7(kJ/K)

wh ere: mj is the total mas s of every material type used.

Cpj is its heat capacity pe r unit mass.

Norm ally every supplier of these reactors gives information about the type of material the vessel

is made off and the thickness it has. For this particular case it has been calculated that the thermal

capacity of the vessel ( neglecting the inserts) is at about 238.6 kJ/K.

An experiment carried out heating amounts of 60 Kg of water with a constant power of 4 kW

and the vessel insulated (heat losses neglected), using the first technique (2.2.1) and using eq.

(2.2),

gave a value of 256 kJ/K for the whole thermal capacity of the vessel and inserts. Using the

fast injection method (2.2.2) to determine the value of the heat transfer barrier, with the reactor

properly insulated, a large variation between 23 and 431J/K was found between five experiments.

This experimental error is due to the small AT measured.

A calculation using data available for the thermal capacity of the heat transfer barrier was made

and the value found is 38.9 kJ/K

glass => n y C p g = 3.6-800(Kg-J/Kg/K) = 2.9(KJ/K)

metal => m

m

- C

p m

= 72-500(Kg-J/Kg/K) = 36.(K J/K)



103

Comparing these values, it is possible to conclude that the theoretical prediction of the thermal

capacities is rather accurate in accordance with the values experimentally found, taking into

account that the thermal capacity of the inserts was not calculated.

3 .-

Ca lcu lation of heat transfe r coefficients

3 . I . L N I K O D U C T I O N

Almost all the operations carried out in chemical reactors involve either the production or the

absorption of heat. The knowledge of the equipment capacity for heat transfer is very important

for the characterisation of the dynamic behaviour of the system and is, therefore, of great

importance for the safe and economic design of the process.

Heat flow is defined as the speed at which heat is exchanged from a hot source to a cold

receiver. Both systems are usually considered indepently because their heat transfer dynamics are

different There are three main distinct mechanism s in which heat can be exchange d: conduction,

convection and radiatioa

Many different types of vessels and cooling/heating systems are used in chemical processes.

For batch ch emical reactors, external jackets and internal coils are the most co mm on methods to

control the reaction mixture temperature. This chapter will deal with jacketed vessels, but all the

items described hereafter are also applicable with slight modifications for coils and for other

similar types of equipment.

Heat transfer in a stirred chemical reactor with an external jacket can be represented in a

generalized form as is shown in figure 3.1.

Figure 3.1. Heat transfer from a chemical reactor to an external jacket.

The general equation to describe heat transfer dynamics is the energy balance, which can be

described as the time evolution of reactor tem perature:

dt r

L

ff '

m i = l

removed

(3.1)



104

Newton's law defines the heat removed through a wall as a proportional part of the temperature

difference betwe en both sides, which is called driving force (3.2 ). This p roportionality involves

the overall h eat transfer coefficient, U, and the heat transfer area, S):

^removed = U -S-(T

m

- T

e

) (3.2)

The magnitude of the driving force depends on the operating mode. There are three main

modes: adiabatic, isoperibolic and isothermal. In the adiabatic mode, no heat exchange occurs

betw een reaction mass and surroundings, that means qrem oved = 0- The isoperibolic mode is

characterised by a constant inlet temperature in the jacket, whereas in the isothermal m ode the

reac tor tempera ture is controlled by mean s of adjusting the jac ket tem per ature . In the latter case,

the dynamics of the heating/cooling circuit becomes important.

For jacketed chemical reactors, the main heat transfer phenomena is forced convection, which is

produced either by stirring effects inside the vessel or by the circulation flow of the heat transfer

fluid through the jacket. Heat conduction through the wall may be important, depending on the

material of w hich the reactor is made .

The exchanging of heat by means of forced convection can be described simply with the

following equation:

dq =

h-SdT

(3.3)

The proportional constant h is referred to as the partial heat transfer coefficient. For a jacketed

reactor, h is applied to the internal and external sides of the reactor w all. Th e internal heat transfer

coefficient depends on the reaction mixture properties and on the stirring characteristics while the

external depends on the heat transfer fluid properties and its fluid-dynamics regime inside the

jacke t. These coefficients mu st be evaluated experimentally [9].

The final parameter is the heat exchange area. This is practically constant for batch processes

because its changes are due only to density variations in the reaction mixture. However, for

semibatch processes the heat transfer area will increase as a function of the feed rate. Further,

there is also an increase of the heat transfer area due to the vortex generation in reactors that do not

have baffles inside, and this will depend on the stirrer characteristics and physical properties of the

fluid [10].

The main objective of this chapter is to show how to predict from dimensional analysis the

overal l heat t ransfer coefficient , and to describe the procedure with which evaluate i t

experimentally. After the heat transfer coefficients are modelled or experimentally evaluated for a

small laboratory chemical reactor, a procedure to scale-up the process to a pilot plant and/or to a

larger production vessel is presented.

3.2. HEAT TRANSFER IN AGITATED VESSELS

For a tank within which a chemical process is carried out, the heat exchanged with the heat

transfer fluid is calculated by taking into account all the thermal resistances between the reaction

mix ture and the heat transfer fluid. Th e overall heat transfer coefficient, U , introduc ed before, is

determ ined by two different partial or individual heat transfer coefficients and the wall resistance,

or in other term s, the overall resistance to remove he at can be described as the add ition of three or

mo re resistances. Thes e are attributable to:



105

- Internal film from reaction mixture.

- Wall thermal conductivity.

- External film from circulating heat transfer fluid.

Th e gen eral expression for overall heat transfer resistance is:

U " h

+ H w +

D h (

3

.

4

)

o 1 1

Where: hg and hj are the partial heat transfer coefficients related to the internal and external

films respectively, and R

w

is the wall resistance. The term

D Q / D J

is the ratio of areas to take into

account the diameter difference betwe en the inside and the outside of the reactor w all.

It should be noticed that every liquid can produce a layer or deposit of extraneous materials on

the heat transfer surface, which will provoke a time-modification of both partial heat transfer

coefficients. In these cases, the heat transfer resistance increases considerably due to the fact that

this type of materials normally have a lower thermal conductivity. This effect is referred to as the

fouling or dirt factor, and should be avoided or, if this is not possible, taken into account as a

further resistance to heat transfer.

3.3.

THE DETERMINATION OF THE INTERNAL HEAT TRANSFER COEFFICIENT

From dimensional analysis, using the Nusselt equation (3.5), it is possible to correlate empirically

the internal partial heat transfer coefficient as a function of operating conditions and mixture

properties by means of equation (3.6).

Nu = f (Re, Pr, Vi) (3.5 )

h

0

= a

0

N

a

9 2

° (3.6)

w here : otQ is a cons tant.

According to equation (3.6), only the stirrer speed can modify the value of the internal partial

heat transfer coefficient for a given reactor, with the same mixture and temperature conditions

inside it The value of

OLQ

is described by dimensionless analysis (Nusselt equation) with equation

(3.7):

Da-Pn

- o - ^ o ^ P ^ V l '

4 0

-

K

where : 0 IQ, 620 ^30> ^40

a r e

constant for every system.

(3.7)



106

When the power generated in the reactor mixture is small, the viscosity number (Vi) can be

neglected , if temperature difference between the mixture and the heat transfer fluid is not so large.

Assum ing that

O Q

has a constant value u nder the conditions previously men tioned, it is possible

to determine experimentally the value of hg, using the Wilson plots [11]. For every vessel, the

values of hg and

(XQ

must be experimentally d etermined in orde r to derive the characteristic values

for a specific system. The correct values of II Q and

< XQ

can be simply obtained using eq. (3.4).

W ith the sam e operating conditions in the jacket, R

w

and hj will not change, and hg can be

mo dified varying only the stirrer speed. A straight line can be plotted in a graph using eq. (3.8):

1

U

f

R

+

- ^

A

V

1 1

+

^LN

920

a

o

a

(3.8)

The experimental procedure to evaluate the overall heat transfer coefficient, U, is described in

section 3.7.

If the stirrer speed pow ered at -620 is plotted against the reciproca l of U, a graph such as that

shown in figure 3.2 is produced. The slope of the straight line is the reciprocal of

<XQ.

When the

stirrer speed has no effects on the value of ho (N—»°°), 1/U gives the constant value for the wall

and partial external heat transfer resistance due to the heat transfer fluid film.

U

- T

_ R

w

+

"

D l

h .

Na

20

Fig. 3.2.- Wilson ploter for hg experimental determination.

Ex tensiv e characterisation work has been carried out by B ourn e et al. [14] for different agitator

types. Th e values of the constants reported are given in table 3 .1. The values found in their work

for the exponents and constants were contrasted with those found in the literature, and a standard

deviation for the predicted and the experimental ho was calculated for all cases.



107

Table 3.1- Exponents and standard deviation for different impellers and Re regimes.

impeller

turbine

turbine

anchor

ar-chî

anchor

pfaudler

pfaudler

gate

gate

Re range

8<Re<46000

8<Re<46000

5<Re<70

70<Re<600000

70<Re<600000

9<Re<55000

9<Re<55000

12<Re<300000

12<Re<300000

OlO

0.42

0.42

1.0

0.29

0.35

0.27

0.33

0.55

0.47

620

0.694

2/3

0.38

0.678

2/3

0.7

2/3

0.65

2/3

630

1/3

1/3

1/3

1/3

1/3

1/3

1/3

1/3

1/3

640

0

0

0.14

0.14

0.14

0

0

0.14

0.14

s %

3.2

8.4

11.3

4.2

6.9

4.5

9.8

5.6

6.9

3.4. THE DETERMINATION OF WALL RESISTANCE

Theoretical evaluation of wall resistance is normally straightforward for standard chemical

reactors, because of the specifications provided by the manufacturers. These specifications

normally include the type of material used in the construction of the vessel, the thickness of the

walls and the type and characteristics of possible paints or coating covering the walls in order to

protect the reactor from corrosive agents.

W all resistance is described w ith the following equation:

R

w

=

R

0

-Lnh/D

0

)

(3.9)

wh ere: ^ is the thermal cond uctivity of the wa ll.

DQ and Dj are respectively the internal and external diameters of the cylindric wall.

If the wall of the reactor is made of different films of different materials, each resistance should

be calculated separately for every one, and the addition of these will give the overall resistance

value. Detailed information about the thermal conductivity ^ , of the mo st comm on materials used

to build chemical reactors can be found in the literature [3].

3.5.

THE DETERMINATION OF THE EXTERNAL HEAT TRANSFER COEFFICIENT

Determination of the external partial heat transfer coefficient for a given vessel can be done

following the dimensional analysis mentioned previously for the calculation of the internal one.

Again, the Nusselt equation (3.5) can be used to correlate empirically the influence of the flow of

the circulating heat transfer fluid through the ja ck et T he N usselt equation gives:

h

1

= a

1

Q

e

21

(3.10)

where: a\ depend s on the heat transfer fluid properties and the shape of the jack et



108

From the equation (3.10), and assuming that a\ is kep t in such a cond itions that there are no

temperature changes, the variation of Q

e

is the only parameter that can modify the value of the

external partial heat transfer coefficient, due to the film of the heat transfer fluid. The value of a j

is a function of the heat transfer fluid properties and is defined by dimensional analysis with

equation (3.11):

e„

a . = 0

11 D

^-Pr

3 1

- V i

4 1

P.-D,

S

f

- H

f * e

21

(3.11)

where:

G J J ,

62 1, 63 1, B41 are coastant for every system.

Following the procedure used for the linearisation of the internal heat transfer coefficient as a

function of the stirrer speed, it is possible to represent the external partial heat transfer coefficient

as a linear function of the heat transfer fluid flow if it is pow ered to the correct ex pone nt for each

system. The expression to plot is:

1_

u

\

V ° J

D

r°S

• Q ,

21

(3.12)

The experimental procedure to evaluate the overall heat transfer coefficient, U, is described in

section 3.7.

A graph similar to the one proposed by Wilson can be produced, with the heat transfer fluid

flow powered to -621 against the reciprocal of U. This also produces a straight line whose slope

is proportional to the reciprocal of ctj, and it gives a constant value when the heat transfer fluid

flow has no influence on U (high Re num bers), comp ared with the partial internal heat transfer

coefficient and the wall resistance. This plot is show n in figure 3 .3 .

Fig. 3.3 .- Wilson plotter for hj experimental determination.



109

M any different autho rs [12, 13 , 14, 15] have reported stud ies on Nusselt 's dimens ionless

equation for different systems through a large range of Reynolds numbers (Re), and have often

reported similar values for the exponents ©21 • ®31

a n (

^

®4\-

T h

e

typical values for 02

\

631 and

041 are respectively 2 /3 , 1/3 and 0.14. The constant 6 J J which is used to multiply the whole

equation have been reported to range from 0.2 to 0.8, mainly varying due to system geometry. In

the same system, it varies with the fluid dynamics regime, increasing at about 40% from the

laminar flow (Re<400) to the fully developed turbulent flow (Re>10000). The exponent for the

Prandtl Number (631) is set to 1/3 in nearly all the main relevant works, and the viscosity number

is usually found to be 0.14, though different values have been reported ranging from 0 for small

process vessels to 0.18 for bigger ones.

3.6. THE DETERMINATION OF THE OVERALL HTC DURING A CHEMICAL REACTION

In som e cases it may be useful to know the variation of the overall heat transfer coefficient during

a chemical process. It might happen during a chemical reaction that the physical properties of the

mixture change drast ical ly and, with them, i ts heat t ransport characterist ics. Under such

con dition s, the internal heat transfer coefficient m ight decre ase due to the variation of the reaction

mixture properties, and a larger quantity of heat than expected can be accumulated in the reactor,

increasing the temperature of the mixture. In such cases, undesired reactions may take place and,

in the worse case, reaction mass can lead to a thermal runaway.

In order to avoid this situation, the evaluation of the heat transfer coefficient time dependence

during a chemical process can be done. This technique was p roposed for the Mettler RC1 reactor

calorimeter [20], and it has been tested for a simple chemical reaction. Its performance is now

described.

The desired reaction is carried out under normal conditions, and the temperature profiles of the

reaction mass and the heat transfer fluid (also the temperature of the reagents added if the process

is semi-batch) are stored in a computer file. After this, the reaction is performed again under the

same conditions, but adding a well known and constant ammount of heat (qh) to the mixture, by

means of an electric heater, during the whole process. This heat flow input should be small

enough in order not to affect the reaction conditions, (basically the temperature), but it must

produce a significant change between reactor and jacket temperature. Temperature data is also

recorded in this case.

Using the equation for the energy balance (3.1) for both cases, and subtracting one from the

other, it is possible to obtain equation (3.15).

dT

m s

dt

dime

dt

1 [q

x

- US(T

m s

- T

e s

) - K ^ T ^ - T

a

) - Q

a d

Cp(T

m s

- T

a d s

) ]

1 [q

x

- US(T

m c

- T

ec

) - r y -T ^ - T

a

) - Q

a d

Cp(T

m c

- T

gdc

) + q

h

]

(3 .13) , (3.14)

whe re: s and c refer to the experimen t without and with qh respectively.



no

To develop this equation (3.15), it is assumed that the chemical reaction occurs exactly in the

same way and rate, the heat input by the stirrer and any other different inserts are the same in both

cases, as is the ambient temperature.

U S =

dTn

d t

dTm

d t

q

h

- K / T ' V

T m

c) -Q

a d

C p (

T

a d c -

T m

c -

T

a ds

+ T m

s )

A T

S

-

A T

C

(3.15)

where: q^ is the heat input

r is the thermal capacity of the reactor and its contents

dTm i/dt is the derivative of reactor temperature w ith (c) and w ithout (s) heat input

AT] is ( T

m

- T

e

) with (c) and without (s) heat input

T

a

di is the temperature of addition, with (c) and w ithout (s) heat input

Ki is a constant for the heat losses to the surroundings.

Using this equation with all the points of both experimental profiles, it is possible to obtain a

good time profile of the heat transfer coefficient, even the noise introduced when calculating the

derivative of the reaction m ixture temperature (see figure 3.4).

Continous heat transfer coefficient calculation using equation (3.15) has been performed for

two different experiments on isothermal and isoperibolic mode, when adding 0.500 Kg of water

during 30 min. to 1.000 Kg of water.

1100

10.50-

10.00-

7.00

6.50

6.00

180 360 540

T T

US (IS0THERMAL. MODE)

US (ISOPERIBOLIC MODE)

US

(EXPERIMENTAL DATA)

T

720

900 1080 2 6 0 1440 1620

Fig. 3.4.- Calculations under isoperibolic mode (light line), isothermal mode (thick line)

and from previous and posterior evaluation (straight line).



I l l

This method can be applied under either isothermal or isoperibolic modes. If it is applied under

isoperibolic mode, it should be taken into account that the additional heat input will increase the

reactor mixture temperature. In order not to modify the reaction rate, jacket temperature should be

reduced on the same amou nt

The value of the constant for the heat losses should be determinated for every process at the

final temperature, using the experimentally evaluated heat transfer coefficient and the energy

balance for the steady state (eq. 3.16 ). It will be mo re accur ate if all the hea t input sources are

experimentally measured.

K

_ US(Tm - Te) + q

a ( 3 1 6 )

1

(Ta - Tm )

where: q

a

is the po wer inp ut by the stirrer.

3.7. PRACTICAL EXAMPLES

The re are two different metho ds to measure the overall heat transfer coefficient using calorimetric

principles. The first one uses a control system to keep the reactor temperature constant while a

kno wn pow er is given to the mixture, which causes a decrease of jacke t temp erature. The second

one is in isoperibolic mode, where a known power is given to the mixture and the reactor

temperature is allowed to reach a steady state. In both cases the measure of the AT generated will

be used to determine the value of U. The overall heat transfer coefficient can then be calculated

using equation (3.17):

US =

s

A T

m r

A T

, n o '

AT, .=

In

AT

e

. m eo .

(3.17)

where: AT[

n

Q and A T

m

j are the temperature difference betw een the mixture and the jacket

before and during the power input (when reactor temperature steady state is reached)

respectively.

Experimental Wilson plots with different liquids were carried out with a reaction calorimeter

using the first technique [16]. A plot for toluene at different temperatures and 5 different agitator

speeds is shown in figure 3.5.

The second technique described has been used to determine U for water in a 100 1 standard

chem ical reactor [ 17]. Th e results of this experimen tal

OQ

evaluation and the Reynolds exponent

are shown in figure 3.6.



112

y . 0.0076 » 0.0022X

y - 0.0076 * 0.002X

y - 0,0074 . 0.0022X

y - 0.0072 ♦ 0.0O25X

y - 0 , 0 0 6 7 * 0.0031

R-0,99

H - 0,96

R.0 .96

R-1.00

H-0.99

°.

5

Na

A

-.694

Figure

3.5.-

1/U

vs.

Na for

toluene

at

different

Temperatures.

1/U

1AJ -0 . 0 016 » 5,803e-4 Wa -0.7 R - 0.98

Na

A

-0.7

Figure 3.6. 1/U vs. N a

u

' ' for water at different stirrer speed.

4 .-

T he

c h a r a c t e r i s t i c s

of

mix ing

dev ices .

4.1.

TYPES OF EQUIPMENT.

Many different types of stirrers ar e used to agitate chemical mixtures. Among them, impeller,

anchor, turbine and gate are th e ones mainly used. For batch and semibatch reactors, normally

only one stirrer is used and it is generally axially centered in th e reactor with th e paddles close to

th e bottom of i t

The anchor agitator is normally operated at a few rpm. It generates tangential flow which can be

accompanied with axial flow depending on the mobility of the product. It is placed in the centre of

the reactor and has the shape of the vessel outline, ensuring a low wall clearance. The height of the

tw o blades usually ranges from 0.5 to 0.8 of the agitator diameter.

The

impeller

agitator

obtain

optimum

results

at

an

agitator

diameter

of

0.5

to

0.8

of

the

vessel

diameter. It usually rotates at more rpm than the anchor. It is normally arranged in the centre of the



113

reactor, and with a minimum of bottom clearance. The agitator sucks in the product axially and

ejects it radially. By installing baffles in the vessel, the efficiency is considerably improved,

especially in the lower viscosity range. It is considered to be a reliable all-purpose agitator over a

wide viscosity range.

The gate agitator produces a double ring turbulence conveying the product out of the middle of

the blades and deflecting it at the vessel wall to both sides. Suction is produced both from the

re^Cujr DOLtom and from the liquid surface. Moreover, it develops a uniform shearing head above

the entire filling height. It is applied for homogenizing services throughout the whole viscosity

range. This type of agitator is specially suitable for the high-viscous range with good results even

at small Re (Reynolds number) with a relatively low power input

Th e turbine ag itator covers ap proxim ately 1/3 of the reactor diam eter and can be fitted w ith a

variable number of blades. The conveying flow is normally ducted to the vessel bottom. It is

especially suitable for dispersing services. Power consumption is only slightly affected by

viscosity increase.

Often, baffles are installed in stirred tanks in order to cut the liquid flow inside the reactor,

allowing a better mixture. The baffles can be placed in many different places and in many different

ways.

The use of baffles is optional but they are efficient and advantageous in mixing throughout the

whole turbulent flow range. Depending on their size and position they more or less convert the

tangential flow into an axial flow. Moreover, they increase the turbulence within the vessel and

reduce the formation of vortices, although this is at the expense of power consumption.

The use of probes and other types of inserts in the reactor will also produce a non

homogeneous flow, and vortex generation (if no baffles are present) can be really different,

depending on the whole reactor geometry.

For homogenizing tasks, all the stirrers can be used, but there is, however, an optimum Re

range for each agitator, where shorter mixing times can be obtained with less power consumption.

The application limits of every agitator depends on the minimum Re number required by means

of the physical properties of the mixture. Baffles are recommended in the turbulent flow range

whereas they may be omitted in the laminar range.

4.2. POWER INPUT BY M IXING.

The calculation of the power input disregarding mechanical loss is calculated using the following

equation:

P = N e N

3

- d

5

- p

(4.1)

In the first instance, power calculation is reduced to defining the dimensionless Ne number

(power num ber).

N e = f( agitator shape , Re, d/D, b/d, H/D) ,4

2

)

where: P = power requirem ent

Ne = power number.

N = agitator speed.



114

d = agitator diameter.

p = density of the mixture.

Re = Nd

2

p/|J-

D = vessel diameter,

b = height of blades.

H = height of the vessel.

Normally the course of the Ne is plotted against Re. The influence of baffles in mixing

processes is more important at large Re num bers, having no effects o n pow er consumption w hen

Re has sm all values.

The power transmitted by an agitator to a mixture in agitated vessels has mostly been

determined mechanically by measuring the torque transmitted by the shaft. If it is not possible to

.do this, a calorimetric m easurement can be carried out.

With a properly insulated vessel in which heat losses are negligible, the following equation can

be applied to calculate the power given to the mixture:

U-SAT

=

- (

m

m

-

C

p m

+ n

V

C

P

t } - ^ + P (4.3)

In a steady state (dT/dt = 0), and without any external power input, the agitator is the only

pow er input source. Then, i f the U S value is know n (previously evaluated), and the AT

generated is measured, it is possible to calculate the power input by means of agitating.

Data for predicting the power given by different stirrers can be found either from the

manufacturing company or from the literature [18].

4.3.

HEAT TRANSFER AREA INCREASE DUE TO VORTEX G ENERATION.

The stirring speed in chemical reactors does not only modify the internal partial heat transfer

coefficient, but can also produce an important change of heat transfer area. This is applicable for

the vessels that do not have baffles or inserts inside (see figure 4.1). Heat ex chang e area increases

with stirrer speed, and thus, the proportional factor that multiplies the temperature difference in

Newton's law for heat transfer also increases.

The heat transfer area is defined as the surface wetted by the reaction mixture. It can be

calculated as a function of the volume of the ma ss added plus the stirring effects (vortex) with the

following expression:

2(V

- V J

S = S +

m B

- + AS (4.4)

B R v

v

'

wh ere: S = who le heat transfer surface.

S B = reactor bottom surface.

ASy = increase of surface du e to the vortex.

V

m

,

VB

= Mixture and bottom volume respectively.

Rfj = vessel internal radio.



115

A theoretical model to predict the increase of heat transfer area due to the vortex generation was

developed [19] using the modified Navier Stokes equations. This model is valid for a steady

rotational laminar flow of a newtonian fluid around a vertical axis, and without radial and vertical

speed. The expression deduced from this equations is:

N?R

S

H

v

=-

2g

(4.5)

where: H

v

= increase of height due to the vortex generation.

N

a

= stirrer speed.

RO = reactor radio,

g = gravitational strength

Figure 4 .1.- heat transfer area increase due to the vortex.

The validity of this model for a common chemical reactor is very restricted, due to many non-

ideal agitating effects. These non-ideal effects are caused by the vertical and radial movement of

the fluid produced by the stirrer, the interaction of the reactor fittings that cut the rotational flow,

as well as the interaction of the fluid with the reactor wall, which may depend on the mixture

physical properties such as viscosity and surface tension.

4.4. MODEL OF INFLUENCES ON HEAT TRANSFER AREA INCREASE.

In accordance with the theoretical result given by equation (4.5), it is possible to describe the

increase of heat transfer area due to vortex formation with the assumptions previously numbered

as equation (4.6).

AS = (2JIR J H

v

v

0 v

(4.6)



116

Experimental results show that this increase in the heat exchange area is not independent of

liquid volume, type of agitator, and physical fluid properties. In order to correct the non-idealities

of such an assumption, the value of N

a

in the equation (4.5) was multiplied by a factor, f, that

depends empirically on all the characteristics mentioned above. Hence, eq. (4.6) can be write, for

a determined reactor and geometry, as follows:

A S ^ K ^ f N f (4.7)

wh ere: K i is a constant that depends on the geometry of the reactor

f is a correction factor for the non -idealities

According to [18] the factor must be correlated with the discharge rate which depends on the

power number given by equation (4.8). Substituting f by this term and rearranging equation (4.7)

the following relationship is obtained (4.9):

K

3 \

Po = K -(Re) -(F r) (4.8)

AS

V

= C

1

R e

C z

F r°

3

N* g(V

m

) (4.9)

wh ere: g(V m) is a function of the reaction mass volum e.

Intuitively, this function has to follow an exponential inverse behaviour, that means with less

volume the increase in height must be bigger than with more volume present in the reactor. The

correlation that fits the experimental data best is:

9 (V

m

) =

V

- V

T m

V

T

C

4

(4.10)

where: C i , C 2 , C3 and C4 are constants that were calculated ex perim entally for four

different agitators using several different fluids and mod ifying th eir vo lum e, the temperature and

the stirrer speed [21].

5.- The Scaling-up of batch reactors .

5.1. INTRODUCTION.

In the Chemical Engineering Industry, one of the main problems to solve is how to carry out a

chemical reaction in a produ ction plant under the same c ond itions as in the laboratory. The

manufacturing of a product requires large vessels in order to be economically viable for the

company, which can lead to unforeseen problems in the laboratory, i .e. heat released, mass

transfer.



117

There is a procedure which should be followed through the laboratory experimentation to the

industrial production which can contribute substantially to safe reactor design thus avoiding

accidents.

This procedure concerns the full calorimetric study of the mentioned reaction, beginning with

small amounts of reagents (for example using DSC or adiabatic calorimetry), followed with bigger

quantities (i .e. using heat flow calorimetry), and scaling-up from this reactor to the plant one,

s o ^ n m e s also going through a pilot plant reactor stage before produ cing the final design.

Tem peratu re control of the reaction vessel is essential for the safety an d performa nce of a given

process. The proper knowledge of the heat transfer coefficients play an important role for a

satisfactory scale-up procedure, because often it is necessary to ensure that the temperature

evolution in the large vessel will be the same as that in the laboratory one. Thus, once the thermal

respo nse of the vessel and the heat of reaction (from calorimetric studies) are kno wn , the scale-up

procedure can be applied. For the first larger runs, a large safety margin should be conserved in

order to account for any unexpected behaviour of the reaction mixture during the process.

5.2. RULES FOR BATCH AND SEMIBATCH REACTORS SCA LE-UP.

The two main phenomena in which special care has to be taken for scaling-up from laboratory to

plant reactors are heat and mass transfer. The main parameter for the former is the overall heat

transfer coefficient, while for the latter the interfacial area through which the diffusion of chemical

species takes place is of great importance.

The mass transfer phenomena will not be considered in this chapter, but the most important

thing to remember is that the interfacial area per unit volume should be constant in both reactors

for the right scale-up of a process. If the main limiting factor for a chemical reaction is the

diffusion of the species from one phase to the other, the reaction rate will change in the same

proportion that it has changed the interfacial area per unit volume.

5.2.1.- Scaling-up to a geometrically similar plant reactor. For this case it is necessary to conserve

geometrical similarity (shape factors, i.e. relations between diameters and height, blades, inserts)

and thermal conditions (reactor and jacket temperature).

It is not so difficult to design a bigger reactor geometrically similar to the laboratory one, but for

the overall heat transfer coefficient approximation, a complex experimental work should be

performed.

It has been defined previously a general procedure to determine the film heat transfer coefficient

for a chemical reactor with equations (3.5), (3.6) and (3.7).

For the plant reactor (P) as well as for that of the laboratory (L), these equation s are applicable.

If Sjo p is not kno wn b ut the vessels are geometrically sim ilar, the ratio of Nusse lt analogies of the

plant and laboratory reactors may be applied. Since the properties of the reaction mixture remain

constan t for the same process at the same tem perature, this ratio can be drastically simplified.

Rearrang ing of the equations and using hoL determined w ith the laboratory reactor, hQp for the

plant reactor is calculated at the same tem perature using equation (5.1):

fD.VcO

4 / 3

h

0P

= V '

v S

v

L

y

V

2 / 3

,

N

L

' V i

p

>

0.14

Vi.

(5.1)



118

In the case of geometrically similar reactors and if hydrodynamic conditions remain the same

(Newtonian fluids), scale-up involves only a change of heat transfer area and the results can be

viewed with confidence.

With the procedure presented before it is enough to scale-up a process even if no data is

available for the plant reactor.

5.2.2.- Scaling-up to a non geometrically similar plant reactor. More accurate calculations should

be performed if possible to use the material properties. With this information there is no need to

have geometrical similarity between reactors. The use of Nusselt's relation for the film inside the

reactor can be expressed in the following manner

h

0L = V

4

o

d N a

2

0

Y I / 3

go

J

J

V^

2

c

D

g

0 / 3

,

2 / 3

Na„

(5.2)

The first therm involves the geometry of the reactor and inserts (Rn), the second refers to mixture

properties (Mp) and the third is a relation between the stirrer speed and a reference o ne.

The calculations involve the experimental determination of 6 J O L by means of the Wilson

method, using a low viscosity solvent with a well behaved boiling point and vapour pressure.

9 J O P

is determined following the same procedure used for

0JOL-

The overall heat transfer

coefficient U can be experimentally determined as it is proposed for heat flow calorimeters [ 16]

and described in section 3.7.

1

U

9

10P

R

n

3

Mp^[

Na/Na,

R

+

- ^

A

1 1P

(5.3)

Fo r the develo pm ent of this equation it has been assum ed that 620 = 2/3 , 630 = 1/3, and that

the viscosity number can be neglected. The last therm of this equation is called the apparatus

resistance. Now, for the plant reactor, it is possible to get the 9iop value from the slope of the

Wilson plot, because either Rn and Mp are known (Mp can be calculated from the bench scale

reactor Wilson's plot). Once it is evaluated, any unknown Mp can be calculated if a new plot is

done with the same reactor, with the goal of avoiding any possible lack of mixture properties data.

For accurate data acquisition, the vessel should be insulated from the surroundings. Viscosity

data is necessary at the reaction temperature and at the estimated wall temperature, if there is a

large temperature difference between reactor and jacket temperature.

Th e best results are obtained if the linearisation with the Wilso n plot using a Reyno lds exponent

2/3 is good and heat transfer measurements have been accurately carried out in the plant reactor.



119

5.3. DOSING CONTROLLED REACTIONS (SEMI-BATCH).

With the known resistances due to the reaction mixture (h^p) and the apparatus (h^p), the overall

heat transfer coefficient can be calculated. The maximum heating/cooling power can be estimated

with the larger reactor and jacket temperature difference. The heat transfer area can be calculated

using the reaction mixture volume inside the reactor, thus available power (q

a v

) is obtained by

means of.

q

a v

= U S - ( T

m

- T

e

)

( 5 4 )

Heat of reaction and proper reaction temperature are known approximately from laboratory

experiments, by means of the different types of calorimetric analysis. From the available power

plus data on the heat of reaction, a minimu m dosing time for an isothermaly controlled reaction can

be approximated by:

t _

A H

dos q

a v

(5.5)

This applies for an addition of a liquid at the same temperature of the reaction mixture. It is

possible sometimes to add a warmer or a colder fluid depending on the requirements of the

reaction, having a heating or cooling influence according to the needs of the process. The heat

involved in this case should be added to the available po wer as it is described in equa tion (5.6):

q

a v

= U S ( T

m

- T

e

) + q ^ C p

d o s

- (

T

m "

T

d o s

) (5.6)

5.4. SCALE-UP APPLICATION EXAMPLE.

An exam ple of scale-up from a 2 1 laboratory reactor to a 100 1 pilot plant reactor will be done in

this section. Data from a calorimetric study carried out by Bourne, Buerli and Regenass [14] using

a heat flow calorimeter with a Pfaudler stirrer will be used in order to calculate the internal heat

transfer coefficient of a Pfaudler reactor, using the same type of stirrer [7].

The evaluation of

HQ

for the plant reactor has been done in troducing a know n electrical power to

the water inside the reactor and waiting for all temperatures to reach the steady state. Using

equation (3.13 ), U was calculated and the plot show n on Fig. 1 represents the reciprocal of U

against the reciprocal of Na raised to the power of 0.7.

Bourne et al. adjusted eq. (5.7) for the 21 reactor. Calculations of hg at the temperatures of 19

and 25 °C stirring water at 100 rpm are presented in table 5.1.

N u = 0 . 2 7 - R e

0 7

P r

1 / 3

( 5

.

7

)



120

1 / U - 0.0018 ♦ 6.074a-4 Na«-0.7 R - 0.98

1/U - 0,0019 < 5 .M3« -4

-

Na* -0 .7 R - 0.99

EI 1/U(25 C)

• 1/U(19 C)

1. 2

NaM) .7

Figure 5 .1 . - 1/U vs. Na~0-7 for the 1001 reactor filled with 80 Kg of water.

Table 5.1.- Values used in eq . (5.5) to calculate hg.

values

Re

P r

k/D

ho

calculated

T=19°C

7273

7.220

5.219

1375

T=25°C

8378

6.154

5.305

1463

Using data from Figure 5.1, rig evaluated for th e 100

1

reactor agitating at 50 , 100 and 150 rpm

at 19°C and 25°C are compared with the ones obtained scaling-up from the 21 reactor to the 1001

one,

by means of equation (5.1). The same exponent for Re used in (5.7) has been used to rise the

relation between stirrer speed for both agitators. The equation used in this case ha s been

5.1.

This

comparison is shown in table 5.2.

Table 5.2.- comparison between scaled-up/evaluated hg values.

RPM

hO

scale-up

(19)

hO evaluated (19)

hO scale-up (25)

hO evaluated (25)

50

1762

1588

1875

1449

100

2797

2580

2976

2354

150

3665

3426

3900

3127

These calculations have been carried out considering for the calorimetric reactor d=0.067 and

D=0.114 , and for the 100 1 reactor d=0.350 and D=0.508, where d is th e stirrer diameter and D is

the reactor diameter.

N O T A T I O N

c

:

parameters

for

correlations.

Cp : Specific heat capacity, J-Kg

l .

K

- l



121

d,D

f

g

h

H

K

L

m

M p :

N

N

a

Q

q

p

R

Rn

S

T

t

U

U S

V

G r e

a

r

A

e

X

n

p

X

S u b

0

1

a

B

dos

e

g

i

J

: diameters

empirical factor for vortex increase

gravitational acceleration, nvs"2

partial heat transfer coefficient

Molar enthalpy (liquid), J-mol"^ orHeight.m

dimensionless constant or Coefficient of heat losses, W-K"

1

laboratory

mass,Kg

mixture properties

Nu mb er of species, stirrer speed

Stirrer speed s~*

Volumetric flow, m^-s"

Thermal flow, W

power, plant

Rad ius, or resistance

reaction number

Surface, m^

Temperature, K

time,

s

Heat transfer coefficient, W-nT^-K'l

Effective heat transfer coefficient, W-K"l

Volume, rrP

ek symbol s

Constant in a heat transfer correlation,var. dim.

Thermal capacity, J-K"'

difference, variation

Param eter of a heat transfer correlation

Thermal conductivity,

W-m"^-K"'

Dynamic viscosity, kgm~l-s~l

Density, kg-m^

Time constant, s

s c r i p t s

A t the surface, internal side m

At the surface, external side P

Stirrer or ambient R

Bottom r

Dosing T

Therm ovector, heated loop t

glass v

Input w

Species x

Reaction mixture, metal

plant

Reactor

radial

Total

tank

Vortex

Wall

reaction



122

L : Liquid, laboratory

Dimensionless groups

Fr

Ne

Nu

Pr

Re

Po

Vi

6.-

: Froude number,

: power number

: Nusselt number,

: Prandtl number,

: Reynolds number,

for stirred tank,

: Power number,

: Viscosity ratio

References .

Axial

N

a

2

-D

a

-g- l

u-D-r

1

t i - C p - r

1

p

m

-Q-D-S-l -Li - l

P m - N a ' D a

2

- ^ "

1

q a - P m ^ - N a "

3

^ -

5

R j u l k ^ a t w a l l

( 1) Rasm ussen , B. (1988) 'Occurrence and impact of unw anted chem ical reactions', J. Loss

Prev. Process Ind., 1, 92.

( 2) Barton, J.A. and Nolan, P.F . (1989) 'Incidents in Chem ical Industry due to Therm al-

Runaway Chemical Reactions', Chemical Reaction Hazards, London Press Centre, London.

( 3) Dubb el (1981) Taschenbuch fur den Maschinenbau, Auflage, Springer.

( 4) Ku man a, J.D., Kothari, S.P. (1982) 'Predict storage-tank heat transfer precisely', Chemical

Engineering, March, 127-132.

(5 ) R.H . Perry and C.H. Chilton (1973) Chemical Engineers Ha ndbo ok, 5th ed., M c Graw-

Hill, New York.

( 6) M cCa be, W .L. and Smith, J.C. (1956) Unit Operations of Chem ical Engineering ,

Mc Graw-Hil l , New York.

(7 ) Pfaudler reactor Type: AE-100

( 8) Private comm unication from Dr. Hernand ez, H. FIRE S Project, J.R.C. Ispra (VA ), Italy.

( 9) Kern, D.Q . (1950) Process Heat Transfer, Mc Graw-Hill, New Yo rk.

(10) Zaldivar, J.M., Hernandez, H. and Barcons, C. (1990) 'Developm ent of a Mathematical

Mo del and Num erical Simulator for a Reaction Calorimeter FISIM , RC1 Version', technical

note n° 1.90.109, J.R.C. Ispra (VA), Italy.

(11) Wilson, E.E. (1915) Trans A.S.M.E. ,37-47.

(12) Ch apm an, F.S. and Holland, F.A. (1965) 'Heat Transfer Correlations for Agitated Liquids

in Process Vessels', Chemical Engineering, 1, 153-158.

(13) Ch apm an, F.S . and Holland, F.A. (1965) 'Heat Transfer Co rrelations in Agitated Vessels',

Chemical Engineering, 2, 175-182.

(14) Bo urne , J.R., Buerli, M. and Rege nass, W. (1981) 'Heat transfer and power measurements

in stirred tanks using heat flow calorimetry', Chemical En gineering Science, 3 6, 347-354.

(15) Bro oks , G. and Su, G.J. (1959) Che m. Eng. Prog .,Oct., 54.

(16) RC 1 Operating Instructions (1986) Mettler Instrumente AG , CH-860 6 Greifensee.

(17) Private comu nication from Zaldivar, J.M., FIRES Project, J.R.C. Ispra (VA ), Italy.

(18) Uh l, V.W . and Gray, J.B. (1966) M ixing: Theory and Practice, vol 1&2 , Academ ic Press,

N e w Y o r k .

(19) F.A. Holland (1973 ) Fluid flow for Chem ical Enginee rs, Edw ard Arnold, L on do n.



123

(20) Hoffman W . (1989) 'Qdos Qflow Qaccu and all these things', RC 1 3rd International User's

forum.

(21) Zaldivar, J.M., Hernandez, H. Barcons, C , Nom en, R. and Semp ere, J. (1990), 'Heat

Transport for Immiscible Liquids in Agitated Vessels', Proceedings of the 5th Mediterranean

Congres on Chemical Engineering.Barcelona, 1,176-177.





MODE LLIN G AND SIMULATION FOR SAFETY ANAL YSIS OF B ATCH

REACT ORS AND STORAGE TANKS

H.J. HERNANDEZ

Joint Research Centre,

Institute for Safety Technology

Process Engineering Division,

21020 Ispra (Va), Italy

ABSTRACT. The application of mathematical modelling and numerical

simulation to hazard analysis is discussed. The principles of

mathematical modelling are described, with particular reference to

batch reactors and storage vessels where runaway reactions can take

place.

Two representative cases are presented in order to show the

applicability and limits of numerical simulation in assessing the

safety of a batch process by calculating critical operating conditions.

1 . I n t r o d u c t i o n

Process analysis can be based on experimental investigations or

mathematical modelling, whereby the behaviour of a system can be

simulated either experimentally or by solving a mathematical model.

In this manner, the design and optimization of industrial processes

can be supported by appropriated techniques where the objective is to

reproduce the desired behaviour of the system under "normal" operating

conditions.

The safety assessement of processes can also be based on simulation

techniques, but this requires additional information about the

"off-normal" functioning of the system. However, in this case the

experimental work must employ specialised equipment and/or reduced

scales,

because the consequences of the associated hazards. Therefore,

the mathematical modelling becomes an important tool as guide and

complement of the experimental research and to carry out the scale-up

of the process, respecting the safety constraints.

Nevertheless, whenever a mathematical model is used to asses the

safety of a process, special attention must be paid because of the many

assumptions usually introduced during the formulation of the model. In

fact,

safety calculations are frequently made by applying conservative

assumptions that do not always guarantee a safety improvement, because

of complex interdependencies between the process variables.

The objective of this work is to describe the principles of

mathematical modelling based on a Chemical Reaction Engineering

125

A.

Bemtizi and J. M. Zaldivar (eds.). Safely of Chemical Batch Reactors a nd Storage Tanks, 125-145.

© 1991

ECSC.

EEC,

EAEC,




126

a p p r o a c h , a n d t o f i n d o u t t h e a p p l i c a b i l i t y a n d l i m i t s of t h i s

t e c h n i q u e t o t h e h a z a r d a n a l y s i s o f b a t c h p r o c e s s e s . F i r s t l y , a

g e n e r a l mo d e l i s p r e s e n t e d i n o r d e r t o d e m o n s t r a t e t h e c om p l e x

i n t e r a c t i o n i n v o l v e d , an d t h e l a r g e q u a n t i t y of d a t a t h a t i s r e q u i r e d .

S e c o n d l y ,

t h e

f o r m u l a t i o n

a n d

a p p l i c a t i o n

o f

s p e c i f i c

mod e l s

f o r

a

b a t c h r e a c t o r a nd a s t o r a g e v e s s e l i n wh i c h r u n away r e a c t i o n s c an t a k e

p l a c e a r e d e s c r i b e d .

2 . M a t h e m a t i c a l m o d e l l i n g

2

.

1

GENERAL MODEL

Consider a system consisting of a mixture of (Nc) chemical species

confined in a volume (Vm) of fixed coordinates.

The state of the system, represented by the temperature(Tm), the

pressure(p), and the concentration of different species

(Cj),

changes in

time and space according to the chemical reactions taking place, and to

the transfer of

mass,

energy and momentum. These phenomena are

interdependant, and so must be considered simultaneously. However, for

the systems studied here, the transfer of momentum is not strongly

coupled, and may be determined separately (e.g. by means of

dimensional analysis).

Let consider first, the characteristics of these phenomena, that

will be introduced into the fundamental equations.

2 .1.1. Chemical reaction.

A chemical reaction is characterised by the

kinetic function that expresses the rate of matter transformation,

which depends on the state of the system (see complete description of

symbols in section

4

:

r. = r. T

m

,C.,p (1)

The knowledge of the rate of reactions and the stoichiometric

coefficients Vj:, allows the calculation of the net rate of production of

each

species[1]:

Nr

/

V . r.

X ^ *■

1

Rj = ; , V

H

r

(

; j=l,...,N

c

(2)

i = l

Where Nr is the number of independant chemical reactions.

2.1.2.

Mass transfer.

The mass transfer is mainly due to velocity and

concentration gradients.

For each species j, the molar flow can be defined as:



127

N. = C. v + J. ; j = l,

. .

.,N

C

(3)

Where the two terms represent respectively the molar flow of

species j by convection and conduction.

In the case where the difussional terras due to temperature and

p r e s s u r e radients are negligeable, and where the total concentration

is constant, the conduction term may be expressed by:

i i J : 3 - 1 / • •

•

/N

c

(4)

Where Dj is the difussivity coefficient of j within the mixture

2.1.3. Energy transfer. The relevant impulsive forces leading to the

energy transfer are the gradients of velocity, temperature and

pressure. A concise form of the equation for the energy flow within

this system is [3]:

e = p

m

(U + l/2v

2

)v + N

w

+ n • v (5)

Where,

the three terms represent respectively the internal and

kinetic energy flow by convection, the thermal energy flow and the work

done by the system.

The mathematical representation of the state variables of the

system is based on the fundamental principles of conservation, which

can be expressed as mass and energy balances. These balances can be

written in the following form:

Mass balance for each species j

3c.

- ^ = R. - V • N. ; j = l, ..,N

C

(6)

Energy Balance

§ = -

v

. V U - - U V . N

w

+ p V • v]

(7)

Equations 6 and 7 are strongly coupled, and their solution needs the

following information:

state equations for

U=U(p,Tm,Cj),

p=p

(p

m

, T

m

, Cj)

and

ri=ri( T

m

,Cj,p) ,

expressions for the mass and energy flows as functions of

gradients and transport coefficients

• expressions to take into account the variation of all parameters

with temperature, pressure and composition.



128

2.2.

PARTICULAR MODELS

2.2.1.Storage Vessel.

Consider a vessel of symetric geometry specified

by CT, (where

<T=0,

1 or 2 for a slab, cylinder, or sphere), containing

an isotropic medium where physico-chemical processes may take place.

The characteristics of such a system permit to assume one-dimensional

transfer of mass and energy.

The mass balance equation is obtained directly from equation 6,

introducing the characteristics of this system: no velocity gradients

and mass flow by diffusion expressed by:

V • N.

a

2

c

3x

2

3c.

£

\_

x

3x

(8)

Where Dj= constant

Then equation 6 becomes:

3c.

:

3t

3

2

c.

3c,

l

+ - ^

3x

2 x

3x.

;j=l,...,N

r

(9)

With the boundary condition at the center of the vessel, x=0 :

= o

; j = l, . . . ,N

C

(10)

The temperature time-profile is obtained by modifying the energy

equation 7, as follows:

• cancelling the velocity terms:

v»Vu, and pV»v/p

m

,

• replacing the internal energy by the enthalpy function:

3u

_ 3H

3t

3t

V-

dp

dt

(11)

and neglecting the term Vdp/dt, which is small compared with the

enthalpy term,

• introducing the enthalpy change of the mixture and substituting the

concentration variation by the mass equation 9,

• introducing the Fourier law for heat conduction,

N.,

A .

m

V

T

(12)



and the definition of enthalpy change due to reaction:

A H

C

. = / V . ,H . ; j = l , . . . , N

r

j = i

( 1 3 )

129

The t i m e - p r o f i l e of t e m p e r a t u r e r e a d s :

3 T „

dt Cp„

3x

2 x

3x_

r

i = l

( 1 4 )

With the boundary conditions at the center of the vessel, x=0 :

3x

0

(15)

and, at the wall of the vessel, x=Xo,

5T

m

3 T

P

_ u

K

~d^

"

x

?~d^ X

p

( T e

"

T

^

(16)

2 . 2 . 2 .

S t i r r e d Batch Reac tor.

In a typical batch reactor, the

diffusional phenomena are negligeable, due to the elimination of

composition gradients by the stirring.

The integration of the continuity equation 6 over the reactor

volume Vm, including the mass input from the surroundings, gives the

time-profile of composition for each species j:

dC,

"dt

3

R.

+

^

3

V „

(F,

F

c

) - C

dV

m

i

dt

;j=l,...,N

C

(17)

The temperature profile is obtained, by simplifying the energy

balance (eq. 7 ) , as in the case of the storage vessel, adding the terms

corresponding to the exchange of mass and heat with the surroundings:

dt

r

m

+r

/

c

(T - T ) - V

j = l

\

r.AH.

+ q

(18)



130

3 . Application cases

3.1. SYNTHESIS OF ETHYL GLYCIDATE

The objective of this study is the optimization of an existing process,

taking into account the potential hazard of thermal explosion. The

process is described in detail in the reference [4], where emphasis was

placed on obtaining the thermo-kinetic data required for the solution

of the mathematical models.

3.1 .1 . General description and thermo-kinetic data.

The ethyl glycidate

is obtained by epoxydation of the ethyl acrylate by the

peroxycarboximidic acid, which is prepared "in situ" by the action of

hydrogen peroxide on the acetonitrile in an alkaline medium. The raw

materials and products are:

raw materials

H2C=CH-COOC2H5

CH

3

-C H

2

OH

CH3CN ========

H2O2 CO3K2

A nd e t h a n o l a s s o l v e n t

p r o d u c t s

CH2-CH-COOC2H5

CH3-C0-NH2

o

2

The reaction scheme is the following:

1) CH3 CN +

H

2

02

>

2) CH

3

-COOH=NH + H

2

02

3) CH

3

-COOH=NH + H

2

C=CH-COOC

2

H

5

>

4) CH

3

-COOH=NH >

5) H

2

C = C H - C O O C

2

H

5

)

CH

3

-COOH=NH

CH3-CO-NH2 + H

2

0 + 0

2

CH

2

-CH-COOC

2

H

5

+ CH3-CO-NH2

decomposition product

decomposition product

The main problems of this process are the high exothermicity and

instability of the peroxycarboximidic acid, which decomposes (reaction

4 ) , and reacts with the hydrogen peroxide at low temperatures (side

reaction 2) . The objective is to determine the optimal operating

conditions, (temperature and initial composition), that minimize the

reaction 2 and 4 and the decomposition of ethyl acrylate (reaction 5 ) .

The thermo-kinetic parameters were obtained by "thermal flux"

calorimetry[4]

.

These results are presented in table 3.1.

This process is implemented in a standard 500 1 glass lined reactor

in semi-batch operation mode. The main characteristics of such reactor

are described in table 3.2.



131

TABLE 3.1. Thermo-kinetic parameters. Ethyl glycidate synthesis

N ° r e a c t .

1

2

3

4

5

A H i ( k J r a o l

- 5 4 , 4 3

- 2 5 5 , 3 9

9 , 6 3

- 1 0 2 , 9 6

- 6 7 , 8 3

-1 )

A i

1 , 90 - 108

6 , 2 6 - 1 0

2

°

1 , 21 - 1014

6 , 86 -1020

3 , 0 6 - 1 0 6

E i ( k J i n o l

- 1

)

4 5 , 0 2

1 1 7 , 6 5

8 3 , 3 2

1 2 4 , 3 5

1 2 2 , 6 7

f i ( c o n e . f u n c t i o n )

f i = c

A

- c

B

f

2

=

C

B

- C R

f 3

=

C

C

- C R

f

4

= c

R

0 / 5 5

f 5 = C

C

TABLE 3.2. Equipment data. Ethyl glycidate synthesis

Glass lined reactor

dimensions: hight, H R = 0,8 m

ceramics film: thick., Ei = 0 002 m

steel

wall:

thick., E2 = 0,013 m

heat capacity, T R = 51,7 kj K~l

Heat exchanger

jacket diameter =

0 027

m

diameter, D R = 1,0 m

conduct., X \

=

1.2 W m-lR-l

conduct.,

X.2 =

6.5 W m-iK

-1

Cp

c

Pc

^c

Thermo-vector:,

heat capacity,

density,

viscosity,

thermal conductivity,

X

c

temperature range, Tc

flow, Q

c

T e m p e r a t u r e c o n t r o l l e r

P . I . D . c o n s t a n t s : p r o p . = 7 , i n t . = 12 0 s ,

J k g

k g m

kg irf

■IK-

'S

-1

I s - 1

W m

_ 1

K~

K

m

3

s

1

-1

Water

4 , 1 9

1 0

3

1 . 1 0

3

1 1 0

- 3

0 , 6

Brine.

2 , 7 8 1 0

3

1 , 2 5 1 0

3

1 1

1 0

- 3

0 , 5

T m i n = 2 8 3 Tm i n = 2 5£

2 , 0 8 1 0 ~

3

d i f f . = 60 s



132

3.1.2. Typical operating procedure.

The normal conditions for this

process are indicated in the following recipies:

• Charge the the reactor with a mixture (225 1) of following

composition:

- 1 mol of Ethyl acrylate per 1.72 mol of acetonitrile

- 2.5 vol. of ethanol per 1 vol. of ethyl acrylate

• Put stirring at 1.67 s~l, and maintain the mixture at a

temperature of 303 K

• Introduce, over 3.5 h, 70 1 of a mixture with composition:

-

1.95 mol of

hydrogen peroxide

(30

%wt)

per mol of

ethyl

acrylate introduced.

3.1.3. Simulation.

This system was simulated, by solving numerically

equations 17 and 18 , which have been modified to include the algorithms

of

a

temperature controller

and the

influence

of

operating conditions

on the heat exhanged [4] .

The results of the simulation, with the operating conditions

described above, are shown in Fig. 3.1, which contains the time-profile

of the relevant variables:

3.1. a/ temperature of the reaction mixture and of the external

cooling,

3.1.b/ thermal fluxes generated and removed,

3.1.c/ concentration of reactants and

3.1.d/ concentration of products.

Thereafter, the critical conditions have been found by means of

succesive simulations with different temperature set-points

and

different feeding rates of the hydrogen peroxide. Selected results of

these simulations are presented

in

the figures

3.2 to 3.6.

3.1.4. Concluding remarks.

Under normal operating conditions, this

process is carried out at a low temperature (< 303

K) ,

generating a

moderate thermal flow that may be removed with a low cooling capacity.

However, the process is very sensitive to slight modifications of the

operating conditions, which easily activate the side reactions, leading

to a thermal excursion. Additionaly, the release of oxygen can cause an

overpressurisation of the system.

In general, safety improvement

of

this process result

in a

reduction in yield. A compromise between the safety and performance

criteria could be achived by increasing the proportion of hydrogen

peroxide, both with a slower rate of introduction.

Finally, a higher cooler capacity (e.g. with sodium chloride

solution), is recommended, which allows a larger margin of safety.



Taav wat ur B ( C )

3 . 1 .

a

Thermal f low fcw)

6 4 . 0 -

SHNEHET REMOVED

Concentration (nol/lt)

5.00.

4.0i

0 25 50 75 100 125 150 175 200 225 250

— - — - - Tim e (rnn)

CH3CN H2 02 ACflYLATE ACID E-fl

Concent r a t i on ( r ao l / l t )

2.00r

1 . 2 0 -

0 . 00

AC-AMIOE SLYCIDTE FW C*

FIGURE 3.1. Simulation results of ethyl glycidate synthesis with "normal operating conditions".



Tannarature ( C) 3.2.a

Thermal flow (kVO

32.0-

lB.O-\

MIXTURE THEBMOVE

-25. V-

5.00-

Concentration (ml/It)

Concantratlon (rnol/lt)

2.00 i

1.00-

0 29 SO

C H 3 C N

-

H 202

75 100

"*>» 1 i i JBBU.VSI

125 190 179 200 229 290

Tlaa tan)

1 . 6 0 -

1 . 2 0 -

0 . 4 0 -

0 29 90 79 100 129

AC^MUDE 6LYCUJTE BM C« "

175 200 229 250

T I M tun)

ACHYLATE ACDJE-H

FIGURE 3.2. Simulation results of ethyl glycidate synthesis with T

set

=303 K, Feed rate H

2

0

2

=35 1/hr



B4.0

4S.0

32.0

16.0

0.0

r«apsr*tura

\

A

Co

—j 1 1~

9

1 i

3.1

,

/

. m u m

29 SO 75 100 IBS ISO 173 200 223

— — TlaB 0m)

MIXTUFE THEHHOVE

S.O

Tharml flow (kH)

1 . 0 -

-a.o-

—I u-

5.0"

*-

0 23 50 79 lOH I B 150 173 200

SHOVED

Tlao (an)

9.00]

Concentration tool/It)

3.3 .C

O.Ol

2.001

Concsntnatlon taol/ltl

1.20-

0.80-

0.40-

190

178 BOO 223 250

Tlae (on)

0 25 80 73 100 12S ISO 170 200 228 250 0 25 90 73 100 125

CHSCS

-

" H 20 2~ ~ ACHYLATE AC IBM "* "" ACHWIOE 6LYCHJTE 5* '~

C* '

FIGURE 3 . 3 . S i m u l a t i o n r e s u l t s o f e t h y l g l y c i d a t e s y n t h e s i s w i t h T

s e t

=2 98 K, Feed ra te H

2

C>2=20 1/hr



Tmparatura (*C)

3 . A.»

64.0-

16.0

\

0.0^

0 25 SO 73 100 125 150 173 BOO 225 250

. - - - - - T i n * (on)

MIXTURE TWHMOVE

5.0,

Ttwoml flow IkW

3 . 4 . 6

5 . 0&

Con c«n t r«t lon ( ao l / l t )

3 . 4 . c

3 . 0 0 -

2.00 i

1 . 0 0 -

JSaMLyoJ

28 50 75 100 1 2 3 1 5 0 173 2 0 0 2 2 5 2 5 0

Tlaa (on)

C o n c e n t r a t i o n t a o l / l t )

2 . 00r

3 . 4 . d

1 . 2 0 -

0 . 4 O -

O.OO

25 50 73 100 123 150 175 200 225 2fi

AC AMWe BLYKOTE SS CK ™ ""

H3CN H 20 2 ACHYUkTE ACIOE-R

FIGURE 3.4. Simulation results of ethyl glycidate synthesis with T

set

=298 K, Feed rate H

2

0

2

=35 1/hr



Taaporatura

( CI

SO.Of-

6 4 . 0 -

S . S . a

TTisml flow tkX

- 7 . 0 -

-11 .0 -

-1S.0

1

0 24 48 72

G E N E R E T R E M O V E D

Concentration

(asl/lt)

Concentration (Ml/It)

a.OOr

i . a o -

0.00'

0.40-

0.00*-

168

192

216 240

T i m

(an)

0

24 48 72 96 120 144 1M 192 216 240 0 24 48 72 96 120 144

EHSCN" SaniT" ACHYLATE A C ID M " " ACÂMIDE 6LYCH>TE BM ci

FIGURE 3.5. Simulation results of ethyl glycid ate synthe sis with T

s et

=293 K, Feed rate H

2

O

2

=20 1/hr



Tsaparaturs C)

Tharm l flaw (kW

3.B.0

-83.0

1

GENBST REMOVED

Concentration (Hol/lt)

Concentration tol/lt)

S.B.d

CH3CN H202

ACHYLATE ACIDE-fl

1.60-

l.ao-

0.80-

o.ooi

AC-AMIDE BLYCIDTE

R*

FIGURE 3.6. Simulation results

of

ethyl glycidate synthesis with T

set

=293

K,

Feed rate H

2

0

2

=3 5

1/hr



139

3.2. STORAGE OF CYCLOPENTADIENE

The cyclopentadiene, in liquid state, is an intermediate reagent in

many organic syntheses. However, this product is very unstable even at

low temperatures, when it dimerizes exothermically to dicylopentadiene,

which is the stable form until the boiling point, 170°C (see ref. [5]) .

The objective of this study is to determine whether is worth to

store the cyclopentadiene, by predicting its stability under storage

conditions.

3.2.1. G eneral description and thermo-kinetic data.

The dimerization

reaction of cyclopentadiene is:

2C

5

H

6

====> C10H12 + AH

(2) cyclopentadiene dicyclopentadiene

The thermo-kinetic parameters were determined by calorimetry [4]

and compare favourably with those reported in reference [5]:

• Heat of reaction, AH: -3,86 9-10

4

J-mol"

1

• Heat capacities, Cp: cyclopentadiene dicyclopentadiene

1,71 1,64

J-g-l-K-l

• Rate of reaction, r:

r = A-exp(-E/RT)-C

s

With: A =

1,34-106

s

-l ,

E = 6,47-10^

J-mol-l

,

T he t h e r m a l c o n d u c t i v i t y was c a l c u l a t e d u s i n g t h e f o l l o w i n g

c o r r e l a t i o n fo un d i n r e f e r e n c e [ 6 ] :

X =

3 , 5 9 - 1 0 - 3 - C p - (p 4 /3 ) / ( M l/3 )

W h i c h g i v e s :

C y c l o p e n t a d i e n e , X = 0 , 1 1 3 W - m - l -K

- 1

D i c y c l o p e n t a d i e n e , X = 0 ,1 1 0

T h e d i f f u s i v i t y c o e f f i c i e n t w as c a l c u l a t e d a s s u m i n g , a

s e l f - d i f f u s i o n p hen om en on u n d e r i d e a l c o n d i t i o n s [ 6] :

D

=

=

n

KT

v

v

*y

O b t a i n i n g , D

s

= 4 , 3 3 - 1 0 "

9

m Z - s "

1



140

3.2.2. Calculation of storage conditions.

This

case

was

simulated,

by

solving numerically equations 9 and 14. The critical conditions are

determined

by

means

of

succesive

simulations,

fixing

the

characteristics of the vessel and following the behaviour of the

mixture

for

different

storage

temperatures.

The following case was used as a reference:

steel spherical vessel: storage conditions:

radius,

X() = 0,10 m concentration C

s

=12157 mol-lt

-1

surface,

So = 0,27 m

2

coefficient of heat exchange:

thermal

capacity,

r

R

=l-103

J-K-I

U

=

35

W-m-2-K-l

The

results

of

the

first

simulation

run

with

a

storage

temperature,

T

c

=283

K,

are

shown

in

the

figures

3.2.1

and

3.2.2,

which

show how the temperature and concentration profiles, change with time.

It can be seen that the reaction runs away after nine hours.

Succesives

simulation

runs

with

lower

storage

temperatures

lead

to

the

critical

values:

T

c r

=

279

K,

for

Xo

=

0,10

m

The t e m p e r a t u r e p r o f i l e s f o r t h e s e c o n d i t i o n s a r e shown i n

f i g u r e s 3 . 2 . 3 and 3 . 2 . 4 .

I t i s i n t e r e s t i n g t o c omp a r e t h e s i m u l a t i o n r e s u l t s w i t h t h e

a n a l y t i c a l

c r i t e r i o n

o f

F r a n k - K a m e n e s t k i i [ 7 ] w h i c h

e x p r e s s e s

t h e

c r i t i c a l s i z e of a v e s s e l a s :

8 • • RT^

r

cr m cr

cr

AH ■ E ■ A ■ exp(-E/RT

cr

)

This

criterion

yields

the

following

critical

storage

conditions:

T

C

r

=

275.8

K,

for

Xo

=

0,10

m

Finally,

the

previous

calculations

were

repeted

for

vessels

of

different sizes. The critical values found by simulation and by the

Frank-Kamenestkii

equation

are

shown

in

the

Figure

3.2.5



141

350

Temperature (K)

TIME (hr)

3 3 4 . 0 -

31B.0

3 0 2 . 0 -

2 B 6 . 0

2 7 0 . 0

0 . 5 0 .5 R

R ad iu s (R 0 .10 m)

C o n c e n t r a t i o n ( m o l / l t )

3 . 7 . 0

TIME (hr)

15.00

12.80

1 0 . 6 0 -

B.40

6 . 2 0 -

4 . 0 0

0 . 5

0 . 5

FIGURE 3 . 7 . S i m u l a t i o n r e s u l t s o f c y c l o p e n t a d i e n e s t o r a g e

T

storage

=283

K



142

320.0

310.0

300.0-

290.0-

280.0

270.0

Temperature (K)

3.8.a

TIME (hr)

0.92

2.93

4.90

6.85

8.83

10.82

12.74

14.47

16.29

18.28

20.27

22.21

24.17

26.12

28.02

30.01

32.00

33.93

0.5

0.5 R

Radius (R 0.10 m)

320.0

310.0

300.0

290.0-

2B0.0

270.0

Temperature (K)

3 . a . b

TIME (hr)

33.93

35.95

3 7 . 7 1

39.65

4 1 . 5 8

43.5B

45.5B

47.55

49.52

5 1 . 4 1

53.38

55.32

57.34

59.28

6 1 . 2 3

63.02

0 . 5

0 . 5 R

Radius (R 0 .1 0 m)

FIGURE 3 . 8 . S i m u l a t i on r e s u l t s o f c y c l o p e n t a d i e n e s t o r a g e

T

s t o r a g e

=279

K



143

FIGURE 3 . 9 . C r i t i c a l c o n d i t i o n s o f s t o r a g e o f c y c l o p e n t a d i e n e .

C o m p a r i s o n o f s i m u l a t e d a n d F r a n k - K a m e n e s t k i i r e s u l t s .

300.0

X )' 10'

Critical temperature

(K)

3.2.3

Concluding remarks.

Under adiabatic conditions, dimerization of

cyclopentadiene will produce a temperature rise of approximatively 350

K. This means that secondary reactions that become significant at

temperature greater than 550 K, may be activated by the main reaction,

leading to a thermal explosion.

The above discussion confirm the high potentail hazard of

storing important amounts of cyclopentadiene, which requires a

relatively low storage temperature.

As far as possible, the processes where the cyclopentadiene is

an intermediate, should be integrated, in order to avoid the storage of

this compound.

Concerning the difference between the two calculation methods

presented here, it is due to the fact that the Frank-Kamenestkii model

does not take into account the influence of extent of the reaction

neither a resistance of heat exchange with the sourroundings, while,

both were included in the numerical simulation.



144

4

Conclusion

The m a t h e m a t i c a l m o d e l l i n g for hazard p r o c e s s analysis appears

particularly attractive and beneficial because the difficulty of carry

out appropiate experimental investigations under dangereous conditions.

However, the formulation of a model for safety assessement should

be oriented to the representation of the significant features of the

process, with an awareness of the implicit assumptions from a safety

point of view.

The main limitation in applying the t h e o r e t i c a l approach

presented here is the lack of knowledge of the chemical process. A

reliable model would require a large quantity of data, which are rarely

available.

In

practice,

accurate

data

are

only

found

for

a

limited

range of process variables and do not provide enough information for

the

safety

study.

In

the

future,

the

problem

of

lack

of

data

may

be

reduced

by

the

application of identification and estimation techniques, which provide,

on-line or off-line, determination of parameters of the model.

5 N o t a t i o n

A

C

Cp

Cp

L

D

E

e

F

H

J

K

N

Nw

N

Na

n

P

q

R

r

S

T

U

U

V

v

v

X

Pre-exponential factor

Molar concentration,

Specific heat capacity,

Molar heat capacity of a chemical species,

Diffusivity,

Activation energy,

Energy flux,

Molar flow,

Molar enthaply

(liquid),

Molar flux by conduction,

Chemical equilibrium constant,

Molar flux by convection and conduction,

Heat flux,

Number

Stirrer speed

Molar

Hold-up,

Pressure

Thermal flow,

Rate of chemical production,

or Gas constant,

Rate of reaction,

Surface,

Temperature,

Internal energy,

Heat transfer coefficient,

Volume,

Average

velocity,

Local velocity,

Radius,

depends on kinetics

mol-m

3

J Kg l K l

J mol i K l

m

2

■s-1

J -mol

-1

W-m-2

mol• s

_ 1

J mol

m o l - m

-

2 • s

_ 1

depends on k

mol-m

-

2• s

1

W-m-2

m o l

K g - m - 1

W

m o l

m

J - r n o l

m o l

m2

K

J

W-m

m

3

m -

s

m -

s

m

m-

-2 .

-1

■ l

3

1

3

K

2

S

K

s

1

1

1

1



G r e e k s y m b o l s

145

r

n

v

n

P

Thermal capacity, J-K~l

Thermal conductivit y, W-m

_1

-K~

Dy namic vi scos ity, Kg-rrrl-s

Stoichiometric coefficient, reactant(-), product(+)

Partial order of reaction

Mo me nt um flux, Kg-irrl-s

Density, Kg-m

3

Vessel geometry, 0=slab, l=cylinder, 2=sphere

S u b s c r i p t s

c

e

i

m

R

S

heat transfer fluid

External

Reaction

Reaction media

Reactor

Output

E

h

J

P

s

X

Input

Heating

Species

Wall

Set-point

Radial

6.References

[1] LEVENSPIEL 0. (1972), Chemical Reaction Engineering, John Wiley,

New York.

[2] TREYBAL

R.E.

(1955),

Mass transfer operations,

Mc

G raw-Hill,

USA.

[3] BIRD R.B., STEWART N.E. and LIG HTFOOT E.N. (196 0), Ttransport

Phenomena, John Wiley, New York.

[4] HERNANDEZ H. (1987), "Contribution a la Simulation de Systèmes

Chimiques orientee vers

l'Analyse

de Securite", Ph.D. thesis,

U.T.C., Compiegne.

[5] WILSON P.J. and WELLS J.H. (1944), "The chemistry and utilisation

of cyclopentadiene", Chemical Review, N o . 3 4 , pi, Pennsylvania.

[6] REID R.C., PRAUSNITZ J.M. and SHERWOOD T.K. (1958), The Properties

of Gases and Liquids, Mc G raw-Hill, New York.

[7] GRAY P. and LEE P.R. (1967), "Thermal Explosion Theory", Oxidation

and Combustion Review, vol. 2, Elsevier, New York.





RISK ASSESSMENT METHODOLOGIES

N.A.LABATH

Consultants in Advanced Technologies

Via L. Maggiore 41

21038 Arolo di Leggiuno (VA)

Italy

1. Introduction

Qualitative and Qualitative Risk Assessment have been applied

to new and existing installations to ensure that the hazards

associated with the plants are acceptable to employees and

the public. Quantitative Risk Assessment expresses the

magnitude of a hazard on an absolute numerical scale thereby

providing plant designers and management with the necessary

data to take measures aimed at reducing the risk to

acceptable levels. It is frequently used to compare the

effects of alternative safety measures.

The assessment methods can be broken down into three areas,

as follows :

- Methods used to identify sources of accidents and the

ways in which they could occur.

- Methods used to estimate the likelihood of occurrence

of accidents.

- Methods used to estimate the potential consequences of

accidents.

Only the first two areas will be covered in the following

sections.

Accidents can be prevented by anticipating how they may

occur.

Having identified how accidents could occur, several

other questions may then have to be considered. What is the

likelihood of the accident occurring ? What would be the

consequences of such an accident ? What measures could be

taken to eliminate the particular hazard or if this is not

possible to reduce the likelihood or consequences of the

accident ? Would implementation of such measures be

justified ? The identification stage remains the most

important step in safety assessment however, if the

existence of a hazard is not identified, no action can even

be contemplated. This essential stage in the assessment

prodedure involves rigorous consideration of all situations

in which the potential for harm may exist in order to

identify those which are hazardous, followed by a

disciplined analysis of the combinations or sequences of

147

A. Benuzzi

and

J. M.

Zaldivar

(eds.).

Safety of


a nd

Storage

Tanks, 147-159.

© 1991 ECSC, EEC, EAEC, Brussels a nd Luxembourg. Printed in the Netherlands.



148

events which could transform this potential into an

accident.

This stage in the assessment of an installation is called

hazard identification. It is essentially a qualitative

process,

although aspects may be revealed which require

calculation, for example, analysis of transients to

establish the boundaries of safe operation.

2. Hazard Identification Techniques

Many hazard identification methodologies are available to be

applied at differrent steps of the project. Most of them are

listed in Table 1.

Table 1 : Hazard Identification Methodologies

Process/System Checklists

Safety review

Relative ranking : DOW and Mond Hazard Index

Preliminary Hazard Analysis

What-if analysis

Failure Mode and Effect Analysis

Hazard and Operability Analysis

Fault Tree Analysis

Human Error Analysis

The first four methodologies are normally applied in the

initial steps of an engineering project.

The others are preferently used when most design features

and details are defined.

This paper deals mainly with the last procedures and their

possible developments or extensions.



149

3. Hazard

a n d

O p e r a b i l i t y A n a l y s i s

3.1 GENERAL DESCRIPTION

The method of hazard and operability studies (HAZOP) is now

well established as a means of identifying at the detailed

design stage potential hazards and operability problems.

HAZOP is a technique for systematically considering

deviations from the design intent, by the application of

guide words, to an operation or a process flowsheet. It can

be carried out at an early stage on a conceptual flowsheet,

in which case only safety aspects are usually noted, or at

the detailed design stage line by line on a Piping and

Instrumentation Diagram (P & I) . In this case all deviations

which are undesirable, either for safety or for operability

are noted.

The technique can be applied to an existing plant but in

this case the scope for action will be limited whereas

during plant design options should, as far as possible, be

kept open until the process has been studied in this

rigorous manner. One particular situation where the

technique is found to be particularly useful, in the case of

existing plant, is where modifications are under

consideration. If a HAZOP study has been carried out on the

original design and adequate records are kept then only a

limited amount of work would be required to consider the

implications of the modification.

The study is based on a very generalised procedure capable

of application in a wide range of circumstances and which

generates a number of searching questions. These questions,

of the "What happens if?" type, are asked in an ordered but

creative manner which ensures a thorough and systematic

coverage either by an individual working alone or by a

multi-disciplinary team.

The method adopted is to search the proposed design,

systematically looking for every notional deviation from the

norm and to decide whether these deviations are trivial

ones,

operational problems or constitute a potential hazard.

It is usually applied to flow diagrams whether these are

detailed P & I diagrams, block charts for unit operations or

flow charts describing an operational activity. This search

is done by the application of a carefully chosen list of

guide words or standard phrases to the process parameters

for each integral part of the design or system. Such a list

of guide words should promote unrestricted, free ranging,

logical thought to detect virtually all conceivable process

abnormalities. The method can be applied to any type of



150

plant or operation, irrespective of the degree of

complexity, provided that only a suitable list of guide

words is selected. There are several variations of these

lists of guide words. Some are intended for specific

situations and the guide words will reflect

this.

Other

lists are designed to be far more wide ranging in

application.

Table 2 : A comprehensive list of guide words

Process variables

Main guide words

FLOW

PRESSURE

TEMPERATURE

LEVEL

PHASE CHANGE

COMPOSITION

NO SUPPLY

DISCONTINUUS

OPERATION

LEAKS

EXTERNAL EVENTS

Low / High / No / Reverse

Low / High / Vacuum

Low / High / Below 0 °C

Low / High

Vapour / Liquid / Solid

Contaminants / Composition

Change

Energy / Compressed Air /

Nitrogen / Cooling water /

Vacuum / Steam

Start-up / Shut-down /

Emergency Shut-down /

Maintenance Activities

Flanges / Small Pipes /

Pump Gaskets

Tube Rupture / Vessel

Rupture

Vehicle Collision / High

Winds / Flooding / Fire

Earthquakes / Aircraft

Crash



151

A rather comprehensive list of guide words and their

possible "states" is presented in Table 2 for most important

process variables and other events of interest.

Each guide word is applied to the "integral part". How each

deviation might be caused and what the possible consequences

of it may be, are then considered. The kind of questions

that ought to be asked at this stage of the procedures are :

- Could there be no flow ?

- What are the consequences of no flow ?

- Are the consequences hazardous or do they prevent

efficient operation ?

- If so, how could it arise ?

- How will the operator know that there is no flow ?

- If so, can we prevent no flow (or protect against

the consequences) by changing the design or method of

operation ?

- If so, does the size of the hazard or problem

justify the extra expense ?

Having completely examined one part of the design and

recorded any potential hazards associated with it, or

remitted for detailed separate consideration, the study

progresses to focus attention on the next part of the

design.

The examination is repeated in the same fashion

until the whole section of the design, etc. under

consideration has been reviewed.

3.2 FAULT PROPAGATION IN HAZOP STUDIES

The objective in HAZOP studies is to identify deviations

from design intent which may give rise to safety or

operability problems. This necessarily involves some

exploration of the possible causes and consequences of the

deviations.

It is not, however, the purpose of the study to

make a detailed analysis of these causes and consequences.

If this is considered necessary, it is carried out as a

separate exercise using such techniques as fault trees.

Nevertheless, since a HAZOP study does involve in some

degree the detection of fault paths, the method may be

regarded as one of a member of techniques developed in

recent years for the exploration of fault propagation in

process plants. The fault tree aspects of HAZOP studies are

illustrated by work described by Lihou

(1) ,

who has

developed a method of encoding the written results of a

hazop studiy to produce a set of fault trees for the plant.

The completeness of the fault trees so produced necessarily



152

depends on the completeness of the fault propagation

information produced by the HAZOP study.

In normal HAZOP studies the exploration of fault

propagation by the study team is unsystematic and

fragmentary. This is to be expected, since the systematic

determination of the fault propagation pathways is not the

object of the HAZOP study. These considerations indicate

that there are likely to be difficulties in constructing

fault trees from HAZOP study records.

3.3 OTHER FEATURES

The main advantages of the procedure are :

- Several minds with different engineering

backgrounds address the problem.

- Very detailed results

and the drawbacks :

- Considerable time and manpower required.

- Not all causes are investigated.

Many interesting comments regarding other important

features of HAZOP studies as well as some application

examples can be seen in references (2) and (3 ).

4.

Fault Tree Analysis

4.1 GENERAL DESCRIPTION

It is a deductive technique that focuses on one particular

accident event and provides a method for determining causes

of that accident event. The fault tree itself is a graphic

model that displays the various combinations of

equipment/component failures and human/operator errors that

can result in the accident event of interest. These diagrams

must start from an event which has been identified by some

other method.

The technique is essentially binary, i.e., the events or

states in a fault tree are generally assumed to be those

which can be identified as existing or not existing. In

reality there is a whole spectrum or multiplicity of failure

possibilities, some will constitute a state of partial

failure others may be total. Decisions must be taken about

what degree of partial failures constitutes a "failure" in a

fault tree.

The result obtained is a set of combinations of

failures/conditions (cut-sets) that being present

simultaneously produce the accident event. These cut-sets



153

may be limited by the number of component failures to

consider or by its probability of occurrence, in order to

minimise the work of result analysis.

These sets can also be ranked qualitatively (number of

failures/errors required to produce an accident) or

quantitatively (probability of having an accident).

The strength of Fault Tree Analysis as a qualitative tool

is its ability to break down an accident into basic

equipment/component failures and human errors.

It requires a complete understanding of how the

plant/system functions, the interconnections between the

different components or subsystems, operating procedures,

failure modes of every component and their effects on the

plant.

4.2 PROBABILISTIC EVALUATION.

Fault trees also provide a basis for quantification of the

frequency or probability of the undesired event, provided

data is available for the frequency or probability of the

various events or states appearing in the fault tree. Even

if this data is very limited, the important contributory

factors can often be identified. This enables effective ways

of reducing the likelihood of the top event to be

determined.

4.3 FAULT TREE CONSTRUCTION

The construction of a fault tree follows a rigorous and

methodical process. Starting with the top event the analyst

poses the question "What are the immediate precursors or

causes of the event or system state?". This question is then

applied to each of these sub-events until the analyst is

quite satisfied that all credible root causes, which could,

albeit in combination with other causes in the tree, lead to

the realisation of the top event, have been discovered and

included.

In the construction of fault trees, the analyst makes use

of various symbols. Symbols known as gates describe the

logical combination of input parameters necessary for an

output to be propagated up the tree. The two most widely

used gates are the "OR" gate and the "AND" gate :

- OR : An output is propagated from an "OR" gate if any

one or more of the inputs exist at any time.

- AND : An output is propagated from an "AND" gate if

all the inputs exist at the same time. Note that this does

not mean that these input events or states must happen



154

simultaneously. If, for example, a protective system is

failed on demand, the time at which the protective system

became unable to react to demand is irrelevant.

There are more complex gates which are sometimes used to

show conditions or sequences. The use of certain gates can

complicate quantification of a fault tree. Examples of these

complex gates are the "EXCLUSIVE OR" and the "SEQUENTIAL

AND"

gates. Take for instace the "EXCLUSIVE OR" gate, if an

input A or an inut B exists then the output will be

propagated but should both inputs A and B exist, then the

output will not be propagated. A "SEQUENTIAL AND" gate,

sometimes known as a "PRIORITY" gate, can be used in

situations where the output, for example an explosion, will

only propagate if one of the inputs, an inflammable gas

release,

is closely followed by a second input, an ignition

source (note the flammable gas must be in the combustible

range).

4.4 USE OF FAULT TREES IN HAZARD IDENTIFICATION

The main use of fault trees in the overall context of hazard

identification is to structure the failure logic although

they are also used for identification of the causes of top

events. Fault tree construction provides a powerful prompt

to the analyst to consider ways in which situations

appearing in a fault tree can arise thereby identifying

causes.

This prompting action is not structured and so

cannot be guaranteed to be exhaustive. For this reason it

may be wise to apply "bottom-up" techniques, such as FMEA or

HAZOP to parts of the system to improve the likelihood that

all important causes are included.

Because Fault Trees are labour intensive, i.e., require

specialist expertise to perform the analysis and can involve

very detailed analysis of components and operations, their

use in the process industry has mainly been limited to the

analysis of critical areas. Hazard and operability studies

can provide an exhaustive way of going through deviations

but it does not provide any structure for combinations of

events. The techniques are therefore complementary and

should not be seen as alternatives.

Fault trees tend to be equipment oriented therefore the

analyst must be aware of this and ensure that sufficient

attention is given in other areas for instance human errors.

Human errors can be incorporated into the technique but the

main problem here is in identifying them.

Fault tree analysis provides a powerful technique for

identifying and structuring the contributory causes to a



155

given top event. The analyst must be aware that causes

appearing in the tree could lead to other top events which

may be just as serious. This is another good reason for not

relying solely on one technique to provide a thorough

analysis of the situation.

Some application examples can be seen in references (2) and

(4).

5. Plant Dynamic Simulation to Evaluate Top Event Conditions

(DYLAM Methodology)

The increasing complexity of chemical sites nowadays,

combined with the diversity of dangers in various parts of

them, calls for a more synthetic and representative way of

plant and process description for risk and safety analysis

as well as fault detection purposes. Towards this direction

the DYLAM methodology offers a solution since it takes

account at the same time of process physics and system

performance, two domains which are normally separated by

current probabilistic techniques.

Since accidents proceed according to the values assumed by

certain physical variables, such as temperature, pressure,

concentrations, etc.

,

as a function of time and to the

occurrence of logical events such as lack of intervention of

protective systems, control actions, human operator faults

(which happen at random

times),

dynamic analyses are more

appropriate for representing such phenomena because they

depict more adequately the real accident sequence. This

advantage is greatly reinforced when responses of control

systems and/or of human operators are of concern because the

real time period for their intervention can be quite

precisely defined.

In such a way, design parameters and operating procedures

can be analysed in detail, helping the decision making

process and the fault diagnosis for accident prevention.

5.1 DYLAM TECHNIQUE

The DYLAM technique and its related computer program is a

methodology which has been developed at the Joint Research

Centre of the European Community, Ispra, Italy, and it is

still under amelioration. The basic characteristics of the

method have been extensively described elsewhere (5-6) and

in this lecture we are going to shortly summarise and stress

these aspects which become important for the elaboration of



156

our example, as they are synthetically represented in Table

3.

The technique has two main parts. The first one (steps 1 to

4) consists of generating all the possible system state

configurations by the combination of the different component

states. Every one of these configurations is finally

represented by giving appropriate parameter values to a set

of parameteric equations, which contain both logical and

physical information. The second part (steps 5 to 7) solves

numerically the corresponding equation set in order to

foresee the physical consequences of the event sequences

generated, and it verifies whether the TOP conditions are

satisfied

(i.e.,

if some physical variable has reached

certain threshold value).

The process under analysis is described by a set of

component models, obtained by a quantitative failure mode

and effect analysis, resulting in logical analytical

relationships characteristic of each component. Such models

should be developed for each single component, but if this

tends to be very CPU-consuming by increasing considerably

the number of sequences to be analysed, the grouping of

single components in macro-components is advisable.

DYLAM provides all the nominal sequences that produce one

or more TOP conditions and the evolution of the physical

variables of interest for those sequences. On the other

hand, the probability distributions of the top conditions

are given as a function of time, taking into consideration

both statistical and functional failure dependencies. It

must be stressed that the functional dependency

consideration is made possible just because of the step-by-

step procedure in the evaluation of the physical variables

along the transient state and is has been implemented in the

new version (DYLAM 2) of the code (6 ).

In order to minimise the number of numerical solutions,

which are generally most CPU consuming, steps 2, 3 and 4 of

Table 3 are performed as soon as an event sequence has been

generated and before proceeding to the physical consequence

evaluation. In that sense, the maximum order of simultaneous

failures to be considered and the cut-off probabilistic

limits are key factors in the total CPU time of the

analysis.



157

T a b l e

3 :

S t e p s

o f

D Y L A M p r o c e d u r e

1) Event sequence generation (based on component models).

2) Sequence are generated until the maximum order specified

is reached.

3) Analysis of passive states to cancel those sequences

where all components are in passive state.

4) Verification that sequence probability is not lower than

the cut-off value established by the user.

5) Numerical solution of equation set or dynamic simulation

of the plant to predict the physical consequences of the

respective sequence of events.

6) Verification of TOP event conditions and selection of

minimal TOP TIME PATTERNS.

7) Results :

i) Reliability parameters.

ii) Physical evolution of every minimal sequence that

reached at least one of the TOP event conditions.

The first and the fifth steps presented in Table 3 are

strongly interrelated because components should be modelled

according to the way in which the numerical solution

requires parameter values to calculate the system

performance.

The numerical solution of the equation set, characteristic

of each system, may be performed in several ways according

to the complexity of the system, as applications in the

nuclear and chemical field can show. Main alternatives are :

a) The process equipment is represented by simplified

formulas including some delay times to take account of

transient situations.

b) The system is represented by transient simulators,

the running times of which are considerably low as to be

used directly, without simplification. The requirement of

this alternative is that the simulation running time must be

reduced to as little as possible for any combination of



158

failures. The accuracy of this code should be compatible

with the uncertainties which are present in the other steps

of risk assessment.

5.2 CASE STUDY

An application of DYLAM to chemical plants falling in the

second case indicated above is described elsewhere

(6) .

The

chemical plant analysed is a batch plant for sulfolane

production; it is divided into two parts : the addition unit

and the hydrogenation unit. The process can be summarised in

the following chemical reactions :

Addition reactor :

S02 + C4H6 > Sulfolene

C4H6 : butadiene

Hydrogenation reactor :

Sulfolene * H2 > Sulfolane

Sulfolane : tetrahydroditiofene-1-1 dioxide.

The first reaction is exothermic and reversible; the higher

the temperature, the smaller the amount of products

obtained.

The second reaction is irreversible, exothermic, and needs

a catalyser to proceed at an acceptable rate.

The DYLAM methodology was applied only to the addition

reaction and the respective facilities.

5.3 RESULTS OBTAINED

Two complete analysis were made, the difference between them

lying in the consideration or not of the operator corrective

actions for certain emergency situations.

The following parameters were considered :

- 13 components and event variables (without operator

corrective

actions).

18 components and event variables (with operator

corrective actions)

- Maximum top event seguence order : 4

- Sequence probability threshold : 1.0 x 1 0

- 8



159

Different top event conditions were assumed, regarding

maximum pressure to be obtained for all failure combinations

generated by DYLAM. Results obtained and discussion are

detailed in reference (7).

It was concluded that with DYLAM method olo gy, t he complet e

prob abili stic and physical related info rmation for all the

possible and significant combinations of failures or

compo nent states were obtained, giving thus the p aram eter s

which help the reliability engineer to judge about the

adequacy of the different design alternatives from the

standpoint of plant safety.

The simulation of a large number of possible accidental

sequences which is made possible by the automated technique

implemented in DYLAM, offers the designer a very strong body

of knowledge to understand malfunctions and their effects.

Therefore, it may give a great aid in applications directed

towards operator support systems and fault diagnosis.

References

1. Lihou, D. (1980) Oyez Publications Symposium on Safety

Promotion and Loss Prevention in the Process

Industries, London.

2.

Lees,

Frank P. (1980) Loss Prevention in the Process

Industries,

Butterworths, London.

3. Roach, J. and

Lees,

F. (1981) The Chemical Engineer,

456-461.

4. Labath, N. ,

Real,

M., Huespe, A. and Masera M. (1986)

Reliability Engineering 14 , 223 -24 3 .

5. Amendola, A. and Reyna, C. (1984) EUR 9224 EN

6. Amendola, A. and Reyna, C. (1987) T.N.I.87.128, JRC;

Ispra

7. Amendola, A., Labath, N. , Nivolianitou, Z. and Reyna, C.

(1988) The Int. J. of Quality & Reliability Management

5, 48-59





C O N T R O L T E C H N I Q U E S

C. MOUSSAS

Control Systems Laboratory

University ofPatras, Patras, Greece

Present address: J RC

Ispra Site

Safety Technology Institute

Ispra (VA), 1-21020

ABSTRACT. In this paper, first a description of the general configuration of a batch process computer-

controlled system is given. Then, some process control techniques are reviewed. Emphasis is plased on

the so-called

adaptive

control

techniques

which appear to be very effective in controlling batch processes

over a large range of operating conditions. In fact, the need for adaptive control arises from the fact that

the traditional feedback controllers (State Feedback, PID, e.t.c.) may work well for a given application,

but they need to be retuned whenever the conditions of the underlying process, or the process itself,

change. Fine chemical plants represent typical examples. The basic concepts of the various design

methods are presented, without getting into many technical details and mathematical derivations.

1 . Introduct ion

The introduction of digital comp uters to chemical process plants has been started approximately 3 0

years ago. Even in the first applicat ions, improvements in product quali ty and process

reproducibility were immediate, since the sequencing of the process steps was being done in a

more consistent and systematic way. With the increasing development of microelectronics, digital

computers became smaller, more powerful, and less expensive. At the same time, new theoretical

results in control theory, specially suited for computer-controlled systems, appeared in the

literature. As a result, advanced controllers can now be implemented in a fast and inexpensive

manner. Also, the substitution of many process units by microprocessors led to the idea of

distributed control systems, where specific control functions are imp lemen ted by means of

microprocessor-based devices which are supervised by a general-purpose digi tal computer.

Because of their complexity, batch chemical processes lend themselves to the application of such

advanced control systems. Major improvements include increased production, better product

quality, cost reduction, and safer plant operation. O n the other han d, there is an inevitable increase

in the complexity of the overall system which dictates the need for better personel training, and

elevates the role of process operators

[1].

2 . Batch Process Com puter Control

2 .

1

.

BATCH PROCESS DESCRIPTION

161

A.

Benuizi and J.

M.

Zaldivar (eds.). Safety of Chemical Batch Reactors and Storage Tanks, 161-200.

© 1991 ECSC, EEC, EAEC, Brussels and Luxembourg. Printed in the Netherlands.



162

Batch chem ical processes consist in the manufacturing of

a

product by proces sing raw materials in

a discontinuous way. Usually, the batch reactor includes an agitator, a cooling/heating jacket, a

condenser and a feeding system. Important batch process variables are, among others, the reactor

temperature, the jacket temperature, the reactor press ure, and the feed rate. In all cases, the reactor

temperature, as well as its variations, play an important role in both the quality of the

manufactured product and the safe operation of the plant, and they can be directly controlled by

means of the fluid tem perature circulating in the jacket. In the case of highly ex othermic reactions,

temperature control may also be performed by controlling the reactant feeding rate, i.e. semi-batch

operation. Other control variables can also be controlled indirectly, since the reactor temperature

definitely affects the reaction rate, as well as the pressure. However, difficulties in controlling the

above m entioned quantities arise form the following facts.

First, some of the process variables may not be easy to be measured, and thus they have to be

inferred by using other available measurements.

Second, many of the process variables vary considerably throughout a batch, and they never

achieve a steady state. This is an unavoidable situation, since it is inherent in every batch process.

Third, startups and shutdowns are normal procedures which have to be automated effectively,

since they represent one of the most difficult phases with respect to control.

Finally, a batch process plant must be able to operate in a wide range of operating conditions,

so that various desired products can be manufactured.

In spite of the above difficulties, batch chemical processes can be effectivelly controlled with a

high degree of reliability and safety, by a proper selection of a process control system [2]. This

requires a good understanding of the batch process characteristics, and a careful consideration of

the process control needs. In the following section we discuss some common control system

configurations, paying more attention to the so-called Distributed Control Systems which are

mostly used today.

2 . 2 . BATCH PROCESS CONTROL SYSTEMS

2.2.1.

Classification. Commonly, the existing batch process control systems can be classified into

the following three general categories [2] :

1. Systems based on P rogramm able L ogic Controllers (PL C).

2.

Direct Digital Control (DDC) Systems.

3 .

Distributed Control Systems (D CS).

In the first category, the control system is build around microprocessor-based programmable

controllers w hich sequence the process and they can handle a limited amou nt of control functions.

These systems are suitable for small to medium scale batch processes, and where there do not

exist frequent changes in the manufactured product specifications. The main reason is that PLC

units provide two-state(on/off) control functions, and thus, complex controllers are more difficult

to be both programmed and modified. However, as long as no advanced control techniques are to

be implemented, they represent simple, well-functioning, and highly reliable control systems.

They can also be easily expande d by the introduction o f either new PLC u nits or just I/O

hard w are. It is imp ortant to men tion that PL C's are beco ming mo re and more powerful and they

can now be equiped with A/D and D/A modules in order to implement special analog control

functions, such as PID controllers.

In the second category, the control system uses a minicomputer for direct control. That is, a

computer handles all the required control actions, and its output control signals act directly to the

specific final control elements, or other process units. Whenever continuous time signals are

involved, the necessary transformations are performed by means of A/D and D/A converters. Note



163

that these functions can also be implemented on the computer. Futhermore, by appropriate

programming, advanced control techniques can be easily applied. DDC systems are suitable for

medium to large scale batch processes, having complex requ irements. A mon g their drawbacks is

their poor expand ability. Also, their complex harware and software usually requires highly trained

personel.

In the third category, microprocessors, designed to perform specific tasks, are responsible for

all the required functions of the control system. Through a communications link they are all

connected to a general-purpose computer which acts as a supervising unit. The supervising

computer does not act directly to the various process elements, but it rather sends appropriate

requests to the specially designed microprocessor-based units which, subsequently, transform

these requests into actions applied directly to the process. Similarly to DDC systems, distributed

control systems are appropriate for medium to large scale batch processes. Furthermore, they are

far more expandable. They also provide more standard functions and they require less

programming skil ls. With respect to PLC based systems, they provide more sophist icated

operaror interface, and they are able to implement advanced control algorithms as well as better

recipe handling functions. On the other hand, PLC based systems tend to be less expensive for

smaller plants. On the wh ole, distributed control system s are mu ch mo re flexible than PLC and

DDC systems, and they are the most appropriate for processes where either the product

specifications are frequently changing, or different products are manufactured.

The main idea in a DCS is that the implementation is totally distributed, and supervision of the

various units is performed through levels of increased centralization. This leads to the notion of

different levels of functionality in a batch process control system. According to the previous

discussion, we can identify two main levels of functionality which will be referred to as the

regulatory control level and the superviso ry control level, respectively [3]. Specifically, the

regulatory control level contains the microprocessor-based units as well as any existing manual

control functions, while the supervisory control level contains the supervising computer together

with its peripherical units. In the following subsection we discuss these two levels in more detail,

and we identify the specific control functions that each one of them can handle.

2.2.2. Functiona lity Levels. Figure 2.1 show s a distributed con trol system which has been

divided into three basic levels of functionality. Level 1 contains the various process elements, that

is , valves, pumps, agitator, measuring elements e.t .c, level 2 represents the regulatory control

functions, and level 3 the corresponding supervisory control functions. In order to make a clearer

distinction between levels 2 and 3, we now consider some general control functions which are

common to all batch chemical processes. A predefined recipe which determines the specific

product to be produced and also selects the appropriate operations which are to be performed, will

contain the following actions [4] :

- feeding of the raw materials

- strirring of the reactor components at certain speeds

- following a desired temp erature profile

- measuring various process variables

- checking the proper function of valves, pumps, e.t.c.

- discharge of the product

- reporting, during and after the batch

The execution of the above actions can be obtained by a combination of sequence and

continuous control, including the following b asic control functions :



164

- actuation

- sensing

- interlocking

- regulatory (continuous) control

- recipe handling

- sequencing

- failure detection

- data handling and reporting

Terminals

^ i a p

> ^

V*

SUPERVISING

COMPUTER

t

LEVEL 3

J

* l

\

Pr in te r 1

Disc

J

Terminals

s a

MICROPROCESSOR-BASED

UNITS

- Operator Interface

- Single Loop controllers

- Weighting subsystem

- A/D converters

- ' - . L J .

mrm

Communicat ions

Link

LEVEL 2

Panels

PROCESS

LEVEL 1

Figure 2.1 - Functionality levels

Actuation, applies electric signals to pumps and valves, required for the feeding of the

components, or the discharge of the product.

Sensing, includes all the data aquisition d evices, as well as A/D and D /A converters.

Interlocking, prevents different valves to be open at the same time, whenever this is not

permitted.

By regulatory, control we mean the application of control algorithms for controlling important

process variables such as temperarure, pressure, flow, e.t.c.

Recipe handling, manages the execution of a specific recipe through the process units, and

sequencing, determines the steps to be followed within each of the process units.

Failure detection, handles any irregularities which are detected in the process, actuates alarms,

and takes recipe-based corrective actions.



165

Data handling and reporting, is the function which organizes data from various devices, and

makes them available as reports, or it transmits them to other systems.

We now turn to the classification of the above control functions with respect to the

functionality levels. As we can see in figure 2, the regulatory control level, or level 2, is directly

connected to the process equipment and to other output devices, while the supervisory control

level, or level 3, acts on the process by giving specific requests which are subsequently executed

by level 2. That is, it is not directly connected to the process. Thus, actuation and sensing

definitely belong to level 2. Simple, well-defined regulatory control functions (e.g. PID), are also

included in level 2, as well as safety interlocks which should not be bypassed by a plant operator.

On the other hand, recipe handling, data handling and reporting functions usually belong to level

3 ,

together with any advanced regulatory control algorithms and any flexible interlocking

functions. Sequencing and failure detection control functions, can be divided between the two

levels, depending mainly on the complexity of each function. The equipment used in level 2 must

be totally error-free, thus requiring low complexity. It must also be protected against changes. On

the other hand, level 3 equipment can be quite complex and it should be able to change whenever

operation conditions, product specifications, or safety measures, change.

2.3. BATCH TEMPERATURE CONTROL

In this section, we discuss in some more detail the regulatory control function. As we mentioned

above, this part of the batch control system deals with the application of control algorithms for

controlling important batch process variables. The m ost important controlled variable is the reactor

temperature, which plays an important role in the quality of the manufactured products and in the

safety of the operation. Therefore, varying temperature profiles from batch to batch, lead to

inconsistent, or unacceptable, product quality. In the beggining of a typical batch reaction, heat is

introduced, so that the reactor temperature is initially raised until a specific value, called the set

point, thus initiating the reaction. Then, for an exothermic reaction, cooling is applied to keep the

temperature close to the set point. Towards the end, heating may be necessary in order for the

reaction to be com pleted.

This heating/cooling procedure can be performed by manipulating the temperature of the fluid

circulating in the jacket of the reactor. To this end, either two fluids, that is steam for heating and

water for cooling, or just one fluid which is externally heated or cooled, can be used. In the letter

case the jack et tem perature is changed by opening and closing va lves. Wha tever the case is, the

control algorithm has to provide a value for the jacket temperature, given values of other process

variables such as reactor temperature, reactor pressure, feeding flow, e.t.c. For the design of such

control algorithms, various techniques are discussed in the next chapter. Emphasis is placed on

the so-called adaptive control techniques which appear to be quite effective in controlling chemical

processes.

3 . Contro l Techniques

3 . 1 . INTRODUCTION

3.1.1.

General Control Considerations.

Control systems are found in all sectors of industry, such

as chemical industry (quality control of desired product), space technology (flight control), power

system s (energy co nsum ption ), robotics and others. In fact, our every-day life is greatly affected

by some type of control system (car, air-conditioning, electronic devices e.t .c). The design of



166

such a system consists in determining the appropriate control signals which will be applied to a

specific p roces s, so that its output satisfy som e prescribed p roperties.

In the chemical industry, process means the operations necessary to put together raw materials

and cause them to react in a prescribed fashion in order to produce a desired end-product.

Generally speaking, the process can be described by an equation of the form

Y = f (X,U,t )

(3 .1)

where Y represents the desired properties of the end product, and it will be referred to as the

output of the process. The letters X and U represent the variables on which the properties depend.

Specifically, let U represent the variable(s) which we can control directly, i.e. the input of the

process. The control system, or controller, can also be described by an equation of the form

U = g (X,Y, t )

(3.2)

where g is a function which realises the following strategy :

1.

Measure the variables X, U, Y of the process at a given time instant.

2. Compare the output Y with the desired value, i.e. the set point, and find the error.

3 .

Based on 1 and 2 above determ ine a new value for the input variable U , in order to

correct any deviation of the error from zero (Controller Design ).

4. Feed the new value back to the process.

A simplified block-diagram configuration of the above procedure is illustrated in figure 3.1.

Set Point

e

A

Controller

u

Process

y

— w

Figure 3.1 - Feedback Control System

According to the above discussion, it is clear that the design of the controller should be done in

such a way so as to eliminate the error, e, in a reasonable period of time. Typically, the design of

the controller is based on some assumed process model as in 3.1. If the model is known, then the

design can lead to satisfactory results. But a complete knowledge of the model, requires a

complete knowledge of the process parameters for all possible operating conditions. If these

param eters are not known, or if they change w ith time, then the performance of the controller will

deteriorate. Unfortunately, industrial processes exhibit time varying parameters, nonlinear

dyn am ics, and mo delling unc ertainties. Since a com preh ensiv e theory for the treatment of

nonlinear systems does not exist, we realise that the controller design for such processes becomes

a very difficult task. In fact, this is where the adaptive control systems come in to the picture. A

typical block-diagram representation is shown in figure 3.2. The controller parameters can be

adjusted by means of the adjustment mechanism, and they usually depend on the difference

between the actual and the desired performance of the overall control system. We can distinguish

two main loops; loop 1, which is the same as that in figure 3.1, and loop 2, which is used to



167

adjust the controller parameters. If the process parameters change, then loop 2 will take a

corrective action by chan ging the param eters of the controller.

Set Point

Loop 2

Controller

Adjustment

Mechanism

Process

Loop 1

Figure 3.2 - An Adaptive Control System

Two very important adaptive control schemes which lead to such control system

configurations are :

1. Self-Tuning Controllers (STC) [5],[6]

2.

Model Reference Adaptive Systems (MRAS) [5],[6],[7]

For the rest of this report we shall be concerned with these two categories. For information about

other important adaptive control schem es see [5].

3.1.2. Self-Tuning and Model R eference Adaptive Control. A block diagram of a self-tuning

control system is shown in figure 3.3.

Desired

Performance

Set Point

^

i

r

Design

i

r

Controller

u

Estimation

Process

. _

y

_ ^



168

Figure 3.3 - Self-Tuning Control System

An assumed dynamic model is associated to the process. Based on this model and on a

controller design procedure, a specific controller can be derived. This controller, which obviously

depends on the model parameters, is then applied to the process. At each time instant the

parameters of the model are estimated from input-output data, and based on these estimates, the

parameters of the controller are computed according to the specific design procedure. We see that

a variety of self-tuning controllers can result from this scheme by co nsidering different structures

for the controller and the estimator. Typical design procedures include the recursive least squares

and projection algorithms, for the estimator design, and the minimization of a quadratic cost

function and pole-placeme nt techniqu es, for the design of the controller.

A block diagram of a model reference control system is shown in figure 3.4. In this case the

desired performance of the control system is described in terms of a reference model. We again

have to assume that the process is described by some mathematical model. The goal is to

determine the adaptive mechanism which changes the values of the controller parameters, so that

the output y of the process be close to the desired ou tput y

m

.

STC systems where originally developed for discrete time systems [9],[10], while MRAC

systems were developed for continuous time systems [11],[12],[13]. Also, MRAC as shown in

fig. 3.4, represent the so-called direct schemes because the controller parameters are directly

updated from the adaptive mechanism. On the other hand, STC as in fig. 3.3, are indirect

schemes in the sense that first the model parameters are estimated, and then the new controller

parameters are computed. However, as we can see in these figures, the two configurations are

quite similar. In fact, we can design MRAC for discrete time systems and STC for continuous

ones ,

as well as, indirect MRAC and direct STC which, as we shall see later in this paper, in

some cases result in identical adaptive control schemes [5],[6],[7].

Desired

Performance

Set Point

w

Reference

Model

1

r

Controller

y

m

u

Adaptive

Mechanism

t

Process

y

*

Figure 3.4 - Model Reference Adaptive Control System

The design of an adaptive control system of the form illustrated in figures 3.3-3.4 is

conseptually simple. As we have already mentioned, the design will result in different schemes

depending on the specific choises of the controller and the estimator. Whatever the choise is, the



169

overall system must satisfy some stability and convergence requirements. Specifically, we require

global stability, which means that the process inputs and outputs remain bounded for all time, and

that the error between the process output and the desired one go asymptotically to zero. Also, in

the case of constant process parameters we require that the estimates converge to the real values.

Since, in principle, adaptive control systems are nonlinear systems, their analysis is quite

complicated and global stability and convergence proofs exist only for some cases and under ideal

situations. An overview of the current stability and convergence results can be found in [5],[6].

Issues associated with the application of adaptive schemes to real nonideal situations, as well as

general guidelines for resolving some practical problems are discussed in [5],[19],[20],[21].

3.1.3 .

Digital Control and Process M odelling.

Nowadays, digital computers play an important

role in the implementation of adaptive schemes. Recent achievements in microelectronics was one

of the main reasons for the developm ent of many different adaptive algorithm s, since their testing

through simulations could be done in a very fast and inexpencive way. Since many processes are

inherently continuous-time, some kind of conversion from continuous-time values to discrete-time

values, which can be direcdy processed by the computer (and vice-versa), is needed. This is done

by using analog-to-digital (A-D) and digital-to-analog (D-A) converters. A block diagram of such

a computer controlled system is illustrated in figure 3.5.

z(t)

h -

A-D

z(k)

Digital

Controller

u(k

D-A

u(t)

Process

y(0

w

measurements

input

output

Figure 3.5 - A Computer Controlled System

One way to design a digital controller for this system would be, first to design an appropriate

continuous-time controller based on the continuous-time process model, and then to make a

discrete-time approximation. The best results that we can expect by applying this approach are the

ones obtained by the continuous-time controller, and in the case that we sample the process fast

enough. In many cases, however, much better results can be achieved if one uses the theory of

discrete-time systems. This will, also, enhance the class of controllers available for a specific

application, as well as it will lead to a better understanding of inherently discrete-time processes.

For a more detailed discussion and representative examples see [14],[15]. For the above reasons,

it is necessary to develod discrete-time models for the continuous-time processes, and then base

the design of digital controllers on them. In the context of adaptive control the usual approach is to

consider that the process is described by the so-called AutoRegressive Moving-Average with

auxiliary input (i .e. the control signal u) model, or ARMAX [5],[6], which for a single-input

single-output process is given by the following equation

A(q"') y(k) = B(q"

1

) u(k-d) + Cfq"

1

) e(k)

(3.3)

where u and y are the process input and output, respectively, e is a stochastic noise variable (white

noise process), and by definition



170

q'VG Osyfc-l) . (3.4)

Any delay between the input and output of the process is expressed through the integer d, for then

d > 1. The polynomials A, B, and C are defined by,

n

A q

1

) = l

+

2 ^ a . q -

i

(3.5)

i= l

m

B(q"

1

)

= X

b

i

q

"

i ( 3 6 )

i=0

n

C t q V ^ C . q

1

•

(3

-

7)

i=0

Th e coefficients a;, bj , and q , represe nt the para me ters of the mo del. At first glance, one

would say that this model cannot represent a highly nonlinear process, such as a chemical

process, since 3.3 is a linear difference equation. However, by allowing the parameters a;, b;, q,

to change (time-varying parameters), we introduce a nonlinear behaviour into our model. In the

adaptive control case, this is done by the estimation mechanism which continuously updates the

model parameters. The use of ARMAX models is furthermore justified by the fact that when

combined with appropriate control and estimation schemes, they lead to adaptive algorithms for

which stability and convergence results can be established. For these reasons ARMAX models

have been extensively used in the literature [5],[6],[17],[18].

3.1.4. Applications. In a recent article, surveying the design of adaptive control system s [2 7], the

author begins with the phrase :

" Adaptive control is now finding its way to the market place after many years of effort"

In fact, even if the first applications of the adaptive control systems appeared in the 1950s in

the context of aircraft flight control, it was only in the 1980s where the development of both the

theory and the computer hardware, allowed for a systematic application of various adaptive

control schemes to the industry. As reported in [5], it was estimated that in May 1988 there were

at least 7000 0 industrial process loops in which adaptive techniques w ere used. A description of

various commercially available industrial adaptive controllers, announced in the 1980s from

com panies in Europe, No rth Am erica and Japan, can also be found in [5]. At least half of them are

based on the PID controller structure, which is the most common technique applied to industrial

processes, and provide automatic tuning of the PID parameters. They are very useful, since it

appears that even today many industrial PID controllers are poorly tuned [27].

Som e recent applications of adap tive control to chem ical reactors are reported in [25], [28]-

[31].

In [25], the generalized minimum variance self-tuning controller (sec. 3.4.2.4) was applied

to a batch chemical reactor (Real Plant). The results showed a smoother temperature profile, than

that obtained by a PID controller, as well as insensitivity to reactant quality. In [28],[29],[30],

applications of various adaptive control techniques to a batch polymerization reactor are described,



171

both to simulated [28],[29],[30] and to pilot plant [30], experiments. The techniques included,

among others, minimum variance and generalized minimum variance self-tuning control (sec.

3.4.2), as well as adaptive pole-placement (sec. 3.4.3). Their performance was showed to be

either

equally

good,

or

better

than

the

performance

of

well

tuned

PID

controllers.

Various

control

objectives were considered, such as isothermal operation, constant rate operation, constant weight

average molecular weight , and specific monome r conversion profile. Finally, in [31], a

modification of the basic minimum variance self-tuning controller (sec. 3.4.2.3) was applied to a

simulated continuous stirred-tank reactor, where it was demonstated that it was more effective

than the basic method. Other numerous applications of various adaptive control schemes can be

found in the survey parers [21], [27] and [32].

3.2. PID CONTROLLERS

Even today, PID feedback controllers are th e most widely used controllers in the industry. The

reason

is

that

they

perform

quite

well

whenever

th e

process

is

of

reasonable

complexity

and

the

control specifications are not very tight. Among their features are th e integral action, which

eliminates steady state errors, or offsets, and the derivative action, which improves the stability of

the closed loop system. Their function can be described, in its simplest form, by the equation

r ■

I

„(,) . KI

e

M

+ Y |=W

d s + T

d T I , (3.8)

L ' » J

where u(t) is th e control signal, e(t) is the control error which equals the difference detween the

output y(t) and the set point y

r

(t), and K, Tj and T j are the so-called PID parameters, namely, the

proportional gain, th e integral t ime, and th e derivative t ime, respectively. In Laplace transform

representation, the above equation can also be written as

U( s ) = K

1 + T ^ - + T .

s

T. s

d

E(s) . (3 .9)

In practice, the algorithm described by 3.8 is subject to various modifications which improve its

performance.

For

examlpe,

in

the

case

of

pure

proportional

control

we

have

u(t) = K e ( t ) . (3 .10)

Since th e goal is the elimination of the error e(t), and since 3.10 implies that u(t)=0 whenever

e(t)=0, we realize that in most cases there will exist a non-zero steady-state error between the

output and the se t point. For this reason, instead of 3.10 we frequently use the equation

u(t ) = K e(t) + A (3 .11)

where

A

is

a

constant

corresponding

to

the

control

signal

when

e(t)=0.

In fact, th e main function of the integral term is the elimination of such offsets. To see this,

consider that instead of 3.11 we use a PI controller, i.e.



172

r i i

u(t) = K |

Z(Q

+ Y

e(s)ds

| .

( 3 1 2 )

L

' »

J

Now

assume

that

after

a

time

instant

t'

we

are

in

steady

state

with

u(t)

=

u(t')

=

u',

while

e(t)

=

e(t') = e' * 0, for t > t'. That is , a non-zero offset. Then, for a t > t' equation 3.12 gives

r r I

I , i f . , . e '-(t - t' ) I

u(t) = K |

e

+ — e ( s ) d s + |

;

f

o r t > t

. (3 .13)

L

°

j

J

Note , however, that the third term of the above expression is not constant, but it depends on the

time

t.

Consequently,

u(t)

is

not

constant.

But

this

contradicts

ou r

hupothesis.

On

the

other

hand,

we se e that for e' = 0 the control signal equals

r}

(s )

ds

0

which

is

constant.

A problem associated with th e integral action of a PID controller is th e so-called

integral

windup,

or

reset

windup,

which appears whenever th e control signal drives an actuator, or final

control element, having limited range. Then, when th e actuator reaches its upper limit, it will

remain there even if the control signal is increasing. Simultaneously, th e control signal will keep

increasing, since the error is not zero and the algorithm cannot detect that the non-zero error is not

due to the magnitude of th e control signal, but rather to th e saturation of th e actuator. This

situation has th e following consequences. When, at some time t, th e error becomes zero, the

integral part stops integrating, but the control signal is so big that the output of the process will

still be increasing, and it will take time before it s derivative changes sign. Therefore, this

behaviour

leads

to

large

overshoots

and

long

settling

t imes.

One

way

to

avoid

this

problem

is

to

use the integral part only when the error is sufficiendy small, thus avoiding the actuator saturation.

Another way is to stop updating the integrator when th e actuator saturates, or keep its value

bounded. This can be done, for example, if we use the following modified form of the integral

part

t

t

■ £-

fe(s)ds

+

^ fe

t

(s)ds

(3 .14)

In

this

case,

the

second

term

integrates

the

error

e

t

(t )

defined

as



173

e

t

( t ) = v( t ) - u ( t ) , (3 .15)

where u(t) is the control signal, and v(t) is the actuator signal. In normal conditions, v(t) = u(t)

and therefore e

t

(t) = 0. On the other hand, when the actuator saturates, e

t

(t) becomes negative and

keeps the integrator output bounded.

As we have already mentioned, the derivative action improves the stability of the closed loop

system. Intuitively, this can be understood if we rewrite the derivative part as

deffl e(t

+

A t ) - e ( t )

d

dt

d

At

This expression implies that the derivative term provides anticipatory action, for the error at time

t+At, thus improving the performance of the controller and the stability of the overall system. If

high frequency measurement noise is present, the derivative term will result in flactuating control

signals whose amplitude will be an increasing function of the frequency. For this reason, the

deriv ative term is often filtered th roug h a first order filter. The n, in Lap lace transform

representation, tthe derivative term becomes

D

=

T 7 T W

E ( S )

<

3

-

17

>

d

where N is an integer, and Tj/N is the time constant of the filter.

Derivative action can also lead to large control signals, and thus to large overshoot, when the

set point changes. Since after such a change, usually, the new value remains the same for a

relatively long period of time, and since the derivative of a constant is zero, it is a common

technique to replace the error e(t) by e^ t) = -y, only in the derivative term . Th e oversho ot can be

even more redu ced, if in the proportional part w e replace e(t) by e

p

(t) = b y

r

- y, w here 0 < b < 1.

Taking into account the above modifications, a more realistic PID controller can be described,

in Laplace form, by the following equation

U(s) = K E

D

(s) +

fE(s)+fE,(s)

T . s T

t

s

K T

d

s E

d

(s)

1+T. s /N

d

(3 .18)

where

E

p

(s) = b-Y

r

(s) - Y( s) (3.1 9)

E(s ) = Y

r

(s) - Y(s ) (3.2 0)

E

d

( s ) = -Y (s ) (3 .21 )

E

t

(s) = V(s) - U( s) (3 .22 )

N is an integer in the range 3-10, T

t

is a rather small constant, and K , Tj , T j are the PID

parameters. The implementation of the PID algorithm on a digital computer requires a discrete-

time model, which must be equivalent to that of equation 3.18 when the sampling period is small

enough. There are many methods to derive such a discrete-time model [14],[38]. In the case



174

wh ere an Euler appro ximation for the integral part and a backw ard-difference approx imation for

the derivative part are used, equation 3.18 becomes

u(k) = Ke

p

(k )+

Khe(k) he

t

(k)

T

;

(q-1) T

t

(q-1)

T

d

( q - l ) e

d

( k )

(3.23)

where k represents the discrete time, and h is the sampling period.

In the following, we present two well known methods for tuning the PID parameters, namely,

the Ziegler-Nichols open loop, or transient responce, method, and the Ziegler-Nichols closed

loop, or ultimative sensitivity, method. [14],[38]. The first method is based on the form of the

process step responce. Specifically, it is assumed that the responce is similar to that shown in

figure 3.6, where R is the maximum slope of the responce and L is determined by drawing the

tangent at that point.

y(t)

Figure 3.6 - Process Step Responce

Then, the PID parameters are obtained as shown in table 3.1.

Table 3.1 - PID parametrs (open loop method)

Controller

Type

P

PI

PID

K

1/RL

0.9/RL

1.2/RL

T

i

3L

2L

T

d

0.5L



175

The second method is a frequency responce method. First, a proportional controller, as in

3.10, is applied to the process. After, the proportional gain is increased until the output of the

process oscillates periodically. At that point, let K

c

be the gain of the proportional controller and

T

c

be the period of the oscillations. Then, the PID parameters are obtained by means of table 3.2.

Table 3.2 - PfD parameters (closed loop methodt

Controller

Type

P

PI

PID

K

0.5K

C

0.4K

C

0.6K

C

Ti

0.8T

C

0.5T

C

T

d

0.12T

C

The PID parameters obtained by using either of the two methods have to be considered as a rough

estimate, and based on them, more accurate values must be derived manually. A more detailed

discussion of the above methods, as well as methods for automatic tuning of PID controllers, can

be found in [38] .

3 . 3 .

PARAM ETER ESTIMATION

3 .3 .1 .

Introduction. As we have already discussed in section 3.2 , estima tion of param eters is a

very important part of an adaptive control system. In the indirect schem e the estimator com putes at

each sampling instant the current parameters of the process model, while in the direct scheme it

computes directly the new controller parameters. We see that a kind of system identification is

performed, where the system to be identified is either the process or, in some sense, the

controller. In both cases, it is assumed that the system can be described by an ARMAX model, so

that the method of least squares can be easily applied. The methods which we discuss in the rest

of this section, namely, Recursive Least Squares (RLS), Projection Algorithm, and Extended

Least Squares (ELS), belong to the so-called on-line, or real-time, parameter estimation methods,

as opposed to the off-line ones. A complete discussion of the various identification schemes can

be found in [6],[16].

3 .3 .2 . Least Squares. Con sider the problem of estimating the param eters of a system whose

behaviour is described by the mathematical model

y(k) = e ^ O O + 9

2

x

2

(k)

e

r

x

r

(k) ,

(3.24)

wh ere y(k) can be thought of as the output of the system , and xi (k) x

r

(k) are combinations

of other variables which can be measured. We w ant to estimate 0 i , . . . ,0

r

, given measurements

of the functions xi (k),. . . , x

r

(k) , so that the output of the real system y (k) be as close to the

variable y(k) as possible. In the context of least squares, as close as possible means that the error

k

e (k )

=

X

[ y ( i )

y + ( i ) ] 2

(3.25)

i=l



176

is minimum. The estimated parameters, at time k, should minimize this error. Equations 3.25 and

3.24 contain the two most important features of the least squares formulation, namely, the

minimization of a squared error criterion, and the linear fashion in which the parameters are

introduced into the model. These two facts allow for an analytical solution to exist. Specifically,

let

x(k) = [

X j

(k ) x

2

(k) - x

r

(k) ]

T

, (3 .26 )

and

e = [ e

1

e

2

- e

r

]

T

>

(3.27)

which will be referred to as the

regression vector

and the

parameter vector,

respectively. Then,

3.24 can be written as

y ( k ) = _ x

T

(k )_9 , (3 .28)

which will be called the regression equation. At time k, the estimate which minimizes the error

e(k) can be show n to be the solution of the equation (see [16],[22])

R( k)- 8(k ) = p(k) , (3 .29 a)

or

where

6(k) = K

1

( k ) p ( k ) , ( 3 . 2 9 b)

m =

2^_x(i)x

T

(i) (3.30)

i = l

and

p(k)

=

2^y*(i)-x

T

(i) , (3.31)

i = l

a matrix of dim ension (r x r) and a vector of dimen sion (r x 1), respectively. A s far as the notation

is concerned, the underscore indicates a vector, the double-underscore a matrix, and the

superscript T the transpose of either a vector, or a matrix. Equation 3.29b implies that,

theoretically, we are able to compute the solution if the matrix R is inversible. However, the

amount of computation needed for inverting this matrix, for large r, makes this approach not



177

feasible for real-time ap plications w here time is an impo rtant factor [22]. For this reason, in many

practical applications the vector 6(k) is computed recursively, and its value at time k depends on

the previous e stimate, at time k -1 , plus new information available at time k -1 . The idea is the

recursive computation of the matrix R and the vector p

a

in 3.29b, based on their values at time k-

1. This leads to the so-called Recursive Least Squares (RLS) algorithm which provides the basis

for many different recursive identification algorithms. In what follows we discuss the application

of the RLS, ELS, and projection algorithms, in the parameter estimation of processes described

by ARMA X m odels.

3 .3 .3 . On-line Estimation Algorithms. The AR MA X m odel, which was introduced in section

3.1.3 , is described by the set of equations 3.3-3.7. Assume that e(k)=0 for all k's (deterministic

case),

so that the process is approxim ated by the model

A C q

1

) y(k) = BCq

1

) u(k-d) , (3 .3 2)

which can be written also as

y ( k ) + a y ( k - l ) + - + a

n

y ( k - n ) = b u ( k - d ) + - + b

m

u ( k - d - m ) , ( 3 .3 3 )

y (k) = -a

1

y ( k - l ) - - a

n

y ( k - n ) + b

0

u ( k - d ) + - + b

m

u ( k - d - m ) . ( 3 . 3 4 )

We see that, for

e

i

=

- V

e

2 = -

a

2 ' - - - '

e

r =

b

m (3-35)

and

Xj(k) = y(k - l ) , x

2

(k) = y(k-2) , . . . , x

r

(k) = u(k -d-m ) , (3 .3 6)

3.34 yields 3.24. Therefore, the application of least squares is straightforward and the solution is

given by 3.29. In the sequel we present its recursive version, i.e. the RLS algorithm, in the case

where the error to be minim ized is given by

k

e(k) =

2 /

k

' [

y(0 " y*W ]

2

• (3-37)

i = l

which is a generalization of that in equation 3.25 .

3.3 .3 .1 .

Recursive Least Squares Algorithm.

Let

9(k) = [ -aj( k) - -a

n

(k) b

0

(k ) - b

m

(k ) ]

T

(3 .38)



178

and

u ( k -l ) = [ y * ( k - l ) - y * ( k - n ) u ( k - d ) - u ( k - d - m ) ]

T

. (3 .3 9)

The argument k-1 in the definition of the vector u indicates that all its components are available at

the samp ling time k- 1 , or before. W ith the above notation, the recursive least squares equations

are as follows ([16],[22]):

9 ( k ) = e ( k - l ) + g ( k ) [ y * ( k ) - _ u

T

(k - l ) _e (k - l ) ] , ( 3 .40)

where

P ( k - l ) - u ( k - l )

g ( k ) =

U u T ( k - l ) . P ( k - l ) - u ( k - l )

( 3

-

4 1 )

and

P(k) = -L[P(k-D-g(k)-u

T

(k-l)-P(k-i)] _

( 3 4 2 )

A.

Equation 3.40 implies that the current estimate depends on the previous estimate, plus the error

y (k) -u( k-l )9 (k- l) resulting by the use of the previous estimate multiplied by a time-varying gain

£(k).

This gain is determined by 3.41 and 3.42, where the matrix P(k) is being interpreted as the

covariance matrix of the estimation error. For the algorithm to work, initial values of the parameter

vector £(0) and the covariance matrix P(0) are needed. Usually, P(0) is chosen to be the unit

matrix multiplied by a constant. A large value of this constant indicates that 6(0) is a poor

estimate, and vice-versa. This w ill, initially, cause rapid chan ges in the estimated parameters Q(k).

The constant X, taking values in the interval

(0,1],

is called the forgetting factor. The choise X=l

will equally weight all the measurements from k=0, while a value of

\< l

will discard old

measurements by weighting more heavily the recent ones. The smaller the value of X. the less

weight into the old measurements wil be assigned. This will allow for parameter tracking in the

case where the parameters are not constant but rather drift. For more details concerning the

specific choise of X, as well as other techniques dealing with time-varying parameters such as

covariance reseting or use of variable forgetting factors, see [5],[6],[19],[21]. Another important

issue associated with the RLS algorithm is parameter convergence. As we have said, the criterion

is the minimization of the error in 3.37. We notice that no requirements about the parameter

behaviour are included in this criterion. This can very well lead to the case where the error goes to

zero,

while the parameters do not converge to the real values. This situation can be avoided if the

vector u(k) possess the so-called persistent excitation prop erty (for a formal definition see

[5],[6],[16]). Practically speaking, a persistently exciting sequence should contain a sufficient

number of frequencies, in its frequency spectrum, so as to allow for parameter updating

[5],

[6],[19],

[21].

Lack of this property can also lead to various

bursting phenomena

[20].



179

3.3.3.2. Projection Algorithm. The above recursive computat ion of th e solution to th e least

squares problem considerably reduces th e computat ional complexity, by avoiding th e matrix

inversion. It is probable, however, that further reduction of th e computation effort be required,

depending

on

the

application

and

especially

in

th e

case

where

the

dimension

of

the

vector

j

is

too

large. Then a frequently used simplified algorithm is the projection algorithm described below.

g ( k ) =_6(k- l )

+

n

, - f

1

„ [ y* (k ) -uT (k - l ) - _6 (k - l ) ] p . 4 3 )

p + u H k - l ^ u t k - l )

where 0 < a < 2 and

3

> 0 .

We see that the step of updating the matrix P(k) has been eliminated, and this yields in a less

complex algorithm. Instead, its rate of convergence will be slower than that in the case of the RLS

algorithm [6],[16].

3.3.3.3.

Extended

Least

Squares

Algorithm.

In the beginning of this section we had assumed that

th e process is described by th e model 3.3 with e(k)=0 for all k. Assume now that th e noise

variables are not zero and that C(q ^)=l . Then the process model becomes

ACq

1

) y(k) = BCq

1

) u(k-d) + e(k) . (3.44)

If {e(k)} is white noise, then the RLS estimates, as described adove, will converge to the true

parameter values. But, if e(k) is a sequence of correlated random variables, then it will produce

biased parameter estimates [16],[18]. This correlation in th e noise sequence is expressed through

the

polynomial

C(q~l)

which

leads

to

a

process

model

as

in

equation

3.3,

with

c,

*

0

for

some

i

>

1, and {e(k)} being white noise. In th e fol lowing we describe th e extended least squares

algorithm (ELS) which, based on this model, produces unbiased parameter estimates [16],[18].

First, we rewrite 3.3 as

y ( k ) + a

1

y ( k - l ) + - + a

n

y ( k - n ) = b

0

u ( k - d ) + - - - + b

m

u ( k - d - m ) +

+ c

0

e ( k ) + c

]

e ( k - l ) + - + c

n

e ( k - n ) . (3 .45)

Then, by defining

9 = [ -a , -a ■•■ -a „ b ••• b

m

c ••• c

n

] (3 .46)

-

L

1 2

n

0

m

0

n

and

u(k- l ) = [ y* ( k - l ) - y* ( k - n ) u ( k - d ) - u ( k - d -m) e ( k ) - e ( k - n ) ]

T

, (3.47)

3.45

yields

y(k)

=

u

T

( k - l ) - e

.

(3.48)



180

Therefore, the RLS algorithm can be directly applied, where now the vector 0 contains also the

correlation coefficients of the noise. No tice, how ever, that the regression vector u ^ k - l ) , which is

supposed to be know n, contains the variables e ( k ) , . . . , e(k-n), for which measurem ents are not

available. For this reason, in applying the RLS we have to replace these variables by

approximations. A possible choise is

e (k ) = y * ( k ) - u

T

( k - l ) - 6 ; k - l ) ; V k ( 3 .4 9 )

i.e. the prediction errors. The method which results by applying the set of equations 3.40-3.42 for

the estimation of the parameters in 3.48 with the above modification in the regression vector, is

referred to as the extended least squares method [5],[6],[16]. Finally, in order to give an example

for the presence of correlated noise, consider the following situation. Let the process model be

deterministic, that is, as in 3.32. Assume that the measurements of the system output are

corrupted by additive white noise. Then, our modelled output is not y(k) but rather y'(k) where

y'(k) = y(k ) + e(k) . (3.5 0)

By substituting 3.50 into 3.32 we get

A ( q "

1

) [y ' (k) - e (k)] = B(q '

1

) u(k- d) , (3.5 1)

A ( q

4

) y '(k) = B(q"

1

) u(k-d) + A(q

_ 1

) e(k) , (3. 52 )

which yields 3.3 for C(q

_ 1

) = A(q

_ 1

) and y(k) = y'(k).

3 .4 . ADAPTIVE CONTROL TECHNIQUES

3.4.1. Introduction. Th e design of adaptive control system s is base d on the idea of simultaneou s

parameter estimation and control. Therefore, by using different parameter estimation methods and

different control design procedures, many adaptive control schemes can be produced. Since

parameter estimation was treated in the previous chapter, we shall now discuss some control

design procedures together with their adaptive versions. Two main categories are considered in

the following sections. In the first category (section 3.4.2), the desired performance of the overall

system is expressed by means of a quadratic cost function, and the design of the controller is

based on the minimization of this function, while in the second category (sections 3.4.3 and

3.4.4), the desired performance is expressed by specifying some characteristics of the closed loop

transfer function which, also, determine the structure of the controller. We shall always assume

that the process is described by an ARMAX model as in equation 3.3 which we rewrite below as

A ( q - ' ) y ( k ) = q - f y q

1

) u(k) + C(q "

) e(k ) , (3.5 3)

with A (q" l) being a stable polynom ial, that is, having all its roots inside the unit circle.



181

In every case which we present below, the resulting controller will be a special case of a

general linear controller described by an equation of the form

V ^ q

1

) u ( k ) = V ^ q

1

) y

r

(k ) - V^q"

1

) y(k) , (3 .5 4)

where u is the output of the controller, y

r

the set point and y the process output. V j, V2 and V3

are polynomials of the backward shift operator q~l.

3.4.2. Generalized Minimun Variance Self-Tuning Controllers.

3.4.2.1. Deterministic One-step-ahead Self-tuning Control. We begin with the deterministic case.

We assume, also, that the process delay is d= l. Then , the process model becomes

A ( q -

1

) y ( k ) = B ( q -

1

) u ( k - D . ( 3 .5 5 )

Let y

r

(k) be the set point, not necessarily constant. Also, define a polynomial P(q~') as

P ( q "

1

) = l+p

1

q -

1

+ - + p

I 1

q -

n

. (3.5 6)

Then, our goal is to determine a control law u(k) which minimizes the following quadratic cost

function:

2

j(k+i) = L

p

(q"

1

)[y(

k + 1

)-yr(k+i)]J

;

k> o . (3.57)

P(q"l) determines the dynamic behaviour in which y(k+l) approaches y

r

(k+l). The way to

minimize J(k+1) is to take its first partial derivative with respect to u(k) and set it equal to zero. In

this case, how ever, w e can simplify the calculations if we notice that the minimum value of J(k+1)

can be m ade equal to zero by requiring that

P(q"

1

) [ y ( k+ l ) - y

r

(k + l ) ] = 0 ; k> 0 , (3 .5 8a)

or, equivalently

P ( q "

1

) y ( k

+

l ) = P ( q -

1

) y

r

( k + l ) ; k>0 . ( 3 .58b)

In order to proceed with the derivation of u(k), we define A (q"

1

), B ( q

- 1

) a n d P ( q "

1

) by the

following equations

A (q

1

) = l+ q - ' A V ') (3-59)

B ( q -

1

) = l + q "

1

B V

I

) (3-60)



182

P(q

_1

) = l + q V f o "

1

) (3.61)

Then, 3.58 can be written as

[ l + q

1

P * ( q

1

) ]y (k+ l ) = P( q

1

) y

r

(k + l) , (3 .62)

y(k+l) = P(q

1

) y

r

( k +l ) - P V ) y (k) . (3 .63 )

By adding the term A (q~*)y(k) in both sides of

3.63

we obtain

A(q"

1

) y (k+ l ) = P (q ' ) y

r

(k +l)+ [A V ) " P V ) ] y(k) , (3 .64)

and using 3.55 we get

B ( q

1

) u(k) =

?(q

l

)

y

r

( k + l) + [A V ) " P V ) ] y(k ) , (3 .6 5)

which yields the following control law :

u ( k ) =

X [P(q-

1

)y

r

(k

+

l)

+

[ A* ( q -

1

) -P*(q

1

) ]y (k) -B*(q-

1

)u(k-l)] .

( 3

.

6 6 )

b

0

We see that the controller output at time k is a function of the set points y

r

(k+l), y

r

(k ),. . . , of

the process outputs y(k), y (k -l ), . . . , and of the previous controller outputs u(k- l), u(k -2) ,. . .

Equation 3 .66 can be written also as

u(k ) = — L - [P (q -

1

)y

r

(k+l)+[A*(q-

1

) -P*(q-

1

)]y(k)] , (3.67)

B (q

1

)

which implies that the roots of B(q~l), i.e. the process zeros, should lie inside the unit circle or, in

other words, the process should be

minimum phase.

This is necessary, in order to have a stable

control law which will remain bounded when disturbances are present. The transfer function of

the closed loop system can be derived by substituting 3 .67 into 3.55, and this gives

A(q '

1

)y(k+l) = P(q-

1

)y

r

(k+l) + [AV

1

) - P * ( q "

1

)]y (k) - (3.68)

By subtracting 3.61 from 3.59 and substituting above, and by defining

y

P

r

(k+l) = P(q"

1

)y

r

(k+l) (3.69a)

and



183

we get

y

P

( k + l )

=

P ( q "

1

) y ( k + l )

,

(3 .69b)

ACqbyCk+l) = y

P

r

(k+l) + q[A(q"VP(q

)]y(k)

,

(3.70)

P ( q

1

) y ( k + l )

=

y

P

r

(k+l)

.

(3 .71)

Therefore,

the

pulse-transfer operator

is

given

by

H( q

1

) = ^ - = V , (3.72)

y

P

( k + l ) P ( q "

1

)

that

is, the

roots

of

P(q~l)

are the

poles

of

the closed loop system,

and

they have

to be

inside

the

unit circle

so as to

result

in a

stable closed loop system.

If

the

model parameters, that

is, the

coefficients

of

A(q" l )

and

B(q" l ) ,

are

known, then

the

computation

of

the control

law

u(k), given

by 3.66, is

straightforward.

If

not, then

we

need first

to estimate them , using

one of

the methods described

in

section 3.3,

and

then com pute

u(k) as in

3.66 where instead

of aj , a2, . . . a

n

,

bQ,

bj , . . . , b

m

, we put

their estimates. This

can be

repeated

in

every sam pling instant

and it

leads

to a

so-called indirect adaptive control schem e.

The

name

is due to the

fact that

the

controller parameters

are not

estimated directly,

but

rather

indirectly, through

the

controller design procedure. Another approach, which leads

to a

direct

scheme,

is

described below.

We

notice that, using

3.69 and

3 .61 ,

the

process model

in 3.55 can

be w ritten

as

y

P

( k + l )

=

B(q"

1

)u (k )

- [A*(q

V p V ) ] y ( k )

•

(3 .73 )

Let

us

define

the

vectors

9

and u(k)

as

6 = [ b

0

- b

m ( a i

-

P i

) - ( a

n

- p

n

)

]

T

(3 .74)

and

_u(k)

= [ u(k) -

u ( k - m )

-y(k) -

- y ( k - n + l )

]

T

,

(3 .75 )

respectively. Th en,

3.73 is

also written

as

y

P

( k + l ) = _ u

T

( k ) _ 9

,

(3 .76)

which

has the

form

of

the regression equation

as in

2.28. Then,

the

parameter estimation methods

of section

3.3 can be

directly applied

for the

estimation

of

the controller param eters. This

can be



184

done in every sampling instant, and it leads to a direct adaptive control scheme. Notice that in both

methods, indirect and direct, the number of the estimated parameters is the same, and equal to

m + n + 1 . We see that in the indirect case the controller design step (i.e. the computation of the

controller parameters from the estimated process parameters), has been eliminated, thus resulting

in a simpler method. This, however, will not be always the case as we shall see in the sequel.

We now turn to the case where the process delay d is greater than one. The process model will

be

A( q

1

)y (k ) = B(q-

1

)u( k-d) , (3.77)

and the control law u(k) should minimize the cost function

J(k+d) = [ P(q

_1

) [ y(k+d) - y

r

(k+d) ] ]

;

k>0 (3.78)

which corresponds to 3.57. Let us proceed as previously, that is, define 3.59 - 3.61 and try to

satisfy 3.58 where instead of k+1 we put k+d. By following exactly the same steps, the

corresponding controller equation of 3.65 will be

B(q"

1

) u(k) = P(q-

l

) y

r

(k+d) +

[ A V V P V ) ]

y(k+d-l) . (3.79)

By solving it with respect to u(k), as in 3.66, we see that u(k) depends on the set points y

r

(k+d),

y

r

(k+d-l), . . . , on the previous controller outputs u(k-l), u(k-2), . . . , and on the process

outputs y(k+d-l), y(k+d-2), . . . Thus, the output of the controller at time k will depend on the

output of the process at future times, and this is an undesirable situation since it leads to a

noncausal controller, or in other words, to a control law which depends on outputs of the process

not yet available. This difficulty arises from the fact that in 3.77 the output at time k+d is

expressed as a direct function of the previous outputs at times k +d -1 , k+d-2, . . . In order to

overcome this problem we can transform the model in 3.77 in another equivalent one, where now

the output at time k+d will be a function of the output at the times k, k - 1 , . . . This can be done by

expressing y(k+d) as a function of y(k+d-l), y(k+d-2), . . . , then, expressing y(k+d-l) as a

function of y(k+d-2), y(k+d-3),. . . , and so on, until we arrive at the point where everything is a

function of y(k), y(k- l) , . . . A more systematic and compact way of performing the above

transformation is the following. First, we solve a polynomial identity of the form

P(q"

1

) = A(q

) S(q"

1

) + q"

d

Ttq"

1

) (3.80)

which has a unique solution for S(q

_1

) and T(q

_1

) (see [6],[14]), defined by

S(q"

1

) = l + s ^ + ' - H - s ^ q - " *

1

(3.81)

and

K q '

1

) =

V

T

1

q "

1

+

- + T

n l

q -

n + 1

, (3.82)



185

respectively. We define, also, the polyno mials BS (q~l) and BS (q" l) by the equation

BSCq"

1

) = BCq-^SCq"

1

) = b

Q +

q 'B S V ) . (3 .83)

Then, the steps corresponding to 3.62 - 3.64 are as follows. Substituting 3.80 into

PCq'

1

) y(k+d) = PCq'

1

) y

r

(k+d) (3 .84)

yields

[A(q"

1

)S(q"

1

)+q"

d

T(q"

1

) ] y(k+d) = P(q

l

) y

r

(k+ d) , (3 .85 )

or

A ( q "

1

)S(q"

1

)y (k+d) = P(q

1

) y

r

( k + d ) - T ( q "

1

)y(k ) . (3.8 6)

Using 3.77 and 3.83, the last expression becomes

B(q"

1

)S(q"

1

)u (k ) = P(q

1

) y

r

( k + d ) - T ( q ' ) y ( k ) ( 3 .8 7 )

and

[ b ^ q ^ B S ^ q -

) ] u ( k ) = P ( q '

1

) y

r

( k + d ) - T ( q

1

)y (k ) , ( 3 .88)

respectively. Then, the control law is given by

u(k) = - L [ P(q -

1

)y

r

( k + d ) - T ( q -

1

) y ( k ) - B S * ( q -

1

)u (k - l ) ]

( 3

. 8 9 )

b

0

where, now, u(k) is a function of the set points y

r

(k+d) , y

r

(k+d-l), . . . , of the process outputs

y(k),

y(k-l), . . . , and of the previous controller outputs u(k-l), u(k-2), . . . , i .e. it represents a

causal controller. Notice that 3.89 reduces to 3.66 when d=l.

For the adaptive controller based on 3.89, it is interesting to consider the direct and indirect

schemes in more detail. Specifically, for the indirect case we have the following algorithm :

Algorithm 3.1 (Indirect Schemel

1) Estimate the model parameters (coefficients of A(q~l), B (q "'))

2) Compute T(q "

) and S(q"

J

) by solving 3.80

3) Compute u(k) as in 3.89

4) k=k+ l ; go to 1

We see that the controller design is now rather complicated, when compared with that in the case

of d=l, since the solution of the equation 3.80, at each sampling instant, is required. For the



186

direct case we proceed as follows. First, we multiply both sides of 3.80 by y(k+d). Then, by

combining the result with the model equation 3.77, we get (compare with 3.73)

PCq^yOc+d) = BS(q"')u(k) + TCq^yCk)

wh ich, by defining approp riate £ and u(k) vectors, can be transformed to a regression equation

similar to 3.76. Therefore, as in that case, the parameter estimation methods of chapter 2 can be

used in order to directly estimate the controller parameters Tj and bsj. Thus, we have the following

algorithm:

Algotithm 3.2 fDirect Schemel

1) Combine 3.77 with 3.80, and form a regression equation

2) Estimate the coefficients of this equation (controller parameters)

3) Compute u(k) as in 3.89

4) k= k+ l ; go to 2

Therefore, we don't need to solve 3.80 at each sampling instant, and this fact greatly simplifies

the computational effort of the adaptive scheme. On the other hand, we notice that the number of

estimated parameters in the indirect scheme is less than that in the direct one. Specifically, in the

indirect scheme we need to estimate n+m+1 parameters, while in the direct one the corresponding

number is n+m+d. Thus, it may happen that the computational effort introduced by step 2

(algorithm 3.2), is bigger than the simplification that the algorithm provides, and as a result, its

overall performance can be worse than the performance of an indirect scheme. That is, there is a

trade-off between the two algorithms, and the choise depends on the specific degrees of the

polynomials B(q~l) and A(q~l) and on the delay d, as well as on various robustness and stability

considerations [5],[6].

At this point a comm ent on the sam pling rate is in order. Assum e that the model 3 .77 describes

a continuous-time process w ith a delay of D seconds. Then, by approximating it by a discrete-time

model we introduce the delay d which, clearly, depends on the sampling rate and it increases

when the sampling period decreases. In order to be more specific, if h is the sampling period,

such that D is a multiple of

h,

then

d = ^ + 1 . ( 3 . 9 0)

h

Since we are interested in reducing the compu tational effort of the parameter estim ation algorithm

as much as possible, we must not choose a very small value of h. On the other hand, we must

keep its value small enough, so that the discrete model adequately describe the process. More

details on the selection of the sampling period in implementing discrete-time control systems, can

b e f o u n d i n [ 5 ] , [ 1 4 ] , [ 2 1 ] .

The controller described by 3 .89 is usually referred to as the one-step-ahead controller because

the criterion which is based on, takes care only of one step ahead ((k+d)th sampling instant).

Criteria including the system behaviour for a set, or horizon, of future sampling instants lead to

control techniques such as Model Predictive Control [23], or Generalized Predictive Control [24].

3.4.2.2. Weighted Control. Frequently, the method described above produces control signals

whose magnitude is quite large. This is due to the specific form of 3.78 which does not include



187

any requirements about u(k). One way to put a weight on it, is to consider a cost function of the

form

2

J

1

(k+d)= [ P(q

_1

)[y(k+d)-y

r

(k+d)] J + l-

u

2

(k) ; 1>0 , (3.91)

and minimize it with respect to u(k). Intuitively, this criterion implies that a situation like

y(k+d)=y

r

(k+d) being achieved by a lagre value of u(k) will be avoided, since even if the first

term of the right-hand side of 3.91 is zero, the second one will result in a very large value of

Jj(k+d). Therefore, it may be preferable to reduce the absolute value of u(k) in order to produce a

smaller value for Jj(k+d). For the same reason, a control law based on 3.91 can produce an offset

in the steady state responce of the closed loop system. A slight generalization of the cost function

wh ich alleviates this problem is given by the following :

J

2

( k + d ) = [ P ( q "

1

) [ y ( k + d ) - y

r

(k+d ) ] ] + l . [

u

( k ) - u ( k - l ) ]

2

; 1>0 . (3.92)

W e see now that the weighting is placed on the increm ents of the control signal, rather than on the

signal itself. The term u(k)-u(k-l) can be rewritten as (l-q"')u(k) and by defining Q(q~l)=l-q~l,

3.92 becomes

2

J

2

(k+d)= L P(q"

1

)[y(k+d)-y

r

(k+d)] J + l.[Q(q

1

)

u

(k)]

2

; 1>0 . (3.93)

This form leads to different criteria when different expressions of Q(q~^) are applied. The general

case will be treated later in the context of stochastic self-tuning controllers. For this special case of

J2(k+ d) it can be show n, by diffentiating with respect to u(k), that the control law is given by

u ( k ) =

J _ [ l u ( k - l )

+

b

0

[ P ( q -

1

) y

r

( k + d ) - T ( q -

1

) y ( k ) - B S * ( q -

1

) u ( k - l ) ] ]

( 3

.

9 4 )

b

0 +

l

Notice that if 1=0, then equation 3.89 results. Also, if we just remove the term lu(k-l), then the

resulting controller equation is the one which minimizes Jj(k+d). As both cases are simple

generalizations of the controller in 3.89, their adaptive versions can be obtained in exactly the

same manner as described before. Their application will produce control signals of reduced

magnitude with respect to the previous cases, and for this reason they are useful when constraints

on these signals exist. We must keep in mind, however, that specific maximum or minimum

values of u(k) are not included in 3.93.

The controller equation 3.94 can also be written as

u ( k )

, P ( q -

1

) y ^ d

)

- T ( q ^ ) y ( k )

B ( q -

1

) S ( q -

1

) + ( l / b

n

) ( l - q

1

)



which implies that it is not necessary for the process to be minimum phase, as long as, the roots

of the denominator of 3.95 are inside the unit circle. Also, by substituting 3.95 into 3.55 we can

easily obtain the closed loop pulse-transfer o perator, given by

H ( q ' ) - - ^ = , / ^ ,

r

. (3.9 6)

yP(k+d) BCq-^PCq-Va/boXl-q-VCq-

1

)

which implies that also the roots of B(q~ l)P(q~l)+(L /bo)(l-q~l)A(q "l) should lie inside the unit

circle, in order for H(q"') to represent a stable closed loop system.

3.4 .2 .3 . Minimum Variance Self-tuning Control. So far we considered the deterministic case,

where C(q"l)=0. In the stochastic case we assume that disturbances are present, which can be

mod elled as a random noise process, say

{h(k)}.

This leads to a process model as in 3.53. In that

model, {e(k)} is a white noise random process and C(q~l) is a polynomial representing any

correlation betw een the random variables of

{h(k)},

whose roots should be inside the unit circle.

We can also assume that co=l[17],[18]. Furthermore, we assume that the random variables e(k)

have zero means and finite variances. Thus, the output of the process y(k) will also be a random

variable and therefore any criterion describing its desired behaviour should include some kind of

probabilistic expectation. In the simplest case, the control law u(k ) mu st minim ize the expectation

J(k+d) = E{ [y(k+d) - y

r

( k + d ) ]

2

} , (3.9 7)

given measurements available at time instant k. Notice that for y

r

(k+d)=0 V k (regulat ion

problem), the criterion becomes the minimization of the output variance. The resulting controller,

when co mbined with the RLS parameter estimation method, leads to the minimum variance

self-

tuning regulator, originally proposed in [9].

In order to minimize the expectation in 3.97 we proceed as follows. First, we determine two

polynomials S(q~l) and T(q~l), defined by 3.81 and 3.82 respectively, by solving the polynomial

equation (compare with 3.80)

C(q"

1

) = A(q-

) S ( q

1

) + q

d

T t q

1

) . (3 .98)

Then, a multiplication of both sides by y(k+d) yields

C ( q "

1

)y (k+d) = A(q"

1

)S(q"

1

)y(k+d) + T(q"

1

)y(k) , (3 .99)

or, equivalently

y

( k + d ) =

A ( q

"

1 ) S

1

( q

"

1 )

y (k + d) + ^ - y (k ) , ( 3. 10 0)

C ( q

1

) C ( q

1

)

and using 3.53 we have that



189

y (

k + d

) = 4 r % ^ u (k )+ S( q-

1

)e (k+d)

+

â

:

l

y ( k )

.

CCq

1

)

CCq"

1

)

(3 .101)

Thus, 3.97 equals

B S

^ ( k ) 3 ^ y ( k ) -

y r

( k

+

d )

-,2

CCq

1

)

CCq

1

)

+EnS(q-

1

)e(k+d)] (3.102)

because {e(k)} and {u(k)} are assumed to be independent, and furthermore, y(k) is independent

of each one of the random variables e(k+d), e(k+d-l), . . . , e(k+l). Finally, since the second

term of 3.102 does not depend on u(k), we require that

^ml

m+

ml

yik)

.

yik+d)=0

CCq"

1

) CCq"

1

)

which yields the control law

(3.103)

u(k)

= J -

[C(q-

1

)y

r

(k+d)-T(q-

1

)y(k)-BS*(q-

1

)u(k-l)]

,

(3.104)

b

0

i.e. the same as that in 3.89 if we chose P (q "') =C (q "') . The m ain difference is that while in the

deterministic case this control law sets the error P(q~l)[y(k+d)-y

r

(k+d)] to zero, in the stochastic

case the minimum value of J(k+d) (eq. 3.97) is given by

W

k + d

) =

E

{ [

s

( q

1

)

e

(

k

+

d

) ]

2

.

= V a r [ e ( k + d ) ] + S j V a r [ e ( k + d - l ) ] + - + s ^ j V a r [ e ( k + l ) ] . (3 .1 05 )

However, the various assumptions pertinent to the stability of both the control law in 3.89 and the

overall closed loop system in the deterministic case, apply also to this case for C(q~l)=P(q~l).

The adaptive version, or minimum variance self-tuning controller, will be a combination of the

controller in 3.104 with a parameter estimation technique. If C(q~l)=l then the RLS algorithm

will suffice, while if C(q"l) is a polynomial of a degree greater than zero, then the ELS method

should be used. As before, either the direct, or the indirect schemes can be applied.

3.4.2.4.

Generalized Minimum Variance Self-tuning Control.

We now present a generalization of

the above controller, which has been introduced in [6], based on the cost function

J(k+d)

=

E {

[P(q-

1

)y(k+d)-R(q-

1

)y

r

(k+d)]

2

+

[Q(q

1

)u(k)]

2

) (3.106)



190

which generalizes 3.97. P(q"'), R(q"^) and Q(q"^) are polynomials in q~l where, generally

speaking, Q(q"*) weights the control signal, R(q~l)y

r

(k+d) represents a filtered version of the set

point, and P(q ) greatly affects the dynam ics of the closed loop system . The expectation is

conditioned on system input-output data available at time k. If we remove the expectation, we

have a generalization of 3 .93 for the deterministic case.

The control law which minimizes 3.106 can be shown ([25]) to be given by

Rfa-VOc+d) - (^(k+d/k)

u(k) = —

i

— ^ \ , (3.107)

(q

0

/b

0

)Q(q

1

)

where qo=Q(0), brj=B(0), and <j)

v

(k+d/k) is the least-squares prediction ([22]) of P(q"^)y(k+d)

given data up to k, and it is given by

.

=

T V W + B S ^ M k )

" C(q"

1

)

where BS(q

_ 1

) has been defined in 3 .83. T (q

_ 1

) and S(q"

1

), defined by 3.81 and 3.82

respectively, are determined by solving the polynomial aquation

C(q"

1

)P(q"

1

) = A(q

1

) S ( q "

1

) + q ^ q

1

) . (3 .109 )

By combining 3.107 and 3.108 we get

C ( q W

W

. T ( q ' ) y ( k )

;

B S ( q

1

) + (q

0

/b

0

) Q ( q -

1

) C ( q -

1

)

and the closed loop system output is given by

[ B S ( q -

1

)

+

( q

0

/b

0

) Q ( q -

1

) C ( q -

1

) ] e ( k ) + B ( q -

1

) R ( q -

1

)y

r

(k)

y(k ) = : i ; ; • (3 .111 )

P ( q -

1

) B ( q

1

) + (q

0

/b

0

) Q ( q -

1

) A ( q -

1

)

Thus, this method can be applied also to non-minimum phase processes for which the roots of the

denominator polynomial of 3.111 are inside the unit circle. Notice that if in 3.110 we set C(q"

1)=1, then the resulting control law will be either the one which minimizes 3.106 when the

process model is given by 3.44 with e(k) being white noise, or that which minimizes 3.106 in the

deterministic case (i.e. drop the expectation) where the process model is as in 3.77.

The adaptive version is obtained by combining 3.110 with one of the parameter estimation

algorithm s described in section 3.3 . In the indirect case one has to estimate the coefficients of the

polynomials A, B and C at each sampling instant, and then apply 3.110 by using their estimates.

In the direct case the controller param eters, that is the coefficients of T(q "' ), B S(q

_1

) and C(q

_ 1

) ,

can be estimated by means of 3.108 which can be written as



191

n

^/k+d/k) = T C q^ y C y+ B S C q V C k )- ^ c.cfyk+d-i/k-i) . (3.112)

i=l

Thus, upon defining vectors Q and ]i(k), by

-

9

= ^ 0 V V l

b S

0 ^ f

b S

m +

d - l "

C

l " V "

C

n ]

T

(

3

-

113

)

and

u(k) = [ y ( k ) - y ( k - n + l ) u ( k ) - u ( k - m - d - l )

< | > y ( k + d - l / k - l ) - < t ) J ( k + d - n / k - n ) ]

T

(3 .114)

respectively, it becom es

(fyk+d/k) = u

T

(k ) -9 (3 .115)

which is a regression equation, as in 3.28, hence the RLS method can be applied. Notice however

that <t>

v

(k+d/k) is not known because it depends on the parameters, and for the same reason the

vector u.(k) is not completely known. Therefore, an approximation of these quantities has to be

used (compare with ELS). Specifically, we can put instead,

ty(k+d/k) = u

T

( k ) 6 ( k ) ( 3 . 1 1 6 )

where f)(k) is the previous parameter estimate and the symbol "

A

" ov er u i mp lies that the <>-

components in 3.114 have been calculated also by 3.116. Finally, once the estimates of T(q~l),

BS(q"l) and C(q"l) are available, the control law can be readily computed by 3.110.

The choise of the polyno mials P(q"^), R(q ) and Q(q "') depen ds on the specific requirements

of the closed loop system behaviour. A s we mentioned above, P(q"^) affects the closed loop poles

and if, for example, Q(q~l)=0 then equation 3.111 shows that the roots of P(q"^) become poles of

the closed loop response. In the case of sudden set point changes, R(q"*) can be chosen, for

example, as

R(q"

1

) =

T

-—

(3 .117)

1 - rjq"

1

so that to filter the set point. This will be advantageous in many cases since it will reduce the

magnitude of both the control signal and the overshot, at the expense of slower tracking. In this

case r should be chosen such that P(1)=R(1) in order to avoid a steady state offset. Finally, Q(q"

1) is used in order to reduce the magnitude of the control signal. Equations 3.91 and 3.92

represent two such examples forQ(q"^)=l and Q(q"')=l(l-q"'), respectively. More details on the

choise of the above polynomials can be found in [6], [21], [25], [33] and [34].



192

3.4 .3 .

Adaptive Controllers B ased O n Pole Placement. In section 3 .4.2 we presented a class of

adaptive controllers which were based on control laws having the form of equation 3.54. In all

cases, these control laws were the result of a minimization of a quadratic cost function as, for

example, in 3.106. In this section we follow a different approach. We assume from the beggining

that the controller is described by an equation as in 3.2 which, by changing the notation, we

rewrite as follows

P(q

_1

)u(k) = R(q

_1

)y

r

(k) - TC q^M k) . (3.118)

Our goal will be to determine appropriate polynomials P(q"^), R(q~') and T(q"'), such that the

closed loop responce possess desired prorerties. For example, we can ask that the poles of the

closed loop transfer function be in prespecified locations (pole placement). The closed loop

responce can be determined by combining 3.118 with the process model 3.53. This gives

q

d

B ( q -

1

) R ( q -

1

) y

r

(k ) + C(q-

1

) P ( q -

1

) e (k )

( 3 u 9 )

A(q-

1

)P(q

1

) + q^BCq-ÎXq

1

)

The specific degrees of P(q~l), R(q~*) and T(q~l) depend on the imposed requirements. Note that

we can always take prj=P(0)=l.

In the sequel we discuss the pole placement self-tuning controller, following the approach

which is used in [5] (originally proposed in [35]). For other approaches and more details see also

[6],[21],[36]. The main idea is to place the poles of the closed loop system in some desired

locations by an appropriate choise of the polynom ials P(q~*), R(q ) and T( q" l). From 3.119 we

see that the closed loop poles are the roots of the polynomial (A P+q "^B T)(q" l). Therefore, P(q"^)

and T(q"l) can be determined by equating this polynomial with another one, representing the

desired pole locations, and then solving an algebraic equation with respect to P(q"^) and T(q"l).

By choosing only the poles, however, the behaviour of the closed loop system is not completely

known from the beggining, since the polynomial P(q~l) appears also in the numerator of 3.119.

The same holds for T(q"^), since in some cases we select R(q~l)=T(q~l). Thus, if we want that

the imposed requirements completely specify the behaviour of our system, then the closed loop

zeros must be specified as well.

We consider the deterministic case, for then 3.119 becomes

y « - ,

q

y ? " ' ,

, y , « . (3-.20)

where the process model is given by 3.77 (For extensions to the stochastic case see [5],[6]). Our

objective is to choose the P (q

_ 1

) . T(q

_ 1

) and R(q

_ 1

) such that

y ( k ) =

q d B m ( (

;

}

y

r

(k ) , ( 3 .121)

where B

m

( q "

1

) and A

m

(q "

1

) represent the desired zero and pole locations, respectively. That is,

we require that



193

y(k) q^B(q-

1

)R(q-

1

) q X C q '

1

)

( 3 m )

Yr(k) A(q

1

) P ( q -

1

) + q

d

B ( q

1

) T ( q -

1

) A ^ q "

1

)

By comparing the nominators of the above equation we see that, first, some (or all) of the zeros of

the open loop system (roots of B(q~ l)) can beco me zeros of the closed loo p system, and second,

other zeros can be added by means of R(q~l). On the other hand, roots of B(q"l) which are not

desired as roots of B

m

(q~l), have to be cancelled by the denominator of the middle term of 3.122.

Hence, they should be included in P(q~l). Specifically, let B~(q~l) contain the open loop zeros

which appear also in B

m

(q~l), and let B+(q~l) contain those which are cancelled. Then according

to the above discussion we must have that

B(q'

]

) = B V ' j B - f q

1

) (3.123)

and

P ( q

1

) = P

1

(q -

1

)B

+

(q -

1

) . (3 .12 4)

Furthermore, notice that the controller equation 3.118 can be written as

u ( k ) = ^ J - y

r

( k ) - ^ 3 J . y ( k ) . (3.125)

P (q

_ 1

) P(q

_ 1

)

This implies that the roots ofP(q"l) should be inside the unit circle, for the control law to be

stable. Therefore, B

+

(q~l) must contain only well-damped zeros of the open loop transfer

function. That is, only these zeros can be cancelled. The rest must be included in the zeros of the

closed loop transfer function. For this reason B

m

(q~l) will be given as

BJq"

1

) = ffJq^B V) . (3.126)

where B

m

'(q"^) contains additional desired zeros. As we mentioned before, these will be

provided by the polynomial R(q~'), for then

RCq

1

) = R ^ J B ' J q

1

) . (3.127)

We didn't take just R(q"

1

)= B

m

' (q"

1

), because the term Rj(q"l) will be useful afterwards. In the

light of the above definitions, the left-hand side of 3.122 b ecom es



194

y ( k

) q -

d

B

+

(q -

1

) B - ( q -

1

)R

1

(q -

1

) B ^ ( q -

1

)

y

r

(k) A ^ P , ( q ^ B V

1

) V B V ^ B X q ^TCq

1

)

(3.128)

q^B^q-^R.Cq"

1

)

AC q^P ^q

1

) + q^BCq-^TCq

1

)

Until now we dealt with the closed loop zeros. The corresponding poles can be determined by

the denominator of 3.128. Normally, we would equate this term with A

m

(q"l) and solve with

respect to P i( q "' ) and T(q~l). A slight generalization is to solve the equation

A C q -b P /q ^ + q V C q ^ T C q ^ A J q - b R j C q "

1

) . (3.129)

This will assure that a solution exists independently of the order of A

m

(q "

1).

Notice that R \ (q" *)

has already been included in the nominator of 3.128 (by means of R(q~l)), so as to be cancelled.

Hence, w e have that

y(k) _ q-Xtq-Xtq-

1

)

Yr(k) A

m

( q -

1

) R

1

( q

1

)

dr> /„-l>

(q .e .d .) . (3 .1 30 )"

a

B

m

(q~')

AJq"

1

)

The above procedure can be applied also to non-minimum phase systems, since only well-

damped zeros are cancelled. Equation 3.129 is the so-called Diophantine equation, and it is

discussed extensively in [5],[6],[14]. Note that it is a generalization of 3.80. In fact, many of the

control design procedures presented in section 3.4.2 can be shown to be special cases of this zero-

pole placement technique [32].

An indirect self-tuning controller based on the above procedure can be summarized in the

following algorithm :

Algorithm 3.3 (Indirect scheme)

1) Specify polynomials A

m

(q

_ 1

), Bjjj'tq"

1

) and Ri(q

_ 1

)

2) Estimate A(q~l) and B(q~l) (model parameters)

3) Determine B+fq"

1

) and B-(q

_1

)

4 ) So l v e 3 .1 2 9 f o r P

1

( q -

1

) a n d T ( q -

1

)

5) Calculate Ptq"

1

) and Rfa"

1

) by 3.124 and 3.127

6) Compute u(k) by 3.125

7) k= k+ l ; go to 2

In order to get a direct scheme we first multiply 3.129 by y(k), and then combine the result with

the process model in 3.77. This yields the equation

A ^ q ^ R / q ' ^ y C k ) = q

d

B - ( q "

1

) [ T ( q -

1

) y ( k ) + P ( q

1

)u ( k ) ] . ( 3 .131)



195

The idea is to use this equation in order to directly estimate the controller polynomials T(q"l) and

P ( q " l ) . But as we can see, 3.131 is not linear in the parameters (i.e. it doesn't have the linear

form of equation 3.28) because B~(q"l) multiplies both T(q~l) and P(q~l). In the simplest case,

we can make it linear by taking B"(q"l)=l, but now the method is not applicable to non-minimum

phase systems since all the process zeros are cancelled. Other approaches dealing with this

nonlinearity are described in [5],[27],[32].

3.4.4. Model R eference Adaptive Controllers. A block diagram of a model reference adaptive

control system (MRAS) is shown in figure 3.4 (sec. 3.1.2). The idea is to express the desired

behaviou r of the closed loop system by means of a reference mod el, and then design the controller

in such a way so that the closed loop system "follow" the reference model as close as possible.

Originally, model reference adaptive control systems were developed in the continuous-time

domain where the process was described by state-space equations [11],[12],[13]. Later, the

interest was moved more to the transfer function representation and also to the discrete-time

domain [5],[6].

Traditionally, the design of MRAS was based on stability criteria, which means that the

adaptive control laws were being derived in such a way so as to assure the stability of the closed

loop system. In order to illustrate the early ideas we now present an example where the design of

the adaptive controller is based on the Lyapunov stability criterion [37 ]. As sum e that the process

is described by a first-order differential equation

y( t ) = -a y( t ) + bu( t ) , (3 .1 32 )

where y(t) is the process output, u(t) is the process input, and a,b are constant but unknown

parameters. The problem is to find an adaptive control law such that y(t) follow the output y

m

(t)

of a reference mo del, given by

y

m

W = -a

m

y

m

( t )

+

b

m

u

m

( t ) . (3 .13 3)

We see that a controller of the form

u(t ) =-Cj( t )y( t ) + c

2

( t )u

m

( t ) , (3 .13 4)

when applied to 3.132 yields

y(t) = -[a +b

C l

( t ) ]y ( t ) + [bc

2

( t ) ]u

m

( t ) . (3 .13 5)

The above equation implies that if a and b were known, then a choise of C2(t)=b

m

/b and

c i ( t )= (a

m

-a)/b would suffice. But, since a and b are unkown constants, we proceed as follows.

We first define

e(t) = y

m

(t) - y(t) , (3 .1 36 )

to be the output error. Then , by combining 3 .133 with 3.135 we get



196

e(t) = -a

m

e ( t ) - d

1

( t ) y ( t ) + d

2

( t ) u

m

( t )

where

and

dj(t) = a

m

- a - bCj(t)

d

2

(t) = b

m

- b c

2

( t ) .

( 3 .137)

(3 .138)

(3 .139)

Our goal is to appropriately adjust dj(t) and d2(t) so that e(t)—»0, dj(t)—>0 and d2(t)—>0 as

t—>+°°.

Le t d^(t) and d2(t) satisfy differential equa tions of the form

d,( t ) = g

L

(e, y, y

m

)

d

2

(t) = g

2

(e, y, y

m

)

Then the quadratic function

V(e,d

1

,d

2

) = l

b - s g n ( b ) - e

2

( t ) + ^ - d j ( t ) ^ - d

2

( t )

(3 .140)

(3 .141)

,X

x

X

2

>0 (3 .142 )

is a candidate Lyapunov function for the dynamic system described by the equations 3.137, 3.140

and 3.141 [7]. Th is system will be stable, accord ing to the Ly apu no v stability criterion, if the

derivative of V(e,di,d2) with respect to time is negative semidefinite, and this is achieved by

choosing [7]

and

d

1

(t) = X

1

[ b s g n ( b ) ] e ( t ) y ( t )

d

2

( t ) = - y b s g n ( b ) ] e ( t ) u

m

( t ) .

Then, cj(t) and C2(t) will be given by

6

1

(t) = -X

1

s g n ( b ) e ( t ) y ( t )

and

(3 .143 )

(3 .144)

(3 .145)

c

2

( t ) = X

2

s g n ( b ) e ( t ) u

m

( t ) , ( 3 .146)



197

respectively, and they represent the adaptive laws. Notice that the sign of the parameter b is

assumed to be known. Also, in order to get a uniformly asymptotically stable system, further

properties on the reference input signal u

m

(t) must be imposed. Finally, since the adaptive laws

3.145 and 3.146 directly adjust the controller parameters, the above procedure corresponds to a

direct MRAS. For details, as well as extensions of the above method to more general cases, the

reader is referred to [7].

We now consider the case where the process is described by a transfer function model, in the

discrete-time domain. Specifically, we assume that the process model is given by 3.77 which we

rewrite below as

A C q

1

) y(k) = q^BCq'

1

) u(k) . (3 .14 7)

The objective is that the process output y(k) follow a reference output y

m

(k) determined by a

reference model given below

A

m

( q

4

) y

m

( k ) = q '

d

B

m

( q

1

) u

m

( k ) . ( 3 .148)

In order to derive a suitable controller form, let Pj(q"l) and T(q~l) be polynomials satisfying

the algebraic equation

AmCq"

1

) = P / q V t q '

1

) + q"

d

T(q

X

) . (3 .149 )

Multiplication of both sides of 3.149 by y(k) yields

A

m

( q ' ) y ( k ) = P / q ' l A t q ' l y f k ) + q

d

T ( q -

1

)y ( k ) , ( 3 .150)

and using 3.147 we get

A

m

(q "

1

)y(k) = q"

d

[P

i

(q -

1

) B ( q "

1

)u(k) + T(q"

1

)y(k)] . (3 .15 1)

By comparing 3.151 and 3.148 we see that a controller of the form

P

1

(q

1

)B(q-

1

)u(k) = B J q ' V ^ ) - TXq-'jyOO (3.152)

would cause y(k)=y

m

(k), in the case of known model parameters. If they are unknown, they can

be estimated using equation 3.148 together with a parameter estimation method. This procedure

results in a indirect MRAS. If, on the other hand, equation 3.151 is used instead, then the

controller parameters can b e directly estimated, thus resulting in a direct sch eme.

By comparing equations 3.149 and 3.152 with 3.129 and 3.118, respectively, we notice that

the above model reference adaptive control scheme can be considered as a special case of the pole

placement design technique, by taking u

m

(k )=y

r

(k), B~(q~l)=l and Ri(q~l)=l, corresponding to

the case where all process zeros are cancelled and no additional zeros are introduced.



198

4 . C o n c l u s i o n s

Adaptive control systems result from the combination of two basic techniques, namely, controller

design and parameter estimation. In the general case, the resulting system is a time-varying

nonlinear dynamic system which may be very difficult to analyse. For this reason, theoretical

results exist only for some classes of adaptive control systems.

In the previous chapters we gave a description of self-tuning controllers and model reference

adaptive systems which represent two of the most important classes of adaptive systems for which

stability and convergence results have been established. Also, numerous applications of these

schemes have revealed that they are quite effective in controlling a large number of industrial

processes. Both methods require the existence of a mathematical model which should adequately

describe the process. Usually, the model is given in discrete-time representation since the

implementation is done by means of digital computers. Typical examples are the so-called

ARMAX models. Based on such models, various controller design methods can be applied, as for

example, general ized minimum variance, pole placement, model fol lowing, e .t .c . Final ly,

identification schemes based on the recursive least squares (RLS) are usually applied since they

appear to be the most appropriate for real time applications.

5 . R e f e r e n c e s

[I] G. Stephanop oulos, Process Control with a Com puter " , CHEMTECH, pp. 251-256,

April 1987.

[2] D. B. Leach, Specifying a Batch Process C ontrol System ", Chemical Engineering, pp.

115-122, December 1986.

[3] L. W. Craig, Control Structure for B atch Reactor Control", P lant/Operations Progress ,

Vol. 8, No. 1, pp. 35-39, January 1989.

[4] M. Rood huyzen, Guidelines for the Implementation of Batch C ontrol in a Distributed

Control System ", Journal A, Vol. 30, No. 1, pp. 33-40, 1989.

[5] K. J. Astrom and B. W ittenma rk, Adaptive control ", Addison Wesley, 1989.

[6] G. C. Go odw in and K. S. Sin, Adap tive filtering p rediction and control ", Prentice Hall,

1984.

[7] I. D. Landa u, Adaptive control: The model reference approach ", Marcel Dekker, 1979.

[8] I. D. Lan dau,

Com bining model reference adaptive controllers and stochastic self-tuning

regulators

", Automatica, Vol. 18, No. 1, pp. 77-84, 1982.

[9] K. J. Astrom and B. W ittenmark , On self tuning regulators ", Automatica, Vol. 9, pp.

185-199, 1973.

[10] D. W. Clarke and P. J. Gaw throp, Self-tuning controller ", Proceedings of IEE, Vol.

122, No . 9, pp. 929-934 , Sept. 1975.

[I I] R. V. Monopoli, Model reference adaptive control with an augmented error signal", IEEE

Trans,

on Automatic Control, Vol. AC-19, No. 5, pp. 474-484, Oct. 1974.

[12] D. P. Lindorff and R. L. Carroll, Survey of adaptive control using Lyapunov design ",

Int. Journal of Control, Vol. 18, No. 5, pp. 897-914, 1973.

[13] I. D. Landau, A survey of model reference adaptive techniques-Theory and applications ",

Autom atica, Vol. 10, pp. 353 -37 9, 1974.

[14] K. J. Astrom and B. W ittenmark, Comp uter controlled systems: Theory and design ",

Prentice Hall, 1984.



199

[15] E. I. Jury, Sampled-data systems revisited: Reflections, recollections and reassessments ",

Trans,

of ASME, Vol. 102, pp. 208-217, Dec. 1980.

[16] L. Ljung and T. Soderstrom, Theory and practice of recursive identification ", M IT Press,

1983.

[17] B. Friedlande r, System identification techn iques for ad aptive signal processin g ", Circuits

Systems and Signal Processing Journal, Vol. 1, No. 1, pp. 3-41, 1982.

[18] K. J. Astro m and P. Eykhoff, System identification-A survey ", Automatica, Vol. 7, pp.

123-162, 1971.

[19] B. W ittenmark and K. J. Astrom , Practical issues in the implem entation of self-tuning

control

", Autom atica, Vol. 20, No . 5, pp. 595 -605 , 1984.

[20] B. D. O. Anderson, Adap tive systems, lack of persistency of exitation and bursting

phenomena ", Autom atica, Vol. 2 1, No. 3, pp. 247 -258 , 1985.

[21] D. E. Sebo rg, T. F. Edga r and S. L. Shah, Adap tive control strategies for process control:

A survey ", AIChE Journal, Vol. 32, No. 6, pp. 881-913, June 1986.

[22] S. T. Alexan der, Adaptive signal processing: Theory and applications ", Springer Verlag,

1986.

[23] C. E. Garcia, D. M. Prett and M . M orari, Model predictive control: Theory and practice -

A survey " , Automatica, Vol. 25, No. 3 , pp. 33 5-348 , 1989.

[24] D. W. Clarke, C. Mohtadi and P. S. Tuffs, Gen eralized predictive control - Parts I,II",

Automatica, Vol. 23, No. 2, pp. 137-160, 1987.

[25] D. W . Clarke and P. J. Gaw throp, Implementation and application of microprocessor-

based self-tuners ", Autom atica, Vol. 17, No . 1, pp. 233 -244, 1981 .

[26] A. Papo ulis, Probability, random variables, and stochastic processes ", McGraw Hill,

1984.

[27] K. J. Astro m, "

Adaptive feedback control

", Proceedings of IEEE, Vol. 75, No. 2, pp.

185-217, Feb. 1987.

[28] C. Kiparissides and S. L. Shah, Self-tuning and stable adaptive contro l of a batch

polymerization reactor ", Automatica, Vol. 19, No. 3, pp. 225-235, 1983.

[29] W. R. Cluett, S. L. Shah, J. M . Martin-Sanchez and D. G. Fisher, Adaptive predictive

control of a polymer reactor ", 32nd Canadian Chemical Eng. Conference, Vancouver, pp.

1313-1323 ,

Oct. 1982.

[30] V. K. Tzouanas and S. L. Shah,

Adaptive pole-assignment control of a batch

polymerization reactor ", Chemical Engineering S cience, Vol. 44, No . 5, pp. 1183 -1193,

1989.

[31] A. V. Papadoulis, C. A. Tsiligiannis and S. A. Svo ronos,

A cautious self-tuning

controller for chem ical processe s ", AIC hE Journal, Vol. 3 3 , No . 3, pp. 401-409, M arch

1987.

[32] K. J. Astrom , Theory and applications of adaptive control-A survey ", Automatica, Vol.

19, No. 5, pp. 471-486, 1983.

[33] D. W. Clarke and P. J. Gaw throp, Self-tuning control", Pro ceed ings of IEE, Vol. 126,

No. 6, pp. 633-640, June 1979.

[34] P. J. Gaw throp, Som e interpretations of the self-tuning controller ", Proceedings of IEE,

Vol. 124, No. 10, Oct. 1977.

[35] K. J. Astrom and B. Wittenmark, Self-tuning controllers based on pole-zero placement ,

Proceedings of IEE, Vol. 127, pp. 120-130, 1980.

[36] D. W. Clarke, Model following and pole-placement self-tuners ", Optimal Control

Applications and Methods, Vol. 3, pp. 323-335, 1982.



200

|37 ] K. S. Narendra and P. Kudva, Stable adap tive schem es for system identification and

control

", IEEE Trans, on Systems, Man, and Cyb ernetics, Vol. SM C-4, No. 6, Nov.

1974.

[38] K. J. Astrom and T. Hagglund,

Automatic Tuning of PIDControllers

", ISA, 1988.



EARLY ON-LINE DETECTION OF RUNAWAY INITIATION

J .M. ZALDIVAR COMEN GES


Joint Research Centre

Safety Technology Institute, Process Engineering Division

1-21020 lspra (Varese), Italy

ABSTRACT. In the early stages of a runaway reaction, when the rate of heat generation exceeds

the rate of heat removal by a small amount, it may be possible to restabilize the control of the

reactor by taking emergency actions. The problem is to detect these potentially hazardous

situations in sufficient time to allow the necessary counter-measures to be taken. In this paper, a

general overview of the different techniques for early detection of potentially dangerous situations

will be given and the advantages and disadvantages of each technique w ill be discussed.

1. Introduct ion

Normally, the temperature of a reactor in which exothermic reactions take place is controlled by a

cooling system. If, for some reason (e.g. loss of cooling, loss of mixing, etc.), the rate of heat

generation exceeds the rate of heat removal, the temperature of the reacting mass will begin to rise.

This will cause an increase in the rate of heat generation, due to the exponential dependence of the

reaction rate on the temperature, and the process will continue to accelerate producing a large

amount of heat in a very short time with the consequent dangers for people, installations and

environment.

However, in the early stages, when the rate of heat generation exceeds the rate of heat removal

by a small am ount, it may be possible to restabilize the control of the reactor by taking emergency

actions such as full cooling, fast injection of a suppressant or dumping the reactor contents. The

problem is to detect these potentially hazard ous situations in sufficient time to allow the necessary

counter-measures to be taken to avoid temperature and pressure excursions associated with the loss

of control of such processes. The early detection of these potentially hazardous situations is,

consequently, of great importance in the safe and economic design and operation of a plant.

Control of potential thermal explosion hazards once had to rely on laboratory measurements of

process chemistry and direct control of process variables within fixed limits on the plants. In recent

years,

new techniques have been developed allowing a better understanding of the chemical

reaction [1,2] and improving the methods to control it.

Although the so called off-line tests, performed under laboratory conditions, are necessary, and

should be carried out for each new process, there are some disadvantages which must be taken into

account when the results are evaluated [31. Off-line tests are not totally representative because the

properties of materials being used in the plant are never exactly the same as those of a laboratory

201

A.

Benuzii

and J. M.

Zaldivar

(eds.).

Safety of


and

Storage

Tanks, 201-226.

© 1991

ECSC,

EEC,

EAEC,

Brussels a nd

Luxembourg.

Printed in the Netherlands.



202

sample. Another disadvantage is the fact that in these tests there is an implicit assumption that the

"worst case" conditions have been identified, and consequently there is the possibility that

unexpected hazards will remain undiscovered. Moreover, in the real processes there are

unpredictable disturbances that affect the process behaviour and can not be simulated in the

laboratory tests. However this can be partially compensated by performing the tests under

conditions (temperature, pressure, initial concentrations, etc.) more severe than those forseen for

the process.

Complementary to these tests, there is another type of procedure to recognize the potential

hazard. These procedures are called on-line supervision, and are carried out in real time, with the

real reaction mixture, equipment and operating conditions. Because of the development and the use

of digital computers, the level of sophistication has increased from simple supervision of directly

measurable variables to complex signal analysis, treatment, and estimation techniques that allow

prediction of state variables or parameters, not directly measurable, to be included in the criteria for

hazard detection. The disavantage of on-line methods is that the information appears only when the

process is outside of the desired conditions and normally in a dangerous state. From all these

considerat ions, i t can be shown that both techniques (off-l ine and on-l ine) should be

complementary.

Ta ble 1. Differences betw een off-line and on

Offline

laboratory

sample

simulated conditions

without disturbances

sensitive to the choice of test conditions

conditions more severe than real process

information obtained before process design

line prevention measures [3].

On-line

actual process materials

process equipment

real conditions

with disturbances

non sensitive

information appears only when the

process is outside desired

conditions

There is a fundamental requirement that early detection should provide sufficient time for plant

operators to correct the deviation from safe operation. However early on-line detection of

hazardo us states is difficult [4] because a chemical process is described by a large num ber of state

variables, such as temperatures, pressures, concentrations, etc. and only some of these can be

measured on-line with an acceptable response time to allow the information to be used for the

detection procedure. Particularly for batch chemical reactors, the difficulties are increased due to the

wide range of processes that are carried out, and their complexity, strong non-linearity and time-

dependen ces (in a batch cycle there is no steady state).

2 . Early on- l ine Detect ion Techniques

2.1.

DETECTION SYSTEM

A process (see fig. 1) can be described by an equation of the form:



203

y =f{x, n, w, ©}

(1)

where n(t) and y(t) are the measurable input and output variables, w(t) represents non-measurable

disturbance signals from the process and its manipulating and measuring equipment, © non-

measurable process parameters, and x(t) non-measurable state variables. The process parameters

are constants or slow time-variable coefficients, while the state variables are time-dependent.

Disturbances

Control

va r iab les

T ><

( t ) |

Figure 1. Representation of a process with measurable input variables a, measurable output

variables y and non-directly measurable disturbance variables w, process parameters © and state

var iables St.

If a process fault (a non-permitted deviation of a characteristic property which leads to the

inability to fulfil the intended purpose) appears, it has to be detected as early as possible. In order to

accomplish this objective, the detection system (see fig. 2) consists of the following parts:

- Interface with the process in order to acquire data (monitoring).

- Criteria to distinguish between dangerous situations and non-dangerous ones (detection)

- Procedure for triggering off the alarms (diagnosis and evaluation)

After the detection system has found a fault in the process, the decision abou t the co unter-measures

to be adopted has to be made .

D i s t u r b a n c e s

Control

var iables

i

PROCESS

DETECTION

SYSTEM

Measured

var iables

r

A l a r m ?

Figure 2. Block diagram of a detection system.

The methods for early on-line detection can be divided into two categories depending upon the



204

quantities being used [5]:

- Measurable signals.

- Non-measurable state variables, process parameters or characteristic quantities.

In the former case, measurable information about the status of the process is used in order to detect

a malfunction. In the latter case, it is necessary to develop estimation methods and process models

in order to calculate the non-measurable quantities that will be used afterwards in the criteria for the

detection system.

2.2. MEASURABLE SIGNALS

2.2.1.

Limit checking. Measurable input iu(t) and output y(t) variables can be directly used to

monitor changes in the process. The method consists of on-line measurement of a determined

variable checked against preselected limit values. The hazard identification criterion is:

y

(

<yXt) < y

;

2)

This is referred to an absolute value check. If the measured variable exceeds the set limit, alarm

or automatic counter-measures must be initiated. The most common is temperature supervision [3],

but recent theoretical studies show that detection procedures based on pressure are more suitable in

certain conditions [6]. However for practical applications the sensitivity and reliability of the sensor

play an important role to determine the choice of the detection system.

A number of other variables: pH, viscosity, thermal conductivity, etc. are also easily measurable

and can be used for some processes, for example, oxidation can be a dangerous secondary reaction;

therefore the oxidation-reduction potential (Redox) of the reacting medium is a good measure in

order to detect initiation of these reactions at its earliest stage.

The limits are usually so set that a large enough distance to the non-return point is retained on the

one hand, while avoiding false alarms on the other. In general these measures are easy and cheap to

install and can have good predictive capacity, but they are completely dependent on knowledge of

the process and are unsuitable for detection of unexpected dangers.

2.2.2. Supervision of the rate of increase and/or acceleration. The limit check can also be applied to

the derivative of the signal. The hazard identification criteria in this case is:

dy=

dt

dy

;

< — <

dt

ty

dt

3)

for the rate increase, and

o V ,

< J .

2

J

4<

dt

2

^

dt

A

4)

for the acceleration.

The loss of control of exothermic batch or semibatch processes is characterised by thermal and



205

pressure excursions of the reacting mass due to the large amounts of heat released in a very short

time. That means that the derivatives of temperature and pressure or derivatives of the rate increase

can be used to predict the runaway excursion.

Th e m ethod of supe rvising the rate of temperature or pressure rise is not as cheap or as simple as

temperature or pressure measurement, because amplification and filtering are necessary before

reliable derivative can be calculated. Since the "safe" temperature or pressure need not be specified,

the independence and selectivity of this method is higher, but depends also on specific kovvledge of

the system in order to define the limits.

The method of monitoring the acceleration is similar to the previous method; the predictive ability

is however higher.

2.2.3. Frequency analysis. A physical process can be described either in the time domain, by the

value of some quantity as a function of time, or in the frequency domain, where the process is

specified by giving its amplitude as a function of frequency. The method to change from one

representation to another is by m eans of the Fourier transform equations:

y(co) = y( t) -e

i r a t

-dt

y(t)

J

y(co)e"

1 C D t

-dco

(5)

(6)

Output signals Y(t) often consist of lower frequency components with large magnitudes which

mainly determine the nominal values of the signal, and higher frequency components with small

amplitudes which give additional information on the inner state of the process. Some attempts have

been made to identify frequency signal patterns and to pinpoint process errors from the changes in

their corresponding frequency behavior. A simple approach [7] consists of representing the

frequency response by its amplitude ratio and phase angle (see fig.3) and then defining the upper

and lower limits tolerated in the case of a change in the typical pattern obtained when the process is

operating under normal conditions.

Real axis

Figure 3. Polar representation of the transfer function with the tolerance limits.



206

Simple bounds at one frequency are not very effective for fault detection. Instead, fault

dictionaries need to be prepared in which bounds are placed at several different frequencies or more

comp lex characteristics need to be examined [8].

2.2.4.

Recipe-based supervision.

Th e hazard identification criterion is the devia tion of some

characteristic values, or of status of different parts of equipment from the "recipe". The procedure

consists of observing the time record of one or more process variables or parameters, computing

simple statistics of the variables, and carrying out elementary tests to detect faulty operation.

Normally the practical application of this method is through control charts [7], which are a

graphical means of representation and analysis (see figure 4).

When the process is subject only to variations due to random fluctuation, such as that

engendered by environmental changes, internal mixing conditions, etc. then it is possible to say that

it is "in statistical control". If some change takes place via a non-random change, such as

engendered by a deterministic component added to the process variable, the process is "out of

statistical control". Consequently, "in control" means that the same probability distribution will

continue to represent the observed variable as the process goes on. The objective of control charts

is to provide a visual observation of the measured variable and to detect the category change as

soon as possible after it occurs.

•

• m

•

• •

• m

Upper control limit

. . ' •

• •

Lower control l imit

T i m e

Figure 4. A process quality control chart.

This method is completely specific for a process, fully dependent on knowledge, data available,

and judgements. For these reasons it is better for continuous processes at steady-state rather than

for batch processes in which all the variables change with time and there is no steady-state that can

be used as a reference.

The predictive ability and selectivity are given by the quality of the evaluation and specification of

the hazard limits.

2.2.5. Detection of the progressive increase of heat evolution. The hazard identification criterion is:

'Generated

r\

(7)

dt

where qc.eneraied '

s t n e

P

o w e r

generated by chemical reaction. The principle applied is based on a

simple heat balance:



207

F

dt

U S ( T

m

-T

c

)

(8)

Power generated = power used to increase the temperature of the reaction mixture + power

removed by the jacket.

From expression (8) it is possible to obtain:

dt

P

d t

2 dt

supposing MCp and US independent of time.

^ d ( T

m

- T

c

)

(9)

.......

t

.. .

>o

mm

^Potent ia l ly dangerous

Jzone J~r

d r

Figure 5. Delimitation of the potentially dangerous region [9].

The criteria of eq. (7) defines two different regions separated by the line dq^dt =0. The region in

which the heat output of the reaction declines can be considered non-hazardous. However two

other zones in the region in which the heat output of the reaction inc reases, can be discarded from

the potentially dangerous region (see fig.5). In the former, the power accumulated in the reaction

mixture increases and the power removed through the jacket decreases; this is due to deliberate

heating of the heat transfer fluid by the control system and, in principle, is not dangerous. In the

latter, the heat removed increases and the heat accumulated decreases, so in this situation the

reaction is under control. Hence, for the purpose of hazard recognition it is sufficient to check the

following two expressions:

d

2

T

n

d t

2

> 0 and

d ( T

m

- T

c

)

dt

(10)



208

For the evaluation of these criteria there is a comercially available system, that was developed by

Hub [3], and is called OLIWA. Figure 6 shows an idealized form of the flow diagram of the

OL1WA system.

OLIWA MONITORING

SYSTEM

Figure 6. Diagram of the OL IWA (On-LIne WA rning) system.

The strong point of the OLIWA system is its independence of knowledge about the supervised

process. It is the only on-line method, which in principle does not require any setting, adjustment,

or information on the process or equipment. A nother advantage is that only the measurement of two

temperatures is necessary for the hazard identification. The disavantage is that disturbances, always

superimposed on the measurement signal, become amplified and considerably affect the result of

the evaluation. Hence, digital filters of high order and also various auxiliary algorithms must be

employed to smooth out the differential coefficients and to avoid false alarms.

In practice, positive values of the derivatives are allowed up to upper limits Ei and £2, and the

alarm is triggered off only if these limits are exceeded by a time interval greater than

A t

m

j

n

.

The

variables E\, £2

a n

d

At

nl

j

n

must be adjusted for each process [9].

2 . 3 .

NON -MEASU RABLE STATE VARIABLE S, PROCESS PARAM ETERS OR

CHARACTERISTICS QUANTITIES

If a mathe matical model of the process exists, the state of the reactor can be reconstructed from

measurable variables, which will allow predictive calculation of the future status or at least,

evaluation of new criteria based on these non-measurable quantities. That means that highest

predictive power and selectivity can be reached and hence better early detection of hazardous states

can be ob tained.

Figure 7 illustrates the general structure of a model-based detection system. Firstly, all the

know n inform ation about the process is put in the form of a ma them atical m odel that normally

consists of a set of algebraic and differential equation s. This m odel is solved on-line by num erical

procedures in order to obtain the whole state of the batch reactor.



209

In addition to the available measured variables, the model-based detection system must be

supplied with all the control variables, and the initial and operating conditions. The simulated

variables must be compared with the measured variables; a non-zero difference will indicate an

incorrect calculation in the model that can be due to unknown disturbances, unknown initial

conditions, erroneous parameters, etc. Consequently, the model must be corrected from process

measurements. The method to correct these deviations is by minimizing the error using estimation

techniques, for instance, a state variable observer (deterministic case) [10] or state variable filter

(stochastic case) can be used [11].

Control

va r iab les .

1

PROCESS

Disturbances

Measured

v a r i a b l e s ^

Error between

predicted and

0

bserved respons

Mathemat ica

model of the

process

State var iables,

paramete rs ,

x i i a iac te r i s t i c

Est imat ion

techniques

quar tities

Pattern

recognit ion

(Cr i te r ia )

*

M o d e l - b a s e d

d e t e c t i o n s y s t e m

Alarm ?

Figure 7. Block diagram of a model-based detection system.

Once the whole state of the system is estimated and the error between predicted and observed

responses has been minimised by modifying parameters in the model, different criteria can be

applied using data estimated.

It is possible to divide these m ethod s, depend ing on the type of quantities in which the safety

criteria is based [5]:

- Non-measurable state variables

- Non-measurable process parameters



210

- Non-measurable characteristic quantities

2.3.1.

Non-measurable state variables. As was pinpointed before, once all the state variables of the

system are known, different criteria based on non directly measurable parameters can be applied.

For instance, Gilles and Schuler [12] developed another criterion for the definition of dangerous

reaction states by examination of the inflection of phase trajectories for dimensionless temperature

and conversion variables:

C - C T T"

A

0

A l

m

- l i r ^ E

a

x, = — , x„

C

4

'

2

T _ R T

m

(11)

They demo strated that for a batch reactor in which a simple reaction, with decom position behaviour

(nA

—»

products) , takes place and in which a proportional controller regulates the temperature of

the jacket, the phase trajectories show a positive inflection when the reaction is self-accelerating,

and that all points in the phase plane for which the conditions:

dx_ d x„

— - > 0 an d — - ? - > 0

d x

i dx^

(12)

apply are dangerous reaction states.

Similar procedure, based on conversion, can be applied if the criteria of eq. (7) is used and q

G

is

defined as:

q „ = V

m

-AH-r (13)

lG ~ ' m

and hence,

dq,

^ T = V

m

A H . |

(14)

supposing that the volume of the reaction mixture does not change considerably during the reaction

(approximately true for batch processes).

This type of criteria can be extended and applied only if the conversion can be measured or

inferred on-line. The measurement of this variable is difficult or expensive in most cases,

consequently model based techniques for estimating the conversion are necessary for the use of

such as criteria.

An other similar approach was followed by Bonvin and Saner [1 3]. They developeded an on-line

procedure for supervising the operation of batch reactors with the aim not to detect runaway

initiation but the entrace of a disturbance in the system . Th e general procedu re was based on the

estimation of the rate of heat production by two different methods. The former used kinetic

reconstruction from temperature and time measurement, eq. (13), to infer the conversion and the

heat evolution of the reaction. The latter used calorimetric reconstruction based on a model of the



211

reactor to estimate the total heat which evolves in the reactor, eq. (8). The difference between the

two estimates indicated that a disturbance had entered the system. For example, if during a reaction

there is a disturbance in the heat transfer coefficient (U) due to a stirring problem, the estimation of

the rate of heat production using the calorimetric approach will not be correct because it is based on

the calculated value of U by simulation, while the kinetic approach does not depend on the reactor

model, and consequently will not be affected.

2.3.2. Non-measurable process param eters. Process parameters are constants or slow time-

dependent coefficients which appear in the mathematical description of the relationship between the

input and the output of the mathematical model, i.e. overall heat transfer coefficient (U), heat

transfer area (S ), kinetic parameters, heat capacity (Cp), etc.

There are no applications in literature for tine use of these parameters for safety criteria for batch

or semibatch chemical process, but for instance, if the kinetic parameters are changing it is normal

to infer that an unexpected reaction has taken place and this could be used for detecting

decomposition reactions. The following method, practically the same as that for non-measurable

process variables, should be used for this purpose [5]:

- Establishment of the process equation for the measurable input and output variables by theoretical

modelling.

Y ( t ) = f { U ( t ) , © } (15)

- Determination of the relationship between the model parameters 6; and the physical proce

coefficients pj:

© = f(p ) (16)

- Estimation of the model parameters 9; as results of measurements of the signals Y(t) and U(t).

- Calculation of process coefficients:

P = f '(© ) (17)

and determination of their changes Apj.

- Possible process fault can be pinpointed if there are changes in the Apj coefficients.

2.3.3. Non-measurable characteristic quan tities. Normally the checking.of characteristic quantities

can give im portant inform ation on the inner state when s upervisin g larger plants 15], but for small

installations such as those used in batch or semibatch processes they do not seem to be very

adeq uate. Examples of characteristic quantities are:

- Efficiency (e.g. all types of engines and mach ines, heat exc hange rs)

- Energy consumption per unit time (e.g. stirrer, pumps)

- Wear per unit time

These characteristic quantities must be determined from measurable variables:

:SS



212

n = g{u,Y}

Mostly, static relationships are sufficient.

(18)

3 . Experimental and Analyt ical results

3.1.

DESCRIPTION OF EXPERIMENTS

3 .1 .1 . Materials and Method. The reaction ch osen for this set of expe rime nts to test the

possibilities of early detection of runaway initiation, was the esterification between propionic

anhy dride and 2-bu tanol [14]. This reaction has some ad vantages that mak e it very interesting for

safety studies:

- Hom ogeneous reaction

- No danger of decomposition reactions.

- Reaction rate variable in function of catalyst (strong acid, i.e. sulphuric acid)

- Autocatalytic behavior for 0.8% sulphuric acid, in the sense that the maximum of the reaction rate

is reached at approx. 5 0% of conversion . This imp lies that the early detection is more difficult due

to this accelerating phenomena.

( C H J - C H J - C O ^ O

H +

CHj-CHOH-CH^CH

CH -CH -COOH

3 2

CHj -CH2-COOCH-CH -CH

CH

The system investigated was a 1:1 molar mixture of 2-butanol and propionic anhydride. The

process was carried out in a RC1 reaction calorimeter [2] of 2

1

of volume. Initially the =6.8 mols

of 2-butanol containing 0.8% in weight of sulphuric acid were added to the reactor, and allowed to

reach thermal equilibrium, the same number of mols of the propionic anhydride were then rapidly

introduced (=10 s.). Different series of experiments in isoperibolic (modifying the jacket

temperature) and isothermal conditions (varying the reactor temperature set-point) were performed.

3.1.2. Isoperibolic experiments [14]. Figure 8 represents a set of isoperibo lic experime nts

(constant jacket temperature).

The initial drop in the temperature of the reacting mass is associated with the endothermic

mixing of the reagents. The effect of jacket temperature on the rate of reaction can be seen from the

changes in the reactor temperature-time profiles, with high temperatures leading to exothermic

runaway.

Table 2. Jacket temperature for the different isoperibolic experim ents.

Experiment

El

E2

E3

E4

E5

E6

T e H O

293.9

295.7

298.2

300.7

303.2

308.2



213

n 1 1 1 r

0 1200 2400 3 6 0 0 4 8 0 0 6 0 0 0 7 2 0 0 8 4 0 0 9 6 0 0 tBOO 12000

Time (s)

Figure 8. Esterification reaction: Isoperibolic experim ents.

3.1.3 . Isothermal experiments [14]. Figure 9 represents "isothermal" experiments m odifying the

reactor temperature set-point.

~\ 1 1 1 T 1 1 1 r

1300 2600 3900 5200 6500 7800 9 t» tt+ 00 11700 13000

Time (s)

Figure 9. Esterification reaction: Isothermal experim ents.



214

Table 3 . Jacket temperature for the different isothermal ex periments.

Experiment

E7

E8

E9

Tm set point (K)

296.4

304.2

313.2

Figure 10 shows the experiment E9. The "strange" behaviour of the cooling jacket temperature

is explained due to the fact that when the RC1 alarm system started (the maximum reactor

temperature parameter was set at 100 °C), the emergency cooling programme was triggered off and

the safety valve was opened to increase the cooling power. Afterwards, when the reactor

temperature was decreasing and the emergency was cancelled, the RC1 tried to mantain a 50 °C

difference between T

m

and T

e

in order to protect the glass reactor against breakag e.

410

1

150

I

300

I

450

1 1 1

600 750 900

Time (s)

1

C50

I

1200

050 S »

Figure 10. Esterification reaction: Isothermal experiment E9. Temperature-time profiles for the

reactor (Tm) and jacket (T

e

) respectively.

3.2. OLIWA TESTS

The OLIWA system was tested using the esterification reaction described above. The OLIWA

system has three different alarm levels [15]: a/ Pre-alarm (flashing light with increasing on-time

and constant cycle), b/ Alarm (acoustic signal and flashing light together, with increasing on-time

and constant cycle), c/ Extreme danger alarm (continuous acoustic and optical signals).

Two independent temperature sensors were placed in the reaction calorimeter in order to

measure the reactor and jacket temperature, and connected to the OLIWA system. The signals of

these two m easu res, the first and second deriv atives of reactor tem pera ture, as well as the first

derivative of the temperature difference between reactor and jacket, and the alarm level were

recorded independently of the RC1 data acquisition system.



215

376

"T

752

T

1128

n 1 1 1 r

« H B 80 2256 2632 3008 3384 3760

Time(s)

Figure 11. Reactor and jacke t temperature of the experimen t E5.

10

d 2 T m / d t 2 « W

^f-

Akrm level

T n 1 ^ T

-

^ 1 1

1128 "604 B80 2256 2632 3008 3384 3760

Time(s)

Figure 12. Values of the two variables of the criteria used by the OLIWA system and alarm level in

experiment E5.

Figure 11 and 12 show a typical isoperibolic experiment and the OLIWA results. There are two

alarm s, the first at approx. 927 s and the second at approx. 1408 s, which con vert into an extreme

danger alarm, while the time for the maximum temperature is approx. 1969 s.



216

The results of the OL1WA experiments show that potentially dangerous reaction states can

be detected in the early stages if the reactions proceed slowly at the beginning. In the case of

autocatalytic or radical type behaviour the time for taking counter-measures is reduced due to the

fact that the self-heating process is enhanced by the effect of the concentration in the Arrhenius

expression for the reaction rate and in some circumstances the OLIWA is not useful.

M oreove r, the existence of an alarm does not imply that the system will runaway (see figure 8,

E l ) ,

because perhaps all the reactants will be consumed. Consequently, the installation of such a

device should provide a warning, but should not substitute the judgment of the people in charge of

the plant.

3 .3 . DEVELOPMENT OF AN IN-HOUSE WARNING SYSTEM

The OLIWA system is a dedicated equipment with its own micro-processor and can be used

simultaneously for five reactors or storage tanks. In the case of a single system, if a reliable on-line

estimate of both temperature derivatives can be made, then the criteria given by eq. (10) can be

used as a part of the warning system of the installation, and this can be carried out in a personal

com puter or as part of the control system.

3.3.1.

Signal treatment and noise suppression. The numerical methods for differentiation, i.e. eq.

(19) for five centered points and eq.(20) for nine centered points are affected by the disturbances

superimposed on the measurement signal. This can lead to rate estimates that amplify this effect

making the use of these values for early warning detection very difficult (see figure 13.a).

f (

X

) = _L_ [f(V

2 h

) -8f(x

0

-h)+8f(x

0

+h)-f(x

0

+2h)]

( 1 9 )

0

12h

fYv

^

- 1 F3f(x

n

+4h)+16f(x

n

+3h)-36f(x

n

+2h)+48f(x

n

+h)-48f(x

n

-h)

U

°

;

" 2 8 0 h o o o o o

f-36f(x

0

-2h)-16f(x

0

-3h)+3f(x

0

-4h)] (20)

where h is the interval between successive x values.

There are many available techniques for minimizing the noise in the calculation of the

derivatives, but only very simple digital filters will be considered in this section. A more

comprehensive treatment of digital filtering is available elsewhere [16, 17].

- Exponential filters: If we denote the samples of the measured variable as x

n

_i, x

n

... and the

corresponding filtering values as y

n

_i, y

n

... where n refers to the current sampling instant, the eq.

(21) gives the filtered measurement as a weighted sum of the current measurement x

n

and the

filtered value at the previous sampling instant y

n

.i . This is a single exponential smoothing (see

figure 13.b)

y

n

= a x

n

+ ( l - a ) y

n l

(21)

a is defined as ,



217

a =

(22)

At

+ 1

where At is the sampling period and if the time constant of the filter. Limiting cases for a are: oc= 1

(no filtering), a=0 (the measurement is ignored).

Another similar filter is the double exponential or second-order filter, which offers some

advantages for eliminating high-frequency noise (see figure 13.c).

y

n

= Yaxn+(

2

-Y-a)y

n

_

r

( l-a)( l-y)y

n 2

(23)

a and y

are

defined in the same way as previously

r-

» ■

6

4

2

0

-2

-4

■6

-t

-D

lETm/dO' ld

- 1 1 1 r

-

85

370 555

740 525 110

Tn»(i )

a/

1295 H80 66 5

y dflm-Te)/«

• U 2

(CTm/dO*

1*3

»

370 555

740 925 II I

fine (a)

H » 1565 B50

b/

(CTm/dt2*l*3

IB 370 555

- 1 1 1 T

740

925 110

TVre(i)

C/

C-j

0

- 4 -

-6 -

■ « -

- t -

^

*

dam-T«)/dl'l i2

(OTm/iM'UJ

J

_v

K80 B65 - B50 o K 370 555

740

925 II D

Trt»(j)

d/

1295 1460 K 5 850

Figure

13.

Derivatives

of

criteria

from

eq.

(10)

in

experiment

E5.

a/

Single

exponential

filter,

Tp=20

s,

b/

Double

exponential

filter

tpi=

7

s

and

Tp2=

8

s,

c/

Moving

average filter,

=

20

points.

-

Moving

average

filter:

This

filter

averages

a

specified

number

of past

data

points,

by

giving

equal

weight to each data point (see figure 13.d).



218

y

n

:

n

i=n- j+ l

(24)

where

j is

the number of past data points that are being averaged.

Comparing

the

three different filters and using

the

same arbitrary margin

for

th e level

of

derivatives and

for

th e time interval

in

which they must exceed these limits,

the

detection

is

achieved at 1556, 1504 and 1400 s respectively. The same type of treatment was carried out for

exper iment E9,

the

results

are

shown

in

figure

14. In

this case

the

t ime

for the

maximum

temperature was 556

s.

Using the same criteria, th e detection

is

achieved

at

364, 348 and 328

s

respectively.

Better results can be obtained applying adaptive filters similar to exponentials bu t using variable

averaging weights [18]

or

Kalman filters [11]. The disadvantage

is

that extra computat ion

is

required

but

they

provide

standard

error

estimates

that

ca n

be

used

in

formulating

decision

rules,

reducing the false alarm risks.

T

« -

36-

24 -

E -

- 0 -

- 24 -

- 36 -

- 48 -

1

.

91

dCTm-WUtf

1

<tZrm/*2 U3

112

63

204

255

306

Tn«(i )

357

40B

A

■y

459

5

6 0 -

4 8 -

36 -

24 -

0 -

0 -

- 0 -

- 24 -

- 36 -

- 4 8 -

D

(

51

dCIm-T.y*'li2

/ ( B W d B ' U J

IK

83

204

255

306

Trab)

357

403

-^y

459

5

a/

b/

6 0 -

4 t -

36 -

2 4 -

0 -

-a-

- 24 -

3 6 J

- 4 8 -

1

\

V

1

51

dCIrn-W*

•

U2

/ <ZI>n/iK'U3

IQ

E3

204

255

306

T imd)

d

357

405

459

5

6 0 -

4 8 -

36 -

2 4 -

0 -

0 -

-B -

- 24 -

n36-

- 4 8 -

0

0

1

51

dCTm-T.Vdl

•

U2

\

/

/

dTIm/da l*

112

B3

204

255

306

Th»W

d/

357

l

408

J

/

459

5

Figure

14.

Derivatives

of

criteria

from

eq.

(10)

in

experiment

E9.

a/

Single

exponential

filter,

Tp=20 s, b/ Double exponential filter TFI= 7 s and Tp2= 8 s, c/ Moving average filter, j = 20 points.



219

Moreover, in order to avoid false alarms due to the noise, it is necessary to define a certain limit

value greater than zero. However, this will reduce the sensitivity for small values of derivatives,

that means, the slow starting self-heating processes will be detected later. In order to correct this

problem is interesting also to evaluate [15]:

± f

2

d t > e .

d t

z

(25)

ps

™ I ^ d t > £ ,

dt

4

(26)

3.4. MODEL-BASED APPLICATIONS

A numerical simulator able to reproduce the dynamic behaviour of chemical processes carried

out in a RC1 reaction Calorime ter was developed [29]. Th e results of experimental and simu lated

data of experiment E9 are shown in figure 15.

41) •

1

160

I

320

1

480

1 1 1

64 0 800 960

Time

(s)

I

1120

I

1280

1440

1600

Figure 15. Exp erimental and simulated temp eratures of the reacting mass and the heating/cooling

jack et in a runaway scenario in the RC1 Reaction Calorimeter for experiment E9.

3.4.1. Off-line application. As the simulator exists, the application of criteria given by eq. (10) and

other criteria based on conversion or another non-measurable state variable or parameter may be

carried out. The advan tage of this approach is that the experimental noise can be eliminated. Figure



220

16 shows the application of the criteria given by eq. (10) to the simulated results.

dfJm-Te)/dt«te2

Simulated

I I

204 255 306 357 408 459

Time(s)

Figure 16. Derivatives of criteria from eq. (10) using simulated data.

5t)

Figure 17 shows the evolution of derivatives of criteria given by eq. (12).

60

n i i i i i r

0.02 0.03 0 J0 4 0.04 0.05 0.06 0.07 0.08 0.08 0.09

x1

Figure 17. Derivatives of criteria from eq. (12) using simulated d ata.

3.4.2. On-line developments . Up to now, the model-based criteria for early detection of runaway



221

initiation have been applied off-line, but this technique has been developed to solve on-line the

mathematical model of the process and to correct it by comparison with the real measurement [19-

22].

Some applications for incipient fault diagnosis in chemical process have been reported [23], and

particularly, Gilles, King and Schuler [4,12, 24] who studied the application to detect hazardous

states in a batch chemical reactor.

The first step for a development of such system is the reconstruction of the state of the system

and/or the estimation of some parameters. In order to achieve it, the most common method is the

Kalman filter [11], but other methods can be used (i.e. Lainiotis filters [25], etc.).

Th e mode l of a chem ical pro cess , in this case a batch reactor, can be be represe nted by the

following expression:

x = F ( x

r

x

2

, . . . , x

n >

Q

V

Q

T

...,9

p

) (27)

where x; are the state variables and 0j the model parameters. Through linearization by Taylor series

around any operating point, it is possible to obtain the following stochastic state-space model:

x(t) = Ax (t)+ E n( t) (28)

y(t)=Mz(t)+v(t) (29)

where x is an n dimensional state vector of the process, n is an r dimensional vector of inputs to

the proc ess; y is an m dimensional ind epend ent me asurem ent vec tor; and v is an m dimensional

gaussian random noise vector for the measurements; A,B and M are coefficient matrices with

appropriate dimensions.

The linear model given by eq. (28) and (29) can be discretised under the assumption that a is

constant over a sampling interval. Hence,

\

+

l = *

X

k

+ r

\

+ W

k (30)

y

k

=

M

k

X

k

+ V

k (3D

where, 4>= e

A A l

, T= A-\fy-'iyB and w is an r dimension al gaussian random noise for the inputs.

The equations of discrete Kalman filter recursive algorithm are summarized in Table 4. A more

detailed and rigorous de scription is available elsewhe re [2 6,2 7]. Th e discrete K alman filter gives

an estimate x of the state x at the time sam ple k +1 . This estimate is based on the previous estimate

x

k

and the previous measurement y

k

. K

k

is the filter gain vector that minimizes the covariance P of

the estimation error. Moreover, if some parameters 9, need to be estimated along with the original

state vector, the Kalman filter algorithm can be extended by introducing these parameters in the

state vector [26,27].



222

Table 4. Summary of discrete Kalman filter recursive algorithm

- Prediction:

*

k+

i

=

* k

+

i V

r

A

p

k + 1

= i W L i

+

Q

k

. Q

k

= § K - » f }

- Correction:

K

= P

M

T

M. .P. ,ml ,

+R.

,] R

^ k + 1 ^ k + l ^ k + l l

k+1 k+1 k+1 k+U . ^k

\

+

l

=

\

+l

^J

y

-

M

*^

P

k

+

, =

P

k

+

, -

K

k

+

l

M

k

+

,

P

k

+

l

=

^ V

V

k}

King

and

Gilles

[4,24],

in

order

to

take into accou nt that different fault mode s have

to be

considered,

and

that the w arning system

in

order

to be

efective shou ld

be

able

to

distinguish

betw een the m, applied different filters for every po ssible fault mo del (see figure 18) and using the

information provided

by

the filter abou t the qu ality

of

estimates

it

was possible

to

discriminate

between rival models using the Bayes rule [28].

Process

Filter 1

Normal process

Filter

2

Fault type

1

Filter 3

Fault type

2

Filter 4

Fault type

3

Figure 18. Multiple filter method

for

fault discrim ination using the Baye s rule

to

determine the

model which fits best the measurements.


Early warning detection based

on

temperature derivatives

is

feasible

and

should serve

as a



223

warning for plant operators. Moreover, it can be easily implemented on a microcomputer linked to

ordinary measurement devices.

On-line model based measuring techniques have the highest predictive power and selectivity.

Even though the development of a mathematical model is time consuming, once it has been built-

up, it can be applied not only for safety but also for optimization purposes increasing the yield and

minimizing the time for each batch, and consequently can be justified economically.



224

N O T A T I O N

A

A

B

C

Cp

E

a

H

k

K

IP

q

M

M

R

r

S

T

U

US

m

V

V

<w

%

y

pre-exponential factor

Dynamic matrix of the state

Input matrix

Molar concentration

Specific heat capacity

Activation energy

Molar enthaply (liquid)

Reaction velocity constant

-space model

Ga in vector of the Kalm an filter

Covariance matrix

Thermal flow

Mass

Measurement matrix

Gas constant

Rate of reaction

Surface

Temperature

Heat transfer coefficient

Effective heat transfer coefficient

input vactor

Noise vector of the measurem ents

Volume

Noise vector of the state

State vector

Measured output vector

depends on kinetics

mol-m"

3

J K g - ^ K "

1

J-mol"

1

J-mol"

1

depends on kinetics

W

Kg

J-moH-K"

1

mol -m '^s"

1

m2

K

W-m-2-K-

1

W K "

1

m

3

Greek symbols

Discrete state transition matrix

r

T

e

V

p

X

CO

S u b s

A

a

B

Thermal capacity

Discrete input m atrix

Process parameter vector

Stoichiometric coefficient, reactant(-), product(+

partial order of reaction

Density

Time constant

Frequency

c r i p t s

Actu ator or External cold source L :

Stirrer or inserts m :

Bottom M :

J-K-i

)

Kg-m-

3

s

rad.s"

1

Liquid

Reaction mixture

Measurement



225

c

d

E

e

h

i

J

0

1

Thermovector, cooled loop

Dry part

Feed of reactants

Thermovector, heated loop

Heating

Reaction or Input

Species

At the surface, internal side

At the surface, external side

P

R

r

sp

T

t

V

w

z

Inert gas at inlet

Reactor

radial

Set-point

Total

Hydraulic

Vortex

Wall or Wetted part

Axial

R E F E R E N C E S

1. Grew er, T., Klusac ek, H., Loffler , U., Ro gers, R.L., and Steinb ach, J. (1989)

'Determination and assessment of the characteristic values for the evaluation of the thermal safety

of chemical processes', J. Loss Prev. Process Ind. 2, 215.

2 .

Riesen, R. and Gro b, B. (1985) 'Reaction Calorimetry in Chem ical Process D evelopmen t',

Swiss Chem. 7, 39-43 .

3 .

Hu b, L. and Jone s, J.D. (1986) 'Early On-Line Detect ion of Exo thermic Reactions' ,

Plant/Operation Progress 5, 221.

4. Kin g, R. and Gilles , E.D . (1986) 'Early detection of hazar dou s states in chem ical reactors

with model-based measuring techniques', 5th International Symposium "Loss prevention and

Safety in the Process Indu stries", Cann es 15/19 Septem ber.

5 . Isermann, R. (1984) 'Process Fault Detection Based on M odeling and Estimation Methods-

A Survey', Automatica 20, 387 .

6. Tufa no, V. (1988) 'Mod eling runaw ay reactions in reactors protected with suppression

systems ', J. of Hazardous Materials 19, 225 .

7. Him melb lau, D.M . (1978) Fault Detection and Diagno sis in Chem ical and Petrochemical

Processes, Elsevier, Amsterdam.

8. Tow ill , D.R. and Payne , P.A. (1971) 'Frequency domain approach to automatic testing of

control systems', Radio and Electron. Engr.41, 51 .

9. Cas adei, R. (1977) 'Autom atisierungstechn ik im W andel durch M ikroproz essoren ' in M.

Syrbe and B. Will (eds.), INT ER KA M A-K ongreb , Springer, Berlin, 179.

10. Luenberg er, D.G. (1966) 'Observers for M ul tiv ar iat e System s', IEEE Trans, on Automatic

Control 11, 190 .

11 . Kalm an, R.E. (1960) 'A New App roach to Linear Filtering and Prediction Problem s', J.

Basic Eng. 82 D, 35-45.

12 . Gilles , E.D. and Schuler, H. (1982), 'Early Detection of Ha zardo us States in Chemical

Reactors', Ger. Chem. Eng. 5, 69.

13 .

Bon vin, D. and Saner U. (1988) 'On Line Proce dures for Superv ising the Ope ration of Batch

Reactors', Comput. chem. Engng. 12, 371-376.

14 . Snee, T. (1991), in this course.

15.

OLIW A manual (1985), System Technik AG .

16. Op penh eim, A.V . and Shafer, R. W. (1975) Digital Signal Processing , Prentice-Hall ,

Englewood Cliffs, NJ.

17.

Sebo rg, D. E., Edgar, T.F . and M ellichamp D .A. (1989) Process Dyn amics and Control,

Wiley , New York.



226

18 .

Spe nce, J.P. and No ronha, J.A. (1988) 'Reliable Detection of Run away R eaction Precursors

in Liquid Phase Reactions', Plant/Operation Progress 7, 231 .

19 .

Seborg D .E., Edgar T.F., Shah , S.L.(1986) , AIC hE Journal 3 2, 88 1.

20.

P. de Valliere and D. Bonvin, Application of estimation techniques to batch reactors-II.

Experim ental studies in state and param eter optimization , Co mp . Che m. Eng., 13,11 (1989 ).

21 . Soliman, M. A. and Ray, W. H. (1979) 'Nonlinear State Estimation of Packed-Bed T ubular

Reactors', AIChE Journal 25, 718-720.

22. Kuru oglu, N.R ., Ram irez, W .F., Clough , D.E . (1981) 'Distributed Param eter Estimation

and Identification for Systems with Fast and Slow D ynam ics', Chem. Eng. Sci. 36,1357 (1981).

23 .

W atanab e.K . and Him melblau D.M . (1984) 'Incipient fault diagn osis of nonlinear processes

with multiple causes of faults', Chem. Eng. Sci. 39, 491-508.

24. King , R. (1985) 'Multiple Kalman filters for early detection of hazard ous states', Proceeding s

of Industrial Process Modelling and Control, Hangzhou, 6-9 June.

2 5 .

Lainio tis, D.G . (1971) 'Optimal Ad aptive Estim ation: Structure and Param eter Adaptation',

IEEE Trans. A utomatic Control 2, 160-169.

26. Jazwins ki, A.H. (1970) Stochastic Processes and Filtering Theo ry, Academic Press, New

York, 269.

27.

Gelb, A. (1974) Applied Optimal Estimation, MIT Press, Cam bridge.

28.

An derson , B.D .O. and M oore, J.B. (1979) Optimal Filtering, Prentice-H all, Englewood

Cliffs, N.J.

29.

Zaldivar, J.M., Hernandez , H. and Barcons C. (1990) De velopm ent of a Mathematical

Model and Numerical Simulator for a Reaction Calorimeter. FISIM, RC1 version, Technical Note

N° 1.90.109, Comm ission of The European C omm unities, Joint Reasearch C entre, Ispra (Italy).



EMERGENCY RELIEF SYSTEM SIZING:

IN-VESSEL FLUID FLOWS

J . S . Duffield

CEC Joint Research Centre.

Ispra E s t a b l i s h m e n t

I - £1020 Ispra (Va)

Italy

1. I N T R O D U C T I O N

The occurrence

of an

uncont rol led chemica l runaway reac t ion

in a

ba tch type reac tor

or

storage vessel

is a

frequent event

in the

chemica l indust ry .

The

consequences

of

such

an

event can be benign (but still costly in t e r m s of lost product ion) when the p r o d u c t s are

safely vented

to a

d u m p t a n k

or

similar device,

or can be

d i sa s t rous

in

t e r m s

of the

effect

on

the

env i ronment when

the

p r o d u c t s

are

released

to the

a t m o s p h e r e ,

as for

example

in

the case of the acc idents at Seveso and Bhopa l .

An uncontrol led release to the a tmosphere usual ly occurs due to vessel failure, which

often results from

the

fac t tha t

the

emergency rel ief system

is not

correc t ly sized. Tra

di t ionally

the

emergency rel ief systems were designed assuming single-phase condit ions

in

the vent l ine, whereas in rea l ity often two-phase condi t ions prevai l. Co mp ared to relief

systems designed

to

handle single-phase vapour, two-phase flow requires vent sizes that

are

2 - 1 0

t imes la rger .

An

addi t iona l compl ica t ion ar i s ing f rom two-phase discharge

is

t he r equ i rement to insta l l spec ia l equipment to t r e a t the relieved fluids if they are toxic or

imflamm able . This spec ia l equipm ent

(a

fol lowing lecture wil l t reat this subject

in

more

deta i l )

may

consist

of

knock-out dru ms , vapour- l iquid sepa ra to rs , ca tch tank s, condensers ,

e tc . W h a t e v e r the sys t em the cost of such equipment is not insignificant , therefore it is

i m p o r t a n t

to

opt imise

the

size

of the

relief lines

and

duc t ing ,

i.e.

they should

be

large

enough

to

ensure t ha t

the

peak pressure stays within safe l imits during

relief, but not too

l a rge in order to minimise the a m o u n t of relieved fluid to be t r ea t ed .

In view

of

this interest , much effort

has

been expended over

the

las t decade

in an

a t t e m p t

to

improve

the

unde rs t and ing

of the

basic phen om ena assoc ia ted wi th emergency

relief. For example , the chemica l indust ry has performed m any exper im ents some of which

have been described

in the

open l i t e ra tu re ,

the JRC has a

f ramework prog ram me dea l ing

wi th " Indus t r i a l Haza rds" ,

and a

major effort

has

been

the

work performed

in the

D I E R S

227

A .

enuzzi and J

M

Zaldivar (eds.) . Safely

of

Ch emical Batch Reactors

and

Storage Tanks, 227-253.

©

1991 ECSC. EEC EAEC.

russels

and Luxem bourg. Printed in t he Ne ther lands.



228

(Design Inst i tute for Emergency Relief Systems) project . DIERS consists of a consort ium

of 29 companies under the auspices of the American Inst i tute of Chemical Engineers and

was formed to generate experimental data on large-scale vessels undergoing ei ther runaway

reac tion s or exte rna l heat ing (e.g. by extern al f ires or loss of coo ling), and to develop

m eth od s for the safe design of emergency relief system s to handle the se even ts. Significant

progress has been made but th is knowledge i s by no means comple te .

This lec ture wil l conc ent ra te on wh at hap pen s wi thin th e vessel dur ing emergency

relief,

and an a t tempt wi l l be made to highl ight the basic phenomena tha t a re present (and tha t

have to be modelled) during the transient and how they interact and affect the course of the

t ransient . Reference wi l l be made to the computer code RELIEF, which i s current ly be ing

developed a t the JRC to model such s i tua t ions and most of the i l lust ra t ive ca lcula t ions

presented in this lecture have been made using this code.

The important aspect of two-phase cri t ical f low through the vent l ine wil l be left to the

next lec ture . I t is perh aps w orth men t ioning however, tha t i t i s the beh aviour w i thin the

vessel that determines the entrance condit ions to the vent l ine, and the errors associated

with calculat ing these condit ions usually have a much greater effect on the calculated vent

flow th an the likely spre ad of values th a t would res ult from usin g different crit ical flow

models .

2.

REACTOR RELIEF PH EN OM EN A

The s i tua t ion under considera t ion can be a ba tch reac tor or s torage tank conta ining a mul t i -

component l iquid mixture in which a chemical (usually exothermic) react ion occurs. If due

to malfunctioning the generat ion of react ion heat in this mixture exceeds the heat removal

capacity of the equipment a thermal runaway process wil l occur which is strongly enhanced

by the Arrh enius- type tem per a tu re dependency of reac t ion ra t e . W hen this s i tua t ion can

not be cont rol led by opera t ional measures , the tempera ture wi l l r i se to leve ls where the

vola t ile com pone nts of the liquid reac tan t mix ture s ta r t to evap ora te . At h igh tem pe ra tu re

levels also gas may be produced as a result of undesired secondary decomposit ion react ions.

This volume product ion leads to an increase of system pressure and in order to prevent

over-pressurisat ion of the reactor vessel i t is necessary to discharge the fluid mixture from

the vessel at an adequate rate . For sizing the emergency rel ief system, required by safety

rules,

i t i s necessary to dispose of adequate computa t ion models which must be based on a

correct descript ion of the chemical conversion, of mass transfer between l iquid and vapour

phase, of two-phase fluid dynamics and of the interact ions between these processes.

2 .1 LEV EL SW ELL

Chemical react ions can be the cause of a r ise in pressure in a closed system by increasing

the vapour pressure of the system and/or by genera t ing non-condensible gases as reac t ion

or unw anted decom posi t ion pro duc ts . Even endo therm ic reac t ions can cause a pressure

increase if the react ion products are gases, or l iquids which are more volat i le than the

reac tants . Exothermic reac t ions a re potent ia l ly more dangerous as in addi t ion they ra ise

the tempera ture of the reac tants and hence acce lera te the chemica l reac t ion.



229

Often in the l i terature dist inct ion is made between the mechanism of this pressure rise

so tha t s impl i f ica t ions can be made to the mathemat ica l t rea tment of re l ie f system siz ing.

The fol lowing dist inct ions are usually made:-

(a) "Vapo ur pressure" or " temp ered" system s, in which the pressure gene ra ted by the

reac t ion i s due to the increasing vapour pressure of the reac tants , products and/or

iner t solvent as the te m per a tu re r i ses .

(b) "Gassy" sy stem s, in which the pressure is due to the produc t ion of a per m ane nt gas

by the reac t ion.

(c) "Hybrid" systems, in which the pressure rise is due to both an increase in vapour

pressure and permanent gas genera t ion.

For such systems a number of analyt ical tools and formulae can be used to calculate the

vent s ize for a par t ic ular overpressure . These "hand ca lcu la t ional" me thod s usual ly t r ea t

the vessel as a single calculat ional node having uniform propert ies. The obvious difficul ty

arises when this assumption is not val id and when i t is not known a priori w ha t t ype

of sys tem is exp ected . An excellent review of exist ing vent sizing m eth od s of this ty pe is

given by Duxbury and Wilday [1,2].

When a runaway react ion is in progress there is a volumetric source in the l iquid phase

resul t ing f rom evapo ra t ion an d/ or reac t ion gas prod uct io n. T he bubbles of vapo ur an d/ or

gas generated within the l iquid tend to rise through the l iquid and disengage at the l iquid

surface. If the rise velocity is sufficiently high then d rople t entr ain m en t can o ccu r.T he

bubbles during their residence in the l iquid occupy volume and so cause the l iquid level to

rise or "swell" . Figu re 1. shows quali tat ively this ph eno m eno n.

W hen th e set pressu re is reached and the re acto r or sto rag e vessel relieves the n the

pressure fal ls and the evaporat ion or "flashing" increases markedly. This causes the l iquid

level , or to be more precise the "two-phase mixture level"*, to r ise further and if this level

reaches th e vent pos i t ion two -phase venting wil l occu r. Th e dep ress uris at ion rat e of a

system is direct ly proport ional to the volume flow rate exit ing the system and since this,

under c r i t ica l f low condi t ions, i s inverse ly propor t ional to the mixture densi ty enter ing the

vent l ine the capacity to reduce the system pressure by venting is strongly reduced when

the mixture level reaches the vent posi t ion. In a runaway si tuat ion if the volume production

ra te due to evapora t ion and/or gas product ion i s grea ter than the vented volume f low ra te

the system press ure will increase. Therefo re, the abil i ty to describe th e m otio n of the

two-phase mixture level is one of the most important aspects of reactor rel ief modell ing.

2.1.1

Interfacial Mom entum Transfer

Th e genera l a rea of in te rfac ial mo m entu m t ransfer in pool systems conta ining arbi t ra ry

fluids an d subject to depre ssuris at ion is st i l l an open ar ea of resea rch. Th ere is a pau city

of experimental data part icularly for high viscosi ty fluids from which real ist ic models can

be developed. Th e problem reduces to the descr ipt ion of the mo t ion of bubb les wi thin a

The two-phase mixture level

separates

the region which is predom inately liquid (possibly containing

vapour

bubbles)

from the region which is predominately

vapour

(possibly containing liquid droplets) and

is

usually deSned as the position

where there is a discontinuity in the axial void fraction profi/e



230

cont inuous l iquid phase and the mot ion of drople ts wi thin a cont inuous vapour phase , and

how this motion changes with void fract ion. In a bubbly l iquid in a pool where wall effects

are negligible, the frict ion or drag exerted by the l iquid on the bubble surface determines

how fast the bubb les rise with in the l iquid. Th is fr ict ional force in com pariso n to th e

buoyancy force decreases markedly as the bubbles increase in size. As the void fract ion

increases the rate of sl ip of the vapour past the l iquid increases unti l the si tuat ion arises

when the l iquid begins to break up in to drople ts and the vapour becomes the cont inuous

phase. The drag between the droplets and the vapour increases as the droplet size decreases

and so the sl ip decreases. At the extremes of al l l iquid and al l vapour flow the sl ip must

obviously be zero, and at some intermediate void fract ion the sl ip wil l be a maximum where

the bubbles have their maximum size. Therefore, the phasic veloci ty difference should vary

with void fraction in a way similar to as is shown in figure 2.

To descr ibe th is mot ion one has to look a t the phasic momentum t ransfer . The equa

t ions that describe this process are usually formulated in terms of mixture or drif t f lux

mo del [3] or a two-fluid mo del

[4].

In the dr i f t f lux model the phasic momentum equat ions a re replaced by a mixture

momentum equation and the relat ive veloci ty between the phases is described by a steady

st at e corre lat ion . I ts val idi ty is l imited to si tu at io ns wh ere accelerat ion and wall fr ict ion

forces can be neglected. For most pract ical cases i t has been found that an equation of the

form:

U

r

= U

v

-U, = ^

0 0

a

m

( l - a ) "

(1)

correlates experimental data for bubbly flow in vert ical pipes well , where

Uoo

represents the

term ina l r ise velocity of a single bub ble. Th e depe nden ce of /«, up on fluid prope rt ies has

been de term ined exper imenta l ly by Pebbles and G arber[5] , and for bubbles of d iam eter up

to 1 or 2 cms is given by,

Uoo

= 1-53

For bubbles wi th a la rger d iameter than

g c r A g

1 / 4

(2)

r

b

Z

2c

9Ql

1 / 2

(3)

then

Uoo = y/gn

(4)

T he two-fluid m odel uses a se pa rate par t ial differential equ ation to describe the m otio n

of each phase and if one assumes that the pressure difference between the vapour and l iquid

phases is negligible, the momentum equations averaged over a constant cross sect ion can

be wri t ten in the form:



231

dag

v

U

v

dag

v

U

v

2

dp da . ,

-

V

\-a—

+

A

m

+ p

int

—

=

-n

-

F

wv

- a e „ f f + r

m

t / ,

n t

15)

dt az az az

for

t h e

vapour

phase

and ,

9(1

—

a)piUi

9 ( 1 -

a)giUi'

2

.

.dp

da

,

.

„ . . . . .

—

'

+

—

'

+

(1

-

a)-f-

-

A

m

- p

in t

—

=

Ti-F

w

,-(l-

a)etg

- T

m

U

int

(6)

at

az

az

az

for th e liquid phase .

where th e t e rms: -

- r

m

{7,-„

t

represents th e momen t um t ransfer due to phase change .

-

A

m

is th e added mass t e rm re la ted t o iner t ia l effects. I ts value is impo r t a n t only

for high velocity accelerat ing flows.

- r; is t h e interfacial drag force per uni t volume .

■ îu(v,i) i

3

'

n e

phasic wall friction force.

- Pint f f is a differential t e rm appea r ing in non establ i shed flow.

T he interfacial drag force r< is th e force t h a t develops when one of th e phases a t t emp t s

to move faster t h a n t h e othe r and acts so as t o re t a rd t h e faster moving phase . The

magn i t ude

of

th is

force

depends

on

th e

shape

of

th e

vapour- l iquid

in terface ,

th e

relat ive

velocity and th e phasic prope r t i e s .

To solve th is sys t em one has to specify a corre la t ion for th e interfacial drag force. If a

force balance is made on a single bubble it can be shown t h a t

[6]:

3ag,U?C

d

n = - — (7)

8 rf,

The basic empir ic ism of t h e two-fluid mode l enters in de te rmin ing th e values of C j and TV

In th e par t i cu l a r case of pool boil ing or flashing in la rge diame te r vessels (such as

ba tch

reac to r s

or

s to rage

t anks)

th e

velocities

are

low

and

th e

t empo ra l ,

accelera t ion

and

convective t e rms in th e momen t um equa t ions can be neglected as to o can th e t e rms re la ted

to wall friction and momen t um t ransfer due to phase change . Thu s in th is case t he re is

l i t t le to choose between th e drift flux approach and th e two-fluid mode l except t h a t th e

drift flux mode l general ly requires less comput ing t ime .

We have chosen for th e i l lustrat ive compu t a t i on s presented in th is pape r to a dop t th e

drift flux approach , and to descr ibe th e phasic velocity difference as a function of void

fract ion. The expression chosen is given below which incidental ly is equivalent to figure 2.

a

m

1 -

a)

U

v

U

t

=

Upool

■

_

J (8)

maxK

1

max)



232

where

a

max

is th e void fraction w hich gives th e te rm a

m

( l - a ) " i t s m axim um value .

The denomenator is a scal ing factor which ensures that the maximum value of the sl ip is

given by

U

poo

i

irresp ective of the value of void fraction at which it occ urs . T he coefficients

m and n describe bubbly flow and droplet f low respectively, they have been fi t ted to ex

pe r imenta l da t a .

U

poo

i

is closely related to equa tion (2) and con tains a physical pro pe rty

sz±±£

a n

d

c a n

be thought of as a characterist ic bubble veloci ty representat ive of

a pool s i tua t ion.

With the constant 1 .53 , U

pool

i s ident ica l to equat ion(2) and corresponds to the churn-

turbulent regime as defined by Zuber [7]. This defini t ion has much success in describing

drift f lux experiments where gas is bubbled through a l iquid column in reasonably small

diameter tubes, say up to lOcms. However, there is a general awareness that this value

significantly underpredicts the rise veloci ty in flashing pool si tuat ions. For a more detai led

discussion reference should be made to the fol lowing art icles by, Fi l imonov[8], Styirkovich

[9],

G ard ne r [10], and K atao ka and Ishi i [11]. Pres ently we are using a co ns tan t t h at

has been obtained from fi t t ing equation (8) to data from available flashing experiments.

To improve the modell ing further more experiments are required, part icularly for viscous

fluids.

2.1.2 Effect of Level Swell on Vessel Depressurisation

Recently a number of vessel depressurisat ion experiments have been carried out in the

Mult iphase Mult icomponent (MPMC) test faci l i ty of the JRC [12]. Shown in figures 3 and

4 are two similar tests with water, where the only difference was the ini t ial f i l l ing of the

vessel. In figure 3 the initia l filling was 98% which ens ured s ignificant tw o-p has e v en ting ,

whereas in figure 4 the fi l l ing was 65%. Subsequent analysis has indicated that at a f i l l ing of

65 %

the two-phase mixture level did not reach the top of the vessel and al l vapour venting

occu rred. Th us a com pariso n of figures 3 and 4 indica tes w ha t effect two-p hase venting

has on the depr essu risat io n. I t is clearly seen th at th e rate of dep ress urisa t ion is strongly

reduced when two-phase condi t ions occur in the vent l ine . This becomes more important

when the ini t ial condit ions are not as in the tests i .e . an inert f luid at steady state , but a

chemically react ing fluid undergoing a thermal runaway.

2 .2 M U L T I C O M P O N E N T E Q U I L I B R IU M

So far we have restric ted our discussion to a single com pon ent f luid, w here as in the p rocess

indust ry we are usua l ly dea l ing wi th mul t icomponent mixtures made up of f lu ids of

signif

icantly different volat i l i t ies and physical pro per t ies. To add ress this pro blem we assum e

th a t th e mul t icom ponen t m ixture consis t ing of l iquid and sa tur a te d vapou r i s in phase

equil ibrium. This may be expressed as:

X

vi

= KtX

H

(9)

where X

v

i is the mole fract ion of com pon ent t in th e vapou r phas e, Xu that in the l iquid

phase and

K{

is the phase equil ibrium rat io. If the vapour mixture behaves as an ideal gas



233

th e par t i a l pressure p,- of componen t i in th e vapour mix tu r e is p ropo r t i ona l t o th e mole

fraction X„< resul t ing in :

Pi = pX

vi

(10)

If

th e

liquid

mix tu r e

also

behaves

ideally

and

follows

Raou l t ' s

law

t h e

pa r t i a l

pressure

Pi

is p ropo r t i ona l to th e liquid mole fract ion

Xu

and to t h e vapour pressure of th e pure

componen t a t th e same t empe r a t u r e :

Pi = P.iXu (11)

As appea rs from eqs(10) and (11) for ideal mixtures th e phase equi l ibr ium ra t io Ki is :

Ki = *± (12)

P

For

ideal

gas

behav iour

of

th e

vapour

mix tu r e

th e

mole

fract ion

X„,-

is

equa l

to

t h e

volume

fract ion ¥ „,•. Eq (9 ) t hen can be t r ansfo rmed i n to :

Y,i = KiXu (13)

The re la t ions between th e componen t mole fract ions and th e componen t concen t ra t ions

are:

x

i^h^

{14)

M

>

2^ i M(

■ i

L- i

u

{

where Mi is th e componen t molecular weight .

Given th e componen t mole fract ion mix tu r e t he rmophys ica l prope r t i e s such as en tha lpy ,

densi ty , specific hea t etc . can be calculated using th e usua l mixing rules .

For non-idea l liquid mixtures e qu a t i o n ( l l ) is replaced by

Pi = P.i-XiiT,- (16)

where n is th e activi ty coefficient of componen t t .

The above descr ipt ion can be displayed graphical ly by wha t is known as a phase equi-

l ibr ium d i ag r am . Figure 5 shows a typical phase equi l ibr ium d i ag r am for a bina ry mix tu r e

of componen t s A and B. Suppose t h a t we have a liquid in which th e liquid mole fract ion

of componen t

A

XAU

=

0.25 and t h a t th is mix tu r e has an in i t ia l t empe r a t u r e

T\.

If th e

fluid is hea ted , vapour begins to be formed a t th e so-called bubble po in t t empe r a t u r e

(,„(,.

The

vapour

formed

has

a

much

higher

concen t ra t ion

of

componen t A {

in

th is

case

th e vapour mole fraction Xx„,- is a round 0.7) . If, similarly, we had s t a r t e d wi th a vapour

of compos i t i on

X*

v

i

= 0.25, and the vapour was cooled i t would begin t o condense a t th e



234

"dewpoint" Tdcw In this case, the condensed l iquid wil l have a composit ion XAH of around

0.05.

2 .3 C H E M I C A L R E A C T I O N

An ongoing chemical react ion is a potential source of both volume (due to the genera

t ion of new prod uc ts) and he at . Consider a general chemical process in the l iquid pha se

which involves two reactants A and B undergoing an irreversible react ion according to the

stoichiometr ic formula

n

A

A + n

B

Bi— *n

c

C + n

D

D (17)

The instantaneous conversion ra te of reac tant A can be expressed by an Arrhenius type

t empera tu re dependency :

n,A = k

0

\C,^\

m

\C,^]

n

exp[-E/RT) (18)

where : k

0

is an empirical factor, m and n are the react ion orders for A an d B, E is the

ac t iva t ion energy ( in J /kmol) , R i s the gas con stant and X is the ab solute tem pe ra t ure .

The heat source if the react ion is exothermic, or the heat sink if i t is endothermic is

obtained from the enthalpy change of the react ion or from the differences in the heats of

format ion of the reac tants and products .

2 .4 N O N - E Q U I L I B R I U M E F F E C T S

Thermal non-equi l ibr ium has been observed in many vesse l depressur isa t ion exper iments

containing non-reacting fluids (see for example Friedel et al [13] and Friz [14]. This non-

equil ibrium is often referred to as the boil ing delay, and results from the fact that , fol lowing

the opening of the vent the vapour space depressurises but there is a delay before bubbles

are formed in the l iquid and boil ing occurs to bring the system back towards equil ibrium.

In react ing "vapour pressure" systems a significant boil ing delay would mean there

would be a delay in the cooling effect by evaporat ion and the react ion rate would continue

to rise. Fortunately, in react ing systems the means by which the system pressure rises in

the vessel in the first place is usually by the boil ing of the more volat i le components and/or

the produ ct ion of gas f rom the reac t ion. Th is mean s tha t wi thin the l iquid phase th ere

already are plently of nucleat ion si tes and sufficient interfacial area to l imit the departure

from equ il ibrium . It is expe cted therefore, tha t the rm al non -equil ib rium effects with in the

vessel will have a negligible effect on the venting process.

3. MO DEL LING PRINCIPLES

Having described the key phenomena associated with reactor rel ief we wish to provide some

i l lusta t ive computa t ions to highl ight the importance of these phenomena. For th is we wi l l



235

make use of the code RELIEF, which is being developed here at the JRC; the sal ient features

of which wil l be described below. Ha nd calcu lat ional m eth od s, derived from the D IER S

pro gra m m e, wil l not be discussed here and the read er is referred to pape r of D ux bu ry and

W ilday [1,2] for furth er de tail s.

In modell ing the in-vessel f luid behaviour an at tempt is made to separate as far as possible

the physica l , physico-chemica l and thermokine t ic phenomena assoc ia ted wi th the mul t i -

component phase-equi l ibr ium and wi th the exothermic l iquid phase chemica l reac t ion f rom

the phenomena per ta ining to the two-phase f lu id dynamics. The ra te of vesse l depressur i -

sat io n and th e rate at which fluid is discharged from the vessel dep end on the fluid d yn am ic

phenomena in the vent l ine and on the two-phase f low behaviour of the mul t icomponent

mixture inside the vesse l . Both phenomena are model led but major a t tent ion needs to be

given to the mult icomponent two-phase fluid behaviour in the vessel because the vent mass

flow rat es depen d strong ly on fluid dyn am ic con dit ions at th e entran ce to the vent l ine. In

the i l lustrat ive calculat ions shown later a simplified cri t ical f low model has been selected

to compute the mass f low through the vent l ine , taking the s tagnat ion pressure and f lu id

mixture densi ty as the pr ime governing parameters .

The treatment of volume production in the vessel , which is due to evaporat ion of volat i le

components from the l iquid and to gas production by chemical react ion, is an element of

key importance in the ana lysis . Vapour product ion dur ing the vent ing process i s assoc ia ted

wi th externa l hea t input , a l iquid phase volumetr ic hea t source due to ongoing exothermic

chemical reac t ion and the change of system pressure w i th t ime. Ga s pro duc t ion can resul t

f rom the ongoing chemica l reac t ion or through secondary decompost ion reac t ions.

The key features of the in-vessel fluid flow model are:

* Vert ical discr et isat io n of the vessel into control volume elemen ts for which c ons erva tion

laws per ta ining to the separa te phases a re appl ied.

* Formula t ion of mass conserva t ion equat ions for individual components in each of the

phases .

* Formula t ion of phasic energy equat ions for the component mixtures .

* Descript ion of the relat ive motion between phases with an algebraic phase sl ip (drift-

flux) model.

* Irreversible chemical react ion in the l iquid phase formu lated as one of arb i tra ry o rder in

te rms of reac tant concent ra t ions wi th a tempera ture dependency given by an Arrhenius-

type expression.

The fol lowing hypotheses and assumpt ions a re present ly made:

- miscibi l i ty of al l components in the l iquid phase

- uniformity of pressure over the flow cross section

- the wall fr ict ion and accelerat ion terms in the momentum descript ion can be neglected

- the kinet ic energy terms in the energy equations can be neglected



236

- axial conduction and axial mass diffusion in the fluid can be neglected

- thermal equi l ibr ium between l iquid and vapour phases (no superhea t a t onse t of the

depressur isa t ion process)

- d is t r ibut ion of components be tween phases governed by phase equi l ibr ium re la t ions

- phase equil ibrium relat ions based on ideal gas behaviour (Dalton's law) and on ideal

l iquid solut ion behaviour (Raoul t ' s law)

I t i s wo rth point ing ou t tha t most of the above assump t ions do not represen t l imi ta t io ns

of the analy sis. Th eir el imination however requires specification of add it ion al rela t ions

conta ining para me ters th a t have to be de termin ed expe r imenta l ly (e .g . in case of non-

equil ibrium, interphase areas and interphase transfer coefficients, for non-ideal l iquid mix

tures act ivi ty coefficients etc .) .

3 .1 C O N SE R V A T I O N E Q U A T I O N S

Conservation laws are applied to the separate phases in one-dimensional Eulerian fini te

volum e elem ents. For the sole pur pos e of simplifying the pre sen tat io n of equ ation s th e

assumption is made that f low cross sect ions at the inlet and outlet boundaries of a f ini te

volume element are equal .

3 . 1 . 1 . Mass Conservation

Here mass conservation for component i is expressed in terms of concentrat ions per unit of

mixture mass. This formulat ion al lows one to separate the concepts of change in chemical

composi t ion and change of mixture densi ty and enables the der iva t ion of phasic mixture

energy conserva t ion equat ions conta ining hea t source te rms, assoc ia ted wi th chemica l re

ac t ions.

The vapour mass conservation equation in discret ized form for a component t can be

wri t ten as:

A(ag

v

fi

vi

)

_

A(G

vf

i„j)

^ y + r

m i

+ a r „ i (19)

A similar equation for the l iquid phase is:

A((l-a)

eifMi

) A ( G ,

W ;

)

^ = y T

m i

+

(1

- a)ru (20)



237

In the above equat ions a re :

Q„

and

QI

the m ixtu re densi ty in the v apour and l iquid

phase, /*„,- and fin the component mass concent ra t ions in mass per uni t of mixture mass

(which is equivalent to the component mass fract ion) in vapour and l iquid phase, G„ and G/

the vapour and l iquid mass flow rates, T

m

; t he componen t i n t e rphase mass t r anspor t r a t e

per unit of element volume, r„,- and ru the component mass product ion ra te in the vapour

and the l iquid phase per uni t of phase volume, g iven by equat ion( l8) . Physica l parameters

on the right hand side of equations(19) and (20) represent t ime average values during the

t ime s tep ( t ime centered va lues) . Pa ram eters und er the di fference op era to r a t the r ight

hand side pertain to the inlet and exit boundaries of the element.

3 . 1 . 2 . Energy Conservation

Neglec t ing the cont r ibut ions of k ine t ic energy and of axia l conduct ion to energy t ranspor t

the energy conservation equations formulated in terms of enthalpies, in discret ized form,

are for the vapour mixture :

H^BvK) A(G „/i„) Ap„

^ = y + n.„,r

m

+ qh

v

+

a

~^ I

2 1

)

and for the l iquid mixture:

A ( ( l - a ) e i M A (G iM .

r

. . . . .

>A

PI

-£1 y n

v

,T

m

+ qhi +

(l-a)—

(22)

W h e r e qh

v

and qh[ are the external he at inp ut pe r unit of elemen t volum e to vap our

and l iquid respectively, the mixture enthalpies are given by :

hv =J2î

h

" (

2 3

)

i

h

i = ^2îhii

(24)

where h

v

i i s the compo nent entha lpy in the vapou r phase a t system pressu re and tem

pe ra tu re and hn the component l iquid phase entha lpy a t the prevai l ing l iquid tempera ture

and componen t sa tu ra t ion p re ssure , and h„ , i s the vapour mixture sa tura t ion entha lpy a t

the vapour-l iquid interface.

The left hand term and the first r ight hand term in equations (21) and (22), represen

ta t ive of energy accumula t ion and energy convect ion, conta in a change in mixture entha lpy

(over t ime and distance respectively).

The above equat ions can be developed fur ther by taking in to considera t ion tha t the

component composi t ion in the separa te phases may change due to occurrence of chemica l



238

reac t ions and mas s t ransfer processes . The a im is to de termine th e to ta l volume p rodu ct ion

ra te per e lement . This can be wri t ten as:

'/'tot =

$p +

V'chem + V W (2 5)

Equat ion(25) expresses tha t the to ta l volume product ion ra te per e lement foot is due to

changes of pressure and temperature in the gas phase (\£>

p

) , a volume source term associated

wi th chemica l conversion (V^m) and volume product ion by phase change (il>

va

p)-

The ra te a t which components a re produced by chemica l reac t ion [r

v

f,r

ti

) is direc tly

related to the reactant conversion rate taking account of the stoichiometry of the react ion

equat ion. Note tha t i f the te rm rpciiem dominates equat ion(25) then even an endothermic

react ion can cause a r ise in pressure.

The to ta l volume product ion ra te in the vesse l can be found by summing the cont r ibu

t ions for al l e lements in the vessel . Equating the total volume production rate in the vessel

to the total volumetric f low rate exit ing the vessel yields the value of the depressurisat ion

rate within the vessel .

3 .2 A X I A L D I S T R I B U T I O N O F V O L U M E F L O W , V O I D F R A C T I O N A N D

C O M P O S I T I O N

With the known va lue of the e lementa l volume product ion ra te the mixture volumetr ic

flow rat es a t the element b oun darie s can be successively evalu ated a nd from p hase sl ip or

interfacial fr ict ion relat ions, as described in sect ion

2 .1 .1 ,

the phasic e lementa l volumetr ic

flow rate s and the elemen t void fract ion can be calcu lated . Th e elem ental com pon ent

dis t r ibut ion over the vapour and l iquid phases can then be ca lcula ted using the component

mass conserva t ion equat ions and the phase equi l ibr ium equat ions.

4. ILLUSTRA TIVE CALCU LATIONS

Calcula t ions wi l l be presented tha t sequent ia l ly inc lude the phenomena tha t have been

descr ibed above . Th e a im is to highl ight the imp ortanc e and re levance of cer ta in par am eter s

dur ing vent ing and to demonst ra te the complexi ty of the process .

4 .1 H Y D R O D Y N A M I C A N D M U L T I C O M P O N E N T A S P E C T S

The hydrodynamic capabi l i ty of RELIEF has been extensive ly tes ted in a recent benchmark

exercise carried out at the JRC [12]. Here various blowdown experiments using pure com

ponent fluids in different sized test facilities operating at different pressures were compared

to various code calculat ions. Some of these calculat ions were performed "blind". Figure 6

shows a comparison of such a bl ind predic t ion using RELIEF wi th the exper imenta l va lues

for the depressurisat ion of a vessel ( top venting) containing the refrigerant R114.



239

In the following eight figures (7

-

15) the importance

of

pha se equ il ibrium , interfacial

frict ion and vent locat ion wil l be considered. In all these cases chem ical reac t ion is a b

sent so the vapour p roduc t ion and subsequent level swell are due only to phase change

and vapour expansion. The s i tua t ion considered

is

the vent ing

of a

typica l type

of

ba t ch

reac to r or s torag e tank . The vesse l is cylindrical and po si t ioned vert ical ly with the vent

posi t ioned e i ther at the top of the reac tor or at the bo t to m . Th e vesse l was given the

fo l lowing d imens ions : he igh t=4 .17 m, i n t e rna l d i ame te r=0 .305 m, ven t d i ame te r=0 .02

m.

It was descret ised into 100 axial elements. In pr inc iple any n um ber of com ponen t s can

be t rea ted wi th the model but for these ca lcula t ions we wi l l res t r ic t our a t ten t ion to two

components and wil l chose fluids that have dissimilar vapour pressures.

The

fluids chosen

are the refrigerants R-l l and R-22; f igure 7 shows the vap our press ure curve s for these two

subs t ances . In all the calcula t ions the vessel is ini tial ly filled to a relat ive height of 60%

w i t h

an

in i t ia l mix ture comp osi t ion

of

20% (mass)

of

the vola t i le comp onen t and 80% of

the less volat i le component .

To test the importance of l iquid-vapo ur eq uil ibrium the re sults of two calcu lat ion s wil l

be shown.

The

f irst t rea ts the b inary mix ture

as a

t rue m ix tu re

in

which th e com posi t ion

changes dur ing the t ransient due to pha se equ il ibrium effects, the second keeps the com

posi t ion constant (pseudo one-component ) wi th the proper t ies kept equal to t hose of the

b ina ry mix tu re

at

the in i t ia l condi t ions. Figures

8

a nd

9

show the pressure and tem pera

ture histories for the two cases. Notice that the pressure of the pseudo one-component f luid

remains always above the two component f luid but t ha t t he t em pera tu re a lways rema ins

below.

4 . 1 . 1 .

Phase Slip and Vent Location

Of crucial importance is the abil i ty to describe th e ext ent of th e l iquid "swell ing' ' which in

turn defines the onset and durat ion of two-phase condit ion at the e nt ranc e to th e vent l ine .

In figures (10

-

15), the important effect

of

pha se sl ip and v ent loc at ion

is

d e m o n s t r a t e d .

In these figures two si tuat ions are considered, ie . both top and bottom venting of a vessel

conta ining a t rue mix tu re of the two refrigerants R - l l and R -22. To i l lus trate th e effect

of interfacial fr ict ion two values of sl ip have been taken; the first calculated using equation

(8) and is labelled "with slip" in the figures, the second is rep rese ntat ive of a hom ogeneous

m i x t u r e or foam, obta ine d by pu t t ing s l ip to zero and is labelled "no sl i p" .

Figure 10 shows the vessel void fraction evolution for the case

of

to p ven ting w ith sl ip.

The initial swelling of the liquid is clearly seen and after about 5 seconds t he m ixt ur e level

reaches the top of th e vessel; this signifies th e be gin nin g of two-phase ven t ing. No te th a t

a secondary mixture level

is

formed near th e m iddle

of

the vessel after ab ou t 10 seconds

which s teadi ly moves upwards and af te r about 50 seconds reaches the to p of th e vessel.

At th is t ime there is a significa nt axia l void profile in the vessel. La ter in t he t r ans i en t at

t im es bey ond 100 seconds (not shown

in

th e figure

so as to

avoid confusion) the m ixtu re

level moves downwards from the top and stops when the blowdown is complete, giving the

final si tuat ion with the remaining l iquid in the lower p ar t of th e vessel. Fig ure 11 shows

the same void fract ion evolut ion when sl ip

is

p u t

to

zero (homogeneo us condi t ions) and

a

cha racte rist ic foamy b ehav iour is seen. After 20 seconds the vessel is com pletely fi lled w ith



240

a uniform mixture, and the void fract ion becomes a function of t ime only and not vessel

height . No set t l ing out of the fluid wil l occur at the end of the transient .

Figures 12 and 13 i l lust ra te wha t happ ens in the identica l case wi th b ot t om vent ing.

For the case where there is phase sl ip one again sees a moving mixture level but in this case

i t steadily moves downwards at an almost constant speed. At about 40 seconds the vessel

is voided and the vessel pressure will then fall rapidly (see figure 14). For the homogeneous

case with no sl ip the transient is characterised by the mixture level remaining at the height

of the ini t ial f i l l ing and with a constant void distr ibution below this level .

The consequence of there being an interphase sl ip on the global parameters is vividly

shown in figures 14 and 15. Th e system pre ssure histo ries are shown in figure 14 and

de m on str ate s the stron g influence of bo th vent pos i t ion and phase sl ip. O ne shou ld no te

th at th e curves for top and bo tto m venting show even a quali tat ively different beh avio ur,

and that for a certain period of t ime top venting can result in the highest pressure. Figure

15 show s th e correspon ding norm alised m ass inventory histories where significantly different

masses are vented. This can have major consequences when one has to consider the design

of dow ns t ream equ ipment .

4 .2 C H E M I C A L R E A C T I O N T Y P E A N D S C A L E D E P E N D E N C Y

Two types of chemical react ions wil l be considered, the first is typical of a polymerisat ion

react ion where the more volat i le component is converted into the less volat i le component ,

the second i s a decomposi t ion reac t ion forming a gaseous product . Calcula t ions were per

formed where sl ip was modelled, again using by equation(8) and where sl ip was put to zero.

The two components had vapour pressures that differed by a factor of ten and the ini t ial

m ass fract ion for each com pon ent was set to 80% for the mo re volat i le com po nen t an d 20%

for the less volat i le com po nen t . Th e vent l ine was posi t ion ed a t the to p of the vessel and the

relief valve was set to open at an o verpressure of ab ou t 10%. Fig ure 16 show s the influence

of phase sl ip on the pressure history, and demonstrates that for this type of react ion a sl ip

between the phases reduces the tendency for runaway.

T he influence of vessel dim ensio n is show n in figure 17 wh ere calc ula tion s have b een

performed for two vessel having th e same volume b ut wi th different le ngth s ( 0.4m and

4.0m ). A comparison of figures 16 and 17 leads one to believe that the effect of reducing

the vessel height has a similar effect to th at of increasing th e pha se sl ip. Th e ph ysical

explanation for this scale effect is that within the vessel bubbles rise with the same veloci ty

independent of vessel height so their residence time in the liquid is larger for longer vessels.

This results in an increase in the "swelling" of the liquid for the longer vessel and hence

increases the probabil i ty of obtaining two-phase flow condit ions at the entrance to the vent

l ine.

Th is in turn reduces significantly th e pressure rel ieving capab il i ty of a given vent

geometry.

It is interest ing to see whether these conclusions are universal ly val id or are specific

to react ion typ e. Figu res 18 and 19 show similar calcu lat ions for the deco mp osit ion of

hyd roge n pero xide. Th is react io n has been studied in deta i l beca use we have recently

performed such exper iments here a t the JRC. Here one sees tha t the tendencies a re exac t ly

the reverse of those seen with the polymerisat ion react ion.



241

To explain this one has to appreciate that the l iquid mixture is ini t ial ly subcooled

and the gaseous phase i s pr imari ly composed of oxygen f rom the decomposi t ion reac t ion,

which has no late nt heat of vap orisat io n associated with i t . There fore, the pressu re an d

temperature within the vessel are effectively decoupled. Once the relief valve opens (sa 100

seconds into the transient for a rel ief set pressure of 2 bar) the vessel pressure remains close

to the outer pressure unti l the onset of runaway, and oxygen is vented from the vessel . For

homogeneous condit ions (zero phase sl ip) or for sl ip when we consider the longer vessel

more l iquid swell ing occurs. If the mixture level reaches the elevation of the vent l ine then

two-phase fluid wil l be vented and since the temperature and pressure are decoupled there

is no feedback on fluid temperature (and hence react ion rate) of any increase in vessel

pressure due to th is ear ly two-phase vent ing. Of importance however , i s tha t reac tant mass

is vented in this case. Th us when run awa y occurs the re is less hyd roge n perox ide in the

vessel if hom ogen eous co ndit ion s or the longer vessel are consid ered. Th is the n res ults in

lower peak pressures than the corresponding cases where inter phase sl ip is modelled or a

shorter vessel is considered.

4 .3 VE N T SIZING

As an example of how RELIEF can be used to size a venting system, or to calculate the

consequences of using an exist ing system for a given react ion, we wil l consider the hydrogen

peroxide decompostion now in more detai l . The results presented here refer to a vessel of 1

m

3

with an ini t ial f i l l ing of 60%. The l iquid composit ion is 20% H

2

0

2

and 80% H

2

0. The

rel ief valve was set to a very small overpressure so that the vent can be assumed to be open

at a t ime close to zero. Figures 20 and 21 show the results from calculat ions using three

different vent diameters. The first assumes a zero vent diameter and therefore represents

the closed adiabatic case. The other two calculat ions have vent diameters of 2cm and 5 cm

respectively.

Figu re 20 shows the tem per a tu re his tor ies and wh at is imm edia te ly app aren t i s th a t the

vent size has a negligible effect on the ini t ial heat up ph ase (say up to 6 m in ). Th erea fter,

up unt i l the maximum tempera ture i s achieved, the di f fe rences a re mainly be tween the

closed vessel and the vented vessel . This means that for a vented vessel the t ime for the

ons et of runaw ay is to a fi rst app rox ima tion in dep end ent of th e vent area. On e should also

note th at th e value of peak te m pe rat ur e is l i t t le affected by the ventin g process, ra ngin g

from 184 C for the adiabatic case to 175 C for a vent diameter of 5cm.

Figu re 21 show s the corre spo nding pressu re histories and here one sees th at vent size

has a significant effect on the press ure. Th e tem pe ra tur es an d pressure s are effectively

decoupled. The reason for th is i s tha t dur ing the hea t up and runaway the system pressure

is always above the saturat ion value of the mixture, which means that the gaseous phase is

virtual ly entirely made up from the oxygen l iberated from the decomposit ion react ion. In

fact boiling of the liquid only occurs after all the H

2

0

2

has been consum ed and the pressure

fal ls below the saturat ion value. This occurs at 7min 40sec for the 5cm vent and at 8min

35sec for the 2cm vent where a dist inct change in the gradient of the temperature trace can

be seen.



242

Norma. operation

h

Mixture level

i<

o o

O O (

Runaway situation

£

Vapou.

r generation

Fig

1.

M i x t u r e level does no t reach

vent location, practically al l

vapour venting

Reactor level swell

Mixture level reaches vent

location, two-phase ver.tin

_

>

o

>

LJ

u

ex

u .

u .

a

£

o

o

_ l

Lu

>

I/ ]

a

0 .50

0.

40

0 .30

0.C0

0 .10

0 .00

■

/ \

■ / \

:

/

V

/

-

. . I . . . . F . . . . 1 . . 1 - . . . t

0.

20

0 . 50

0 .

70

VOID

FRACTION

Fig

2. Phasic velocity difference as a function of void fraction



243

2. 40

2 . 20

2 . 00

1.80

1.60

1.40

1.20

1.00

fV

^

■

\

•

\

:

N .

\ . ;

^ - ^ _ _

:

TIME

I s a c )

Fig

3. Depressurisation history for two-phase venting

2 . 4 0

2 . 2 0

2 . 0 0

1.80

1.60

1.40

1.

20

1.00

\

N .

^ ^ ^ - .

•

-

-

-

-

_ ^ ^

~~ ~~-

4 0 . 0

TIME I s o c l

Fig

4. Depressurisation history for all vapour venting



244

' d ew

h

T

bub

T)

l \

-X \

1 ' >v

-

r

- - t - - ^

- f

_

r

i i

r-£t*„

i

'

* . , , ;= 0.25 1

I I . I I

= 0.7

100%

B

100%

A

Fig 5.

Phase

equilibrium

diagram

for

a

binary

mixture

of

components

A

and

B

-z .

n-

i

ft

I d

u.

0-

7.00

6.00

5.00

2.00

1.00

0.00

K

- ^

•

\ ,

\»

\ \«

\

¥

»

-

_

E X P E RIME NT

/

V P R E D I C T I O N

^ ♦

^ - - V

TIME

( S )

Fig

6.

Vessel

depressurisation

of

refrigerant

R114;

blind

prediction



245

*

-

S

S -

•s ^ ^

R-22/ sS^

y ^ ^

/ ^^

s^

/ >^

y^

/ y^

/ ys

/ j r

R-iy

/

240.

280. 320.

Temperature (Kalvin I

Fig 7. Vap our pres sure of R-ll and R-22

Timm ( s e c o n d s )

T n*e t seco nds 1

Figs 8. & 9. Pressure and t empera tu re histories for a

pseudo one-component Quid and for a two component Quid



246

Vo i d F r e c t io n

Fig 10. Axial void profile evolution

Top venting - with phase slip

60 . 0

50 . 0

40 .0

30 . 0

20 . 0

10 . 0

:

;

0

se

' I i

■

1

2

1 j

i

]

5s

■ r ' '

l

'

JJ J

/ :

1 j — '

1

i i

i i

;

1 i

i i

i i

j 10 s j 20 s

■

i

j 1

i i

i i

i

| i

i

1

i , i .

-* - • ■ 7 1 ' '

T

1

I

i

i

|

i 5 0 s

1

0 .<0 0. CO

Vo i d F r a c t I o n

Fig

11 . Axial void profile evolution

Top venting - without phase slip



247

eo.o

8 0 . 0

7 0 . 0

SO.

0

4 0 . 0

3 0 . 0

2 0 . 0

1 0 . 0

0 . 0

:

:

- /

/

/

/

/

/ /

/ /

-

i

0

sec.

10 s

20

s

30 s

40

s

i-»

r

■

i

i

■

|

■

i

■

.

-

.

■

;

jS — ;—-

r

--7—-;-- . . .

0. «0 0 . 60

V o i d

F r o c t I o n

Fig 12. Axial void profile evolution

Bottom venting - with phase slip

BO.

0

BO.

0

70 . 0

50 .

0

40 . 0

30 . 0

20 . 0

10.0

0 .0

:

:

-

:

-

0

,

. . . . . . . . .

sec.

r

10 s\

1.

. . . . .

20 s

. . . . i

■ ■ ■

30 s

i i . i ■ ■ ■

-

-

.

/

s j

|

i

:

0.40 0.60

Void FroctIon

Fig

13. Axial void profile evolution Bottom venting

-

without phase slip



248

60 .

120.

T l « « ( s e c o n d s )

Fig 14. Pressure histories

for

different inter phase slip

and

venting modes

0 so

0. BO

0.70

0 . 60

0. 50

0.

40

0 . 30

0 . 20

0 . 10

0

00

^ \

\

^

^

- \ \ ^ ^ ^ \

\

\

^ ^ ^ ^ ^ ^

top

venting/with slip

' \ \ ^ ^ _ _ J

\

\

:

\\

x

\\ \

\ \ top

venting/no slip

\\

^

\\

^

\\

N :

\

\

x

\ \

x

\ \ \

; \ \

ottom \ \ \

with slip \ \

s

\

~~\

—

N

-

\ \ n o slip """""--^

v_ \ .

6 0 . 120.

T i r>« ( s e c o n d s ]

Fig 15.

Mass inventory histories for different inter ph ase slip and venting modes



249

ao.

120. lco. 20a.

TIHE ( seconds )

Fig 16. Influen ce of inter p h a s e slip on the pressure history

a. 10- o

Polymerisation reaction

long vessel

BO.

1 2 0 .

rinE I atconda )

Fig 17. Influence of vessel length on the pressure history



250

90 . 0

BO.

0

70 . 0

60 . 0

50 . 0

40 . 0

30 . 0

20 . 0

10 . 0

0 .0

■ ■ ■ , . . . . | i ■ i . ] ■

|

i

ecomposition reaction

|

1

1

1

1

//

h

/

/

J

■

with slip

■

\

\

\

\

\ \ n o slip

T l f l E s t c o n d a

Figl8 . Influence of inter phase slip on the pressure history

9; 20 . 0

400.

500.

TIME I s e c o n d s

Fig

19. Influence of vessel length on the pressure history



251

1 1 ] ■ ■ ■ ■ ■

0 cm

.X

ii \ ■

\

1 V S cm

:

4 :00 0 :00

Fig 20 . Influence of valve size on the t emper a tu r e history

Fig 21 . Influence of

va lve

size on the pressure history



252

REFERENCES

1) H.A. Du xbu ry, A .J. Wilday, ICh em E Sy m p. Series No 102, 175-186, 1987.

2) H .A. D uxb ury , A .J. Wilday, "Efficient design of reac tor relief sys tem s"

Interna t ional Symp. on Runaway React ions, Boston, Massachuse t t s , March 1989.

3) W .B . Wal l is , "One-dimensional Two-phase Flow ", M cGraw Hi l l , New York 1969.

4) M . Ishii "The rmo -Fluid Dyna mic Theory of Tw o-Ph ase Flow ", Eyrol les , Par i s . 1975.

5) F.N . Peebles , H.J . Ga rber , Ch em E ng Prog r , Vol49, 88-97, 1953 .

6) M. Ishi i , N. Zuber, "Drag coefficient and relat ive veloci ty in bubbly, droplet or part ic

ulate f lows", J.AIChE, Vol25, No5, 843-855, 1979.

7) N. Zub er , J . Hench, Rept n o. 62G L100, Genera l Elec t r ic Com pany, Schenectady, N.Y . ,

1962.

8) A.E. Fi l imonov, M.M. Przhiylkovski , E .P. Dik, I .N. Pe t rova , Teploenerge t ika 4(10) ,

22-26 ,

1957.

9) M .A. Styr ikovich, A.V. Surnov, Y .G. Vinok ur , Teploenerge t ika 8(9) , 56-60, 1961.

10) G.C. Gardner , "Frac t ional vapour content of a l iquid pool through which vapour i s

bubbled", Int . J. Mult iphase Flow, Vol 6, 399-410, 1980.

11) I . Kataoka, M. Ishi i , "Drift f lux model for large diameter pipe and new correlat ion for

pool void fract ion", Int . J. Heat and Mass Transfer, Vol (30) 1927-1939, 1987.

12) A.N. Skouloudis, "Fifteen benchmark exercises on vessel depressurisat ion with non-

react in g fluids", E U R 12602 EN , 1989.

13) L . Fr iede l , 5 th In t . S ym p. on Loss Preve nt ion, paper 4 3 , Can nes, 1986.

14) G. Friz , W. Riebold, W. Schulze, "Studies on thermodynamic non-equil ibrium in flash

ing water" , OECD Specia l i s t s meet ing on t ransient two-phase f low, Toronto, Aug 1976.



253

NOM E NCLA T URE

C

C

P

E

Y

G

U

h

P

R

r

ffc

T

V

X

9

F„

C

d

D

H

K

Concen t ra t ion

specific heat at constant pressure

act ivat ion energy

volume fract ion

axial mass flow rate

velocity

entha lpy

pressure

gas constant

component mass product ion ra te per uni t of phase volume

bubble radius

abso lu t e t empera tu re

volume of computa t ional e lement

component mole f rac t ion

accelerat ion due to gravity

wall friction force

drag coefficient

hydraul ic d iameter

phase equi l ibr ium ra t io

k g m "

3

J k g ^ K -

1

Jkinol"

1

m

3

/ m

3

k g s -

1

m s "

1

J k g -

1

N m "

2

J k m o l ^ K -

1

k g m

- 3

s

_ 1

m

K

m

3

kmol/kmol

m a

- 2

k g m

- 2

s

- 2

m

Greek symbols

a

vap our volume fract ion m

3

/ m

3

T

m

phase change in t e rphase mass t r ansp or t r a t e kg m

_ 3

s

_ 1

\i com pone nt mass concen t ra t ions

g densi ty kg m

- 3

surface tension N m

- 1

<7

r f

volume prod uct ion ra te m

3

a

_ 1

n interfacial dra g force k g m

_ 2

s

- 2

7 ac tiv ity coefficient

Subscr ipts

t component

/ l iquid pha se

v vapour phase

s sa tu ra t ed

in t interface





E M E R G E N C Y R E L I E F S Y S T E M S I Z I N G : V E N T L I N E F L U I D F L O W S

A .

B E N U Z Z I

Institute of Safety

Technology,

JRC Ispra,


21020 Ispra.

(VA), Italy.

A B S T R A C T . This lecture is a review of the methods developed to calculate the critical flow during the

emergency pressure relief of a chemical reactor or a storage tank. The fundamentals of the single-phase

and two-p hase critical

flows

are discussed but the emphasis is put mainly on the simplified formulations

recently developed (DIERS) in order to provide quick and simple-to-use vent sizing methods appropriate

for safety requirements.

1 .

I n t r o d u c t i o n

Th e scope of t h i s l ec tu re is t o r ev iew th e ca l cu l a t ion me th od s cur re n t ly employed

to eva lua te the c r i t ica l mass f lux G ( = pu ) i n t h e ven t ing l i ne wh en for some reaso n

( runaway reac t ion o r ex t e rna l f i r e ) t he p re ssure i n t he reac to r (o r s to rage t ank) r eaches

the "se t" va lue or the va lue a t which the pressure re l ie f device wi l l be ful ly open. I t i s

we ll know n th a t u nd e r t hese cond i t i ons two -pha se f low wi ll m os t l ike ly occur / l / and

tha t t h i s s i t ua t ion repre sen t s t he mos t seve re r equ i rement fo r t he ven t s i z ing . In f ac t ,

t he p re ssure r i se i n t he reac to r i s r e l a t ed to t he vo lume inc rease p roduced by vapour o r

gas genera t ion due to the e ffec t of the energy sources . Pressure re l ie f requi res a ba lance

b e t w e e n t h e v o l u m e t r i c v a p o u r / g a s g e n e r a t i o n r a t e a n d t h e v o l u m e t r i c d i s c h a r g e f l o w

r a t e . F ig . 1 t ak en from / 2 / an d re fe r red to s ty re ne p rop e r t i e s a t 0 .5 M P a , shows t h a t

bo th the mass f l ux

G

a n d t h e t w o - p h a s e d e n s i t y

p

decr ease as th e in le t void f rac t ion a

inc reases . In con t ra s t , t he vo lume t r i c f l ow

G/p

i s found to increase as

a

increases; for

pure gas f low (a = l ) G/p i s ab ou t 20 t im es la rger th an for a l l - l iquid (a = 0) flow.

As a consequence , two-phase f lows need l a rge r ven t a rea s compared to pure gas f l ows ,

in ord er to assu re the sa m e rel ie f capa c i ty . I f a l imi ted pre ssu re increase ( e .g: 20% of

the se t p re ssure ) i s t o l e ra t ed dur ing the ven t ing , a s ign i f i can t r educ t ion in t he ven t

area wi l l be possible . Therefore the eva lua t ion of the mass f lux G for two-phase f low

con di t i on s repre sen t s a key s t e p in t he emergency re li ef sys t em s (ER S) des ign . Th i s

lec ture wi l l be l imi ted to f lows in the fol lowing boundar ies (see Fig . 2 ) :

Tubes ( l ong p ipes ) wi th cy l indr i ca l o r annu la r geome t ry , cons t an t o r va r i ab l e

c ross sec t ion and a rb i t r a ry inc l ina t ion . Fr i c t i on losse s a re a lways impor t an t .

Nozz le s cha rac t e r i zed by va r iab l e c ross sec t ion (con ve rg ing /d ive rg ing ) an d

shor t length which de termines negl igible f r ic t ion losses .

255

A. Bemtzzi and J. M . Zaldivar (eds.). Safely of Chemical Batch Reactors a nd Storage Tanks, 255-284.

© 1991

ECSC,

EEC,

EAEC,




256

Ori f i ce s (d i aphragms) which a re supposed to r epre sen t t ubes wi th ze ro -

length . Specia l cases a re rupture disks , sa fe ty re l ie f va lves and wal l breaks

which a re r epre s en ted by com bina t ions of t he p rev ious ly ment io ned e l em ent s .

1.1. UNSTEADY-STATE SINGLE PHASE CRITICAL FLOW

A lth ou gh t he the ory of s ingle -phas e cr i t ica l flows is wel l kn ow n, ne ver th e less i t is

worthwhi le to reca l l here i t s basic aspec ts in order to make easier the extension of the

form ula t io n to two -ph ase cr i t ica l f lows. Co nsid er ing a f low sy ste m formed by a pipe

a t t ached to a cons t an t p re ssure r e se rvo i r on one end and to a l a rge rece ive r on the

o t h e r e n d , w h e n t h e d o w n s t r e a m p r e s s u r e is r e d u c e d b e l ow t h a t of t h e u p s t r e a m v a l u e ,

a p re s sure g rad ien t i s se t up in t he p ip e an d th e f low beg in s . A s t ea dy -s t a t e i s r eached

when the pressure gradient forces a re ba lanced by the f r ic t iona l and iner t ia l forces . I f

t he t he rmodynamic s t a t e o f t he f l u id i n t he ups t ream re se rvo i r i s kep t cons t an t , de

c reas ing the downs t ream pre ssure wi l l p roduce an inc reased f low ra t e un t i l a max imum

va lue is r eache d . A t t h i s po in t , fu r the r r e duc t ions in t h e do w ns t rea m pre s sure wil l p ro

du ce no effec t. T he ma xi m um f low ra te va lue is ca l led "cr i t ica l" an d rep res en ts a l imi t

in t he d i scha rge p rocess t ha t has t o be de t e rmined wi th accuracy in many eng inee r ing

p r o b l e m s .

The c r i t i c a l f l ow usua l ly occurs when the Mach number i s equa l t o one a t t he

sma l l e s t c ross sec t ion o f t he p ipe . In t h i s cond i t i on a do w ns t re am pe r tu rb a t i on (e .g :

change o f p re ssure ) canno t be t r ansmi t t ed ups t ream and the f l ow ra t e i s no longe r

inf luenced by the changes in the rece iver presssure . Le t us consider the se t of par t ia l

di f fe rent ia l equat ions descr ibing the t ransient compressible f low in a rec t i l inear p ipe of

var iable c ross sec t ion A and inc l ina t ion 0 wi th re sp ec t t o t he hor i zon ta l p l an e .

at ( M ) + h ( M « ) = 0 ( M a s s )

f t (pAu) + j ^ (pAu

2

) + f^ (Ap) = -x

T

w + Apg cos 0 ( M o m e n t u m )

j

t

[Ap (h + £ ) ] + f

z

[Apu (A + T ) ] = X9w + ApgucosO ( E n e r g y )

(1)

w h e r e p, u , p and h a re f lu id densi ty , ve loc i ty , pressure and spec i f ic entha lpy, respec

t i ve ly . In add i t i on , T

W

a n d q

w

a re shear forces and he a t f lux a t th e wal l of th e pip e , x i s

a coe f f i c i en t ob ta ined th rough appropr i a t e cor re l a t i ons and g is t h e g rav i ty acce l e ra t ion .

Equa t ions 1 ) have to be coup led wi th t he cons t i t u t ive l aw:

P = f(p,h) (2)

t o c lo se t h e s y s t e m . E q u a t i o n s l ) c a n b e e x p r e s se d in m a t r i x fo r m / 3 / :



257

(4)

a n d A , B , r a re funct ion s of p ,

u, h

Eigenvalues of the system 3) a re given by the solut ion of :

det(B - AA ) = 0 (6)

which i s a t h i r d o rde r po lyno mia l . Th e roo t s o f 6 ) dep end on th e co m po ne n t s of

/ . T h e s o u r c e t e r m s r e p r e s e n t e d by r do no t p lay any role in eq ua t io n 6 . T he rea l

pa r t o f any roo t A( r ) j g ives t he ve loc ity of s igna l p ro pa ga t io n a long the cor r e sp ond ing

c h a r a c t e r i s t i c p a t h i n t h e z, t p l ane . Th e ima gina ry pa r t o f any com plex roo t A( i)

t

-

g ives t he ra t e of g row th o r decay o f t h e s igna l p rop ag a t in g a long i t s r e spec t ive pa th .

For a hype rbo l i c sys t em in which a l l t he roo t s o f 6 ) a re r ea l and non-ze ro , t he number

o f b o u n d a r y c o n d i t i o n s r e q u i r e d a t a n y b o u n d a r y p o i n t c a n b e s h o w n t o e q u a l t h e

num ber o f cha rac t e r i s t i c l ine s en t e r ing t he so lu t ion reg ion a s t increases . I f system 1)

is appl ied in the par t icular spa t ia l region 0 < z < L a n d t h e b o u n d a r y c o n d i t i o n s a t

z = L a re exa m ine d, i t fo l lows th a t as long as any A,- i s less th an zero , som e bo un da ry

in form a t ion m us t be supp l i ed in o rde r t o ob ta in t h e so lu t ion . If, on the o the r h an d , a l l

t h e A,- a re g rea t e r t h an o r equa l t o ze ro , t he n no bo un da ry co nd i t i o ns a re needed a t

z = L a nd th e in t e r io r so lu t ion is una f fec ted by con d i t i on s bey ond th i s bo un da r y . A

c r i t ica l ( choked) cond i t i on ex i s t s w hen no in fo rm a t ion can p ro pa ga te in to t he so lu t ion

reg ion f rom the ex t e r io r . Such a cond i t i on ex i s t s a t t he bounda ry po in t z = L w h e n :

Ay = 0 for so m e j' < 3 (7)

A, > 0 for all i f j (8)

These a re t he ma thema t i ca l cond i t i ons sa t i s f i ed by the equa t ions o f mot ion fo r a

f lowing f lu id when reduct ion in downst ream pressure ceases to cause an increased f low

r a t e .

I t i s wel l -known tha t the choked-f low condi t ion for s ingle-phase f low occurs when

the f lu id ve loc i ty just equals the loca l sound speed.

1.2. STEADY-STATE SINGLE PHASE CRITICAL FLOW

For s t eady-s t a t e f l ow the t ime de r iva t ives i n equa t ions 1 ) become ze ro and the ma t r ix

equa t ion 3 ) r educes t o :

B

A

f = r

(9)



258

and the f low is c r i t ica l when the fol lowing condi t ions a re ful f i l led somewhere a long the

pipe :

det[B) =

0 (10)

det

( B P > ) = 0 t ' = 1 ,2 ,3 (11)

W h e r e B ^ is t h e m a t r i x o b t a i n e d by s u b s t i t u t i n g in ( B ) t h e i co lumn wi th r .

F ig . 3 t aken f rom / 4 / shows in a (p , z ) p l ane , for a nozz l e , t h e curve de t (B ) = 0

a long which the ve loc i ty a ssumes the c r i t i c a l va lue , sepa ra t ing the uppe r subc r i t i ca l

reg ion f rom the lower supe rc r i t i c a l r eg ion . In t he same d i agram the curve det (Ti^

1

') =

0 i s t h e l ocus o f m ax im um v a lues for t he p re s sure i n t h e supe rc r i t i c a l r eg ion an d

th e locus o f m in im um va lues for t he p re ssure in t h e subc r i t i ca l r eg ion . Th e p o in t

S{Pa

z

c) rep res en ts con di t io ns 10) an d 11) s im ul ta neo usly fulf il led . E qu at io n 11) i s

a compa t ib i l i t y cond i t i on which ensure s an inde t e rmina te i ns t ead o f an imposs ib l e

solut ion of 9) a t the c r i t ica l sec t ion.

I f f r ic t ion and head effec ts a re negl igible and the c ross sec t ion area i s constant , the

ene rgy ba l an ce equa t io n can be w r i t t e n fo r s t ea dy s t a t e t u r bu len t flows / 5 / a s fo llows:

udu + vdp = 0 (12)

w h e r e v = l / p i s th e spec if ic volum e of th e flu id an d the co nt in ui ty eq ua t ion c an b e

expressed a s :

Gv = u wh ere G i s t h e ma ss flux (kg /m2 s) (13 )

di f fe renc ing 13) wi th respec t to p , one obta ins:

du dG dv . .

dp dp dp

c o n s i d e r i n g t h e m a x i m u m o f G wi th respec t to p i .e .

d

Z,

0

wh ich is th e c r i t ica l

cond i t i on , we ge t :

du dv . .

T

P

= Gmax

Tp

( 1 5 )

and combin ing wi th 12 ) we ob ta in :

dv , .

v + uG

max

— = 0 (16)

o r

~ dv

v

+

Gl

ax

v-=0



,2 l '

d v

\

259

G

» » = - U J

(17)

w h e r e G

max

i s th e c r i t ica l m as s flux, an d p an d

v

t he p re ssure and spec i f i c vo lume ,

respec t ive ly , a t the exi t of the discharging l ine .

2 .

P e c u l i a r i t i e s o f T w o - p h a s e C r i t i c a l F l o w s

Two-phase c r i t i c a l f l ow of a s ing le -componen t mix tu re i s much more compl i ca t ed than

t h e c o r r e s p o n d i n g s in g l e p h a s e flo w d u e t o a n u m b e r of p h e n o m e n a / 6 / . T h e s e a r e :

1) change of phase , boi l ing ( f lashing) or condensa t ion; 2) s l ip or re la t ive ve loc i ty be

tween the phases; 3 ) f low pat te rn (or f low regime) and 4) possible depar ture f rom

t h e r m o d y n a m i c e q u i l i b r i u m . T h e fir st of t h e s e p h e n o m e n a o c c u r s b e c a u s e t h e r e is a

p re ssure va r i a t i on a long the l i ne . Gene ra l ly , t he ex i t qua l i t y (pe r cen t vapour by mass)

increases for low ini t ia l qua l i ty va lues and decreases for h igh in i t ia l qua l i ty va lues , i f

t h e expa ns ion i s a ssu me d to be i sen t rop ic / 7 / . S l ip t akes p l ace ma in ly becau se th e

vapour phase i s l e ss dense than the l i qu id phase and , t he re fo re i s more in t ens ive ly ac

ce l e ra t ed by the ac t ing fo rces . Fr i c t i on be tween the phases and l i qu id en t ra inment by

the va po ur t end to r educ e th e re l a t i ve ve loc i ty be tween th e pha ses . T hes e p he no m en a

are s t rongly inf luenced by the f low pat te rns ( f low regimes) or , in o ther words, by the

topo log ica l s t ruc tu re o f t he i n t e r face be tween the phases . In F ig . 4 t he ma in f low pa t

t e r n s a r e d e p i c t e d . I t is e v i d e n t t h a t m a s s , m o m e n t u m a n d e n e r g y e x c h a n g e s b e t w e e n

the phases wi l l be s t rong ly dependen t on the f l ow reg ime occur r ing . However t he f l ow

reg ime p red ic t ion and the eva lua t ion o f t he f l ow reg ime t r ans i t i ons a re p rob lems which

s t il l need more re sea rch work . Lack of t he rm od yn am ic equ i l i b r iu m, h as been shown to

exis t in or i fices an d nozzles or , in gen era l , in sh or t p ip es (L < 0 .1 m ) / 5 / . In s ingle-

ph as e cr i t ica l flows, even if th e ve loc i t ies a re high, mo lecu lar re laxa t ion ph en om en a

a re su ff ic ien tly r ap id for t he vap ou r t o be rega rd ed a s i n t h e rm od yn am ic equ i l i b r ium .

For two-phase cr i t ica l f lows, on the cont rary , re laxa t ion t imes for the format ion of new

in te r faces (nuc lea t ion) , hea t , mass and momentum t ransfe r , and the evo lu t ion o f f l ow

pa t t e rns a re comparab le wi th t he t ime spen t by the f l u id i n t he c r i t i c a l r eg ion o f r ap id

p r o p e r t y c h a n g e . W i t h a s a t u r a t e d o r s u b c o o l e d l iq u i d , d e p a r t u r e f r o m t h e r m o d y

namic equi l ibr ium can occur because of the de lay in in i t ia t ion of boi l ing as the f lu id

flows in to a reg ion in which the p re ssure is be low i t s sa tu ra t io n t em pe ra tu re . Th i s

de lay can occur because of the lack of nuclea t ion s i tes for evapora t ion or because of

the shor t t ime o f expans ion , o r bo th . In t he ca se o f sa tu ra t ed vapour which i s coo l ing

dur ing an i sent ropic expansion, nuc lea t ion s i tes a re needed. I f the radi i of the nucle i

a re sma l l , l a rge subcoo l ing can be reached . In t h i s s i t ua t ion a "condensa t ion shock"

or the sudden format ion of a c loud of f ine l iquid drople ts , can develop, g iving r i se to

a

press ure pulse . Ne ver th e less for long pipe s (L > 0 . 1m ) th e e ffec ts of th e lack of

t h e r m o d y n a m i c e q u i l i b r i u m a r e , in g e n e r al , n e g li g ib l e / 7 / . F i g . 5 i l l u s t r a t e s t h e t y p i

ca l p re s sure p ro fi le in a l ong p ipe and the p re sence of equ i l i b r iu m a nd non equ i l i b r ium

regions for two-phase f low.



260

2.1. G O V ERN I N G EQ U A TI O N S F O R TW O - P H A S E CRI TI CA L F LO W S

For uns t eady , compress ib l e , two-phase f lows , t he ba l ance equa t ions cor re spond ing to

th e sys t em 1) a re l i s ted in Tab le I / 8 / t oge the r wi th t h e exp lana t io n o f t h e t e r m s . Th e

va r i ab l e a r ep re sen t s t he vo lum e t r i c f r ac t ion o f t h e pha se A; ( J ^

a

k = 1) )• N ot e

tha t t he number o f equa t ions i s 6 ( i nd ices k an d i vary f rom 1 to 2 , an d rep res en t l iquid

(1) an d vap ou r (2 ) ) ; t he subsc r ip t s I ,g an d m cor re spo nd to l i qu id , ga s (vapou r ) a nd

mix tu re , r e spec t ive ly . The equa t ions o f Tab le I have to be comple t ed wi th appropr i a t e

c o n s t i t u t i v e r e l a t i o n s h i p s d e s c r i b i n g t h e m a s s , m o m e n t u m a n d h e a t e x c h a n g e b e t w e e n

th e phases an d be tween t he pha ses an d th e bo un da r i e s an d wi th t he e .o. s . o f t he l i qu id

an d vapou r . Th e sys t em of equ a t ion s dep ic t ed in Tab le I can be expressed in m a t r ix

form:

w he re th e t ra ns po se of / i s g iven by:

f = ( p . u ^ h ^ U g . h g . a ) (19)

and r i s the source te rm vec tor which i s the r ight hand s ide of the s ix equat ions given in

Tab le I . The ma thema t i ca l c r i t i c a l f l ow cond i t i ons fo r uns t eady and s t eady-s t a t e f l ows

a re fo rma l ly t h e sam e a s t hos e o f t h e cor re sp ond ing s ing le -ph ase ca ses ( eqn s 6 , 7 , 8 ,

9 , 10, 11) , exce pt for th e fac t th a t th e order of th e poly no mi als is 6 ins tea d of 3 . T h e

mo de l p re sen ted in Tab le I , c a ll ed "mech an i s t i c " o r "Tw o- f lu id" , i n p r inc ip l e ap pe a rs

capab le o f r epre sen t ing a l l t he r ecogn ized nonequ i l i b r ium phenomena occur ing in two-

pha se c r it i c a l f lows. I t ha s been used , w i th mino r modi f i ca t ions , i n va r ious com pu te r

cod es re la ted to nucle ar reac to r safe ty ana ly sis . T he f lu id consid ered i s w ate r which is

ve ry we l l cha rac t e r i zed fo r t he rmophys i ca l and fo r exchange p rope r t i e s i n t he two-phase

region . T his i s no t th e case for o th er s ingle-co mp one nt f lu ids, a nd p ar t ic ular ly , for the

m u l t i c o m p o n e n t m i x t u r e s e n c o u n t e r e d i n t h e c h em i c a l i n d u s t r y . Fo r s u c h s y s t e m s t h e

"Two-f luid" approach, due to the lack of knowledge on the coeff ic ients of the equat ions

sho wn in Tab le I , i s d i ff icult to use . Ne ver th e less , f rom th e the ore t ica l p oin t of v iew

the re is no do ub t t h a t it i s t h e more rigorous m e th od .

2.2.

S I M P LI F IED F O RM U LA TI O N S ( H EM , H F M , ERM )

A current s impl i f ica t ion made for the eva lua t ion of the c r i t ica l mass f lux i s the as

su m pt i on th a t t he two-p hase m ix t u r e i s an hom ogen eous flu id wi th li qu id an d va po ur

h a v i n g e q u a l v e l o c i t i e s a n d t e m p e r a t u r e s ( H o m o g e n e o u s E q u i l i b r i u m M o d e l - H E M ) .

The spec i f ic volume of the mixture i s g iven by:

v = v

t

(l - x) + v

g

x (20)

Where x i s the vapour qual i ty . The s tandard expression for the c r i t ica l f low 17)

i s coup led wi th a m om en tu m conse rv a t ion (Be rnou l l i ) / 7 / equ a t ion which fo r a nozzl e

t akes t he fo rm:



" i L Jpo

dp

261

(21)

w h e r e s u b s c r i p t s 0 a n d 1 i n d i c a t e s t a g n a t i o n a n d e x t e r n a l ( d o w n s t r e a m ) c o n d i

t i ons , r e spec t ive ly . For a l ong p ipe the Be rnou l l i equa t ion t akes t he fo rm:

2po

vi

(

1 _ M _

JUL f

H

n

*dH

V

1

Vaj viPo Jo

P

H

J

0

L

' v*dL*+ K

0

v*

0

+2{v{-

v*

0

)

(22)

w h e r e v*,p* a re dim ensio nless speci fic volu m e an d den si ty , respe c t ive ly . L* —

4./L/D i s a d imens ion le ss l eng th (f is t h e Fan n ing fac to r , D is t h e d i a me te r an d L the

length of the pipe) , H i s the ne t change in e leva t ion and

K

0

is th e en try loss coefficient.

T h e t e r m 1

— p\jp

0

r e p r e s e n t s t h e t o t a l p r e s s u r e d r o p b e t w e e n s t a g n a t i o n (0 ) a n d

ex ter na l ( l ) co nd i t io ns . T he s im ul ta ne ou s solu t ion of 17) an d 21) for a nozz le or of

22) for a p ipe de termine the choking f low G

c

and the c r i t i c a l p re ssure r a t i o r\

c

. F ig .

6 i l lu st ra tes th e grap hic solut ion of th e eq ua t io ns 17) an d 21) for a nozz le for f lashing

wa te r . The equa t ion 17) combined wi th equa t ion 20) g ives :

dv

g

dx dvi

(23)

to :

For a s ingle component f lu id 23) can be eva lua ted a t loca l condi t ions according

dv

g

dp

IP

'xX-wr-^

dx^

dp /

h

-±CT

h

2

(24)

(25)

(26)

dvi (vi

dp \

a

f

(27)

In equat ions 23) through 27) 7 i s the i sent ropic coeff ic ient , vi

g

a n d h\

g

a re t he

spec i f i c vo lume and en tha lpy change f rom vapour t o l i qu id s t a t e , r e spec t ive ly , C i s the

l iquid specific heat , T is t h e a b s o l u t e t e m p e r a t u r e , a n d aj i s th e so un d speed in the



262

l iquid pha s e . In 25) a n d 26) t h e eva l ua t i on of

dx/dp

is pe r fo rmed a long i sen t rop ic

a n d i sen tha lp i c p a t h s , respect ive ly . T h e loca l qua l i t y wi t h reference t o s t a gn a t i o n

cond i t i on s can be a pp r ox ima t e d by:

h

lgo

T

CT

(T

x),

^x

0

f —

+ — In [ —

nig

J o

n-ig

\1

0

(29)

<:)h

hlgo ,

■Ig

Hg

(To - T)

(30)

T h e choice d e p e n d s on t h e app l i c a t i on . Acco rd i ng t o / 7 / , fo r a nozzle c on s t a n t

en t r opy

a n d

fo r

a

p ipe

c on s t a n t

en t ha l py

a re

r e c ommend e d .

T h e

Cl a p e y r on

e qu a t i o n :

dp

dT

Tv

lg

(31)

dvi/dp h a s been ut i l ized in a r r i v i ng a t e qu a t i o n s 26 ) , 27) a n d 29 ) . Using 24 ) ,

25) a n d a s s um i ng dvi/dp = 0 , t h e H E M l oca l choking cond i t i on in t h e s imp l e s t form

becomes :

xvg vf

g

(CT-xh

lg

)

IP

+

t.

(32)

In Fig . 7 a compa r i son be tween two - ph a s e cr i t ica l flow mode l s is i l l u s t r a t e d . Cr i t -

ical ma s s fluxes ve r su s s t a gn a t i o n p re s su r e ca lcu la t ed by different mode l s a r e s h own .

T h e H E M p red i c t i on s r e p r e sen t t h e lower b o u n d of all t h e mod e l p red i c t i on s . For ven t

sizing pu r po s e s t h i s is conse rva t ive .

In t h e Hen r y Fauske nonequ i l i b r i um Mode l ( H FM ) / 7 / t h e flow is also homoge -

n e ou s b u t wi t h no ma s s t r ansfe r be tween t h e s t a gn a t i o n a n d t h e chok i ng po in t ( i = i o )

a n d t h e r a t e of flashing a t t h e choking po i n t is s ome specified f rac t ion [N ) of t h e equ i -

l i b r i um

va lue :

xv

g

vf

g

(CT-xh

lg

)

IP

+ N

?

(33)

T h e p a r am e t e r

N

is given by:

N

=

*i

2Ap

Pl

K vf

g

TC

+ 10L

(33a )



263

w h e r e KQ is a dis ch arg e coefficient ( = 0.6 for sh ar p edges orifices) a nd A p th e to ta l

ava i lable press ure dr op be tw een the vesse l an d the end of th e pip e . T he di ff icul ty

assoc i a t ed wi th t h i s mode l i s t ha t N (usua l ly N < < 1 for nozzle flows) is se ns itiv e to

the f low geomet ry . In t he Equ i l i b r ium Ra te Mode l (ERM) i sen tha lp i c cond i t i ons a re

a s s u m e d w i t h N = 1 :

x

0

v

r

v,„CT

0

V

g

Vjg

IP

K

(34)

As a spec i a l bu t i n t e re s t ing ca se , we cons ide r t he sa tu ra t ed in l e t cond i t i on s

[XQ

=

0) and we ge t :

G

c

o r c o n s i d e r i n g t h e C l a p e y r o n e q u a t i o n

h i

(35)

dp (T

dT\C

3 .

M u l t i c o m p o n e n t T w o - p h a s e F l o w s w i t h E n e r g y S o u r c e s

Th e phys i ca l p ro pe r t i e s o f a m ul t i c om po nen t mix tu r e can be de r ived f rom the p rop e r

t i e s o f each componen t accord ing to t he fo l lowing s imple re l a t i onsh ips :

hi

g

= ^ Yi

h

l

gi

vi

g

E

r

« ^ . E*'

C

<

w h e r e Y{ a n d X{ a re t he vapo ur and l i qu id mas s f r ac t ions o f t h e i t h com po ne n t , r e

s p e c t i v e l y . T h e r e f o r e , t h e H E M c o n c e p t c a n b e e x t e n d e d t o m u l t i c o m p o n e n t m i x t u r e s

which are the f lu ids to be considered in the vent ing process of ba tch reac tors .

4 . D I E R S M e t h o d o l o g y

T h e D e s i g n I n s t i t u t e fo r E m e r g e n c y R e li ef Sy s t e m s ( D I E R S ) / 9 / o f t h e A I C h E h a s

d e v e l o p e d r e s e a r c h p r o g r a m m e s t o :

reduce the f requency , seve r i t y and consequences o f p re ssure p roduc ing acc iden t s

p romote the deve lopment o f new t echn iques which wi l l improve the des ign o f ERS

DIERS was fo rmed in 1976 by 29 US and European Organ iza t ions and so fa r has spen t

in r e sea rch work approx ima te ly $1 .6 mi l l i on . The ma in re su l t o f t he DIERS work was

the deve lop me nt o f an ER S s i z ing me th odo logy based on :



264

a b e n c h - s c a l e e x p e r i m e n t a l a p p a r a t u s ( V SP)

a d e s i g n c o m p u t e r p r o g r a m m e ( SA FI R E )

simpl i f ied ca lcula t ion procedures

Due to t he re l evance o f t he re su l t s ob ta ined by DIERS i t i s i n t e re s t ing to r ev i ew he re

br i e f ly t he concep t s on which th i s me thodo logy i s founded .

A de qu a te s i z ing of ER S to p ro t ec t aga ins t R R i s o f ten d i ff icu lt due to unc e r t a in t i e s

(o r l ack o f knowledge ) r ega rd ing chemica l k ine t i c da t a and the rmophys i ca l p rope r t i e s .

Fur the rmore , t he f l u id dynamic behav iour o f RR sys t ems in r e l i e f cond i t i ons depends

s t rong ly on the phys i ca l p rope r t i e s o f r eac t ion p roduc t s which a re p re sen t even in

m i n u t e a m o u n t s .

In t hese cond i t i ons , ca l cu l a t ion me thods a lone canno t g ive re l i ab l e p red ic t ions due

to insuff ic ien t d a t a fo r sys t em ch a rac t e r i za t ion . The re fo re , t he r e is t h e need to t e s t t he

RR sys t em on a sma l l sca l e ( t o r educe the cos t s ) r ep re sen t ing cor rec t ly wha t would

happen a t fu l l sca le in the rea l reac tor .

Fo r t h i s p u r p o s e D I E R S h a s d e v e l o pe d t h e a d i a b a t i c c a l o r i m e t e r V S P / 1 0 / w i t h

the in t en t ion o f mee t ing the fo l lowing requ i rement s :

Handle l a rge ly unknown sys t ems wi th ene rgy re l ea se ra t e s r ang ing f rom 0 .1 to

WW/g.

A sma l l t e s t sample (100ml ) t o a ssure sa fe and easy hand l ing

Direc t ext rapola t ion to la rge sca le : safe but not over ly conserva t ive

Re la t ive ly inexpens ive

The key fea ture of the equipment i s the use of a low hea t capac i ty tes t ce l l (see

Fig . 8 ) which is m a in t a ined in ad i aba t i c cond i t i ons t h ro ug h e lec t r i ca l hea t ing p rov ided

t o k e e p t h e w a l l t e m p e r a t u r e e q u a l t o t h e s a m p l e t e m p e r a t u r e . T h i s s h o u l d r e p r o d u c e

in the ca lo r ime te r t he behav iour o f a " sma l l vo lume e l ement " o f t he rea l r eac to r cha rge

wi th undesidered sca l ing effec ts .

The VSP can be used to measure homogeneous ( foamy) ve r sus non- foamy be

hav iour dur ing re l i e f o f a RR and to d i sc r imina te be tween " t empered" ve r sus "gassy"

s y s t e m s . T h e a p p a r a t u s c a n a l so m e a s u r e t h e r m a l q u a n t i t i t e s a n d o t h e r R R d a t a

( t e m p e r a t u r e , t e m p e r a t u r e r a t e a n d p r e s s u r e t i m e h i s to r i e s a n d h e a t o f r e a c t i o n v e r s u s

t e m p e r a t u r e ) . T h e i n f o r m a t i o n o b t a i n e d b y t e s t i n g t h e R R s y s t e m i n t h e V SP a l l o w s

th e iden t i f ica t ion o f t he rel ie f beha v iour ( t he rm a l and f lu id dy nam ic ) an d p e rm i t s t he

use o f t he compute r code o r o the r ca l cu l a t ion me thods , wi th t he appropr i a t e se l ec t ion

of models .

SA FI R E ( Sy s t e m A n a l y s i s For I n t e g r a t e d R e li ef E v a l u a t i o n ) is t h e c o m p u t e r c o d e

d e v e l o p e d b y FA I / l l / u n d e r a D I E R S c o n t r a c t w h i c h i n c o r p o r a t e s m o s t o f t h e D I E R S

ana ly t i ca l m e th od s . Th e code desc r ibes t he m ul t ip ha se flu id dynam ics o f a ba t ch - typ e

chemica l r eac to r o r s to r age vesse l wi th an E R S . M ix tu re phys i ca l p ro pe r t i e s , r eac t ion

s to i ch iome t ry and k ine t i c s , ve sse l and ven t l i ne geome t ry a re i npu t by the use r . F lu id

d y n a m i c m o d e l a s s u m p t i o n s a r e a l so m a d e b y t h e u s e r. SA FI R E c a n c a l c u l a t e t h e

m i x t u r e b e h a v i o u r ( t e m p e r a t u r e a n d p r e s s u r e r e s p o n s e ) , p r i o r t o r e l i e f s y s t e m a c t u

a t ion a s we l l a s t he subsequen t vesse l mix tu re d i scha rge p rocess t h rough the ERS.



265

T e m p e r a t u r e d e p e n d e n t p h y s i c a l p r o p e r t y d a t a r e q u i r e d

by

SA FI R E inc lude : l iqu id

and vapour spec i f i c vo lume , hea t capac i ty

and

v i scos i ty : l a t en t hea t

of

v a p o r i z a t i o n ,

su r face t ens ion

and

s a t u r a t i o n p r e s s u r e - t e m p e r a t u r e r e l a t i o n .

The

c o d e

is

e x t r e m e l y

ve rsa t i l e

but two

ma jor l im i t a t i ons sho u ld

be

ta k e n i n t o a c c o u n t :

l) the

i nab i l i t y

to

a n t i c i p a t e

the

vapo ur - l i qu id flow reg im e

in the

vessel

for

u n k n o w n s y s t e m s ;

and 2) for

m a n y p r a c t i c a l s y s t e m s e n c o u n t e r e d n e i t h e r

the

r e a c t i o n c h e m i s t r y

nor the

p r o p e r t i e s

of

the

re a c t io n p r o d u c t s

are

sufficiently kno wn

to

fully utilize

the

f lu id dyn am ic m e th

o d s c o n t a i n e d

in

S A F I R E . T h r o u g h

the use of the

e x pe r im e n t a l a p p a r a t u s

VSP

m o s t

of

the

a b o v e - m e n t i o n e d u n c e r t a i n t i e s

can be

r e m o v e d

and the

a p p r o p r i a t e c a l c u la t i o n

m o d e l

can be

se l ec t ed . The re fo re ,

the

c o m b i n e d

use of VSP and

S A F I R E ,

or

s impl i

f i ed fo rmula t ions ,

is the

D I E R S r e c o m m e n d e d a p p r o a c h

to the ERS

s i zing un de r

RR

c o n d i t i o n s

or

ex te rn al f ires.

4.1.

SIMPLIFIED FORMULATIONS.

B a s i c a s s u m p t i o n s

are:

homogeneous equ i l i b r ium (equa l ve loc i ty

and

e q u a l t e m p e r a

t u r e

in

b o t h p h a s e s ) , c o n s t a n t m a t e r i a l p r o p e r t i e s

and

m i x t u r e c o m p o s i t io n d u r i n g

the

v e n t i n g t r a n s i e n t . A c c o r d i n g

to

L e u n g

/ 12/ who has

deve loped

the

f o r m u l a t i o n s

of

t h i s

sec t ion ,

a

s i m p l e r e l a t i o n s h i p

of the

form:

e —

1 =

w ( l / r ? —

1)

w h e r e

r\ = p/po and e = V/VQ)

c an

be

used

to

correlate f lashing choked flow

in

d u c t s

or

nozz les .

The

cor re l a t i ng

p a r a m e t e r

has the

fol lowing simplified form :

,2 r T^, 2

XoVlg

|

CTpvf

g

CTpvf

g

i

2

r^- = a

0

+ -JS- (38)

v

0

hf

a

v

0

hf

T h i s p a r a m e t e r b a s e d

on

s t a g n a t i o n p r o p e r t i e s ,

is

fo rmed

by two

s e p a r a b l e t e r m s :

the f i r s t r ep re sen t s

the

compress ib i l i t y

of the

m i x t u r e

due to the

ex i s t i ng vap ou r f r ac

t i o n a l v o l u m e

and the

second repre sen t s

the

compress ib i l i t y

due to

p h a s e c h a n g e

(or

f lashing) u po n de pre ss ur iz a t io n.

For

flashing flow systems,

the

s e c o n d t e r m

in 38) is

d o m i n a n t u n t i l

a

0

a p p r o a c h e s u n i t y

(all gas

i n l e t ) .

For

non- f l a sh ing f low sys t ems ,

the

s e c o n d t e r m v a n i s h e s

(no

p h a s e c h a n g e )

and w

r educes s imply

to a

0

. In

t h i s

way,

solu

t i ons deve loped

for

flashing flows

can be

e x t e n d e d

to

non- f l a sh ing s i t u a t io ns . Nozz le :

For

a

nozz l e f l ow, subs t i t u t ing equa t ions

37) and 38)

i n to

21) and

u p o n i n t e g r a t i o n ,

w e

get:

G

.

=

{-2

[a;

In

ry

+ - l )

( 1 - 7 ? ) ] } *

W

( i - 1 )

+ 1

(

>

w h e r e

G* =

G / ( p o / i > o )

2

is

a

d imens ion le ss ma ss f lux. C hok ing con d i t i on s

are

found

by

seek ing

the

m a x i m u m

of G (or G*) as p (or

TJ)

is

dec rea sed . Th i s cond i t i on



266

l e ads t o t h e fol lowing t r a n s c e nd e n t a l equa t i on fo r

77

r a t i o :

T]

c

,

t h e so called cr i t ica l p re s su r e

■nl +

w(w

-

2 ) ( 1

- r]

c

)

2

+ 2u

2

lnr]

c

+

2 w

2

( l

-

r?

d

)

=

0

(40)

Afte r 77

c

is f ound , i t s va lue can be s u b s t i t u t e d i n to equa t i on 39) t o ob t a i n G*.

Al t e rna t i v e l y , t h e loca l choking c r i t e r ion given by:

U

c — —j=

(41)

can be used t o ob t a i n t h e s am e r e su l t . The s e so l u t i on s fo r choked flow t h r o u g h a

nozzle a r e r e p r e sen t ed graph ica l ly in Fig .9 , whe r e b o t h flashing a n d non- f l a sh ing flows

a re

di sp layed .

A

cor re l a t ion

deve loped

by

/ l l /

gives

r e su l t s

in

close

a g r e emen t

wi t h

t h e p rev i ous m e t h o d : For w > 4 (low qua l i t y r e g i on ) :

G*

= [0 .6055 + 0 . 1 356 ( l nw ) - 0 . 0 1 3 1 ( l nw )

2

] /w

0

8

( 41a )

a n d fo r

C J

< 4 . (high qua l i t y r e g i on ) :

G*

=

0 . 6 6 /w

0

-

3 9

(416)

Fu r t h e rmo r e , fo r t h e all- l iquid in le t cond i t i on , t h e cor re l a t ion m ay be rep laced by:

G

= 0 . 9 G

L

(41c)

whe r e

GL

is called t h e l imi t ing flow a n d is given by equa t i on 35 .

Hor i zon t a l p ipe : For a ho r i zon t a l long pipe wi t h c on s t a n t cross sec t ion , i n se r t i ng

e qu a t i o n s 37) a n d 38) i n t o 22) we ge t :

4 /

D

2

G *2

»7i - f?2

w

+

(1

- 2 In

w)

2

In

(1 —u)ri2 + w

(1

-

W)T7I

+ C J

(l-u>)r)

2

+ C J

/771

( l - w ) » 7 i + w \772

(42)

whe r e 4fL/D is t h e t o t a l equ iva len t pipe r e s i s t a nc e , 771 = P i / p o a n d 772 = P2/P0 (see

Fig . 10) . In o rde r to ca lcu la t e flow di scha rges f rom a l a rge re se rvo i r , b o t h t h e in le t

a n d exi t cond i t i on s have t o be known . For t h e in le t , G* a n d 771 a r e r e l a t e d t h r o u g h

t h e r e l a t i on sh i p 39 ) , wi t h

77

= 77

Loss en t r y effects c an b e i n c o r po r a t e d i n t o t h e t e rm

4/L/D. For subson i c or unchoked exi t cond i t i on s , P2 = p

a

whe r e p

a

is t h e amb i e n t

back

p r e s s u r e .

For

ex i t

choking

cond i t i on s ,

e qu a t i o n

41)

wi t h

77

c

=

772c

prov ides

t h e

r e l a t i on sh i p be tween G* a n d t h e cr i t ica l exi t p re s su r e r a t i o , 772c- In t h i s way, fo r a

given 4fL/D,

we

have

t h r e e e

e qu a t i o n s

fo r

t h e

t h r e e

u n k n own s , G*, rji,

T)2

C

-

Fig .

10

di sp lays t h e r a t i o of

G

c

fo r p ipe flow t o

GQ

C

co r r e spond i ng t o a nozzle , as a func t ion of



267

4fL/D, for va r ious va lues o f t h e pa ram e te r u> , cover ing bo th flashing an d non -f lashing

f low condi t ions.

Inc l ined p ipe : Gene ra l i zed so lu t ions have been ob ta ined by us ing a d imens ion le ss

" F l o w i n c l i n a t io n " n u m b e r :

gDcos9 p

0

gLcos8 . .

Fi

= — =

j

(43)

w h e r e 6 i s the angle of inc l ina t ion to the ver t ica l . F{ i s a m e a s u r e of t h e d e p a r t u r e

f rom the hor i zon ta l ca se (F { = 0 ) . T h e n o n - d i m e n s i o n a l iz e d m o m e n t u m e q u a t i o n t o

be solved is:

L f

V, [[1-W)V

2

+UTI] \l-G'

2

p]dT]

4f— — — — (44)

which reduces t o equa t ion 42 ) fo r Fi = 0 . Fig . 11 i l lu st ra tes th e e ffec t of an inc l in a t ion

F{ = 0 .2 by com par i son w i th F ig . 10 repre s en t ing the Fi = 0 case . For more de ta i l s

an d for th e exte nsio n of th e "o m eg a" m eth od to inc lu de the effec ts of sub coo l ing in le t

cond i t i ons and the e f fec t s o f t he p re sence o f noncondensab le gases i n t he mix tu re , see

/ 1 2 / .

4.2. VENT SIZING FORMULAE

In th i s sec t ion the mos t com mo nly used me th od s for t he des ign /ve r i f i ca t ion o f E R S a r e

pre se n ted . Th e ca se o f pu re vap our ven t ing is no t cons ide red bec ause i t ha s l imi t ed

app l i cab i l i t y / 1 3 / . Tw o-ph ase flow can usua l ly be expe c ted to occur from a runaw ay

reac to r ven t and the a ss um pt io n o f two -phas e f low shou ld usua l ly be m ad e a s a sa fe

case .

I t i s r eca l l ed tha t t he des ign /ve r i f i ca t ion o f an ERS in such cond i t i ons requ i re s an

a p p r o p r i a t e c h a r a c t e r i s a t i o n of t h e ch e m i c a l s y s t e m c o n c e r n i n g t h e t h e r m o k i n e t i c a n d

f lu id dy nam ic a sp ec t s . Th i s can be ach ieved on ly th r ou gh ad i ab a t i c ca lo r im e t ry t e s t i n g

/ 1 0 / . O ne of th e lec tures of th is Co urs e i s dev oted t o th is top ic . I t is usua l ly preferab le

tha t t he r e l i e f dev ice can ope ra t e a t a p re ssure va lue p

g

("set" value) well below the

m ax im um a l lowable work ing p re ssure (M AW P) of t he reac to r vesse l. In add i t i on ,

the p re ssure dur ing the ven t ing t r ans i en t may be a l l owed to r i se up to a f i xed va lue

Pm{Pm = l - 2 p

s

) before s t a r t in g th e decay pha se . In doin g so , a s igni f icant red uc t ion

of t he ven t a rea a s compared to t he ca se o f ze ro ove rpre ssure (Ap = p

m

— p

a

= 0) can

b e o b t a i n e d .

In order to dec ide which methods are appl icable in a g iven case , i t i s necessary to

def ine the chemica l system as one of the fol lowing types:

a ) "V apou r p re ss ure sys t em s" (or " t e m pe red " ) , i n which the p re s sure gen e ra t ed by

the runa w ay i s du e to t he inc reas ing vapo ur p re ssure of t he com po ne n t s o f t he

r e a c t o r m i x t u r e .



268

b) "Ga ssy sy s t em s" , i n which the p re ssu re is due to t he non -con den sab le gases gen

e ra t ed by the re ac t ion .

c ) "H ybr id sys t em s" , i n which the to t a l p re ssu re i s du e to bo th vap ou r p re ss ure and

gas gene ra t ion .

" V a p o u r p r e s s u r e s y s t e m s " . I n F i g 12 t h e p r e s s u r e a n d t e m p e r a t u r e t i m e h i s to r i e s

of a runaw ay reac to r in ven ted (do t t ed l ine ) an d non-v en ted (con t inou s l ine ) con d i t i ons ,

a r e s h o w n / 1 4 / . I n t h e v e n t e d c a se t h e m a x i m u m p r e s s u r e v a l u e p

m

is reached in a t ime

r

p

= At

p

+ At

v

w h e r e At

v

i s t he t ime requ i red to gen e ra t e hea t for vap ou r fo rm a t ion

d u r i n g v e n t i n g a n d At

p

i s th e t im e (ad iab at ic r ise t ime ) needed to reach p

m

in th e

non-ven ted ca se . I f t he vo la t i l i t y o f t he sys t em does no t change dur ing the ven t ing ,

t h e t u r n a r o u n d i n p r e s s u r e o c c u r s a t t h e s a m e t i m e o f t h e t u r n a r o u n d i n t e m p e r a t u r e

( r

p

= r

t

). Th e gove rn ing equ a t ion s for t h e rel ie f t r ans i en t can be ob t a ine d cons ide r ing

the mass ba l ance :

dm/dt = -GA

45)

o r m = m o — GAt

w h e r e m = pV a n d V i s t he vo lume of t he reac to r {m

3

);

and the ene rgy ba l ance :

mCdT/dt = mq- GAVh

lg

/[mvi

g

) 46)

w h e r e

q

i s th e speci fic power (W /k g) ge ner a te d by th e reac t ion ;

In wr i t i ng equa t ion 46) t he fo l lowing a ssumpt ions have been made :

vapour sens ib l e hea t t e rms a re neg lec t ed

vapour mass i s neg l igeab le

q i s cons t an t ( a su i t ab l e ave rage o f t he va lues a t T

a

a n d T

m

shou ld be used)

G i s cons t an t

hom ogen eous vessel beha v iou r ( two -phase f low w i th no vap ou r d i sen gage me nt )

c o n s t a n t m a t e r i a l p r o p e r t i e s

By combin ing eqns 45 ) and 46) a f t e r i n t egra t ion , we ob ta in :

r = r

a +

g -

vh

'° , (47)

Dif fe ren t i a t i ng equa t ion 47) wi th re spec t t o t ime and pu t t i ng dT/dt = 0, we get :

T=?±-( *-)* 48)

GA \v,

g

qGAj

V

'

by subs t i t u t ion o f t h i s va lue in to equa t ion 47) we ob ta in :



269

^ ^ , (4 9 )

w h e r e A T = T

m

— T

a

is t h e " o v e r t e m p e r a t u r e " c o r r e s p o n d i n g t o t h e " o v e r p r e s s u r e "

A ? = p

m

— p

e

- T he zero ove rpre ssu re case i s g iven by:

m

0

qvi

g

Gvhio

(49a)

Fig . 13 / 1 4 / d i sp l ays t he ven t a rea ve r sus A p show ing th e bene f i t s in t h e red uc t io n

of th e ve nt a re a wh ich can be achieved w i th a l lowanc e of a sm al l ov erp res sur e . Al l -

vapour and a l l - l i qu id ven t ing repre sen t , r e spec t ive ly , t op and bo t tom ven t ing modes

w i t h c o m p l e t e v a p o u r - l i q u i d p h a s e s e p a r a t i o n o r d i s e n g a g e m e n t . T h e t r e a t m e n t i s

s imi lar as the one previously descr ibed; the only di f fe rence in equat ion 46) i s the ra t io

V/m repla ced by V| or v„ . For the zero overpressure , in the case of a l l -vapour f low the

required flow area is given by:

T h e r e c o m m e n d e d v a l u e f o r q i s g iven by /14 / :

q = 0.5C{[dT/dt)

m

+ {dT/dt)

a

)

(50)

w h e r e dT/dt va lues a re me asu red w i th t he ad i a ba t i c ca lo r im e te r . K ey pa ram e te r s fo r

the use o f t h i s me thod a re : V, m o , C, hi

g

, v\

g

, and P — T d a t a .

For a non- reac t ing sys t em sub jec t t o a cons t an t ene rgy inpu t Q(VK) repre sen t ing

the ca se o f a s to rage t ank exposed to an ex t e rna l f i r e , equa t ion 46) becomes :

mCdT/dt = Q - GAVh

lg

/(mvi

g

) (51)

which a f te r us ing a t r e a tm en t s imi l a r t o t ha t i n t he runaw ay reac t ion ca se , y i e lds t h e

fo l lowing express ion fo r t empera tu re :

T

°

c £ c

l n

GA

L GA

V hig t

™o Cvi

g

( g j -

t)

(52)

and the fol lowing impl ic i t equat ion for the vent a rea A:

-

1

4-

m

0

Cvi

g

Q

AT =

T

m

-T

e

=

W

,m

0

QVi

g

GAC

which has t o be so lved th ro ug h i t e ra t ive m e th od s

+

-FT—

(

5 3

)



270

"G ass y sy s t e m s" . Le t us cons ide r t he ca se o f an idea l gas ( accu ra t e enou gh for

low pre ssure cond i t i ons ) i ns ide the co n ta im ent vessel o f an ad i ab a t i c ca lo r im e te r :

n =

pV

c

/RT

c

(54)

wh ere n i s t h e num ber o f moles , V

c

i s t he con ta inment vesse l vo lume (m

3

) a n d T

c

is

t h e c o n t a i n m e n t a m b i e n t t e m p e r a t u r e . D i f fe r e n ti a ti n g y i e ld s :

dn/dt ~ V

c

/(RT

c

)dp/dt (55)

L e t rh g deno te t he gas gene ra t ion ra t e i n kg/s, t h e n :

m

g

= M

w

dn/dt (56)

a n d c o n s i d e r i n g t h a t :

we ge t :

v

g

= RT

p

/[p

p

M

w

) (57)

Q

g

= m

g

v

g

= V

c

T

p

/{p

p

T

c

){dp/dt) (58)

w h e r e M

w

i s th e mo lecular weight of th e gas , p

p

i s t he peak p re ss ure , T

p

i s t h e t em

p e r a t u r e a t p e a k r a t e , a n d

Q

g

i s t he vo lum e t r i c gas gen e ra t ion ra t e eva lua t ed a t t he

peak p re s sure dur in g ven t in g . For an ad eq ua te ven t si ze, we equ a te t h e vo lu me t r i c

gene ra t ion ra t e t o t he vo lume t r i c d i scha rge ra t e :

A = m

0

Q

g

/{m

a

Gv) (59)

w h e r e

m,Q

i s t h e r eac to r cha rge (kg) , m

a

i s th e tes t ce ll cha rge (kg ) , v i s t he homoge

neous two-phase spec i f i c vo lume

— V/mo

w h e r e

V

i s t he r eac to r vo lu me (m 3) , an d

G

i s t he two-phase d i scha rge mass f l ux [kg/m

2

s) , or:

A = m

2

0

Q

g

/{m

e

VG) (60)

Combin ing 60) and 58) we ge t :

A = m

2

0

V

c

T

p

/{m

a

VGp

p

T

c

){dp/dt)

max

(61)

I f t he d i scha rge f low i s eva lua t ed wi th t he incompress ib l e Be rnou l l i ' s equa t ion :

G

g

= (2Ap/v)i (62)

w h e r e A p = p

p

— p

am

b, equ a t ion 61) becom es :



A = V

c

T

p

/{m

3

p

p

T

c

).{dp/dt)

max

{m

3

J{V2Ap)*

271

(63)

"Hybr id sys t ems" a re t hose in which a non-condensab le gas i s p roduced bu t some

of t he reac to r con ten t s vapor i ze du r ing the runaway , p rov id ing a t em pe r in g ef fect . Th e

vent s ize formula i s the equat ion 49) modif ied to account for the fac t tha t the to ta l

p re ssure i s t he sum of t he pa r t i a l p re ssure s o f t he vapour and the gas (p = p

v

+ p

g

)-

T h e t e r m hi

g

/vi

g

i s replac ed by (T p

v

/p)dp/dt / 1 5 / an d the equ a t ion 49) becom es :

A =

qm

0

( ^ ) * + (CAr)i]

2

(64)

T h e t e r m

(p

v

/p)dp/dt

m a y b e f o u n d t h r o u g h a d i a b a t i c c a l o r i m e t r y , a n d

G^

is

g i v e n b y / 1 5 / :

n

i , ,Pv dp

2

T

G

»

+ (

7 A ' C

(65)

4.3.

PRACTICAL EXAMPLE

T h i s e x a m p l e h a s b e e n t a k e n f r o m / 1 4 / a n d / 1 6 / a n d c o n c e r n s a t a n k o f s t y r e n e

m o n o m e r u n d e r g o i n g a d i a b a t i c p o l y m e r i s a t i o n a f t e r b e i n g h e a t e d i n a d v e r t e n t l y t o 7 0 C .

T h e M A W P o f t h e t a n k i s 0.5MPa. T h e p a r a m e t e r s of t h e p r o b l e m a r e :

V

m

0

Ps

T

B

T

a

Pm

T

=

13.16

= 9500

= 0.45

= 482.5

= 0 .493

= 0.54

= 492.7

= 0.662

m 3

kg

MPa

K

K/s

MPa

K

K/s

They have been ob ta ined v i a ad i aba t i c ca lo r ime te r t e s t i ng ,

p rope r ty da t a have been used :

Th e fo llowing m ix tu re

For p = 0A5MPa:

vi = 0 .001388

v

g

= 0 .08553

C = 2470

hi

g

= 310.6

m

3

/kg

m

3

/kg

U/kgK

kJ/kg



272

For p = 0 . 5 4 M P a :

vi = 0 .001414

v

g

= 0.07278

C

= 2514

hi

g

- 302 .3

m3/kg

m3/kg

kJ/kgK

kJ/kg

B a s e d on t w o - p h a s e h o m o g e n e o u s v e s s e l v e n t i n g , the ca l cu l a t ion p rocee ds as fol

lowing:

F r o m e q u a t i o n 50):

and f rom equa t ion 49):

AT = T

m

-T

a

= 10.2K

q

=

1.426kJ/kgs

9 5 0 0 X 1426 , ,

GA = 2 = 256kg/s

{ ( 9 5 0

1

O

6

X

X

O

3

O B 4 M ) ' + (2470X10.2)*}

The two-phase mass f l ux is e v a l u a t e d w i t h e q u a t i o n 41c):

3 1 0 6 0 0 / 1 \ , ,

G = 0.9 = 3 0 4 0 f c o / m

2

s

0 . 0 8 4 1 4 \ 2 4 7 0 x 4 8 2 . 5 , /

y/

A

2

p

= ^ ^ = 0 . 0 8 4 m

2

and D

2

p = 0 . 3 2 7 m ( t w o - p h a s e v e n t i n g )

U s i n g the m o r e t r a d i t i o n a l v a p o u r - v e n t i n g m o d e l , the ze ro ove rp re ssure ca se (equa

t ion 49b) gives:

9 5 0 0 x 1219 x 0 .0 8 4 1 4 , .

GA = = 37kg/s

3 1 0 6 0 0 x 0 .0 8 5 5 3 * '

a n d the c r i t ica l mas s flux, eva lua t ed wi th equ at io n 41b) and w i t h u> = 1.4 gives:

= 1 3 1 0 f c o / m 2 s

0 .66 / 41

1.4

0

-

39

\0.

3 7

= 0 . 0 2 6 m

2

and D

v

= 0 . 1 8 9 m

1310

(a l l -vapour ven t ing)

In

Fig. 14, the

p re ss ure t im e h i s to r i e s , dur ing ven t ing

and

ca l cu l a t ed us ing

the

t w o - p h a s e h o m o g e n e o u s v e s s e l m e t h o d , v e n t d i a m e t e r s D

2

p and Dv, are s h o w n . It is

e v i d e n t t h a t the ven t s ize based on al l-vapour flow wil l lead to vessel fai lure .



Table I: Two Phase Flow Equations

Iner t i a

+ c o n v e c t i o n

d

k

d t

d 7 (

A

«kOk)

A

D

k t

i

h

A«KL>k

D (

Aa

he k

fh

k

+ -^-1

P r e s s u r e

+

A «

k

—

+ Pk

A d d e d

M a s s

+

B

k

In ter fac ia l

P r e s s u r e

+ A p , — —

o z

P h a s e

C h a n g e

= A r

k

= A / '

k

[v,-v

k

)

=

A r

k

( h

k

+ - ^

In ter fac ia l

F r i c t i on

+ Ar

l k

Wal l

F r i c t i on

—

*

k

^

k

w

Inter fac ia l

heat

t rans fer

+

A q

k l

Wal l

heat

t rans fer

+

*k<Pwk

Grav i ty

+ A a

k

y

k

g

z

+ A a

k 0 k

g

z

u

k

C r o s s

S e c t i o n

C h a n g e s

+ R

k

I-a

;i-b

[I-c

d

k

fi d

Where:

—— =

— + — u

k

dt ot oz

n„

ut

=

o

dt

+ u

k

fl

OZ

/ V - l - i r r

r

ik

=

( -D

k

'V

i

B

k

= ( - 1 ) A^n,a

g

i<

m

v,

D g ?>g D| l ' |

_

A

f l a ^ p

+ A p

O ^

fit ot

R

k

=l R (l-«

k

)p,4^

4 oz



274

u>

E

ra

.*:

m

O

O

X

D

"-

(/I

«)

ra

10

6

4

2

-

.

-

-

—

c

CD

TJ

03

W

CO

Q .

n

«:

I -

1<-

10

3

600 -

400 -

E

g

200

at

100 -

60 "

40 -

2 0 -

10

-

- ^ ^ ^ »

-

-

^^^

-

I

e ^

i i i

Styrene

g = 500 kPa /

1 -

G/Q^C \

\ -

100

60

40

20

10

H

4

2

—

w

E,

Q ;

O

CO

m

CO

. w

c

^

ci)

Q .

>.

O

ra

t i

CO

o

"a:

0)

i _

CI)

E

o

0.2 0.4 0.6

Inlet void fraction

0.8

1.0

Fig.

1 : Variation of two-phase density

Q ,

mass velocity G, and

volumetric flow per unit area

G/Q,

with inlet void fraction

(from reference 121).



275

Tubes (long pipes)

Nozzles

y y "if"

Orifices (diaphragms)

Fig. 2 : Ge om et r ies con s ide red fo r c r i t ica l f l ows .

Fig . 3 : Ty pic al (p,z) di ag ra m for a noz zle (from reference /4/).



76

Slug

or

p lug

f low

^

Fig. 4 : Flow patterns in vertical upward f low.

X

o

o Q

O

o

^ 0 ° O

a a

a

o 0

0

o

O

0 o

O

a

o

Non

o

o

—■

-

—

- —

I

-equilibrium . |

\ ^ t

Equi l ib r ium

- L

>

0.1

m -

Lenght ,

L

Fig. 5 : Illustration of typical pressure profile and equil ibr ium and

nonequil ibr ium regions fo r f lashing f lows in constant area

p i p e s f rom re ference HI .



10.

8. -

re

6

6.

x

W

E

O

2.

-

H

2

0 Hom ogeneous Equilibrium

P

0

= 1.1 MPa

x

o

=0.001

r rP -\ 1/2

G = -

2 / vdP

L

y

P

0

J

\ V

i i i i

X

G -

r d v i

dP .

i

-1/2

I

G

c

-

^V/-"

s' \ \

1 \

1 \

1 \

1 \

1

1 1

^ = 0 . 8 8

i I

1

1 '

1

1

1

1

l i

0.20

0.40 0.60

V

_P_

P.

0.80

1.0

Fig.

6 : HEM solut ion for cr i t ical f low of f lashing water through a

nozzle under a pressure drop of

1

MPa (from reference

HI).



278

Experimental

o

LVD

=

0

■

LVD

=

3

A LVD = 3.5

a

LVD

=

6.5

• Friedrich

* Uchida Narig

o Zaloudek

T

•

T

*

LVD

LVD

LVD

LVD

LVD

LVD

LVD

= 12 I

=

I

= 18 I

=

29

I

= 1.5

= 12

=

6

Fauske D = 6 i

Sozzi a nd Sutherland

D

=

12.7

mm

D = 6.0 mm

D = 4.0 mm

D =12 . 7 mm

Mode l

Predictions

i Upper bound flow (Frictionless)

Homogeneous Equilibrium Model (Frictionless)

Moody

(Frictionless)

12

O r

Henry

Fauske

(Frictionless)

Edwards LVD = 12

Henry LVD = 12 (Frictionless)

10.0

9.0

o

- 8.0

X

o

a

7.0

15 30 45 60 75 90 105 120

Stagnation pressure (bars)

Fig.

7 : Discharge of saturated water th rough orif ices, nozzles and

pipes: compar ison between mode l predictions and

experimental

da ta .



279

EXHAUST

& SUPPLY

TYPE I TEST CELL

CLOSED SYSTEM

THERMAL DATA

TYPE II TEST CELL

OPEN SYSTEM

VENT SIZING &

FLOW REGIME DATA

TYPE III TEST CELL

OPEN. SYSTEM

VISCOUS EFFECTS

DATA

F ig .

8 : Sm a l l - sca le tes t eq u ip m en t w i th c lose d and o pe n tes t ee l

designs (from reference /10/).



280

1.2

1.0

0 8

0 6

0.4

0 2

n

_

-

: -r\

- T

D

:

-J

i i

Non- f lash

^ _ P c

• — Gc

/

1

n g

I

f low

1 1

—

1 1 1 1

—

V

Flashing f low

P

c

/Po

^ '

G

c

^ ^

Po Co ^ ^

I 1 1 I 1 1 1 1 1 1

0.01 0.1

0)= n

n

1 10 100

u> = a

0

+ Q

0

C

P

T

0

P

0

(v

ve o

/h

ve o

)z

Fig . 9 : F l a sh i n g a n d n o n - f l a sh i n g ch o ck e d f l o w t h r o u g h n o zz l e s

/12/.

u

100

4fU/D

Fig .

10 : Ch ok ed f l ow d is ch arg e f rom h or i zon ta l p ipe s /12 /



281

u

o

100

4fL/D

F ig . 11 : Ch ok ed f l ow d isch arg e f rom inc l i ned p ip e , w i th F i 0 .2

/12/.

System type

Sealed

Venting

Time into venting

Fig .

12 : Cha rac te r i s t i c t im e in ven ted and no nve n ted runa way s

/14/. /16/ .



282

u.o

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Styrene example

13.16 m

2

9500 kg

-

Computer simulation

[ (SAFIRE)

i i i i i i

0 10 20 30 40 50 60 70

Percent overpressure

i i i i i i

4.5 5.0 5.5 6.0 6.5 7.0

Maximum pressure bar abs.

Fig. 13 : Vent area versus ove rpressure for styrene polym erisation

/14/.

90 120

Time (s)

180

Fig.

14 : Styrene po lyme risation: pressure t ime histories in the

reactor du ring two-ph ase v enting, for two flow areas.

-©•D=0.327 m, and -a-D =0 .189 m .



283

5 . R e f e r e n c e s

/ l /

F i s h e r , H .G . ; ( 1 9 8 5 ) , C h e m . e n g . P r o g r . , A u g u s t , 3 3

/ 2 /

L e u n g , J .C . , F i s h e r , H .G . ; ( 1 9 8 9 ) , J . L o s s P r e v .P r o c e s s I n d . , A p r i l , V o l.

2

/ 3 /

T r a p p , J. A . , R a n s o m ,V .H . ; ( 1 9 8 2 ) , I n t . J. M u l t i p h a s e F l o w , V o l. 8 N . 6 pp 669

- 681

/ 4 /

G i o t , M . ; ( 1 9 8 8 ) , E x p . H e a t T r a n s f e r ,F lu i d M e c h a n i c s a n d T h e r m o d y n a m i c s ;

Shah , Gan ic and Yang Ed i to r s ; E l sev ie r Sc i ence Pub l i sh ing Co .

/ 5 / Faus ke , H. K. ; (1962) , AN L - 6 6 3 3

/ 6 / Wal l i s , G. B . ; (1980) , In t . J. M u l t i p h a s e F l o w , V o l. 6 p p 9 7 - 112

PI Fa u s k e & A s s o c i a t e s ; ( 1 9 8 3 ) , FA I / 8 3 - 2 7 ( D I E R S A I C h E )

/ 8 /

S h e p h e r d ,

I.

M. ; (1989) , Pro c .

of

N U R E T H

-

4 , K a r l s r u h e , O c t o b e r 10

- 13

/ 9 / F i s h e r , H . G . ; ( 1 9 8 8 ) , Sp r i n g N a t . M e e t i n g A I C h E , N e w O r l e a n s , M a r c h 6 - 10

/ 1 0 / Fa u s k e , H . G . , L e u n g , J. C; ( 1 9 8 5 ) , C h e m . E n g . P r o g r . , A u g u s t , 8 1 ( 8 )

/ l l / G r o l m e s , M . A . , L e u n g , J. C; ( 1 9 8 5 ) , C h e m . E n g . P r o g r . , A u g u s t , 8 1 ( 8 )

/ 1 2 / L e u n g , J. C . ; ( l 9 9 0 ) , J. L o s s P r e v . P r o c e s s I n d . , J a n u a r y , V o l. 3

/ 1 3 /

D uxb ury , H. A. , Wi lday , A. J . ; (1989) , In t . Sy m p. on Ru naw ay Re ac t io ns , Bo s ton ,

M a r c h 7 - 9

/ 1 4 / L e u n g , J. C; (1986) , A IC hE Jo ur na l , Vol 32 , N . 10 , pp 1622-34

/ 1 5 /

Fa u s k e

&i

A s s o c i at e s ;( 1 9 8 4 ) , F A I / 8 3 - 4 3 ( D I E R S - A I C h E )

/ 1 6 /

Huff,

J. E . ; ( 1 9 8 2 ), P l a n t / O p e r a t i o n P r o g r e s s , V ol. 1 N . 4 , p p 2 1 1 , O c t o b e r

6 . N o m e n c l a t u r e

o Speed o f sou nd m/s

A Sur face a re a m

2

A M a t r i x of th e coeffic ients of th e t im e-d er iv a t ive t e r m s of th e eqns of m ot i on

B M at r i x of th e coeffic ients

of

t he space -d e r iva t ive t e rm s o f t h e eqn s

of

m o t i o n

C Liqu id spec if ic he a t

J/kg.K

D C r o s s s e c ti o n d i a m e t e r

m

f Vector

of

u n k n o w n v a r i a b l e s

in

t h e eqns o f m ot io n

/ Fr i c t i on fac to r (Fann ing)

Fi F low inc l ina t ion num ber

G M as s f lux kg/m2.s

g Acce le ra t ion o f g rav i ty m/s2

h Specif ic en th a lp y J/kg

H E l e v a t i o n m

K Discharge coefficient

L L e n g t h m

n

N um be r o f moles

m M a s s

kg



284

N Non-equi l ibr ium coeff ic ient

P

q

Qw

R

T

Q

Qs

s

t

T

u

V

X

X

Y

z

P r e s s u r e

Specific power

,

H ea t f lux

G a s c o n s t a n t

Source t e rm vec to r i n t he eqns o f mot ion

Po w e r i n p u t

j Vo lume t r i c g as gene ra t io n ra t e

Specific entropy

T i m e

T e m p e r a t u r e

Velocity

Speci f ic volume

V a p o u r q u a l i t y

Liquid mass f rac t ion

Va pou r m ass f r ac t ion

Sp a t i a l c o o r d i n a t e

Pa

W/kg

W/m2

m2Js2K

W

m3/s

J/kg.K

s

K

m/s

mZ/kg

6.1.

G RE EK S Y M BO LS

a Vo lume t r i c f r ac t ion

j3 Coeffic ient of th e ad de d ma ss te rm s in th e eqns of mo t ion

7 Isentropic coefficient

e Dim ensio nless speci fic vo lum e

r Coeff ic ient of th e in t e rp ha se exchan ge te r m s in th e eqn s of m ot io n

kgm/s

9 A n g u l a r c o o r d i n a t e

77 Dime nsio nles s pressu re

A E igenva lue o f t he ma t r ix o f t he eqns o f mot ion m/s

u>

C o r r e l a t i o n p a r a m e t e r

p D e n s i t y kg/m

3

X Coe ff ic ien t i n t h e wa l l exchan ge t e r m s o f t h e eqns o f m ot ion l / m

T

T im e in t e rva l s

r

t K

Sh e a r s t r e s s Pa

6.2. SUBSCRIPTS

0 Ini t ia l va lue

c C a l o r i m e t e r

t Co m po nen t (1 ,2 )

k C o m p o n e n t ( 1, 2)

j Co m po nen t (1 ,3 ) o r (1 ,6 )

g V a p o u r / g a s p h a s e

v V a p o u r p h a s e

/ L iqu id ph ase

m

M a x i m u m v a lu e

max M a x i m u m v a lu e

s "Se t" va lue

p peak va lue



VENT SIZING FOR TEMPERED VAPOR SYSTEMS

J.C.LEUNG

Fauske & Associates, Inc.

16W070 West 8 3rd Street

Burr Ridge, Illinois 60521 U.S.A.

Introduction

This paper and the accompanying paper address the pressure relief

vent sizing methods for runway reaction systems. In addition, the

fire emergency sizing for non-reactive (storage) systems will be

included because of its prominence in the chemical industry. Runaway

reaction systems can generally be classified as tempered or non-

tempered types, see Table 1. A tempered system is one in which the

reaction heat can be removed by latent heat of vaporization, thus

controlling the runaway reaction from escalation in temperature.

This of course is accomplished by pressure relief venting. Many of

these systems are in fact normally operated in the refluxing mode for

temperature control. The latent heat can be provided by either the

reactant(s) or the solvent(s). However, the latter case presents

special concern If the system loses its solvent via boil-off due to

fire. Note that a tempered system can accommodate a reaction that

gives off noncondensable gases as long as the reaction temperature

can be controlled, we call this type a tempered hybrid system. On

the other hand, a non-tempered system exhibits little or no latent

heat of cooling at all, this is typical of a low vapor pressure

system. If the reaction products are also of low vapor pressure, the

pressure relief requirement can be quite small. But quite often the

reaction product(s) are noncondensable gas(es), these are so-called

"gassy" systems. For these non-tempered systems, the heat release is

largely retained in the runaway reaction mass and if left unattended,

without cooling re-initiation, quenching or dumping, may lead to very

large temperature and pressure excursions.

As might be expected, the vent sizing methods differ depending on

the system type. In this paper only the tempered vapor (or sometimes

being called tempered volatile) system will be addressed. The other

systems will be covered in the accompanying paper.

In the past, several methods of calculation have been proposed for

sizing emergency relief system (ERS) for runaway reactions. One

common, but frequently nonconservative method, is based on vapor

venting alone. As noted by several early observers (Boyle, 1967;

Harmon and Martin, 1970; Huff,

1973),

the most realistic case should

285

A. Benuzzi and J. M. Zaldivar (eds.). Safely of Chemical Batch Reactors a nd Storage Tanks, 285-298.

© 1991

ECSC,

EEC,

EAEC,

Brussels a nd

Luxembourg.




286

be based on the release of a vapor-llquid mixture with two-phase

discharge in the relief system. This conclusion was supported in

part by actual pressure relief experience from industry. This was

also the recommendation of the Design Institute of Emergency Relief

Systems (DIERS) (Fisher, 1985; Huff,

1988),

a consortium of 29 com

panies under the auspices of AIChE formed in 1976 to develop improved

methods for ERS design. The methods presented here are either taken

from this technology or extensions of it.

Theory of Pressure Relief

Simply stated, pressure relief of a runaway reaction requires a

balance between the volumetric vapor generation rate V and the

volumetric discharge flow. This criterion can be derived from first

principles via consideration of mass and energy balance (Leung,

1986).

The above statement must be satisfied at the maximum

(turnaround) pressure during relief. Codes may require this maximum

pressure not to exceed 1.1 times or 1.21 times the design (gage)

pressure of the vessel. In equation form this criterion can be

written as

W

V - - - GA v (1)

v p ^ '

where W is the so-called relief vent rate (kg/sec), G is the dis

charge mass flux (kg/m

sec),

A is the vent area (m ) , p is the fluid

density (kg/m ) discharging from the reactor, and v is the fluid

specific volume

(1/p).

In general the two-phase fluid density

depends on the vapor volume fraction,

a

(or void fraction) via

p - a p

v

+ (1 -

<*)P

£

= (1 - *

P j i

(2)

where

p

and

p.

are the vapor density and liquid density, respec

tively. The discharge mass flux in Eq. (1) also depends on the fluid

conditions and is often limited by the choking (sonic or critical

flow) phenomenon at the minimum discharge flow area.

The volumetric vapor generation rate necessary to remove the ex

othermic reaction heat is given by

Q m q,-, rxn ^rxn ...

V - r - — v (3)

v h

.p

h „ v

v

'

vi v vi

where Q is the total heat release rate

(J/sec),

q is the

specific neat release rate (J/kg»sec), m is the reacting mass at the

point of pressure turnaround, and h . is the latent heat of vaporiza

tion.

Strictly speaking, Eq. (3) should be written as V =

(Q /h „)v „ where v „ denotes the net increase in volume per unit

rxn'

vi' vi . vi

n

_

^

n

p

-

mass upon vaporization. But at low pressure v . - v - v . - v and

Eq. (3) results. The traditional vapor vent sizing formula can be

obtained from Eqs. (1) and (3) with

p — p

and m - m , the reacting

mass at the start of relief venting, i.e.,



287

m q

o

n

rxn

._. ,,

x

W — — r , vapor venting (4)

vi

whereas for a more general two-phase flow condition,

, two-phase venting (5)

m q

o^rxn

h

o

The corresponding equation for vent area with no overpressure, A , is

m q

p

m q

o

n

rxn o ^rxn

. o -rxn o -rxn r , , , .

-i

(6)

vi

p

v vi *v

According to this formula, the term

G/p

, which can be regarded as the

volumetric flow per unit area, plays a key role in determining the

vent size. It is therefore of interest to examine its variation for

a wide range of two-phase flow inlet conditions.

Using styrene properties at 500 kPa, Fig. 1 shows that both the

choked flow mass flux G and the fluid density

p

decrease with in

creasing void fraction a entering the relief piping. In contrast,

the volumetric flow term

G/p

is shown to increase rapidly with in

creasing void fraction. For example, we find in this illustration

that the volumetric flow per unit area is nearly 20 times larger for

all-vapor venting

(a —

1) than for two-phase venting with a = 0.2.

This would translate to vent area of 20 times larger for this two-

phase venting case than for vapor venting, if in fact no overpressure

(i.e.,

pressure above relief set pressure) is permitted. As will be

shown,

by allowing for overpressure, this difference in vent size can

be greatly reduced due to rapid mass (chemical "fuel") depletion in

the case of two-phase venting. By the time the pressure turnaround

criterion is approached

(i.e.,

Eq. (3 )), the mass remained can be

significantly less than the Initial mass prior to venting (i.e., m «

m

Q

) .

Venting With Overpressure

The simplest method of incorporating the effect of overpressure on

vent size is that due to Boyle

(1967).

He defined the required vent

area as that size which would empty the reactor before the pressure

could rise above some allowable overpressure. This can be repre

sented mathematically as

m

^ G A T

(7)

P

Here the emptying time, equated to the pressure rise time At , is

based on the pressure history obtained from adiabatic runaway "com

putation or data in a non-vented system (see Fig. 2 ) . Thus according

to Eq. (7), the vent area continues to decrease with increasing

overpressure. However this method does not yield realistic result as

no overpressure is approached. For the case of zero overpressure,

Eq. (7) would give an infinite vent size (since At - 0) which is at



288

odds with the result presented earlier, Eq. (6 ). This discrepancy is

due to the neglect of the energy balance consideration in Boyle's

method, i.e., the effect of tempering and latent heat cooling has not

been considered. This limitation was overcome in Leung's formula

tion. The relief sizing formula for homogeneous-vessel (or uniform

froth) venting is given as (Leung, 1986 ),

m q

o ^

h 1

1 / 2

m v

n

where

(V

T

)

(8)

q " 0.5 C

p

|^ | + |^ | | (9)

Here q represents the average heat release rate during the overpres

sure venting period, (dT/dt) and (dT/dt) are the self-heat rates

corresponding to the set pressure (temperature) and the turnaround

pressure

(temperature),

respectively (see Fig. 2 ) . For no allowable

overpressure (AT -

0 ) ,

Eq. (8) reduces to Eq. (6) exactly.

The effect of overpressure on vent size can be clearly illustrated

by Eq. (8) together with the experimental data reported by DIERS.

Figure 3 is a dimensionless plot of A/A versus AP/P showing the

homogeneous-venting prediction of Eq. (8) and the styrene relief data

observed in both large (2000

£)

and small (32 i) scale facilities

(AIChE/DIERS,

1986a).

The agreement is encouraging. The discrepancy

is due to the observed vapor-liquid disengagement behavior which

results in lower overpressures than the idealized (homogeneous-vessel

venting) case. Note that by allowing for an overpressure correspond

ing to AP/P of 0.1, Eq. (8) suggests a vent area reduction of about

six times from the no overpressure case (i.e., A/A — 0.15). This

reduction is quite significant and is mostly due to the mass deple

tion via venting, resulting in a much lower total energy release at

the pressure turnaround point.

Figure 3 also depicts that at higher overpressure the relative

reduction in vent area becomes increasingly smaller. This portion of

the curve is in essence operating on Boyle's emptying time theory

with most of the energy release being stored as sensible heat in the

reacting

mass.

The ultimate turnaround in pressure is due primarily

to the emptying of the reactor. Due to the Arrhenius behavior

typi

cal of most reactions, the simple averaging approximation for q, as

suggested by Eq. (9), gets progressively worse at higher overpres

sure,

resulting in some cases a minimum in the area versus

overpressure curve (see Leung and Fisher, 1989). For these situa

tions better approximation of the non-linear heat rate can be given

by

AT

q - C — (10)

P



289

where At is based on the pressure history obtained from adiabatic

runaway computation or data in a non-vented system. An alternative

would be to borrow the results from thermal explosion theory

(Townscend and Tou, 1980) where

P E

A

2 2

T T

s m

(dT/dt)

s

(dT/dt)

r

(11)

can be used to approximate the pressure rise time in Eq. (10 ). Here

E is the apparent activation energy and E /R can be obtained from

the slope of an Arrhenius self-heat rate plot. It is worth noting

that Eq. (8) in combining with Eq. (10) would reduce to Boyle's

formula, Eq. (7) as high overpressure is approached. The above-

mentioned vent sizing methods require the evaluation of two-phase

mass flux G. We shall postpone this discussion towards the end of

the accompanying paper where a complete and generalized treatment for

the mass flux will be presented.

Finally, a very simple method for sizing was advanced by Fauske

(1984a, 198 4b) and this has come to be known as the nomograph method.

In the most recent form it can be represented by (FAI, 1989)

m (dT/dt)

A = 1.5 x 10 — — (12)

s

2

where the particular units are: A[-] m , m [-] kg, dT/dt[=] °C/min,

P [=] psia. This equation was developed based on an overpressure to

set pressure ratio AP/P of 0.2. Note that this is different from

the traditional meaning or 20 % overpressure since by convention the

percent overpressure is defined based on the gage set pressure.

Vapor-Liquid Disengagement

The homogeneous-venting model is an idealized flow regime with no

phase separation at all inside the reactor (Huff, 1982). Because of

its simplicity in treatment and its conservatism, this uniform-froth

model offers a useful tool for ERS design. While a real venting

process falls somewhere between all-vapor venting and homogeneous

venting, the amount of phase separation or disengagement depends

largely on the particular fluid behavior and the vapor superficial

velocity. From studies of gas sparging through liquid columns, two

rather distinct flow regimes have been identified - the bubbly and

the churn-turbulent regimes. These flow regimes are best described

by the drift flux model (Zuber and Findlay, 1965; Wallis, 1969) and

have been used extensively to characterize the in-vessel fluid be

havior during the course of the DIERS research program (AIChE/DIERS,

1986b).

The complete vapor-liquid disengagement criterion can be

stated as follows. If the vessel free-board volume fraction (void

fraction)

a

exceeds the disengagement void fraction

a

, then vapor

venting is predicted. The latter is governed by the following drift

flux relationships for bulk heating:



290

^ - - a

(1 -

a

) for bubble flow (13)

J*.

2 a

D

U 1 - a

n

CO D

for churn flow (14)

where j is the superficial vapor velocity at the top of the vessel.

At the turnaround condition, j is given by

. rxn

n

rxn

■ \ z \

J

g=> h

,p

A h .p A

Ci:>;

° vi V X V* V X

where A is the vessel cross-sectional area. Here U is the bubble

rise velocity given by

U -

^

a

Pjl - P

w

)

1 / 4

r

i V 4

(16)

where the coefficient Ak according to Wallis, ranges from 1.18 for

bubbly flow to 1.53 for cnurn flow. Here

σ

is the surface tension

and g is the gravitational acceleration. Upon solving for aD,

a

D

- 0.5 -

Jo.

25

-

ip

for bubbly flow (17)

a

D

=

2 + IA f

o r c h u r n

flo

w

(18)

where

ip = Q / ( h . p A U ) ,

can be defined as the dimensionless

rxn vi v x

^

superficial velocity. These solutions are presented graphically in

Fig. 4. If a > a

n

, vapor venting (complete disengagement) is

predicted. If a < a., then two-phase discharge upon relief opening

will occur. Under such situations, analytical equations have been

developed (Leung, 1987) for both the bubbly flow regime and the churn

flow regime. However, these solutions are not as simple or explicit

as Eq. (8) for the homogeneous-vessel venting case, but they can be

readily solved by numerical method.

Figure 5 is an illustration of the influence of flow regime on vent

size based on a styrene runaway example (Leung, 1986; Leung,

1987).

Note that the bubbly regime yields nearly the same vent size as the

homogeneous regime. The churn regime, on the other hand, yields

significantly smaller vent size, and in this example the vent size is

nearly the same as the all-vapor venting area if a 40% overpressure

is allowed.

Finally, some useful approximations for these flow regimes are

given here. For bubbly flow the venting process resembles closely to

that of the homogeneous-vessel case particularly when

ij> >

0.25.

According to Fig. 4 or Eq. (17), no vapor disengagement is possible

when the dimensionless superficial velocity

ip)

is greater than 0.25.

For churn flow, significantly more vapor disengagement takes place.

An asymptotic solution was suggested which yielded both simplicity

and acceptable accuracy. The vent area as given by Leung (1987) is



291

^SS[* -

2

^ -

->

- a^ ry t r^ ) ] (")

where

1 r ) - J

|V2

The quantity (1 - T ) is in fact the fraction of mass remaining in the

reactor at the pressure turnaround point. This asymptotic solution

is recommended for AP/P of greater than 0.1. For more discussion

the reader can consult the original publication and a more recent

paper (Leung et al., 1988 ).

Fire Emergency Sizing for Non-Reactive System

The pressure relief system for storage vessel of non-reactive chemi

cals such as solvents is typically designed for fire emergency. The

total heat input from fire exposure Q„ is the product of the wall

heat flux q„ and the wetted heat-transfer area A :

^F w

% - < F \

(21)

Crozier (1985) has summarized various sizing formulae for fire emer

gencies which were all based on vapor venting assumption. His

discussion dealt mainly on the underlying fire heat fluxes assumed in

these formulae. The NFPA (1984) chart was found to be most widely

followed. For a wetted area of less than 19 m (200 ft ), the

average fire heat flux is 63 kW/m (20,000 Btu/h-ft ) . For larger

vessels with A > 19 m , the average fire heat flux actually falls

off due to the fact that larger vessels are less likely to be fully

exposed to fire. It should be noted that a local fire heat flux as

high as 110 W/ra (35,000 Btu/h-ft ) has been measured (API, 1976;

Moodie and Jagger, 1987). This value applies to direct flame im

pingement situations only. Unless the whole vessel is fully engulfed

by the fire, the average flux of 63 W/m is widely accepted (A < 19

m

) .

The fire emergency sizing also depends on the flow regime behavior

of the liquid under consideration. First of all, if the liquid is a

foamy fluid, i.e., the regime is in bubbly flow, then the relief

sizing treatment resembles closely to that for the runaway reaction.

In the case of fire, the dimensionless superficial velocity TJ> is

given in terms of

Q

F

^ - h - T ^ A - i r <

22

>

V f V X <*>

If the available free-board volume fraction

a

is greater than the

disengagement void fraction a

n

, sizing for vapor venting is adequate,

i.e. ,

a

Q

> a

D

- 0.5 - Jo.25 - i> (23)



292

If

ip >

0.25, homogeneous-vessel venting is a close enough approxima

tion. The required vent area is given implicitly by the following

equation (Leung, 1986)

AT -

GAC

in

m

o

Q

F

V

vi

V GA h

vi

V hVi

m C v .

o p vJ

(24)

If TJ>

<

0.25, the venting behavior in bubbly regime can differ

substantially from the uniform-froth case. For lack of any better

method, the relief sizing equations for constant heating in bubbly

regime as given by Leung (1987) are suggested. At present insuffi

cient data exists for further refinement (although preliminary data

suggests that the above methods yield too conservative vent sizes).

For non-foamy system or churn-turbulent fluid, the influence of

external wall heating differs significantly from that of bulk heat

ing.

The vapor is found to nucleate on the vessel wall and upon

detachment forming a boiling two-phase boundary layer, see Fig. 6.

An analysis that describes the void distribution and thickness of the

boundary layer, both of which increase with vertical distance along

the wall has been presented (Grolmes and Epstein, 1985). The amount

of liquid swell as a result of the rising bubble in the boundary

layer was found to be significantly less than the case where bubbles

are created and rising throughout the bulk of the liquid. In fact, a

reported experimental investigation suggests that in venting assess

ments of liquid-filled vessels subjected to external fire, it is

acceptable even to ignore the effects of liquid swell for non-foamy

liquid (Fauske et al.,

1986).

However, the possibility of two-phase

flow to the vent still exists if the velocity of the venting vapor

within the free-board volume is such that a droplet spray is pulled

off the liquid surface and carried by the vapor to the vent (Epstein

et al., 1989). Usually this occurs at a very high quality (vapor

mass fraction) flow condition. Nonetheless, it causes a significant

increase in pressure drop across the vent and particularly detrimen

tal to atmospheric-type storage tanks where allowable overpressure is

very limited. Epstein et al., (1989) has developed a criterion for

the onset of two-phase venting via entrainment consideration, see

Fig. 6. From this criterion, a minimum head space clearance h . can

,

D

, . ,

r

min

be derived,

2 p h ,U„

v vi E

1/2

(25)

where U is the entrainment velocity (or critical vapor velocity for

droplet fluidization) as given by the Kutateladze (1972) correlation

" g P ,

1/4

(26)

Thus if the available head space separation h is greater than h . ,

vapor venting is assumed and the sizing is according to vapor relief

requirement,



293

111

tr

I —

<

DC

H I

0 .

LU

I -

~^

1X1

cc

ID

CO

CO

H I

tr

0_

T IM E I N T O R U N A W A Y

Figure 1. Nomenclature for runaway in unvented system.

J C L B 8 1 0 3 1 H A

£

1 0 — ,

6 0 0 -

Q :

£ 2 0 0

CO

z

LU

Q

— X 6 0

- i

1

4 0

t

ra

CO

O

*-

o

X

o

CO

CO

<

6 -

4 —

2 —

I I I

rn

<

X

n

o

5

i -

- 1

;-

~ ^ -~~~

~

-

"

—

—

-

~ ' ^ - - -

"

~

l

l l l

P

^

4 —

1 1

I 1 I 1

S T Y R E N E

P

0

= 500 kPa

G//3 . , / \

G

1 1 1 1 1

/—

j -

-

—

—

-

\ -

\ -

0.2 0 .4 0 .6 0 .8

INLET VOID FRACTION, a

<

L U

C C

<

CC i'

10 LU E

6

0

a

o

>

Figure 2. Variation of two-phase density (p), mass

flux (G ), and volumetric flow per unit area (G/p)

with inlet void fraction.



294

0.5

0.4

0.3

<

•v.

<

0.2 —

0.1

—

—\

I

O N

0

|

I I

D I E R S I C R E S e r i e s

0

•

D

S c a l e ( J )

V e n t i n g

3 2

Top

3 2

B o t t o m

2 0 0 0 Top

H o m o g e n e o u s V e s s e l

J~

V e n t i n g

o

• ■

o

I

O

—

-

0.1 0.2

AP/R,

0.3 0.4 0.5

Figure

3.

Comparison

of

homogeneous vessel

prediction versus DIERS styrene relief data.

8

<

a

o

»

0.1

0 .01

=—r—

—

-

—

—

—

-

/

'

I

' I ' I ' i

B u b b l y

F l o w

I . I , I .

—

-

—

—

-

—

T

T

m

0.2

0.4

0.6

0.8

1

DISENGAGEMENT

VOID FRACTION,

X

Figure 4. Disengagement void fraction for bubbly

and churn-turbulent flow regimes.



295

0.05

PbAK PRESSURE, bar (abs)

5 5.5 6 6.5

S t y r e n e P o l y m e r i z a t i o n

9500 kg in 13 .16 m

3

T a n k

H o m o g e n e o u s

V e n t i n g

V a p o r

- V e n t i n g

A r e a

i

Bubbly

Churn

20 40 60

PERCENT OVERPRESSURE

Figure 5. Vent area versus overpressure for

styrene runaway example in different venting

regimes.

V a p o r

I C L . 0 1 0 2 0 4 C .A

Figure 6. Sketch of boiling boundary layer

under external fire heat flux and minimum

head space clearance for vapor relief.



296

TABLE 1. Classification of reactive systems

TYPE CLASS SOURCE OF PRESSURE

Vapor System Tempered Vapor (partial) pressure as

driven by temperature

effect.

Hybrid System Tempered Both vapor pressure and gas

pressure.

Hybrid System Non-Tempered Dominated by gas pressure.

Gassy System Non-Tempered Gas pressure due to gas

accumulation within reactor.

Q

F

A

= h - ^ >

f 0 r h > h

m i n <

27

>

where G is the vapor mass flux (G

~

0.61 |P p for vapor choked

flow). On the other hand, if h < h . , then an alternative is to

enlarge the vent area such as to stay just below the droplet entrain-

ment velocity within the vent (Fauske et al.,

1986),

Q-F

A = — . „ , for h < h . (28)

P h „U_, m m

v vi E

Conclusion

This paper provides a state-of-the-art summary of practical vent

sizing methods for tempered vapor systems. Both runaway reaction and

fire emergency of non-reactive storage have been discussed. The

effect of two-phase discharge on vent size can be elucidated and

recommendations are provided for different venting flow regimes.

References

American Institute of Chemical Engineers (1986a), "Phase III

Large Scale Integral Tests, DIERS

III-5,

Experimental Results

for Series III Tests, DIERS

III-6,

Experimental Results for

Series IV Tests, Analysis and Program Summary", Reports sub

mitted by Fauske & Associates, Inc. for AIChE/DIERS.

American Institute of Chemical Engineers

(1986b),

"Emergency

Relief Systems for Runaway Chemical Reactions and Storage

Vessels:

A Summary of Multi-Phase Flow Methods", Report

submitted by Fauske & Associates, Inc. for AIChE/DIERS.



297

American Petroleum Institute (1976), API

RP-520,

Fourth

Editions, "Recommended Practice for the Design and

Installation of Pressure-Relieving Systems in Refineries, Part

I - Design and Part II - Installation", API, Refinery

Division, Washington, D.C.

Boyle, W. J., Jr. (1967), "Sizing Relief Area for Polymerization

Reactors", Chem. Eng. Prog., 63 (8 ), p. 61 (August).

Crozier, R. A., Jr. (1985), "Sizing Relief Valves for Fire

Emergencies", Chem. Eng. Prog., p. 49, October 28 issue.

Epstein, M., Fauske, H. K., and Hauser, G. M. (1989), "The Onset

of Two-Phase Venting Via Entrainment in Liquid-Filled Storage

Vessels Exposed to Fire", J. Loss Prev. Process Ind., Vol. 2

(1),

P- 45.

Fauske & Associates, Inc. (1989), "Reactive System Screening

Tool (RSST) System Manual - Methodology and Operations", FAI

Report No. FAI/89-73.

Fauske,

H. K. (1984a), "A Quick Approach to Reactor Vent

Sizing", Plant/Operations Prog., 3 (3 ), p. 145.

Fauske, H. K. (1984b), "Generalized Vent Sizing Nomograph for

Runaway Chemical Reactions", Plant/Operations Prog., 3 (4 ), p.

213 (October).

Fauske, H. K., Epstein, M., Grolmes, M. A., and Leung, J. C.

(1986), "Emergency Relief Vent Sizing for Fire Emergencies

Involving Liquid-Filled Atmospheric Storage Vessels",

Plant/Operations Prog., 5 (4 ), p. 205.

Fisher, H. G. (1985), "DIERS Research Program on Emergency

Relief Systems", Chem. Eng. Prog., 81 (8 ), pp. 33 -36 (August).

Grolmes, M. A. and Epstein, M. (1985), "Vapor-Liquid

Disengagement in Atmospheric Liquid Storage Vessels Subjected

to External Heat Source", Plant/Operations Prog., 4 (4 ), pp.

200-206.

Harmon, G. W. and Martin, H. A.

(1970),

"Sizing Rupture Discs

for Vessels Containing Monomers", Paper preprint No. 58A, 67th

Nat.

Mtg. AIChE (February).

Huff, J. E. (1973), "Computer Simulation of Polymerizer Pressure

Relief", Chem. Eng. Prog., Loss Prevention Tech. Manual, Vol.

7,

p. 45.

Huff,

J. E. (1982), "Emergency Venting Requirements",

Plant/Operations Prog., 1 (4 ), p. 211

(October).

Huff, J. E. (1988), "Frontiers in Pressure-Relief System

Design", Chem. Eng. Prog., 84 (9), pp. 44 -51 (September).



298

Kutateladze, S. S.

(1972),

"Elements of the Hydrodynamics of

Gas-Liquid Systems", Fluid Mechanics - Soviet Research, Vol.

1. P. 29.

Leung, J. C. (1986), "Simplified Vent Sizing Equations for

Emergency Relief Requirements in Reactors and Storage

Vessels",

AIChE Journal, 32 (10 ), pp. 1622-163 4.

Leung, J. C. (1987), "Overpressure During Emergency Relief

Venting in Bubbly and Churn-Turbulent Flow", AIChE Journal, 33

(6), pp. 952-958.

Leung, J. C , Buckland, A. C., Jones, A. R., and Pesce, L. D.

(1988), "Emergency Relief Requirements for Reactive Chemical

Storage Tanks", Institute of Chemical Engineers Symposium

Series, No. 110, p. 169.

Leung, J. C. and Fisher, H. G.

(1989),

"Two-Phase Flow Venting

from Reactor Vessels", J. Loss Prev. Process Ind., Vol. 2, p.

78.

Moodie, K. and Jagger, S. F. (1987), "Flow Through Pressure

Relief Devices and the Dispersion of the Discharge", Inst, of

Chem. Engrs., Symp. Series No. 102, p. 215.

National Fire Protection Association (1981), "National Fire

Codes",

NFPA-30 Flammable and Combustible Liquids Code, NFPA,

Quincy, MA.

Townscend, D. I. and Tou, J. C. (1980), "Thermal Hazard

Evaluation by an Accelerating Rate Calorimeter", Thermochimica

Acta,

Vol. 3 7, p. 1.

Wallis, G. B.

(1969),

One-Dimensional Two-Phase Flow. Chapter 4,

McGraw-Hill, New York.

Zuber, N. and Findlay, J. (1965), "Average Volumetric

Concentration in Two-Phase Flow Systems", Trans. ASME J. Heat

Transfer, Vol. 87, p. 453.



VENT SIZING FOR GASSY AND HYBRID SYSTEMS

J.C.LEUNG

Fauske & Associates, Inc.

16W070 West 8 3rd Street

Burr Ridge, Illinois 60521 U.S.A.

Introduction

In the previous paper, vent sizing methodology for tempered vapor

systems has been presented. In this paper the gassy system and the

hybrid system are examined. As indicated in Table 1 of the previous

paper, two general types of hybrid system can be found. The type

that does not exhibit any sustained tempering is the non-tempered

type (either due to solvent boiled off or insufficient latent heat of

cooling) and this system exhibits essentially the same characteristic

as the gassy system - the source of pressure is dominated by the

evolved gas mostly. The other is the so-called tempered hybrid

system and as expected, this system exhibits similar tempering

(latent heat of cooling) characteristic as the vapor system.

However, if not properly relieved, the accompanying gas evolution can

cause the reactor pressure to rise much more rapidly. We will ex

amine the relief requirement for these systems and the sizing methods

in this paper.

Theory of Pressure Relief

In general the pressure relief of a runaway reaction requires a

balance between the volumetric vapor/gas generation rate and the

volumetric discharge flow. This criterion can be represented mathe

matically as

m q

o^rxn

,

— T + m m

W \t ° 6

- — ^ — r (l)

or in terms of the required vent area with no allowable overpressure,

[°(P

V

+ P

e

) + (1 - a) pj

A

o

m

0

q

n

r x n •

u +

N

:

' v

+

'

g

>

(2)

299

A.

Benuizi and

J.

M. Zaldivar

(eds.).

Safety of Chemical Batch Reactors a nd Storage Tanks, 299-310.

© 1991

ECSC,

EEC,

EAEC,

Brussels and

Luxembourg.




300

where

p

and

p

are the vapor and gas density, respectively. From

ideal gas law,

p

S

- P M y'RT and

p

- P M /RT. Again the above

equations apply to the case of noôverpressure with an initial batch

size of i , It should be noted that according to the partial

pres

sure definition, the total volumetric generation rate is not equal to

the sum of the vapor volumetric rate (V - m q /h

„ p )

and the gas

volumetric rate (V = m m

/p ) .

In Eqs. (1; and (2; , m denotes the

specific mass rate of gas evolution. Experimentally it ^can be es

timated from pressure rise rate data via

VM

-m ,

Ut /

m

t

°

v

-'meas

where V is the free-board volume the gas occupies in the test ap

paratus, (dP/dt) is the measured pressure rise rate, and m is

the test sample

mass.

Note that in the case of vapor relief, the

vent rate requirement is simply

q

w f

V a

P °

r

m

JventingJ o

rxn

r + m

W

But for homogeneous-vessel (uniform-froth) venting, which

sidered the most conservative, the required vent rate is

.[

m

o

q

r x n . •

r + m

Kl 6

i

o m o g e n e o u s

v e n t i n g I ~ (P M + P M ~)/RT

°

J

V wv g wg

(5)

Thus the difference in relief vent rate between homogeneous venting

and vapor venting is very large and can be given by

..(homogeneous^ _.

,.

.

W ° m /V (1 -

a )p

I venting I

o'

o

r

w

vapor

1

^ventingj

P

(6)

p + p p + p ^ '

v

H

g

H

v

H

g

where

a

is the initial free-board volume fraction in the reactor.

In what follows we will discuss the vent sizing implication and the

merit, if any, for allowing for overpressure in both gassy and hybrid

systems.

Gassy System Vent Sizing

The non-tempered gassy runaway system is deficient in latent heat of

cooling which is used in vapor system to control the runaway by

venting. For the gassy system, the temperature runaway history

remains essentially identical to the adiabatic case even in a vented

environment. Figure 1 illustrates a typical venting scenario for a

gassy system. Due to the continued accumulation of gas given off

from the runaway reaction, the rupture disk soon reaches its relief

pressure and causes the reactor to depressurize quickly to ambient

pressure or to the back pressure imposed on the downstream equipment



301

(Pt.

1 in Fig. 1) . Two-phase flow is not expected since the gas

evolution rate is quite low at this early stage. The assumption of

two-phase discharge would be non-conservative (unsafe) here since it

causes early emptying of the reaction

mass.

After this initial

"blow-off" of the gas, the reactor temperature continues to rise

while the system remains at the prevailing back pressure (Pt. 2 in

Fig.

1 ) . Note that the use of a reclosure-type relief valve would

keep the system pressure at close to the set point with periodic

opening to bleed off the excess gas, but the temperature heatup

profile remains unaltered. As the reaction approaches the maximum

rate prior to complete conversion (decomposition), pressurization of

the reactor will take place (Pt. 3 in Fig. 1 ) , and this will most

likely be accompanied by two-phase discharge. The worst case to

consider is therefore the onset of homogeneous-vessel venting

coinciding with the peak reaction rate (as indicated by maximum dT/dt

or dP/dt

rate),

see Fig. 2. Here the general vent rate equation, Eq.

(5), for gassy system reduces to

m m

o g.max

W

max

p

g

m

o

(7)

Evaluating this requirement at the maximum allowable pressure P

(after substituting Eq. (3) into (7)) yields,

m V /-.„-> max

m

w

_ _o _cfdP]

max m P Idtl

t m

v

J

\

(8)

To estimate the required vent size for the allowable overpressure (AP

= P - P ) ,

m s

W

A = f (9)

where G is to be evaluated at P and at the reactor loading of m /V.

For gassy system, the two-pnase flow can be characterized as non-

flashing flow discharge; this is in total contrast to the flashing

flow regime for the vapor system. A unified treatment for both

regimes has been developed and will be presented later on.

Starting with Eq. (8) and after making a number of conservative

approximations, Fauske arrived at a simple formula in terms of the

maximum pressure rise rate measured in either the RSST (FAI, 1989) or

the VSP equipment,

m (dP/dt)

A

v

_° meas ,, .„

A

-

K

.

—^Jl <

1 0

>

m

where the coefficient K is 3 x 10" for the RSST and 3.3 x 10" for

the VSP (this difference accounts for the different containment

vessel free-board volume). Here the particular units are: A[=] m ,

dP/dt[=] psi/min, P [-] psia.

So far no attempt nas been made to account for the mass loss due to

decomposition and venting. The latter involves a transient



302

(unsteady) calculation during the venting process. This effect is

expected to result in about a factor of two reduction in vent size

from the above methods. Early venting prior to the peak rates re

quires significantly more analysis and physical (flow regime)

characterization. This is best investigated experimentally by the

direct scaling approach as discussed below.

The so-called area-to-charge direct scaling approach (Leung and

Fauske,

1987) offers an alternative method which usually yields a

smaller vent size than the calculational methods given above. This

is because early loss of reactant from the reactor due to two-phase

flow is an advantage for non-tempered systems. Since this loss is

always more effective in the reactor than in the test apparatus due

to much larger superficial velocities, direct scale-up in apparatus

like VSP using top venting is hence possible. A vent size that allow

safe venting of the test sample and empties its content completely

(this is most important) can be safely extrapolated to full scale

based on area-to-charge scaling. Often a number of tests may be

required to narrow in on the size that limits the overpressure to

just below the allowable level.

It should be mentioned here that the Boyle's emptying time formula

(Eq. (7) of previous paper) can yield nonconservative results also if

the pressure rise time At is evaluated at a point where the rate is

substantially less than the peak reaction rate. On the other hand,

it has been found that if the peak reaction rate (m ) was used to

2 max

calculate At , the resulting vent size would be overly conservative.

Hybrid System Vent Sizing

The tempered hybrid system possesses volatile or condensable

component(s) which can be counted on to control the runaway tempera

ture via latent heat of cooling. Figure 3 illustrates a typical

venting scenario for a hybrid system. Although this illustration

uses a reclosure-type relief valve (PSV), the general venting trend

is not much different in the case of a rupture disk. Here PSV would

"lift" first when the system pressure attains the relief set pressure

and bleed off the accumulated gas (Pt. 1 of Fig. 3 ) . The lifting and

reclosing of the PSV might occur many times while the vapor pressure

of the volatile component(s) continues to increase due to rising

temperature. It is not anticipated that two-phase discharge would

occur during these early periodic relief intervals. However, as the

tempering point is approached, the vapor pressure contribution

noticeably increases and the total vapor and gas volumetric rate

rises rapidly. Typically this is the point when two-phase discharge

simultaneous with overpressure venting would take place (Pt. 2 of

Fig. 3 ) . For an adequately sized vent, the pressure would turn

around before the maximum allowable pressure and the temperature

would turn around also. Due to the effect of gas accumulation, the

pressure turnaround and the temperature turnaround do not occur at

the same time (Pts. 3 and 4 of Fig. 3 ) .

The so-called tempering condition is achieved when the evaporative

cooling becomes equal to the reaction heat release. This condition

is attained at the temperature turnaround point (Pt. 4 of Fig. 3 ) .



303

The tempering condition can be determined experimentally in apparatus

like the VSP or RSST. Mathematically we can write the ratio of the

partial pressures as

P

-g _

P x /M

v

v

x /M

g

w

g _

m

- g _

M

.

W

S.

q

^ r x n

h .M

vx . wv

(11)

pressure P,

T \

For vent

In addition, these partial pressures add up to the system total

sizing purpose, one is most interested in

emperature T at the relief device set

pressure P . Thus with P„ equal to P , we can solve for the temper

ing temperature T__ which yields the following vapor pressure

(12)

(T ) -

1 +

This procedure has been demonstrated to yield excellent agreement

with experimental result for hydrogen peroxide decomposition, a

well-

known hybrid system.

The conservative venting scenario is to assume homogeneous-vessel

venting after the reacting mixture has attained the tempering tem

perature corresponding to the relief set pressure (see Fig. 2) .

Analytical sizing equations for such a venting scenario have not been

put forward yet, mostly because of equation complexity. Equation (5)

is ideally suited to estimate the vent rate requirement for no over

pressure, but such a case is deemed overly conservative. Another

somewhat less conservative approach is to modify the former vapor

system sizing formula by Leung (1986)

A -

m q

o ^

m

o \£

1/2

+ (C AT)

P

1/2

(13)

by incorporating the gas accumulation effect on overpressure (Leung

and Fauske, 1987). For a given allowable overpressure AP, the cor

responding "over-temperature" is calculated based on a non-vented

situation, i.e..

AT

AP

(dP/dT)

AP

vi

Vvi

m m RT

° g

a

VM (dT/dt)

o wg 's

(14)

in

ote that in terms of experimental measurement, the second term

the denominator can be replaced by (m V / m a V)(dP/dt)

Typically this term dominates and the available°Af and° hence

A T ^ I S

governed by gas accumulation. The result is quite similar to Boyle's

theory

(1967).

The discharge flow of a hybrid mixture lies somewhere between

flashing flow (for vapor system) and non-flashing flow (for gassy



304

system). A recent development based on simple mixture consideration

has been suggested for the calculation of the discharge mass flux G

in Eq. 13). This will be presented in the next section.

Another vent sizing method for hybrid system is that based on the

RSST technology and the simple equation approach FAI, 1989; Creed

and Fauske, 1990)

suggested:

Based on AP/P of 0.2, the following formulae are

-6

m dP/dt)

A - 5 . 6 x l 0 —

1.5 x 10

p

3/2

s

dT/dt)

for RSST only)

15)

16)

where the units are: A[=] m , m

psi/min, and dT/dt)

[ ]°C/min.

-] kg, P [■

. , The larger

suggested for design. Note that Eq. 15) contains

tion of

psia, dP/dt)

g

[-]

of the two areas is

slight modifica-

the gassy system sizing formula, Eq. 10) while Eq. 16) is

simply the vapor system sizing formula FAI, 1989).

Gassy and Hybrid Flow Discharge

In most of the vent sizing equations presented in this paper and the

previous paper, a two-phase discharge mass flux G appears explicitly

in the vent size equation, such as in Eqs. 9) and 13). In fact for

these analytical vent sizing methods, the procedure can be broken

down to two rather distinct steps. The first step is to calculate

the required vent rate W which is entirely independent of the

dis-

charge flow through the relief device. The second step is to obtain

the required vent area A which, according to Eq. 9), requires the

evaluation of the discharge mass flux. For completeness a general

treatment for evaluating such two-phase discharges is summarized here

Leung, 1990a). The present unified method has the attributes of

yielding the two limiting cases, namely the flashing flow limit for

the vapor system and the non-flashing flow limit for the gassy

sys-

tem. The solution for nozzle flow can be characterized by the

following dimensionless physical groups, evaluated with properties at

inlet stagnation conditions:

a +

1 -

a )p.C

T P

o o

r

SL

p o vo

a inlet void fraction)

o

vlo

vio

a + 1

o

o s

y - P /P

o go o

G* --==£=

0 * 0

P /P eas mole fraction)

vo

o

V 6

normalized mass flux)

Here u is a measure of the flow compressibility of the flashing

component while

a is a measure of the flow compressibility of the



305

non-flashing component. The relative amount is conveyed by the inlet

gas mole fraction y in the vapor phase. The generalized solution

for the normalized two-phase mass flux in a nozz le is given by (Leung

and Epstein, 1991)

G *

a y I n r r

6

- + (1 - a )y

o

y

g o P o - 'go

go

6

g°J

w ( l

"P

V

l n

p ~

+ (1

" vo

+ 1

« ) d - y

g 0

>

1/2

( 1 7 )

For given inlet conditions (i.e., P , T , a , u> , y ) , an additional

expression relating the two partial pressures, P ana P , is needed

before Eq. (17) can be solved for G*. This relationship is

The Dalton's partial

nozzle exit pressure P

(18)

pressure law can be written in terms of the

and the partial pressures:

g°

+ (1

g°

V

(19)

Eqs.

(18) andhus with the downstream pressure slightly below P ,

(19) can be solved for P /P and P /P , which can then be sub

stituted into Eq. (17) for calculating G*. This G* will correspond

to unchoked (subsonic) flow condition. However, as the downstream

pressure is reduced, G* reaches a maximum at the so-called choking

condition. By definition further reduction in downstream pressure

has no effect on G*. At this choked condition, the exit pressure is

given by the choked or critical pressure which is found from the

f o l l o w i n g e x p r e s s i o n

P

- a y I n r

2

- + (1

o

J

go Pgo

P

- «-(i -

y

g 0

)

l n

f~

° vo

1

2

y

g°

a

o

fP 1

- g -

P

I g°J

2

( 1

+

- a )y

o •'go

r p

)

1

- i * -

l g°J

+ ( i - « ) d - y

g 0

)

- y

R

0>

u

fP 1

V

P

0

.

2

1

P 1

V

P

v o

(20)

-.2

+ 1



306

TIME

Figure 1. Typical venting scenario for gassy system.

Homog e n e o u s

Ven t i n g

ca

o

CO

o>

o

•E

a.

T7

■a

T3

N o n - T e m p e r e d

S y s t e m

( G a s s y )

T e m p e r e d S y s t e m s

( V a p o r / H y b r i d )

■TP

'M R

TEMPERA TURE ( R e c i p r o c a l S c a l e )

Figure 2. Sizing approach for tempered and non-tempered systems.



307

PSV

LU

c c

I -

<

DC

LU

Q_

L U

I -

^

LU

CC

Z)

CO

c o

L U

c c

CL

TIME

I C L . 9 0 0 4 1 6 A . A

Figure

3.

Typica l venting scenario

for

tempered hybrid system .

1.4

1

1 I I I

lll|

1 1 I I I

^ - ^ N o n - F l a s h i n g F lo w

I I l l l | 1—I I I I I I I

F l a s h i n g F l o w _

0.8

0 .6

0 4

0.2

1 10

w

- - a

0

+

P o

C

P

T

o

p

o ( W h

v l o

)

100

2

Figure

4 .

Non-flashing

and

flashin g choked flow solu tion s

for

frictionless noz zle discharge.



308

j _

_L

0.2 0.4 0.6

INLET VOID, a

Q

0.8

1.0

Figure 5. Normalized mass velocity and critical pressure

ratio versus inlet void fraction for u) = 10

(y - 0, pure flashing flow; y = 1 , pure

non-flashing flow).



309

This is a transcendental equation for either P /P or P /P as it

R EO v V O

is to be solved simultaneously with Eq. (18) for

6

these critical

pressure ratios.

The solution for flashing flow (y - 0) and non-flashing flow (y

- 1) can be represented quite compactly for all inlet conditions is

shown in Fig. 4 (Leung,

1990b).

At the transition point between

these two regimes is the isothermal gas flow solution (G - 0.606

(P

p

) at u -

a -

1.0). A useful approximation for the flashing

choked flow regime when u> > 10 (for low quality inlet typical of most

homogeneous-vessel venting case) is simply (Leung, 1986)

G - 0.9 - ^ ■

1

(21)

C V

vio T C

J

o

p

Figure 5 illustrates how G* and P /P depends on

a

at various gas

mole fraction, y . At a fixed u — 10 (see definition of co for

a

,

this figure displays the shape of the G* versus

a

curves and the

P /P versus a curves for the entire range of y values (entire

C O O 2 Q

hybrid

regime).

It should be noted also that at the

&

limit of a - 0

(absence of both vapor and gas in the inlet), the current solutions

are in perfect agreement with the choked flow solution for subcooled

liquid inlet (Leung and Grolmes,

1988).

Conclusion

This paper, together with the previous paper, provide a state-of-the-

art summary of practical vent sizing methods for both tempered and

non-tempered systems. Significant advances in the area of two-phase

relief have been made in the past decade and these methods should

serve as valuable tools in ERS design. In addition, correlations and

equations have been developed for calculation of flashing flow, non-

flashing flow, and flashing flow with noncondensable gas through

relief devices. Finally, the tempered hybrid system should deserve

further study as such a development would provide a smooth transition

between the volatile vapor system and the gassy system.

References

Boyle,

W. J., Jr.

(1967),

Sizing Relief Area for Polymerization

Reactors , Chem. Eng. Prog., 63 (8), p. 61.

Creed, M. J. and Fauske, H. K (1990), An Easy, Inexpensive

Approach to the DIERS Procedure , Chem. Eng. Prog., 86 (3), p.

45

(March).

Fauske & Associates, Inc. (1989), Reactive System Screening

Tool (RSST) System Manual - Methodology and Operations ,

Report No. FAI/89-73.



310

Leung, J. C. (1986), "Simplified Vent Sizing Equations for

Emergency Relief Requirements in Reactors and Storage

Vessels",

AIChE Journal, 32 (10 ), p. 1622.

Leung, J. C. and Fauske, H. K.

(1987),

"Runaway System

Characterization and Vent Sizing Based on DIERS Methodology",

Plant/Operations Progress, 6 (2), p. 77.

Leung, J. C. and Grolmes, M. A. (1988), "A Generalized

Correlation for Flashing Choked Flow of Initially Subcooled

Liquid", AIChE Journal, 3 4 (4 ), p. 68 8.

Leung, J. C. (1990a), "Two-Phase Flow Discharge in Nozzles and

Pipes - A Unified Approach", J. Loss Prevention Process

Industries, Vol. 3, p. 27.

Leung, J. C. (1990b), "Similarity Between Flashing and Non-

Flashing Two-Phase Flows", AIChE Journal, 36 (5), p. 797.

Leung, J. C. and Epstein, M. (1991), "Flashing Two-Phase Flow

Including the Effects of Noncondensable Gases", ASME Trans. J.

of Heat Transfer, 113 (1), pp. 269-272 (February).



CALORIMETRY FOR EMERGENCY RELIEF SYSTEMS DESIGN

J.L. GUSTIN

RHONE-POULENC INDUSTRIALISATION

24, AVENUE JEAN JAURES

69151 DECINES CEDEX B.P.166

FRANCE

ABSTRACT. This paper gives an overview of the DIERS methodology for vent sizing

for runaway react ions. The DIERS vent sizing methods rely on experimental data

obta ined under adiaba t ic con dit ions . The theoret ical ba ckg roun d of prac t ical interest

for pseu do-adiab at ic calor imetry is given. This theore t ical ba ckg rou nd provides

methods to correct the data obtained in pseudo-adiabat ic calor imetr ic devices to true

adiabat ic condi t ions.

The experimental methods available for the system characterizat ion and data

acq uisit ion are des cribe d. These experimental m ethods are :

The Accelerating Rate Calorimeter (ARC),

The Vent Sizing Package (VSP),

The closed Dewar experiment,

The Reactive Systems Screening Tool (RSST).

The results obtained with the various methods are compared and the relevance of

these methods to vent sizing is discussed on an experimental and theoret ical basis.

311

A.

Benuzzi and J. M. Zaldivar (eds.), Safety of Chemical Batch Reactors and Storage Tanks, 311-354.




312

1 - INTRODU CTION

Emergency Relief Systems (E.R.S.) are provided on vessels containing a

chemical compound or a mixture prone to undergo a runaway react ion, to

prevent these vessels from exploding.

Normally these vessels cannot resist the pressure generated by a runaway

react ion.

The Design Institute for Emergency Relief Systems (DIERS), a working party of

the AlChE, has issued vent sizing guidelines which take into account the

occurence of two phase f low when the E.R.S. is actuated.

The previous methods issued by the A.P.I, which only took into account gaseous

release could lead to undersizing by a factor of 6-10, should a runaway react ion

be init iated (1).

The DIERS Methodology for vent sizing includes the fol lowing basic steps

Step 1 : Def init ion of the worst cred ible deviat ion of the proces s, to p rovide the

design case for vent sizing.

Step 2 : Characterization of the react ing system behaviour, using pseud o-

adiabat ic experimental techniques. The react ing systems are divided in

three classes :

- High vapor systems

- Gassy reac tions

- Hybrid systems.

Step 3 : Acq uisit ion of the exp erimental data necessary for vent s izing . The

nature of the data required depends on the nature of the react ing

system. The data must be obtained under condit ions close to adiabat ic

for a correct simulat ion of the runaway behaviour.



313

Step 4 : Choice of the vent sizing method and of the two phase f low calculat ion

method, according to the system behaviour.

The purpose of this paper is to describe the experimental methods available for

the system characterizat ion and data acquisit ion for vent sizing and to discuss

the relevance of the various methods on an experimental and theoret ical basis.

The def init ion of the worst credible deviat ion of the process and the discussion

of the choice of the most suitable method for vent sizing and two phase f low

calculat ions, are beyond the scope of this paper.

CHARACTERIZATION OF THE REACTING SYSTEM

Three classes of react ing systems are considered in the DIERS methodology.

1) High vapor systems

High vapor systems are react ing systems where the pressurizat ion of the

enclosure is due to a vapo r- l iquid e qu il ibr ium . The vapor pres sure may be

that of the solvent, the reactants, the products or the react ing mixture.

The vapor- l iquid equil ibr ium must apply during the t ime necessary for the

E.R.S. actuact ion. This must be checked on an experimental basis under

runaway condit ions.

High vapor systems are tempered systems : If E.R.S. actuation allows control

of the pressure in the vessel, the temperature is also control led because the

pressure vs temperature relat ionship is imposed by the vapor- l iquid

equi l ibr ium.

The control of the temperature during the vent actuat ion al lows the control of

the react ion rate in the react ion mixture, provided that the react ion fol lows

the ARRHENIUS law.

These features al low the thermal runaway to be easily control led. The vent

area required is usually less for a high vapor system than for a gassy

react ion.



314

For high vapor systems, the pressure in the vessel does not depend on the

f i l l ing rat io. This al lows laboratory experime nts to be p erform ed in a closed

test

cel l ,

with a high f i l l ing rat io, giving nearly adiabat ic condit ions yet no r isk

of cel l rupture.

For high vapor systems the vent area is est imated by considering the

adiabat ic heat rate at the temperature Tg related to the vent set pressure P

s

by the vapor- l iquid equil ibr ium.

The fol lowing data is required for vent sizing :

- the adiabatic heat rate curve of the reaction m ixtur e,

- the pressure vs tem perature relat ions hip.

2) Gassy reactions

Gassy react ions are react ions in the condensed phase which produce non-

condensable gases l ike CO, C0

2

, N

2

, NO, NgO, 0

2

...

The pressure in the enclosure is due to non-condensable gases only. There is

no vapor- liquid equi l ibr ium.

Consequent ly, the system is not tempered, even if the pressure in the

enclosure is controlled by an E.R.S. there is no vaporization heat sink, the

temperature r ise is unaffected and the chemical react ions speed up with

temperature.

For gassy react ions, the pressure in the vessel depends on the f i l l ing rat io.

The higher the f i l l ing rat io, the higher the pressure r ise and the pressure r ise

rate. In laboratory experiments using closed cells, the f i l l ing rat io must be

kept low to prevent cel l rupture. As a consequence, the experimental

condit ions are far f rom adiabat ic.

Vent sizing for gassy reactions is based on the maximum rate of gas

generat ion measured under adiabat ic condit ions. I t is safe to consider that

this rate is obtained even if the vent is actuated, and to design on this basis.



315

3) Hybrid systems

A hybrid system is a tempered system where non-condensable gases are also

produced by the runaway react ion. Neither the vent sizing equat ions nor the

two phase vent f low equat ions are well established or val idated.

Due to tempering, the vent size is est imated by considering the heat rate and

the non-condensable gas generat ion rate at tempering condit ions e.g. at the

temperature T

s

related to the vent set pressure Pg by the vapor- l iquid

equil ibr ium. The discussion of the vent sizing equat ions for hybrid systems is

beyond the scope of this paper.

In addit ion the behaviour of several hybrid systems may be considered.

Systems with a polymerizat ion fol lowed by a decomposit ion react ion of

the polymers producing n on-con dens able g asses. As long as the

monomers are present, the system is tempered. I t may change to a gassy

react ion when the monomers are consumed. Vent ing is best achieved

when the monomers vapor pressure is available.

Systems where a react ion produces non-condensable gasses in the

presence of a solvent vapor pressure. An example could be the

decomposit ion of an organic peroxide in a toluene solut ion.

The system is tempered (and hybrid) as long as the solvent is present.

In the previous, example, if there is not enough solvent, the solvent is

boiled off and the system behaviour changes to a gassy reaction as in

case 1.

In any case it is necessary to check on an experimental basis that tempering

is available during the time necessary for the E.R.S. to operate. This must be

done under nearly adiabat ic condit ions.



316

3 - PSEUP O-ADIABA TIC CALORIMETRY

3.1 Th erm al Inertia

Experimental methods in calor imetry where the sample enclosed in a test

cel l ,

is al lowed to react with no heat exchange with the outside, are cal led

"Pseudo-Adiabat ic Techniques". This is to emphasize the fact that i t is the

sample and the test cel l which are under adiabat ic condit ions.

In these techniques the heat produced by the chemical react ion causes a

temperature r ise in both the sample and the test

cel l .

The experimental set up is usually able to prevent any heat loss from the

test cel l by maintaining the temperature of the surroundings equal to the

sample temperature or to the test cel l wall temperature.

The way the heat produced by the sample causes an increase in i ts own

temperature and that of the test cel l is characterized by the Phi factor :

Heat capacity of the sample + test cell

$

=

Heat capacity of the sample alone

Under true adia batic con dit ion s, (J) = 1

The Phi factor is greater than 1, provided that there is no heat input from

the outside to the sample.

When a runaway reaction occurs in a chemical plant, the Phi factor is 1.05

or less.

The use of pseudo-adiabat ic techniques to provide data for vent sizing

relies on the possibility of achieving a Phi factor close to 1 and/or

correct ing the experimental data to true adiabat ic condit ions.



317

The experiments are performed by charging the cold react ion mixture in the

test cel l and then by slowly raising the temperature to init iate the react ion.

When the sample exhibits self heat ing, the apparatus assumes adiabat ic

condit ions for the sample and the test

cell.

3.2 Onset tempe rature

The smallest exotherm which can be detected depends on the sensit iv i ty of

the apparatus. I f a given react ion is studied in dif ferent types of apparatus,

the onset temperature observed wil l be lower in more sensit ive apparatus.

The maximum heat rate is also reduced in the most sensit ive equipment,

due to more reagent deplet ion before this point is reached.

The maximum heat rate observed in dif ferent types of apparatus must be

adjusted to the same onset temperature.

3.3 Th eore tical basis

The theory by D.I. TOWNSEND and J.C. TOU [2] for the Accelerating Rate

Calorimeter (A.R.C.) holds for the other pseudo adiabat ic techniques. This

theory assumes that the temperature r ise observed is proport ional to the

degree of conversion and that the rate constant depends on the

temperature according to the ARRHENIUS law. The theory provides a

method of determining the kinet ic parameters of the ARRHENIUS law from

the experimental data e.g. the heat rate curve, dT/dt in log.scale vs T in

reciprocal scale.

The Phi factor is introduced to take into account the deviat ion from

adiabat ic condit ions due to the heat capacity of the cel l .

This theoret ical background provides methods to correct the heat rate curve

dT/dt vs T for the deviat ion from true adiabat ic condit ions.

The adiabat ic temperature r ise A T * _

1

is obtained f rom the exper imental

temperature r ise 4 T * - by the st raight forward relat ion



318

4 T < D

= 1

= 0 .

4 T ( ] ) > 1

The adiabat ic f inal temperature Tf is deduced from the onset temperature

To by

Tf = To + 0 . ATQ^

Furthermore, near the onset temperature To or i f the react ion is zero order,

(i.e.

reactant consumption has no effect on the react ion rate), the adiabat ic

heat rate is obtained from the experimental heat rate by :

For zero order only

A method is proposed to correct the whole heat rate curve but this method

is not satisfactory.

It is necessary to be familiar with the theory by D.I. TOWNSEND and

J.C. TOU to have a good unde rstanding of the correc t ion me thods , de spite

the fact that few f indings of this theory are used for vent sizing purpose.

When the experimental heat rate must be corrected to adiabat ic condit ions

at a temperature far f rom the onset temperature where the react ion is not

"O " order, a method proposed by H.G. FISHER (3) after J. HUFF (4) is best

used.

In this method, the experimental onset temperature or f irst measured

temp erature T ^ is corrected to take into account the deviat ion fro m

adiabaticity :



319

1 R

— + — Ln 0

T

M

E

where

T

o =

T

M =

R =

E =

0 =

adiabat ic onset temperature

f irst measured temperature

ideal gas constant

activation energy

Phi factor

This correct ion takes into account the fact that for a given onset detect ion

sensit iv i ty of the experimental device, the onset temperature would have

been lower if the Phi f ac to r was 0 = 1 .

Then the heat rate curve is corrected for the Phi factor.

The adjusted temperature T» for 0 = 1 is obtained for every measured

temperature T^| by :

T

A

= T

n

+ 0 n \ , - T

n

)

'A " 'o M V

The corrected heat rate /dT \

dt 0 = 1

is obtained f rom the measured

hea t rate / dT \ by

I dt/0

>

1

dT

—

d t _

0 = 1

= 0 -

EXP

E

—

R

/ 1

( - -

\ T

'M

' A / J

dT

dt

0> 1



.20

Correct ion for a dif ferent onset temperature

The react ion rate at any temperature above the onset temperature is

inf luenced by the onset temperature.

The onset temperature of the react ion may be determined experimental ly by

a temperature scan in a pseudo-adiabat ic apparatus. In this case, the onset

temperature depends on the onset detect ion sensit iv i ty of the experimental

device. No exotherm can be measured below the base l ine heat rate on the

heat rate curve. The base line heat rate is given by the rate of temperature

scan.

As dif ferent experimental techniques may produce dif ferent onset

temperatures due to different onset detection sensit ivit ies it is necessary to

correct the measured heat rate to the same onset temperature and to the

same Phi factor, to compare the experimental results.

I f the react ion is init iated by a process deviat ion "by introduct ion", the

react ion is immediately fast whereas in a laboratory experiment, the react ion

is init iated by a temperature scan on the react ion mixture loaded cold in the

test

cell.

The react ion rate under process condit ions can be obtained from this

measured heat rate, adjusted for the dif ference in the onset temperature

and in Phi factor.

The fol lowing correct ion method can be used :

1) The experimental onset tempe rature is correc ted to take into acco unt

the deviation from adiabaticity as previously :

1 1 R

— = — + — . Ln (J)

T

o

T

M

E



321

2) I f a dif ferent onset temperature T^ is considered, any measured

temperature is adjusted for this new onset temperature :

T

A

=

T

o

+ <

f - r r

M

- T

0

)

Then the adjusted heat rate is obtained by :

This correct ion method seems realist ic for simple one step ARRHENIUS

react ions. I t al lows the correct ion of the whole heat rate curve and does

nothing more than changing the onset temperature on the "O" order l ine

once corrected by the Phi factor.

This correct ion method derived from the thermal theory of D.I .TOWNSEND

and J.C. TOU, can also be used to correct the n on-c ond ens able gas

generat ion rate. This is straightforw ard i f the kine t ic param eters for the

gas generat ion are the same as for the heat generat ion.

I f not, the gas generat ion rate must be adjusted using this method in the

absence of any other method.

3.4 Pressure

In addit ion to the kinet ic data the pseudo-adiabat ic techniques al low the

characterizat ion of the system behaviour.

For high vapor systems, the pressure (corrected for inert gasses) in

log.scale is a l inear funct ion of the temperature in reciprocal scale.

The pressure increase during the runaway is also inf luenced by the Phi

factor as the f inal temperature is higher under true adiabat ic condit ions.



322

A deviat ion from an init ial vapor pressure curve may indicate the product ion

of non-condensable decomposit ion gasses.

Alternatively polymerization of the reaction mixture will give a lower

pressure than expected from the init ial pressure curve.

For gassy reactions, experiments in closed cell will often lead to cell rupture

for reasonable f i l l ing rat ios. A prel iminary experiment using an autoclave

wil l provide information on the system behaviour and al low the choice of a

fil l ing ratio which will avoid cell rupture even if the reaction is gassy. A

prel iminary examinat ion of the react ion using DTA and the autoclave should

be carr ied out before any pseudo adiabat ic experiment.

THE EXPERIMENTAL TECHNIQUES

The pseudo-adiabat ic techniques available at the moment are :

- The Accelerating Rate Calorimeter (A.R.C.) manufactured by Columbia

Scient if ic Instruments,

- The Vent Sizing Package (V.S.P.) man ufac tured by FAI an d FIKE,

- The closed Dewar apparatus made from a commercial stainless steel

Dewar f lask,

- The Reactive System Screen ing Tool (RSST) m an ufa cture d by FA I.

We now describe these types of equipment and discuss their relevance for vent

siz ing.

4.1 The Acc elera ting Rate Calorime ter (ARC)

The A.R.C. is manufactured by Columbia Scient if ic Instruments a small f irm

of 75 workers situated in Austin Texas.

The original design was derived from the laboratories of DOW Midland. I t is

the most wide spread pseudo-adiabat ic technique. More than 100 ARC

instruments have been sold.



323

Description of the ARC

The basic pr inciple of this apparatus involves maintaining the sample and

the test cel l under adiabat ic condit ions once an exothermic react ion is

detected.

The calorimeter jack et and the spherical test cel l are show n in f igu re 1. The

test cel l normally contains between 1 and 10 g of l iq uid or sol id m aterial.

The test cel l is connected to a pressure transducer (operat ing range 0-2500

PSIA) and suspended inside a calor imeter jacket constructed from Nickel-

platted copper. The jacket contains eight heaters and three thermocouples.

A fourth thermocouple is attached to the outside of the test cel l . The

operat ing temperature range is 0-500°C. All ARC operat ions are control led

by a microprocessor. The results are obtained on a line printer (raw data)

and on an X-Y plotter (graphs).

Figure 2 shows the heat-wait-search operat ion of the accelerat ing rate

calorimeter.

The sample is f irst weighed in the test cel l to determine the value of the Phi

factor. The test cel l is connected to the l ine to the pressure gauge inside

the jacket and the number three thermocouple is attached on the test cel l

wall.

The user inputs the various parameters which describe the desired

experiment which wil l be carr ied out automatical ly.

The sample undergoes a series of Heat Wait-Search cycles unt i l self-heat ing

is detected through the test cel l wall temperature.

At that point, the condit ions for the test cel l and the sample are

automatical ly kept adiabat ic while the data (Temperature - Pressure - Time)

is stored in the microprocessor.

At the end of the experiment the computer wil l process the data. The

fol lowing graphs are obtained :

- The observed temperature versus t ime f ig.3,



324

PRESSURE

TRANSDUCER

CELL THERMOCOUPLE

THERMOSTAT JACKET

TEST CELL

FIGURE 1 : ACCELERATING RATE CALORIMETER

TEMPERATURE

WAIT

SEARCH

PSEUDO ADIABATIC

TIME

FIGURE 2 : THE HEAT-WAIT-SEARCH OPERATION OF ARC



325

TEMPERATURE

FIG. 3

-TEMPERATURE VERSUS TIME

TIME

F I G . 4

HEAT-RATE VERSUS TEMPERATURE

HEAT RATE

(LOG. SCALE)

TEMPERATURE (RECIPROCAL SCALE)

ACTIVATION

A ENERGY

FIG. 5

ACTIVATION ENERGY

VERSUS TEMPERATURE

TEMPERATURE

A. PRESSURE

LOG.

SCALE

FIG. 6

PRESSURE VERSUS TEMPERATURE

TEMPERATURE (RECIPROCAL SCALE)



326

A

dP/dt (LOG.SCALE)

TEMPERATURE

(RECIPROCAL SCALE)

FIG. 8

PRESSURE RISE RATE

VERSUS HEAT RATE

A k (LOG.SCALE)

5»

TEMPERATURE

(RECIPROCAL SCALE)

FIG. 7

RATE OF PRESSURE RISE

VERSUS TEMPERATURE

dP/dt

A (LOG.SCALE)

dT/di

j.

(LOG.SCALE)

FIG. 9

PSEUDO CONSTANT k

VERSUS TEMPERATURE



327

d T / d t

(LOG.SCALE]

- >

TEMPERATURE

(RECIPROCAL

SCALE)

FIG.

10 : HEAT RATE VERSUS TEMPERATURE

CORRELATION OF EXPERIMENTAL DATA

TEMPERATURE

(RECIPROCAL SCALE/\

> ■

TIME (LOG.SCALE)

FIG. 11 : TIME TO MAXIMUM RATE VERSUS TEMPERATURE



328

- The observed heat rate in Log.scale versus the temperature in reciprocal

scale f ig.4,

- The act ivat ion energy versus the temp erature f ig.5 ,

- The pressure in Log.scale versus the temperature in reciprocal scale f ig.6,

- The rate of pressure rise in Log.scale versus the temperature in reciprocal

scale f ig.7,

- The rate of pressu re rise versus the heat rate bo th in Lo g .scale f ig.8 ,

*

- The pseudo constant k in Log.scale versus the tempe rature in recip rocal

scale f ig.9,

- The correlation of the heat rate data by an estimated heat rate curve

f ig.10,

- The t ime to maxim um rate in Log .scale versus the temp erature in

reciprocal scale f ig.11.

Kinetic interpretation

The act ivat ion energy is obtained from the curve in f ig.5 or from the slope

of the heat rate curve in f ig.4. The order of the react ion is obtained from

the fol lowing relat ion :

E

A

n =

(If "

T

i

R T

M

2

where

Tf = f inal temperature

T

Q

= onset tempe rature

T

M

= temperature at maximu m rate



329

The estimated value of n is checked by the linearity of the plot of pseudo-

constant versus reciprocal temperature in f ig.9.

If the linearity is not satisfactory the value of n needs further adjustment.

Then the adjusted heat rate curve may be compared with the observed heat

rate curve as in f ig.10.

Results of practical interest

The heat rate curve and the kinet ic interpretat ion wil l provide the kinet ic

parameters of the ARRHENIUS law k , E, n, near the onset temperature.

Due to low onset temperature and high Phi factor the heat rate curve may

show that the reaction splits in several separate steps. This is an interesting

result.

The P versus T curve wil l al low the system characterizat ion in the

experimental temperature range.

The heat rate versus pressure rise rate curve may prove that the heat

release and the gas generat ion are due to the same react ion.

If the reaction is a simple one step ARRHENIUS reaction the heat rate curve

and the pressure rate curve can be corrected to true adiabat ic condit ions.

Comment on the results of an ARC run

The results can only be obtained if the experiment comes to complet ion i .e.

I f the test cel l does not rupture. To operate the ARC properly the sample

thermal stabil i ty and the decomposit ion behaviour must f irst be measured

using DTA/DSC and Autoclave experiments.



330

Phi factor

I f the sample react ion produces non-condensable decomposit ion gasses,

the fil l ing ratio of the test cell must be low enough to prevent cell rupture

i.e. to keep the pressure in the ope rat ing range . The sam ple w eight may be

as low as 1 g and the Phi factor 5 to 8 using a S.S. bomb.

If the sample reaction behaves like a high vapor system in an autoclave

experiment, the f i l l ing rat io in the ARC test cel l may be high enough to

achieve a Phi factor as low as 1.2 using a t itanium bomb.

Sensit ivity of the onset detection

Due to the heat - wait - search procedure, the heat rate sensit ivity threshold

for the exotherm onset is as low as 0.02°C/mn. Depending on the sample

heat capacity, the sample mass and the Phi factor, the sensit ivity is better

than 1 wa tt /kg sam ple. This is better than m ost DTA/DSC eq uipm en t.

Effect of Phi factor and sensit ivity of onset detection

The ARC is an apparatus with a good onset detect ion sensit iv i ty. The onset

temperature where the apparatus assumes a pseudo adiabat ic behaviour is

very low compared to other techniques.

The Phi factor typically ranges from 2 to 5 (extreme values 1.2-9).

The Phi factor is high compared to other techniques.

These two features will cause low measured heat rates and will allow

decoupling of complex kinet ics al lowing the separat ion of complex

reactions into separate steps.

Experimental temperature range

In an ARC experiment the onset temp erature T of the exotherm is low due

to the good onset detect ion sensit iv i ty compared to other equipment.



331

The experimental temperature r ise (T

f

- T

Q

) = A T

A B

/ 0 is redu ced due to a

high Phi factor.

The experimental temperature range of the exotherm is shif ted toward lower

temp eratures. This may cause a subseq uent e xotherm not to be inclu de d in

the runaway, which would have been tr iggered in adiabat ic condit ions.

Let us take an example :

I f the onset temperature of an exotherm measured in the ARC is 30°C and

the exper imental temperature r ise 100°C with 0 = 3 , the exper imental

temperature range is 30°C - 130°C.

In a less sensit ive but more truly adiabatic device, the onset temperature of

the same exotherm may be 60°C and the experimental temperature r ise

cou ld be 300°C with <J) ~ 1. Then the e xpe rime ntal te m pe ratu re range is

60°C - 360°C.

In these two experimental temperature ranges, the react ion is not the same.

Further decomposit ion react ions may be tr iggered between 130°C and

360°C wich wil l increase the heat rate and the exotherm. In such a case, the

runaway behaviour is not satisfactorily measured with the ARC.

Conclusion on the relevance of ARC data to vent sizing

The advantages and disadvantages of the ARC experiments in providing

data for vent sizing may be exemplif ied by considering the heat rate curve

of f ig.12 obtained for the phenol + formaldehyde runaway react ion with the

recipe of ref.5.

This heat rate curve shows al l the above mentionned features

- low onset tempe rature

- low ma ximu m heat rate

- de cou pling of several reaction steps



ARC

N 208 - 209

.0)

.M

or/ut

I'HEHOL

'

FORMALDEHYDE REACTION

J

— ' — ' — I A J

- J — I — I — I I I

ldu -

1

-

— - ^ E L M -

C O

Fig.12 : Phenol I Formaldehyde runaway reaction with the recipe of Ref 5

measured in ARC. Note the onset temperature and the maximum

heat rate.



333

and cannot be corrected to adiabat ic condit ions by the known simple

correct ion methods.

In conclusion the ARC is not well suitable for vent sizing because it

operates too far f rom adiabat ic condit ions and gives onset temperatures

and maximum heat rates which are too low.

The other pseudo-adiabat ic techniques are more suitable for vent sizing.

On the other hand the ARC is st i l l a valuable tool for obtaining thermal data

near the onset temperature and detect ing complex react ions which may

look simple under runaway condit ions.

4.2 The Ven t Sizing Pack age (V.S.P.)

The V.S.P. is the commercial version of the DIERS Bench scale apparatus

designed to operate under nearly true adiabat ic condit ions. The f irst

manufacturer was FAUSKE Associates Inc. (FAI), a consultant f rom

Burr.Ridge (I l l inois). After some t ime the manufacturing l icence was given to

Fike,

a

rupture disks manufacturer. At that point some design changes were

incorporated which caused unwanted problems. This has since been

rect i f ied.

25 VSP have been sold so far. The last apparatus was purchased by

Rhone-Poulenc. No other VSP have been sold in the past two years.

A VSP clone is proposed by Dr.SINGH from the Brit ish Fire Research Center

and at least one has been sold to the JRC in Ispra.

The reasons for this lack of interest in the VSP are probably the following :

Some weaknesses in the design of the apparatus.

The VSP cannot be used alone but as a complement to a well equipped

laboratory. The VSP tests are the last to be done in safety studies where

an ERS is needed.

Once the VSP design is understood, the apparatus can be buil t at less

material cost and with more technical ref inement than the commercial

model .



334

The demand for the product is l imited by the high level of expert ise

required to operate it and interpret the results.

The same results may be obtained through closed Dewar f lask

experiments.

Description of the VSP

A descript ion of the VSP and of the test procedures is given in ref.6 see

also f ig.13.

The key feature of the equipment is the use of a low heat capacity test cell

to reduce the Phi factor. The test cel l volume is 116 ml and the wall

thickness is 0.13 mm. A Phi factor of 1.05 is achieved provided that the

temperature control of the heat ing device is correct. The weight of the test

cell is 20 to 30 g. The test cell is enclosed in a containment vessel designed

to withstand pressures up to 200 bar in Europe. The weakness of the test

cel l is compensated by maintaining the pressure in the containment vessel

equal to the test cell inner pressure to prevent cell rupture.

Alternatively an open test cell can be used, especially for gassy reactions.

The heat ing device is a heat ing coi l separated from the test cel l by an

insulation assembly. The auxiliary heater is used to heat the test

cel l ,

when

in temperature scan mode, with a minimum heat rate of 0.3°C/mn. The

outer guard heater is placed on the outside wall of an aluminium can

separated from the can by a uniform layer of insulat ion. A thermocouple is

attached to the inner surface of the aluminium can.

Once the sample heat rate is higher than the temperature scan heat rate,

the auxiliary heater is switched off but the guard heater is used to keep the

temperature of the surroundings equal to that of the test

cel l .

The original design of the VSP did not include a Heat - Wait - Search

rout ine.

The heater temperature and containment vessel pressure are control led by a

computer .



335

PRESSURE

BY PASS

TEST CELL

OUTER CAN

THERMOCOUPLES

NITROGEN

EXHAUST/SUPPLY

®

GUARD HEATER

INNER HEATER

INSULATION

CONTAINMENT VESSEL

FIGURE 13 : VENT SIZING PACKAGE (V.S.P.)



336

Test procedure

The VSP can be used to characterize runaway chemical react ions in a

closed cell as well as in an open or a vented

cel l .

The experimental

information obtained includes Thermal data (closed cell) and f low regime or

viscosity characterization (open cell).

Obtent ion of thermal data

The sample is loaded cold into the closed test

cel l .

The runaway react ion is

init iated by slowly raising the temperature. A constant heat rate mode is the

best choice.

When the exotherm onset temperature is reached, the sample heat rate

becomes higher than the temperature scan heat rate. The guard heater is

then switched on to ensure adiabat ic condit ions for the test

cel l .

The pressure in the containement vessel is control led to fol low the test cel l

pressure.

When the react ion is completed, the power is turned off to the guard heater

and the sample is allowed to cool slowly.

The thermal data includes :

- The temperature T^ versus time curve

- The pressures P^ and

?2

versus time curve

- The heat rate curve

- The pressure rate curve

- The pressure versus temperature curve.

The closed cell procedure is suitable for obtaining thermal data for high

vapor (tempered) systems where the pressure is due to a vapor- l iquid

equi l ibr ium.



337

For gassy reactions or hybrid systems the closed cell bursts readily due to

the high f i l l ing rat io. This exemplif ies the need for a prel iminary test using

an autoclave to detect the product ion of non-condensable gasses. Only the

high vapor systems should be used in a VSP closed cell test.

For test ing gassy and hybrid systems in the VSP the "constant volume

mode" is best used where the gas product ion rate is obtained from the

pressure build up in the containment vessel using a open top

cel l .

To demonstrate the use of the VSP in obtaining thermal data, the heat rate

curve of the phenol+formaldehyde runaway react ion with the recipe of ref .5

is given f ig.14. Note the high onset temperature and the high maximum

heat rate obtained in the VSP experiment.

Flow regime test ing

Flow regime characterizat ion is obtained from blow-down tests using a top

vented test cell.

For the current test cell design, the vent line diameter of 2.5 mm leads to

linear f low ve locit ies of 30 - 60 cm /s. No rmally 40 % to 60 % of the liqu id

wil l be lef t behind fol lowing blowdown transient i f non-foamy behaviour

prevails.

If a foamy regime prevails, no liquid is left behind in the test

cel l .

The test procedure is the following : (see fig.15)

- The containment vessel pressure is set to the value Pg.

- The runaway react ion is init iated and al lowed to reach tempering at Pg.

- The containment vessel pressure is decreased to atmospheric, thereby

init iat ing the blowdown process.

- Whe n the test cel l pressure is equal to atm osp heric, the con tainm ent

vessel is immediately repressurized to prevent further mass loss from the

test cel l . The sample mass lef t behind in the test cel l is determined by

weighing it af terwards.



338

a

en

LL : 1 I LI

L I.I i I..I.I

1

1

1

1 1 1 1 1 L l

1

_43T

I I I 1

I I

I I I 1 I 1 I I I I I 1

I

1

i i i i i i i i i i i i i i l i i i i i i i i n n i i i i i i i i i i i u i

■ ■ r

—

\

jg r

l i .

. . . . . | . . . . . . . _ _ _ .

1

1

-

c F

£°

f

n

z

r;

:

;

:

iV-Z-t~:';E?

'~~ Jr

i

*f \

*r 1

^

4? ' -a -

1

m

3

0

3

~ f

□

D

rff *

- -

&k ~

'•

I l l

6(

«

a

3

I I

] 8(

1 , 1

1 ' , 1

J_LLi . J.L .

:

I

1

I

1 M 1 I I I 1

M I i i m i l H I

1

1

l l l l M l i

r 11

M M M

1

r

) 100 120 HO 170 200

°C)

Fig.

14

Phenol + Formaldehyde runaway reaction with the recipe

of Ref. 5,measured in the VSP. Note the onset temperature

and the maximum heat rate.

Reaction initiated by a temperature scan.



339

r

Ts

,

TEMPERING

- ^

- X

l\

P

'W

\ \

?< , te

R E P R E S S U R I Z A T 1

BLOW DOWN

/

TIME

FIGURE 15 : BLOW DOWN TEST FOR FLOW REGIME TESTING

BLOW DOWN

TIME

FIGURE 16 : BLOW DOWN TEST USING BOTTOM VENTING FOR VISCOSITY TESTING



340

Viscosity testing

The VSP experiment using a bottom vented test cel l and the blowdown

technique is used to characterize the f low regime (turbulent or viscous). A

vent line with L/D ~ 30 and a line length = 100 m m is used to assure

equi l ibr ium f lashing f low condi t ions.

The test procedure is the following : (see fig.16).

Following tempering the by-pass valve is opened to al low a pressure

equalizat ion between the test cel l and the conta inm ent vess el. Then the

blowdown process is init iated.

The f low rate is obtained by measu ring the em ptying t ime A t^ .

The measured f low rate is compared with the two phases f lashing cr it ical

f low rate G given by the ERM model :

dT Y C p

L

If the experimental f low rate is less than the ERM value the flow is viscous.

Comment on the VSP

Advantages of the VSP design

The VSP achieves a Phi factor close to 1 and condit ions close to the

adiabat ic.

Realist ic runaway simulat ion is obtained using the close test

cel l ,

thus

providing suitable data for vent sizing for high vapor systems. Heat rates as

high as 2500°C/mn can be measured.



341

Drawbacks of the VSP

Open cell test ing appears to be expensive because of damage to the

heat ing device.

The heat rate base line corresponds to an onset detection sensit ivity of

0.3°C/mn. This is a poor sensit iv i ty compared with the ARC. Constant

temperature exposures are dif f icult to achieve because of the temperature

drift of the VSP.

The pressure fol low-up in the containment vessel could be better.

VSP clones

Once the basic design of the VSP is understood the performance of the

apparatus can be easily improved by the users. It would be unfair to present

these improvements as a new concept which could just i fy a trade

compet i t ion.

These modif icat ions can be divided into :

- improvem ents to the com puter program

- improvements to the hardware.

The improvements to the computer program are the fol lowing :

- Improvement to the onset detection sensit ivity through a heat - wait -

search rout ine

- Supp ression of the tempe rature dr if t during cons tant temp erature

exposure by better temperature control

- Improvement of the pressure control in the containment vessel to reduce

or delay cel l rupture by fast react ions. This is done by reducing the

control loop cycle t ime in the computer program

- Improvements to the data output, curve print ing



342

- Pressure correct ion for the Nitrogen p ad .

The improvements to the hardware are the fol lowing

- Replace the pressure gauges by piezoelectric gauges, easy to clean with

a range 0-200 bar

- Improve the pressure control in the containment vessel by increasing the

pipe size for nit rogen input, providing a Nitrogen compressor and a

Nitrogen balast close to the containment vessel.

Possibly measure directly the differential pressure between the test cell

and the containment vessel.

- Improve the st irr ing rel iabi l i ty by redesigning the containment vessel and

choosing a better dr iving magnet

- Improve the insulat ion p acking repro duc ibi l i ty by p roviding a sol id

insulat ion block

- Improve open cell and blow-down test ing condit ions by providing a

pressure resistant catch tank outside the containement vessel thus

allowing the test to be aborted if the pressure increases to 200 bar.

To encourage improvements to the VSP we give in f igs 17-19 the results

of a closed cell test on an aqueous solut ion of hydroxylamine sulfate 44 %

by weight. It is a high vapor system. A heat rate as high as 2000°C/mn

and a pressure rate as high as 25 bar/s were measured without cel l

rupture.

Conclusions on the VSP

The basic p r inciple of the VSP is quite in terest ing . The VSP cap abil i ty ca n

be improved by a better design. We are quite conf ident about the future

of this apparatus.



343

10"

103

_

10

2

r

IO

1

10 "

=

lo-'b

10-2

H E A T R A T E

r. '^rrpts^SfrrfK.-f.,

-

rr

p*-f***n: '

l

n" '

- 1 0 0 0 / T ( K )

-3

-2.8 -2.6 -2.4 . -2.2 -2 -1.8 -1.6

.4

(. _ 1.—(.

1—4—|—|—(—J—k_J—I—I—|—l_J__+_4—;--»--l--t-4-l-4-4-+

100 150 200 2 5 0 300 350

F i g u r e

17

103

1 0

2

10 '

inn

P r e s s u r e = f(T)

, . . /

^

-looomK)

-

:

:

1 \.—+-

-2.6 -2.4 -2.2 -2 -1.8 -1.6

4—J....4-4—4—4— 4—4—1~4~-1—l~4-J-4-4-4-4-4--l"M-4-4-4-4

100

150

Figure 18

200

250 300 350



344

DP/Dt = r m

1 0

J

1 0

3

102

1 0 '

h

. 3

c

10"

10-'

io-2

10-3

1 0

J

_

1 ' " " '

..-y^f

.-"""

,*'

"

_

"

- 1 0 0 0 / T ( K )

-2 .8 -2 .6 -2 .4 -2 .2 -2 -1 .8 -1 .6

4-—+—[ —; —I J—i— —J— I—1-—-i—I—1— k—I—1— 4-4—4-4—^-1-4-4-4-4-;-

100 150

2 0 0 2 5 0 3 0 0 3 5 0

Figure 19

Fig. 17-18-19 - VSP closed cell test on 44 % by weight

aqueous solution of Hydroxylamine Sulfate.



345

4.3 The closed Dewar experiment

The closed Dewar experiment was formerly used to determine react ion

onset temperature and adiabat ic induct ion t ime. For this reason it is a wide

spread test ing method.

The use of closed Dewar experiment to provide the experimental data for

vent sizing has been emphasized more recently by R. ROGERS (I.C.I.) (7)

an d the author (Rh one-Poulenc) (5). This is ma de pos sible by the availability

of low Phi factor stainless steel Dewar f lasks achieving a Phi factor of 1.1.

In cont inental Europe the best Dewar is made from the domestic i tems sold

in the superma rkets by Cam ping G az. The same items are also sold in

England by Thermos. These Dewar f lasks are manufactured in Japan and

Korea. The price for 1 I f lask is 300 F.F. The plastic cap on the original item

is replaced by welding

a

thread to hold a cap eq uippe d with

thermocouples, a pressure gauge, a rupture disk and a blow-down valve.

The Dewar f lask is heated in a furna ce the tem pera ture of w hich is

control led so as to be equal to the sample temperature, thus el iminat ing the

heat losses which are essentially from the cap.

The whole assembly, Dewar and furnace can be shaken if necessary and is

shown in f ig.20.

This apparatus must be located in a protected area, and cannot be used in

a convent ional laboratory because of the explosion hazard associated with

its use.

The value of the Phi factor is derived from water experiments.

Glass Dewar f lasks may also be used if necessary but have a larger Phi

factor of 1.8.

The temperature control and data acquisit ion is as good as in the VSP

using the same computer program.



346

The pressure is corrected for the Nitrogen pad.

The outputs include :

- The heat rate curve

- The pressure versus tempe rature curve

- The pressure rate curve

The product ion of non-condensable gasses or the polymerizat ion of the

sample are detected by the deviat ion of the pressure curve from the

previously obtained vapor pressure curve.

The rate of non-condensable gas product ion is derived by the fol lowing

approximate equat ion :

1 d T \

T dt /

derived from the perfect gas law.

To il lustrate the use of the closed Dewar to provide the experimental data

for vent sizing, the heat rate curve and the pressure vs temperature curve

obtained for the Phenol + Formaldehyde runaway react ion with the recipe of

Ref.5 are given figs.21 and 22.

Comments on the Dewar f lask tests

The results obtained with the Dewar f lask are quite similar to the results

obtained with the VSP using the closed

cell.

The pressure resistance of the Dewar f lask is limited to 25 bar which is

enough for most process safety studies. There is nevertheless a need to

determine the further decomposit ion steps to obtain information on the



3 4 7

S A F E T Y V E 1 T

B LO W D O W N

V A L V E

V O ^ * SAMPLE

PRESSURE GAUGE

^ T E ^ T U R E

F U R N A C E

[ I T E H R A T U R E

. - . . 1

F i g u r e 2 0 _ j ) E i A R F L A S K E X P E D I E N T



348

S u l 9 t

Ficni iP :

PHENGL

/ FO nHO L

a: 2 9 0 6 9 0 ( Eaea l au 2B / 6 / 9 0 )

Teago r a tu r a loC)

1

I

■

■

■

?

l a l Mo 1

Lo g

P - « . 2 3 9 3 3 - 2 0 9 1 . 2 8 /

■•

da

a a c o a o o a l t l o n

:

38

1

(T+2271

;y

J <

\ A

i

• , / 1 1

1 . V I I

1

1

/

i

i

i i i

/

i

I

/

1

/

1

/

I

1

i

i -t

/[

/ /

,

> i i

i

i

1

i

T e m o e t a t u r e

l o c i

Sutat

:

PHENOL

/ FORMOL

F l cnu r : a : 2 S G 6 9 0 ( Eaaal mj 2A/B/90 1

Fig.

21 and 22:Phenol + Formaldehyde runaway reaction, with the

recipe of Ref 5. Heat rate curve and pressure vs tenroerature

curve. Reaction initiated by introduction of the catalyst. Dewar

flask experiment.



349

consequences of the uncontrol led runaway react ion.

In some cases where very fast react ions are obtained with moderate f inal

pressure, the Dewar f lask is the best choice because the VSP closed cell

ruptures during the fast pressure build up. A typical example of these fast

reactions is the bulk polymerization of vinyl acetate init iated by a peroxide.

4.4 The Reactive System Scre enin g Tool (RSST)

The designer and manufacturer of the RSST is FAUSKE and Associates Inc.

I t is a simple and low priced piece of apparatus which provides some of the

capa bil i ties of the VSP. The fol low ing data can be ob tained with the RSST :

- The heat rate in a low Phi factor experiment,

- The vapor pressure versus temperature relat ionship,

- The non-condensable gas generat ion rate.

At the moment 30 RSST machines have been purchased.

Description of the RSST

An open, small spherical glass test cel l 10 ml in volume, with a low Phi

factor ( <> = 1.04) is placed in a pressure resistant containment vessel, (see

f i g .

23 and Ref.8).

The apparatus provides a record of the sample temperature and of the

containment pressure. There is a magnetic st irrer. Addit ional reactants can

be introduced into the test cel l during the experiment.

The test cel l holds a single heat ing element that compensates for heat

losses and al lows a temperature scan in the test cel l .



350

FILL

_r

HEATER

TEST CELL

CONTAINMENT.

VESSEL

= 3

.THERMOCOUPLE

®

RESSURE

GAUGE

I PSV

NITROGEN

SUPPLY

-INSULATION

ASSEMBLY

FIG. 23 : SCHEMATIC OF THE RSST



351

The heater is control led by the sample temperature measurement, to

overcome the heat losses and produce a specif ied temperature r ise rate at

that temperature. Nevertheless the temperature control is not by a feed

back loop but by a pre-programmed heat ing.

For a reactive system the linear heat up rate is added to the reaction energy

release so that the heat rate is measured under external heat ing condit ions.

The manufacturer claims that heat rates as low as 0.1°C/mn can be

obtained.

The apparatus must be connected to a regulated Nitrogen supply. The

control unit contains the temperature and pressure amplif iers and the

heater power supply. This unit is connected to a computer to record the

t ime, temperature and pressure during the test.

The apparatus can be easily transported to plant sites, a feature of great

interest when the shipment of the samples is not possible.

Test procedure

High vapor systems

The heat rate data is obtained by sett ing the RSST containment pressure to

some Maximum Allowable Pressure and let t ing the react ion be init iated by a

tempe rature scan . Then the heat rate is measured unde r co nd it ions close to

the adiabat ic or under external heat ing condit ions.

When the boil ing point of the sample under the test pressure is reached,

the vaporizat ion heat sink compensates for the heat rate this al lowing the

detect ion of the boil ing point.

Gassy reactions

For gassy react ions, the non-condensable gas generat ion rate is obtained

from constant volume mode experiments as in the VSP.



352

Hybrid systems

A hybrid system is characterized by repeated tests under dif ferent back

pressures. If the heat rate and the gas generation rate are influenced by the

preset back pressure, the system is hybrid in nature.

Comments on RSST tests

The author is not famil iar with the RSST and so these comments are based

on the experience of other workers.

The results of the Round Robin-test on 25 % Hydrogen Peroxide solut ions

show a good agreement between heat rates obtained in RSST and VSP

experiments.

It is nevertheless likely that as with the VSP, a low heat rate base line

cannot be obtained with the RSST.

The heat rate data obtained with the RSST are influenced by :

- The heat rate of the temperature sca n,

- The insulat ion packing,

- The posit ion of the heat ing resistance with respect to the thermocouple in

the test

cell,

- Any detai l which may inf luence the heat exchange between the test cel l

and the outside.

Given that adiabat ic condit ions are dif f icult to produce and that so many

details may influence the heat rate and gas generation rate data, the results

obtained from RSST experiments look surprisingly good.

In a well equipped process safety lab the VSP is the better choice. The

RSST could be purchased to take advantage of i ts possible operat ion on

plant sites.



353

CONCLUSION

This paper demonstrates the need for experimental techniques achieving

operat ing condit ions close to the adiabat ic for vent sizing purpose.

Due to condit ions far f rom the adiabat ic, the ARC should not be used to obtain

data for vent sizing.

A good experimental device should achieve :

- a goo d onset dete ction sensit ivity,

- a low Phi facto r,

- a fast data acquisit ion al lowing the fol low -up of fast react ions,

- a wide operat ing range to measure the ult imate consequences of

uncontrol led runaway react ions,

- a constant tempe rature exposure capab il ity with no tem pera ture d rif t ,

- the simultaneous acquisit ion of the temp erature and pressure history.

The VSP can sat isfy most of these requirements, once improved by the

customer.

The close Dewar experiment is also a valuable tool but with a pressure range

restricted by the pressure resistance of the Dewar f lask.

The RSST may be useful as a screening tool and is of interest for measurements

on plant sites. The VSP is a more useful device than the RSST.

One should never rely on one technique to produce data for vent sizing. Tests

using at least two or preferably three techniques, including the ARC, provide the

opportunity to detect unexpected react ion changes as well as geli f icat ion

processes which would compromize the rel iabi l i ty of the ERS design.



354

The sample must go through DTA and autoclave tests before using pseudo-

adiabat ic techniques to detect extremely fast react ions and to adjust the

experimental procedure taking into account these basic results.

Hopefully the reader has been convinced of the great util ity of pseudo-adiabatic

techniques in the process safety laboratories.

L I T E R A T U R E

(1) H.G. Fisher, DIERS, an overview of the prog ram .

Loss Prevent ion Symposium.

AlChE Houston National Meeting - March 1985.

(2) D.I. Tow nsen d and J.C. Tou

Thermochimica Acta n°37, PP 1-30, 1980.

(3) H.G. Fishe r, 5

t h

DIERS Users Group Meeting Seattle, Mai 1989.

(4) J.E. Huff, Plant, Op erations Progress

Vol 1 n°4 pp 221-229 O ctobre 1982.

(5) J.L. Gus tin, 6

t h

Symp. Loss Prevent ion and Safety Promotion in the Process

Industry.

Oslo Norway June 19-22 1989 Paper n°75.

(6) H.K. Fauske, J.C. Le ung . CEP Aug ust 1985 p.10.

(7) R.L. Roge rs, The advantages and limitations of ad iaba tic Dewar calo rime try in

chem ical hazard test ing.

Internat ional Symposium on Runaway React ions March 7-9, 1989 - Cambridge

Massachusetts pp 281-292

(8) H.K. Fauske, G.H. Clare, M. Jo Creed , Labo ratory tool for cha racte rizing

chemical systems.

Ibid p.364-371



TREATMENT OF REL IEVE D FLUIDS

Dr.

Jasbir Singh

Hazard Evaluation Laboratory

Ltd.

Fire Research Station Site

Melrose Avenue - Borehamwood

Herts WD6 2BL

1. INTRODUCTION

Runaway chemical reactions are a potential problem in many sectors of the

chemical industry.

The

typical hazard scenario involves

a

batch

(or

6emi-batch) chemical reaction where,

due to an

operator error

or

instrument failure,

the

reaction temperature begins

to

accelerate

rapidly. The rise in temperature is, of course, accompanied by a rise in

pressure and in order to prevent vessel rupture, some means of protection

must be provided.

The common approach for overpressure protection in the industry is to fit

a relief device

to the

reactor vessel

in

question;'the device opens

at a

predetermined pressure and if it is sized correctly, the maximum pressure

can be kept within acceptable limits. The Design Institute for Emergency

Relief Systems

(DIERS),

organized through

the

auspices

of the

AIChE

(ref

1) undertook several years

of

research

to

develop methodology

for

sizing

relief systems to cope with runaway reactions.

The DIERS project however, was completed over five years ago and was

started almost 15 years ago. The emphasis in industry is now changing

such that companies are interested in avoiding the release of chemicals to

the environment in addition to preventing equipment damage. Design

techniques must now be extended to cover the containment of fluids.

There

are two

main approaches

for

achieving these objectives

-

either

to

contain the thermal runaway in the reactor vessel or, vent into an

external tank where the reaction is suppressed (eg. by

quenching).

The

first option is theoretically preferable but not always practical,

particularly for existing units. Venting into an external quench tank,

essentially a compromise between total containment and relief to open

air, has received much support (ref 2, 3) . In order to design such

systems,

it is

necessary

to

generate

the

kinetic

and

physical property

data, under conditions

of the

runaway.

The DIERS work showed that

in

order

to

size relief systems,

the

most

expedient method

is to use

suitable bench-scale equipment together with

simplified design equations. The purpose of this paper is to explore

the use of a similar approach in the design of disposal systems and

discuss a bench-scale device that appears to be suitable.

355

A.

Benuzii

and J. M.

Zaldivar

(eds.).

Sa fety of


a nd

Storage

Tanks, 355-370.

© 1991

ECSC,

EEC.

EAEC,




356

2. FLUID CONTAINMENT EQUIPMENT

Equipment for handling vented fluids, typically a two-phase

mixture of vapour and liquid, are referred to by a variety of

names including blowdown drum, knock-out drum and catch tank.

The objectives of the equipment are typically one or more of

the following:

. separate vapour (or gas) and liquid

. collect the separated liquid

. condense vapour

. cool liquid

The most common device is a knock-out drum, a simple

cylindrical vessel with inlet and outlet nozzles sized

primarily to ensure that the vapour and liquid are

successfully separated. The vessel may be horiz ontal or

vertical (see figure 1 ) , depending primarily on space

limitations.

In either case, the diameter is chosen to be

large enough to ensure that the vapour velocity is below the

terminal velocity of liquid droplets and the length must

provide sufficient time for separation.

The separation efficiency through knock-out drums may be

improved by installation of a wire mesh demister before the

vapour outlet.

A more compact arrangement, frequently more efficient in terms

of separation, is a cyclone connected to a catch-pot; the

cyclone performs the separation and liquid accumulates in the

catch-pot.

In order to reduce the amount of vapour leaving the separation

device still further, it is possible to condense the vapours

by venting the fluid directly into cold liquid (see figure 2 ) ,

so called passive quench, which is commonly used in the

chemical industry. The quench fluid will also serve to cool

(and dilute) the liquid portion - this may be an important

feature of the design in the case of reactive systems because

it will slow any reaction that may still persist.

G enerally, vapour consensation is extremely efficient provided

the quench fluid is at least 10°C below the condensation

temperature.



357

3. VAPOUR DISPOSAL

It is rare for vented fluids to be totally contained in a

downstream knock-out drum or quench vessel. More frequently,

the gas/vapour is vented directly to atmosphere or routed to

a suitable treatment device.

The cheaper option, direct release to atmosphere, is becoming

less common because of increasing environmental concerns.

However it may be still an acceptable alternative in many

cases, depending on the likely frequency of incidents and the

amount and composition of the vapour. Careful selection of

discharge point in terms of height above ground and separation

from buildings, and a high exit velocity to promote rapid

dilution are the two most important design considerations.

If venting to atmosphere is not possible then a number of

options are available in order to treat the gas/vapour:

. vent condenser

. scrubber or absorber

. flare

. incinerator

A vent condenser is simply a dedicated method of removing

small quantities of particularly toxic or corrosive vapours.

The discharge temperature of the remaining gas is selected by

reference to the vapour pressure of the liquid being

condensed; in order to reduce the composition to sufficiently

low levels, cooling with a refrigerant may be necessary.

Scrubbers or gas absorbers may be used in a number of

different situations for treating large quantities of gas

containing a mixture of vapours. Applications are limited to

situations where a suitable solvent for the vapours is readily

available and of course the solvent must then be reclaimed or

suitably discharged. Ideally, emergency relief systems need

to be connected to a unit that is continuously available - for

example, scrubber that is used for routine process streams

with spare capacity. If this is not possible, the dedicated

unit must be continuously operated since it is not possible to

bring it on stream in time, following relief actuation.

Flares systems are the most common method for disposing of

large streams containing flammable gases. The flare itself is

a section of pipe with a specially designed combustion tip.

The tip consists of a pilot light which ignites the gas

flowing through the end of the flare pipe. The flare achieves

the desired objective firstly by converting bulk of the

chemicals to harmless gases (C0

2

, H

2

0 ) , and secondly by

releasing hot gas at a high elevation.



358

Most flares are able to convert close to 99% of hydrocarbons

but other chemicals (e.g. HCN) may be only poorly treated. In

such instances, incinarators may be used. These subject the

gases to a more controlled temperature history and give a

minimum residence time necessary to achieve conversion. Als o,

catalysts are frequently employed to deal with species that

are difficult to treat by heat alone.

4. DESIGN CONSIDERATIONS

4.1 Knock-out-drum

The primary consideration is the velocity of the gas/vapour

leaving the vessel relative to the liquid being separated.

For a vertical drum, this must satisfy:

V* k[(p

L

- s>

g

)/

Pg

\^

2

m/s

with V

TtD

2

/4

where V is the gas velocity through the drum,

p

is the density

L

of the liquid, g of the gas) , Q

g

is the gas flow rate

(m

3

/s) , D is the drum diameter (m) and k is an empirical

constant typically about 0.03 to 0.05. The height of the drum

can be related to the diameter, typically L/D - 3. Horiz ontal

drums are sized in a similar manner, the constant k being

somewhat higher.

The unknown quantity in equation 1 is the gas rate Q

g

from the

drum and this depends on the nature of the reaction vented and

the physical properties of the chemicals.

4.2 Quench Tank

If it is necessary to cool or condense the vented fluids

before separation of the phases, then the amount of quench

fluid M

q

may be calculated from:

M -

M

r

C

r <

T

r ~ T

f

)

+

M

z

X X

C

q

(T

f

- T

0

)

l

'

where M, is the mass of reactants vented, C

r

specific heat of

the liquid reactants, T

r

the reactant temperature (in the

reactor) , T

f

the final temperature in the quench drum, T

0

the

original temperature of the quench fluid, C

q

the specific heat

of the quench fluid, x the weight fraction of vapour in the

reactor and X is the latent heat of vapourization of the

reactants at the reactor venting conditions. This equation

assumes that the amount of non-condensible gas is negligible



359

assumes that the amount of non-condensible gas is negligible

which is usually acceptable for design purposes.

As stated earlier, T

f

should be at least 10°C lower than the

expected condensation temperature of the reactant vapours.

The vapour/gas leaving the quench tank will now be determined

by:

. non-condensible gas from the reactor

. uncondensed vapour

. further continued reaction in the quench drum

The tank volume above the liquid will act to separate this

gas/vapour from entrained liquid. If the flow rate of this

gas/vapor is known, then the top section of the drum can be

sized as a knock-out drum using equation (1).

If it can be shown that the reaction does not produce

non-condensible gas and if the reaction is suppressed after

quenching, then it is possible to totally contain the

incident.

4

. 3

G as/Vapour Disposal Units

4.3.1 Flow From Knock-out drum

The operation of vapour handling equipment such as absorbers,

scrubbers and flares is dependent primarily on the flow rate

from the knock-out drum or the quench device. The composition

may also be important for more detailed considerations but

overall specification can be completed from a knowledge of the

flow rate.

In the case of a simple knock-out drum, operating close to

atmospheric pressure, the first consideration is the flash

from the reactor down to atmospheric pressure. The amount of

vapor produced following adiabatic flashing may be calculated

from:

X

-

C

r< V

r

» >

(3)

where x is the weight fraction of reactants vapourized in the

drum and Tb is the adiabatic flash temperature (the boiling

point of the mixture.) Thus the amount of vapour generated in

the drum is XMr, and the resulting liquid and vapour will be

at a temperature Tb.

After the initial flash down to atmospheric pressure, the

liquid remaining in the drum may continue to react and

generate further gas/vapour.



360

Equation (3) is applicable if the reactor is vented at a

temperature above its atmospheric boiling point (i.e. T

r

> T

b

) .

If the reverse is true the liquid will remain at the reactor

temperature T

r

(no flash cooling) and the gas will be that

vented from the reactor plus further reaction in the drum.

Also, in such cases the reaction rate will be exactly the same

as in the reactor since the reactants are not cooled.

For the situation where the reactants flash down to a lower

temperature, the reaction rate will be quite different in the

knock-out drum, normally much lower corresponding to the

reduction in temperature. If the activation energy E for the

reaction is known, then the self-heat rate in the drum (dT/dt)

d

may be obtained from that in the reactor (dT/dt)

r

using:

i-m,'

l -HSrIBtf

El

1

R[ T

z

T

b

( 4 )

where R is the universal gas constant.

The vapor rate M, resulting from the self-heat is then given

by:

C A (1 -

x) (dT/dt)

d

(5)

M„ =

:

The above equations assume that there is no change in

composition in going from the reactor to the drum, which in

practice will not strictly be true. (This is equivalent to

assuming that the reaction rate is independant of

concentration i.e. zero order.)

4.3.2 Flow From Quench Drum

The gas/vapor rate from a quench drum will of course be lower

than from a knock-out drum depending on the final quench

temperature T

q

.

If the reactants vented into the drum are totally condensible,

then the vapours generated may be calculated from equations

(4) and (5) , with T

b

replaced by T

q

. By venting directly into

the quench fluid, vapours from the initial flash (equation 3 )

are avoided. The vapor rate calculated in this manner is

conservative since reduction in reaction rate due to dilution

by the quench fluid is not considered.

If the amount of quench fluid is large enough then T

q

may be

sufficiently low to prevent further reaction and hence permit

total containment.

If the reaction produces non-condensible gas (typical for



361

d e c o m p o s i t i o n r e a c t i o n s ) , the n clea rly thi s ga s wi ll need to

be rel iev ed from the que nch drum. Th e rate of flow wil l be

identical to that from the reactor plus further gas generated

with in the quenc h drum if the liquid conti nues to rea ct. The

rate of reaction will be determined by the extent of cooling

and dilution by the quench fluid.

5. TESTING OP REAC TOR/ QUEN CH COMBINAT ION

5.1. Runaway Reaction Simulation

Ideall y, a benc h-sc ale unit should prov ide data whi ch can be

interprete d easily and applied simply wit hou t need for c omple x

mod el li ng . Thi s ha s bee n achie ved to a large ext ent in the

case of runaway reaction venting following the work of DIERS.

A device that incorporates essential aspects of the DIERS

equip ment is PHI- TEC I I, shown in figure 3 (ref 4 ) .

This consists of a sample container approximately 130 cm

3

capa city wh ich is susp ende d in the centr e of a set of meta l

p l a t e s . The pla tes totally surround the sample cont ainer and

are elect rical ly heat ed. When a test sample underg oes

reac tion leading to a rise in temp erat ure, the heated plat es

are contro lled to mat ch this temp erat ure, thus elimi natin g

heat losses from the sample.

The sampl e container used in mos t experimen ts is of

0.006

inches wal l thi ckne ss which result s in a very low the rmal mas s

in rel ati on to the ma ss of the tes t sam pl e. Th is aspec t is

normal ly expresse d in term s of the Phi- fact or:

phi = 1 + (MCp),/ (MC p),

where M is the mass and Cp the specific heat, subscript t

refer s to the test cell and s to the samp le mate ria l.

The value of phi in a large scale plant is close to 1.0; using

thin-w alled t est cel ls , PHI-TE C is able to achie ve very

similar values.

In order to prevent the thin test cell from rupturing when the

vapour pressure in the reacting sample rises, a nitrogen

pres sure is exerted out side the

cell. Thus,

as the reaction

p r o c e e d s ,

pressu re equal iz ation is mainta ined by an elect ronic

contro l system. The resul t of thes e desi gn features is that

it is pos sib le to test runaway react ions usin g PHI-TE C and

apply the results directly to large scale equipment.

Extra polat ion of test data is not re quired .

The device can be used for a number of purposes including

chemical reaction screening, kinetic assessment of runaway

reac tions and emerge ncy relief sizing. In term s of exotherm

ons et det ect ion and haz ard scr een ing , it is at least as

sen sit ive as th e AR C (ref 5.) Ho we ve r, wh er ea s the AR C is

limited to maxi mum s elf-he at tracking rate s of 10 to



362

15°C/minute, PHI-TEC II can reach up to about 200°C/minute.

5.2.

Disposal Drum Simulation

In order to simulate the disposal tank connected to a reactor,

low thermal capacity ratio (reflected in the phi-factor) and

adiabaticity constraints need to be observed. Moreover, the

test unit must be capable of being attached directly to the

reaction cell within PHI-TEC. A design that allows this is

shown in figure 4.

This consists of a small pressure vessel containing another

thin-wall

cell.

The vessel is electrically heated and is

held at a temperature identical to that of the thin-wall

cell.

The cell itself is connected directly to the reaction can

within PHI-TEC, the two being separated by a solenoid valve.

The pressure vessel containing the quench cell is fitted with

a small solenoid valve which can be opened or closed as

needed.

Typically, when the valve to the quench cell is opened, the

hot reactants flash down to atmospheric pressure and the

resulting temperature is measured by the thermocouple.

Immediately, the pressure vessel is heated to match this

temperature.

Thus,

the reactants are contained in the

thin-walled cell and the reaction not suppressed by the

thermal mass and at the same time, heat loss is avoided.

If the thin quench cell is left open within the heated vessel,

much higher pressures can be simulated. Normally the

objective is to find conditions under which pressure rise can

be avoided and so even the thin cell is sufficiently strong.

A number of different tests can be conducted with the unit in

figure 4. In all cases, a runaway reaction being studied is

first initiated within the PHI-TEC test cell and at the

appropriate time, the interconnecting valve is opened. The

quench cell can be operated in one of the following

ways:

* the first test could be performed with the vent valve on

the quench open; this would simulate the atmospheric

flashing of the reactants and provide the boiling point

of the flashed reactants.

* in a second test, the valve could be closed after the

initial flash to simulate the runaway reaction that

would ensue after

flash cooling.

* depending on the results, some suitable quench medium

could be added to the cell in further tests to slow down

the reaction still further. Different quantities (and

types) of quench fluids may be examined.



363

If a decomposition reaction is being studied this will be

clear from the results and the rate of gas generation can be

measured.

6. APPLICATION TO A SIMPLE FIRST ORDER REACTION

6.1. Description of Reaction System

The exothermic reaction between methanol and acetic anhydride

has been studied extensively and is found to initiate at

atmospheric temperature (ref 4 ) . If stoichiometric amounts of

the two reactants are mixed in an ice bath and then allowed

to stand, the mixture will self-heat (under adiabatic

conditions.)

The pressure and temperature-time data for a closed

(adiabatic) thermal runaway of this reaction is shown in

figure 5. This shows a characteristic shape - very slow rise

initially and increasing exponentially with temperature. The

rate of temperature rise against temperature is shown in

figure 6. The reaction rate is found to be well represented

by a first order dependence on concentration with the

following Arrhenius parameters:

A = 4.57 x 10

17

sec"

1

E = 17.1 kcal/mole

6.2. Quench Test

The venting and subsequent quenching of this reaction was

studied by allowing the reaction to adiabatically runaway

within the PHI-TEC test cell and then venting into the quench

system at 102°C, 1.85 bar (27 psia) . At this point, the rate

of temperature rise was 21°C/minute. The reactants were vented

into an initially empty quench

cell.

The PHI-TEC venting was

performed through a 3mm dia pipe which was dipped into the

test can. A few seconds after venting, the intermediate

solenoid valve was closed. The quench cell was open to

atmosphere when the venting was initiated, but then closed to

allow adiabatic runaway of the flashed liquid. The questions

to be addressed by the test were:

* temperature following adiabatic flash

* rate of reaction after flash cooling

* quantity of quench solvent needed to reduce the reaction

rate to a safe level.

The temperature-time data for the reaction cell and the quench

cell is shown in figure 7. The vent valve was opened after

about 13.8 minutes into the exotherm - this is clearly

indicated - and then closed a few seconds later. When the

vent was opened, note the rapid initial rise in temperature

within the quench cell as it suddenly warms up from ambient.



364

When the vent valve was shut, the contents in the reaction

cell continued to self-heat, as did the quench cell contents.

The initial information derived from this test is:

* self-heat rate goes down from 21°C/minute in the reactor

to about 7°C/minute in the quench cell

* reactants flash down from 102 to 72°C

* approximately

7 0

of the reactants were vented into the

quench

cell.

At the end of the test about 8 0 % of the

vented material was still in the quench

cell,

hence, the

fraction flashed (ie x) = 0.2.

Hence,

the parameters to be calculated from equations 1 to 3

are immediately available from a single test.

It is interesting to see whether indeed the calculated results

agree with the experimental. Consider first equation 1.

Using the kinetic parameters listed earlier and ignoring the

reduction in reaction rate as given by the concentration term:

(dT/dt)

Q

= 21Exp

1 7

-

l x l

°

9

(_i-\ - (-1-)

» *1 1.987 \3 75/ 1345J

(6)

= 2 .9°C/minute.

This is compared with the experimental value of about

7°C/minute. The difference is at least partially due to the

fact that when the reactants were flashed in the quench

cell,

lighter components will be preferentially stripped. Thus the

concentration will be quite different and extremely difficult

to calculate.

6.3. Effect of Quench fluid

With the data from the above test available, it is possible to

design the quench system. The undiluted (but flash cooled)

reactants still self-heat at 7°C/minute - hence the mixture

must be further cooled and diluted. The effect of quenching

with different quantities of solvent can be assessed directly

from the data. Using equation 2, the degree of cooling can be

calculated and then using equation 1, reduction in the

self-heat rate obtained. The result is shown in figure 8 ;

with the quench fluid equal to the reactant quantity, the

self-heat rate is reduced from 7°C/minute to 0.56°C/minute.

It is quite possible to allow the reaction to continue slowly

in the quench tank and simply vent the vapors that are

generated. The vapor quantity produced at different amounts

of quench is shown in figure 9. In this case the quench unit



365

could for example be directly connected to the flare.

6.4 . Disposal System Design

The degree of cooling required to ensure a safe disposal

system depends on the balance between the self-heat rate and

the heat loss from the tank.

If heat loss from the quench tank due to natural convection is

Q

L

, then at any self-heat rate the amount of vapour generated

^ is:

M =

(M

r

+ M

Q

) (dT/dt)

q

C

p

- Q

L

)

( 7 )

For total containment, the dilution quantity must be chosen

so that the heat generation rate is less then Q

L

(ie H, = 0 ) .

In some instances, in order to completely contain the

reaction, an excessive amount of diluent is needed. In the

case of methanol-acetic anhydride for example, the quench

fluid needs to be several times more than the amount of

reactant. This is clearly impractical for large scale units.

If this situation occurs, then the quench drum itself has to

be provided with a small vent, the size of the vent being

governed by the vapour rate given by equation 7. It is

necessary in such instances to ensure that the venting is slow

enough to prevent liquid carry-over.

Since the vapour rate can be reduced to a low value, it is

possible to vent the vapours to flare, an absorber or

scrubber. The use of equation 6 directly provides the vapour

flow that would be vented to such units.

7. CONCLUSIONS

Design of disposal equipment to treat fluids relieved from

chemical reactors requires the use of standard chemical

engineering design methods in conjunction with the physical

and chemical property information about the reactants and

products.

Pertinent data is difficult to obtain under

realistic conditions without the use of specially devised

instruments. This article has discussed the use of an

adiabatic calorimeter PHI-TEC II for simulation of the

reaction and evaluation of the disposal system. The test data

can be used directly in standard design equations to specify

knock-out drums, quench drums, absorber/stripper columns and

flares.



3 6 6

F R O M R E A C T O R

T O F L A R E ,

A B S O R B E R E TC .

F IG 1 : T Y P I C A L K N O C K - O U T D R U M F O R V A P O R - L I Q U I D S E P A R A T I O N

F R O M

R E A C T O R

C L O S E D V E N T

_ J — t

Q U E N C H L IQ U I D

F IG 2 : P A S S I V E Q U E N C H O F V E N T E D R E A C T A N T S



367

S o l e n o i d

Va lves

n

Ni t rogen

1.

Th r o © R o d l a n l H o s i e r s

1. S i m p l o T h e r m o c o u p l e

3 . M a g n e t i c B a r

P r e s s u r e C o n t a i n m e n t V e s s e l

.

To o

I C e l l

5 . U M a g n a

0 . V e s a u l P r e s s u r e T r a n a d u c o r

7 . B a m p le P r e a t u i t t r a n s d u o o r

F IG 3 : P H I - T E C II R E A C T I O N C A L O R I M E T E R

HEATING COIL

F IG 4 : B E N C H - S C A L E D I S P O S A L C E L L C O N N E C T E D TO P H I - T E C

FROM

PHI-TEC



368

FIG 5:CL0SED VESSEL RUNAWAY: MEOH-ACETIC ANHYD.

PRESSURE

&

TEMPERATURE

Vs

TIME

UJ

en

40 50

TIME[min]

60 70

in

tn

en

FIG 6: METHANOL-ACETIC ANHYDRIDE REACTION

RATE

OF

TEMPERATURE RISE

Vs

TEMPERATURE

80.0

60.0

2 40.0

Li_

O

£

20.0

0.0

I I I L O

i i 1

~r

1 \

i i .v _i i L

i t- — *s- 1 1 L _

25.0

55.0

85.0 115.0

TEMP C)

145.0

175.0



369

FIG

O V E R A L L V I E W

OF Q U E N C H T A N K

AND R E A C T O R

TEMPERATURE

Vs

TIME

■ .

130.0

8.0

12.0

TIME min

20.0

FIG

8 :

VENTING

OF

METHANOL-ACETIC

ANHYDRIDE

EFFECT OF QUENCH QUANTITY ON SELF-HEAT RATE

U J

5



370

F IG

9 :

V E N T I N G

OF

M E T H A N O L - A C F J I C A N H Y D R I D E

EFFECT OF QUENCH ON VAPOR VENTING RATE

2

fe

0.6

0.6

0.4

0.2

0.0

NO QUENCH

J

[ M q

=

1 ' 1 1

Q U E N C H

Q

A N T I T Y ,

M =

R E A C T A N T S V E N T E D ]

' j i

0.5

1.5 2.0

Mq/Mr

2.5

3.0

3.5

REFERENCES

1. H G Fisher, DIERS - An Overview of the Program, AIChE

National Meeting, National Meeting, March 19 8 5, Houston,

Texas, Paper no 55a

2. A G Keiter, Emergency Pressure Relief Discharge Control

by Passive Quenching, International Symposium on Runaway

Reactions, March 7-9, 1989, AIChE

3. S S G rossel, An Overview of Equipment for Containment

and Disposal of Relief System Effluents, J. Loss Prev.

Process Ind., 1990 , Vol 3, Jan

4. J Singh, PHI-TEC: Enhanced Vent Sizing Calorimeter -

Application and Comparison with Existing Devices,

International Symposium on Runaway Reactions, Boston,

March 7-9, 198 9, AIChE

5. Townsend, D I and Tan, J C, Thermo chimica Acta, 37

(1980),

1-30



RUNAWAY REACTIONS: A CASE STUDY

T. J. SNEE

Health

and

Safety

Executive

Buxton

Derbyshire SK17 9JN

UK

ABSTRACT . A simple chemical reaction is used to illustrate the application of thermo-

analytical techniques and theoretical models in determinig critical conditions for exothermic

runaway

in

a

batch

reactor.

A

range

of

thermo-analytical

techniques

are

described

and

compared. Methods of determining th e thermo-kinetic parameters of th e reaction from

thermo-analytical data are discussed. Experimental results are used to predict th e conditions

which can lead to a runaway exothermic reaction in a pilot-scale reactor. The predictions are

compared with the results of experimental studies of exothermic runaway in a 250

1

glass-

lined reactor.

1.

INTRODUCTION

A wide range theoretical and experimental techniques can be used to evaluate hazards

associated with runaway exothermic reactions. This paper illustrates how some of these

techniques are applied to a batch chemical reactor. A reaction system with well established

physical and chemical properties has been chosen in order to demonstrate how thermo-

analytical data can be used to determine safe operating procedures. The methods discussed in

the present work would form part of a formal hazard evaluation procedure.

♦present address: Commission of the European Communit ies, Joint Research Centre,Ispra

(VA),

Italy.

371

A.

Benuzzi and J. M. Zaldivar (eds.). Safety of Chemical Balch Reactors and Storage Tanks,

371-389.

© 1991

ECSC.

EEC.

EAEC.

Brussels and Luxembourg. Printed in the Netherlands.



372

NOTATION

sym bol quantity units

t

to

tf

m

me

m

s

T

T

m

T

e

T

0

A T

a d

AH

E

A

k

n

X

^g

qi

s

u

h i

h0

R

w

£

^

S

V

4>

Vc

R

time

onset time

final time

mass

container mass

sample mass

temperature

reactant temperature

jacket temperature

onset temperature

adiabatic temperature rise

heat of reaction

activation energy

pre-exponential factor

reaction rate constant

order of reaction

conversion

rate of heat generation

rate

of

heat loss

surface area

heat transfer coefficient

external heat transfer coeff.

internal heat transfer coeff.

thermal resistance

of

wall

specific heat capacity

specific heat

of

sample

specific heat of container

thermal dilution factor

critical Semenov number

universal

gas

constant

s

s

s

kg

kg

kg

K

K

K

K

K

k J k g "

1

kj mol"

s-1

s-1

k J s "

1

k J s "

1

m^

W m -

2

W i n "

2

W m "

2

m

2

W -

;

kJkg-1

kJ

kg-1

kJ

kg"

1

1

K-l

K-l

K-l

' K

K-l

K-l

K-l

k J m o l - t K

l i f - 1



373

2.

REACTION SYSTEM

In order to illustrate the principles discussed in this paper it was necessary to choose a

reaction system with the following characteristics:

* a simple reaction system which produces good thermo-analytical data providing reliable

source terms for the theoretical models.

* a reaction system w here reliable data on the physical prop erties of the reagents and

products are available.

* a reaction system in wh ich the rate of heat generation could be controlled by the addition

of small quantities of catalyst to allow a systematic study of the conditions which can lead to

exothermic runaway.

A simple esterification reaction was chosen to meet these requirements so that the salient

features of exothermic runaway can be explored:

C H

3

C H ( O H ) C H

2

C H

3

+ (CH3CH2CCO2O -> C

2

H

5

C02(CH3)C2H5 + C

2

H

5

C 0

2

H

sec.butyl alcohol propion ic anhydride sec. butyl propion ate prop ionic acid

This moderately exothermic reaction can be catalysed by the addition of small quantities of

sulphuric acid.

3 .

HAZARD EVALUATION

Systematic determination of the risk and possible consequences of exothermic runaway should

ensure that safe and cost effective measures for controlling the hazard or mitigating the

consequences can be established. A typical theoretical and experimental assessment would pass

through the following stages:

* Determ ination of the exothermicity of the desired reaction and of any undesired side reactions. (If

the total potential energy release is very low, the risk of exotherm ic runaw ay can be discounted, and

further evaluation is unnecessary.)

* Estimation of the maximum temperature and pressure that could be achieved if the heat from

exothermic reaction were released very quickly (with no heat loss). In this way it is possible to

assess whether, under "worst case" conditions, there is a risk of vessel rupture, release of toxic

reagents or products, secondary reaction, auto-ignition or detonation etc. (If maximum temperatures

and pressures are relatively low, it may be possible to accept the risk of runaway, while ensuring

that the specifications of the reaction vessel are sufficient to achieve total containment.)



374

* Determination of the temperature dependence of the rate of heat generation and the rate of heat

loss so that the critical conditions w hich can lead to exotherm ic runaway can be predicted in order

that suitable control measures can be identified.

* Assessment of the reliability of control measures and the hazard assessment procedure. (If there

remain s a significant risk of loss of control, it is necessary to adopt additional meas ures to m itigate

the consequences of exothermic runaway. These additional measures could include the provision of

an emergency pressure relief system, scrubbing systems, additional containment or plant isolation.)

The information required for the hazard evaluation can be divided into four main areas:

1) Physical properties of reagents and products - usually from published data or simple

measurements.

2) Specifications for process vessels etc. - from data supplied by manu facturers.

3) Reaction exothermicity and kinetic constants.

4) Heat transfer characteristics of reactor.

Physical properties, vessel specifications and heat transfer data are usually readily obtainable.

Definition of the thermo-kinetic properties can be more problematical. The present discussion will

place particular emphasis on the the determination of the thermo-kinetic parameters of an exothermic

reaction from thermo-analytical data.

As a simple example of a hazard evaluation procedure, a proposal to carry out the esterification

reaction in a 250

1

glass-lined reactor will be examined.

4 .PHYSICAL PROPERTIES

Relevant physical properties, and flammability and toxicity data for the reagents and products of the

esterification reaction are listed in Table 1. This type of information is readily obtainable for simple

chemicals. However, in the case of more complex reactions it may be necessary to determine some

of these quantities experimentaly. Uncertainties in, for example, the toxicity data for complex

subs tances, may necessitate additional safety measu res which are not appropriate for simple

substances with well established properties.



375

TABLE 1. Physical properties and flammability and toxicity data for reagents and products of

esterification reaction.

boiling point

(°C)

specific heat

( k J k g K "

1

)

latent heat

(kJ kg"

1

)

flash point

(°Q

long term

expos, limit

(mg m

- 3

)

short term

expos, limit

(mg. m"

3

)

sec.butyl

alcohol

99.5

2.848

544

24

300

450

propionic

anhydride

169

1.796

306

74

(open test)

20

(acet. anh.)

20

(acet. anh.)

sec.butyl

propionate

132

1.944

283

32

(n-butyl)

950

(s.butyl acet.)

1190

(s.butyl acet.)

propionic

acid

141

2.119

431

54

30

45

5. PLANT SPECIFICATIONS

The p resent d iscussion will consider a proposal to perform the esterification as a pilot-scale (250 1)

batch reaction. The specifications for a standard, industrial, glass-lined, jacketed reactor are listed in

Table 2. Specifications for auxiliary equipment such as pumps, feed vessels and pipework, and the

standard operating and handling procedures would form part of a general safety assessment.

Hazard evaluation procedures concerned specifically with runaway reactions would focus particular

attention on the temperature and pressure rating of the reactor and possible catalytic effects from the

materials of construction.

It will be assum ed, for the purposes of the prese nt discuss ion, that the tem pera ture of the heat

transfer fluid in the reactor jack et can be chosen according to the results of the hazard ev aluation

and the requirement for efficient and economic chemical production.



376

TA BL E 2. Specifications of a standard industrial pilot-scale reactor.

working pressure

(barg)

design pressure

(bar g)

test pressure

(barg)

temperature range

(°Q

capacity

(litres)

6 t o - l

6.6 to-1

11.4

-25 to 200

250 (nominal)

334 (total)

jacket

6 t o - l

6.6 to -1

11.4

93

material

glass-lined mild steel

mild steel

6 . THERM AL ANALYSIS

Four types of apparatus have been chosen to illustrate how thermal analysis can be used to

determine the thermo-kineteic parameters of an exothermic reaction:

Differential Scanning Calorimetry (DSC)

Accelerating Rate Calorimetry (ARC)

Adiabatic Calorimetry with Vent Sizing Capability (VSP, PHI-TEC)

Heat Flow Calorimetry (RC1)

6.1 Differential Scanning Calorimetry [1]

The DSC sample (around 10 mg) is held in a sealed container and placed in a measurement cell

whose temperature is increased at a constant rate. The rate of heat evolution (or absorption) from

the sample is measured as a function of temperature with respect to an inert reference material.

6.2 Accelerating Rate Calorimetry [2]

The sam ple for ARC analysis (around 10c) is placed in a container (designed to withstand

substantial pressures) which is subject to stepwise heating, but is held in an adiabatic state between

each temperature step. Adiabaticity is achieved by matching the temperature of the surroundings to



377

that of the sample container. Exothermic reaction or decomposition is detected when, after a

temperature step, the temperature of the system continues to rise due to self-heating of the sample.

If the rate of temperature rise exceeds the detection threshold (0.02 K min"l), stepwise heating is

suspended and an adiabatic environment is maintained as temperature and pressure are recorded as

the reaction proceeds.

6.3 Adiabatic Calorimetry and Vent-Sizing

The operation of the VSP [3] and PHI-TEC [4] is similar to ARC, but thin-walled sample

containers are used so that that the experim ental data is not significantly influenced by the thermal

mass of the container. Rupture of the sample container is prevented by applying external pressure to

match the pressure developed inside the container. These instruments are provided with special

facilities for the design of emergency pressure relief systems for chemical reactors.

6.4 Heat Flow Calorimetry [5]

The rate of heat generation is measured using heat-flow reaction calorimmetry by determining, in a

small jacketed reactor (capacity approx. 2 1), the rate of heat transfer from the reactants to the

surrounding heat transfer fluid. The rate of heat flow is proportional to the difference between the

reactor and jacket temperature. This difference can be related to rates of heat generation, after the

heat transfer characteristics of the vessel have been determined by calibration using electrical

heating.

7 REACTION EXOTHERMICITY

A range of therm o-analytical techniques can be used to determine the heat of reaction. The choice of

technique depends on factors such as: available sample size, required temperature range, maximum

temperature and pressure etc.

7.1 Heat of reaction from DSC

Th e D SC scan for the esterification reaction is show n in Figure 1. Th e reaction is first detected at a

tempera ture of 40°C (the onset temperature) w hen the rate of heat evolution is sufficient to cause a

discernable departure from the baseline. As the temperature is increased further, the rate of heat

generation reaches a maximum value at 75°C and then subsides as the reagents become depleted

until the trace returns to the baseline at 120°C.

The heat of reaction can be determined by integrating the rate of heat generation between the onset

temperature and the final temperature.

1 ^

A H = - J q

g

.d t (1)

to

This integral is given by the area between the DSC curve and the baseline.



378

i

o

CO

0>

o

64 72 80 88

T e mp e ra tu re 'C

96 w

112 120

Figure 1. DSC scan for the reaction between propionic anhydride and sec.butyl alcohol catalysed

by 0.8% H 2SO4 (scan rate 8 K min"

1

).

"E

n

D P - J

1)-^

10"

300

+

PH-TECdota

x ARC data

^ ^ H + H H + ^ ^ H f . , .

- 1 —

312

324 336 348 360 372 384

Temperature

(K)

T

+

+

+

+

T

396 408 420

Figure 2. ARC and PHI-TEC plots of self-heat rate against temperature for the reaction between

prop ionic anhydride and sec.butyl alcohol (no added H2SO4).



379

7.2 Heat of reaction from ARC

The AR C plot of self-heat rate against temperature for the esterification reaction is shown in Figure

2.

Th e reaction is detected at 310 K whe n the rate of self-heating excee ds the detection threshold.

Under adiabatic conditions, the rate of temperature rise increases to a maximum and then decreases

until a final temperature of 392 K is reached when the reaction is comp lete. The total heat evolved

is distributed between the sample and the sample container and the heat of reaction can be calculated

using the expression:

AH = <j).AT

ad

.C

p ( 2

)

where

ms .Cps + mc .Cpc

* =

EITÎ

<

3

>

A typical thermal dilution factor (<j)) for an ARC experiment would be 1.4.

7.3 Heat of reaction from PH I-TEC

The PHI-TEC plot of self-heat rate against temperature for the esterification reaction is shown in

Figure 2. Th e detection sensitivity and the form of the self-heat rate plot is similar to ARC data.

However, the lower thermal dilution factor for the PHI-TEC gives rise to higher self-heat rates and

a larger adiabatic temperature rise. The heat of reaction can be evaluated using Equation 2. PHI-

TEC measurements can be made with thermal dilution factors close to unity.

7.4 Heat of reaction from RC1

Temperature records for the esterification reaction in the RC1 are shown in Figure 3. The reaction

was performed as a semi-batch process (metered addition of the anhydride to the alcohol) with the

reactor tem peratu re m aintained at 75 °C . At the start of the addition, the jac ket tem perature rises

above the reactor temperature in order to compensate for the addition of cold fluid to the hot reactor.

After 60 minutes the addition is complete and the jacket temperature falls below the reactor

temperature to compensate for the heat generated as the exotherm ic reaction proceeds .

The heat of reaction is determined by integrating the difference between temperature of the reactor

and the jacket multiplied by the heat transfer coefficient with corrections for the heat required raise

the temperature of the anhydride to 75°C.

A H =

m JU.S.(T

m

-T

e

).dt (4)

to

At a reactor temperature of 75°C, heat losses to the surroundings through the lid of the vessel are

substantial, and this introduces large uncertainties in the calculated heat of reaction, when the rates

of heat generation are relatively low. At 75°C, with no catalyst, the rate of esterification, and

therefore the difference in temperature between the reactor and jacket, is relatively low and the



380

exothermicity is not determined accurately by heat-flow calorimetry.

343

340

reactor temperature

jacket temperature

— 1 1 1 1 1 1 1 1 —

2 8 0 0 5 6 0 0 8 4 0 0 11200 1 4 0 0 0 1 6 8 00 1 9 6 0 0 2 2 4 0 0 2 5 2 0 0 2 8 0 0 0

Time (s)

Figure 3 . Tem perature records from semi-batch esterifictation in RC1 reaction calorimeter (no

added H2SO4).

8. EXOTHERMICITY DATA AND PRELIMINARY HAZARD EVALUATION

The results of calorimetric measurement of the exothermicity of the esterification reaction are

summarised in Table 4. Large variations can be seen in the values obtained using different

techn ique s. Detailed asses smen t of the reliability of each method is not the subject of the present

work, but Table 4 illustrates the importance of applying a range of techniques, and repeating

measu rements in order to obtain accurate data.

The exothermicity data indicate that if the esterification reaction proceeds rapidly, with no

significant heat losses or thermal dilution, the temperature of the reaction mixture will rise by

approximately 130 K. The consequences of such a temperature rise can be assessed with reference

to Tab les 1 and 2. Th e AR C and PH I-TE C data indicate that an initial temp erature of at least 20°C

would be required for the reaction to proceed at a significant ("economic") rate. A rapid runaway

from this initial temperature would reach the boiling point of the product and give rise to potential

flammability and toxicity hazards (from Table 1). However, the temperature and pressure

specifications of the reactor (Table 2) would be unlikely to be exceeded, so there would be no

significant risk of vessel ruptu re. Such a reactor no rmally w ould be provided a reflux conden ser

and a vent to atmosphere (possibly via a scrubbing system) which would substantially reduce the

potential release of flammable or toxic material. However, assuming somewhat artificial plant

conditions, the exothermicity data indicate that the consequences of thermal runaway would be



381

hazardous but not catastrophic. The preliminary hazard assessment indicates that reaction kinetic

and heat transfer data should be obtained in order to identify the critical conditions which could lead

to exothermic runaway, so that suitable control measures can be adopted.

TABLE 3. Comparison of reaction exothermicities evaluated using various thermo-analytical

techniques.

heat of reaction

(kJ kg"

1

)

differential scanning calorimetry -26 1

accelerating rate calorimetry -28 1

adiabatic calorimetry with vent sizing -3 01

reaction calorimetry -3 06

9. REACTION KINETICS

The rate equation for a simple chemical reaction or decomposition can be written in the form:

£-k.(l-x)* (5)

The temperature dependence of the rate constant (k) can often be predicted using the Arrhenius

equation:

k = A.ex p(-E/R T) (6)

Under adiabatic conditions ,with constant Cp, reactant conversion is directly proportional to the

change in temperature

T - T

0

x = (7)

A T

a d



382

hence the rate of self-heating under adiabatic conditionsis given by :

dT dx AH AH .A.( l -x)

n

1W =

W — .exp(-E /RT ) (8)

d t

<* Cp.<j> Cp.<j)

at low conv ersion (x « 1)

log (dT /dt) = log(AH.A/Cp.<t>) - E/R T (8a)

The critical conditions which can lead to exothermic runaway are normally reached before reactant

depletion causes a significant reduction in the rate of heat generation. This means that, for the

purpose of hazard evaluation, the kinetics of exothermic reaction can be specified by determining

the Arrhenius constants A and E using thermal analysis. The addition of small quantities of

sulphuric acid to the esterification reaction mixture shows how the kinetic parameters can be

strongly influenced by catalytic effects.

9.1 Reaction kinetics from DSC

DS C traces for the esterification reaction catalysed by various concentrations of sulphuric acid are

shown in Figure 4. The increase in reaction rate with increasing acid concentration is seen as a

progressive reduction in the onset and peak temperatures and a progressive increase in the

maximum rate of heat generation.

The shape of the DS C curve is strongly influenced by the concentration depen dence of reaction rate.

DSC is relatively insensitive to the low rates of heat generation at low temperatures or low

conversion of reagents. Interpretation of DSC data can be difficult due to complex heat transfer

between the sample, the sample container and the measurement cell. Although, in principle, it is

possible to determine reaction kinetic constants from DSC [5], adiabatic techniques such as ARC

and PHI-TEC provide a more reliable means of determining the Arrhenius parameters from self-

heat rate data at the start of the reaction.

9.2 Reaction kinetics from ARC

ARC plots of ln(self-heat rate) against reciprocal temperature are shown in Figure 5. These results

show the same dependence of reactivity on sulphuric acid concentration as had been observed using

DS C. The increase in reactivity with increasing acid concentration is seen as a progressive reduction

in the onset temperature (at which the self-heat rate exceeds the threshold value - 0.02 K min"l)

and, at concentrations greater than 0.05% H2SO4, as an increase in the rate of self-heating at the

initial sample temperature.

A linear relationship between ln(heat rate) and reciprocal temperature is predicted by Equation 8a.

The initial sections of the ARC plots are approximately linear, so the Arrhenius parameters for the

reaction can be obtained by linear regression.



383

i

o

o

0.KH2S04

02%H2S04

0.4%H2S(H

0.S5H2S04

0 320 330 340 350 360 370 380 390 400 4 0

Temperature (K)

Figure 4. DSC scan for the reaction between propionic anhydride and sec.butyl alcohol catalysed

by various concentrations of sulphuric acid.

E

2*:

iu -

:

uU

10°^

10-1

-

-

in"

2

HJ

0.4%H2S04

0ZUQSM,

0

0.KH2SO4"

0.05% H2S04 "

«* ° ° o ° o ° ° « ^ ° °«

o° ^ o° o°° c^" ")

0° „°

a

„=°°

y

o^°

o °

c

o o ^ t S >

°

Q

°° o°° 0O°°

."' /

o

„-""

„° „ : 0% H2S04

0.025% H2S04

1 1

1 1 i i i i i

-3.50 -3.40 -3.30 -3.20 -3.10 -3.00 -2.90 -2.80 -2.70 -2.60 -2.50

-1000/T (K-1)

Figu re 5. AR C plots of log(self-hea t rate) against recipro cal temp erature for the esterification

reaction catalysed by various concentrations of sulphuric acid.



384

Reliable ARC data could not be obtained at sulphuric acid concentrations greater than 0.4 %

becaus e, w ith a reactive com positions, significant reaction occurs during the time required to install

the sample in the instrumen t. This effect causes a reduction in the measure d adiabatic temperature

rise.

(The addition of sulphuric acid would not be expected to affect the heat of reaction or the

temperature rise that occurs if adiabatic conditions are established at the start of the reaction.)

9.3 Reaction kinetics from PHI-TEC

The PHI-TEC allows reagents to be introduced into the sample container after it has been installed

in the apparatus. Reactive compositions can be studied by operating in adiabatic mode as soon as

the sample has been assembled. Figure 6 shows PHI-TEC data for the esterification reaction

catalysed by 0.8

%

H 2 SO 4. The difference b etw een initial and final temp erature (110 K)

coresponds closely to the temperature rise measured for less reactive compositions (Figure 2). This

indicates that adiabatic conditions have been maintained from the start of the reaction and during the

course of the reaction when the rate of temperature rise reaches a maximu m value of 500 K min" 1.

9.4 Reaction kinetics from RC1

Figure 7. shows the experimental record for batch esterification reaction (catalysed by 0.8%

H2SO4) in the RC1 with the reactor temperature maintained at approximately 31°C. Equation 5

predicts that, at constant temperature, the maximum rate will occur at the start of the reaction (x =

0).

Figure 7 indicates a maximum rate of heat generation only after substantial proportion of

reagents have reacted (x = 0.5), indicating auto-catalytic kinetics. Auto-accelerating reactions can

result in supercritical (runaw ay) conditions at temp eratures low er than those predicted assum ing

normal kinetics. Detailed discussion and quantification of this effect will be discussed elsewhere.

Figurre 7 shows how reaction calorimetry can be used to determine the concentration dependence of

reaction rate. Reaction calorimetry can be used to deterrmine the temperature dependence over only

a limited temperture range due to the substantial temperature dependence of the heat loss

characteristics of this type of apparatus and problems associated with the detection of rapidly

changing temperatures. The adiabatic techniques (ARC and PHI-TEC) are, in general , more

suitable for determining the Arrhenius parameters of an exothermic reaction.

9.5 Kinetic parameters for the esterification reaction.

The initial sections of the ARC and PHI-TEC plots of ln(heat rate) against reciprocal absolute

temperature (Figures 5 and 6) are approximately linear, indicating that the temperature dependence

of the reaction rate can be predicted by the Arrhenius e quation. V alues for the activation energy and

pre-exponential factor evaluated for the esterification reaction are listed in Table 4



385

10

3

^

10

2

^

10

2

0XH2SO+

0.025* H2S04

3.50

-3.38 -3.26 -3.14 -3.02 -2.90 -2.78 -2.66 -2.54 -2.42 -2.30

-1000/r

( K - 1 )

Figure 6. PH I-TE C plots of log(self-heat rate) against reciprocal tempe rature for the esterification

reaction catalysed by various concentrations of sulphuric acid.

40

E

37-1

34

31

28

25- |

22

19-1

16

13

X)

reactor temperature

jacket temperature

—

1 1 1 1 1 1 1 1 —

850

1700

2550 3400 4250

5100

5950 6800 7650 8500

Time (s)

Figure 7. Temperature records during esterification reaction catalysed by 0.8% H2SO4 carried out

as a batch process in the RC1 reaction calorimeter.



386

TA BL E 4 . Therm o-kinetic parameters evaluated from ARC and PHI-TEC data for the esterification

reaction.

sulpihuric

acid cone.

(%)

0.1

0.2

0.4

0.8

activation energy

(kJ mol"

1

)

ARC

94

97

95

-

PHI-TEC

95

94

94

98

pre-exponential

(s -

1

)

ARC

3 . 6 * 1 0

n

1.8*10

12

1.8*10

12

-

factor

PHI-TEC

4 . 6 * 1 0

n

6 . 6 * 1 0

n

7 . 9 * 1 0

n

7 . 5 * 1 0

1 2

10.

HEAT TRANSFER CHARACTERISTICS

The critical conditions which can lead to a runaway exothermic reaction are determined by the

temperature dependence of the rate of heat generation (from thermal analysis) and the temperature

dependence of the rate of heat loss (from the heat transfer characteristics of the process vessel).

Heat transfer coefficients for a jacketed chemical reac tor can be determined by calculation or,

experimentally, by determining the rate of heat transfer between the contents of the reactor (heated

electrically) and the heat transfer fluid in the reactor jacket.

The rate of heat loss from a well stirred jacketed reactor can be predicted assuming a Newtonian

cooling equation of the form:

qi = U .S . ( T

m

- T

e

)

(9)

where the heat transfer coefficient (U) comprises contributions from the thermal resistance of the

reactor wall and the internal and ex ternal film heat transfer coefficients :

J _

_ 1 _ _J_

U ~ h

0

w +

lu

( 1 0 )

Techniques for determining U are discussed elsew here [6]. A value of U= 180 W m"

2

K~l would

be typical for an organ ic med ium in a standard indus trial glass-lined reactor.



387

11 CRITICAL CON DITIONS

Conditions in a well-stirred jacketed reactor correspond closely to those assumed in the Semenov

model [7] for predicting the critical conditions for exothermic runaway. Under these conditions

(assuming Arrhenius-type temperature dependence for the rate of heat generation) the critical jacket

temperature is given by:

m.AH.A.E.exp(-E/RT

e

) i

V c =

UZRTT

=

e (

u

>

This expression assumes that the critical conditions are reached before the depletion of reagents has

had any significant influence on the rate of heat generation (pseudo-zero order kinetics).

Th e S emenov model has been used to predict the critical conditions for the esterification reaction in

a 250 1 glass-lined reactor. Critical jacket temperatures calculated using ARC and PHI-TEC data are

listed in Table 5.

TABLE 5. Critical jacket temperatures calculated for the esterification reaction in 250

1

glass-lined

reactor.

sulph uric acid critical jacke t temperature (K)

concentration (%)

ARC data PHI-TEC data

0.1 296.0 295.8

0.4 285.1 288.9

0.8 285.6

It is not normally possible to test this kind of prediction experimentally, because of the attendant

hazards. However, in the case of the esterification reaction, where the properties of reagents and

products are well established, experiments to determine the critical conditions which could lead to

exothermic runaway could be performed safely in an isolated 250 1 reactor. The temperature-time

profiles which were observed when the esterification was performed as a batch reaction with water

circulating at 285 K (12 °C) through the reactor jacket are shown in Figure 8.



388

p

CL.

E

C L

OJ -

68-

51-

34-

17-

0 -

I 0.8%H2S(H

i i

i i i

0.4% H2S04

^ — - \ 0.1% H2S04

i i i i

0 4800 9600 14400 19200 24000 28800 33600 38400 43200 48000

T i m e (s)

Figure 8. Temperature records during esterification reaction (catalysed by various concentrions of

H2S04) as a batch process in a standard industrial , pilot scale reactor (250 1 capacity) with the

jacket temp erature maintained at approximately 295 K .

Th e dro p in temp erature wh ich can be seen at the start of of each of the expe rimen tal records

(Figure 8) is due to endothermic mixing of reagents.

The results for

0.1%

H2S O4 show that, after the initial mixing of reagents,the tem perature of the

reactor contents remain at approximately the same temperature as the water circulating through the

jacket. (Analysis of the contents of the reactor after 48 hours indicated that the reaction had

proceeded isothermally to completion.) At a sulphuric acid concentration of 0.4% exothermic

reaction causes the temperature of reaction mixture to rise above the jacket temperature but the rate

of cooling is sufficient to prevent a large increase in the temperature of the reactor contents. At a

sulphuric acid concentration of 0.8% the rate of cooling cannot prevent an acceleration in the rate of

heat generation and a runaway excothermic reaction was ob served.

The experimental data indicate that for the 250

1

reac tor at a jack et tem peratur e of 295 K the critical

acid concentration which can lead to a runaway reaction lies between 0.4% and 0.8%. This result is

broadly in accord with the prediction of the simple Sem enov criterion (Equation 11) using thermo-

analytical data from AR C or PH I-TEC (Table 5 ) .

Au tocatalys is detected using isothermal reac tion calorime try (Figure 7) wo uld lead to critical jacket

tempe ratures low er than those predicted in Table 5. Experim ents over a wider range of acid

con centra tions and jack et tempe ratures than those reported here would be necessary in order to

quantify this effect.



389

12 CO NCLUSION

The application of a simple theroretical model can provide a reasonably reliable prediction of the

critical conditions which can lead to exothermic runaway in a batch reactor. More sophisticated

treatments which take account of the concentraion dependence of reaction rate would provide a

more accurate prediction of the critical jacket temperature. A range of thermo-analytical techniques

should be applied in order to determine reliable input parameters for the theoretical models.

REFERENCES

1) Rogers R.N. and Smith L.C., (1970) 'Application of scanning calorimetry to the study of

chemical kinetics', Thermochimicha Acta, 1, 1

2) Townsend D.T. and Tou J.C., (1980) 'Thermal hazard evaluation by an accelerating rate

calorimeter', Thermochimica Acta, 37, 1.

3) Fauske H.K. and Leung J.C., (1985) 'New experimental techniques for characterising runaway

chemical reactions', Chemical engineering progress, 81(8), 39..

4) Singh J., (1989) PHI-TEC: Enhanced vent sizing calorimeter application and comparison with

existing devices', International Symposium on Runaway Reactions', AIChE, 313.

5) American Society for Testing Materials, (1979) 'Arrhenius kinetic constants for thermally

unstable materials', ASTM E698-79, Nov. 79, Committee E-27, SCE27.02.

6) Ch apm an F.S . and Holland F.A ., (1985) 'Heat transfer correlation s in jack eted vessels',

Chemical Engineering, 15, 175-182.

7) Semenov N.N, (1928) Z. Phys. Chem.,48, 57 1.





REACTION HAZARD EVALUATION

P. F. NOLAN

Department of Chemical Engineering

South Bank Polytechnic

Borough Road

London SE1 OAA

UK

ABSTRACT. The available calorimetric methods are discussed in terms of

the data, which they provide in relation to the stages in the

development of a process. The data produced from calorimetric and other

thermal methods is placed within an overall assessment strategy

incorporating literature searches, calculations and formal quantitative

hazard assessment procedures and these may lead to the definition of a

basis for safety. Against this background a procedure is outlined which

will allow a beginner to establish a chemical reaction hazard assessment

laboratory for an industrial company.

1. INTRODUCTION

The majority of reactions carried out in the fine and speciality

chemical industries are exothermic and have the potential for over

heating to occur in their normal batch or semi-batch methods of operation.

The safety record of the chemical industry is generally good when placed

against the background of the number of reactors in operation and the

quantities and types of materials processed. However, problems have

occurred in the past [1,2] due to:

a. inadequate understanding of the process chemistry and thermochemistry

b.

inadequate engineering design for heat transfer

c. inadequate control systems and safety back-up systems

d. inadequate operational procedures, including training.

Various categories of hazard are inherent in chemicals manufacture.

These can be defined as chemical, operational, toxic and environmental.

The potential for such hazards, singly or in combination, can be present

during the stages of manufacture. (see Table 1)

Incidents have occurred in each of the stages below and hence it is

necessary to be in a position to predict any hazard producing potential

at every manufacturing stage. In particular, it is essential to have an

assessment strategy which links the nature of the chemical reagents, the

reaction with the equipment/plant in use and the operating procedures.

In general, chemical reaction hazards arise from:

391

A. Benuzzi and J. M. Zaldivar (eds.), Safety of Chemical Batch Reactors and Storage Tanks,

391—408.




392

TABLE 1. Stages in Chemicals Manufacture

Assembly/storage of raw materials

Chemical reaction

Holding of reactive substances

Purification of the reaction product

Treatment of waste/cleaning/recovery

Storage of product

Drying/formulation/packaging

Transportation

a. thermal instability of reactants, reaction masses and products

b.

rapid exothermic reaction, which can raise the temperature to

decomposition temperature or cause violent boiling of the batch

c. rapid gas evolution which may be associated with thermoneutral,

exothermic or endothermic processes.

Essentially, an assessment procedure for chemical reaction hazards will

initially define:

a. the chemistry for each stage of the process

b.

the plant design and operating conditions

c. the normal variations in process/plant procedures.

The second stage involves:

a. an evaluation of the potential hazards

b. the specification of safety measures

c. the preparation of a detailed report.

The implementation of the safety measures and their inclusion into the

process and plant design needs to be compatible with production and the

economics of manufacture. Finally, it is necessary to regularly monitor

the safety measures and ensure that they remain adequate.

2. STAGES IN PROCESS DEVELOPMENT

Gibson [3] has defined the stages in the assessment procedure against

the background of the normal development stages of a process. Process

development usually occurs in four stages, primarily defined by the

scale of operation - concept, laboratory bench, pilot plant and

manufacturing scale plant. At each stage, the potential reaction hazard

requires definition. Such continuous definition and in some cases re

definition leads to a comprehensive knowledge of the reaction at the

final,

manufacturing stage. Whilst a continuous development of safety

considerations is recommended, it has to be recognised at the outset that

a substantial amount of the experimental work on reaction hazard

evaluation occurs, in practice, between laboratory bench and pilot plant

scale operations.



393

2.1. Laboratory Scale Development

After the conceptual stage of reaction design, it will be necessary to

carry out some bench-scale work in a fume cupboard. However, prior to

such activity it is necessary to:

a. check the literature for data on potential chemical hazards e.g. use

of Bretherick [ 4 ], NFPA [5] and Austin [6 ]

b.

calculate the heat of reaction and the adiabatic temperature rise for

instantaneous reaction. The latter will enable the maximum

attainable process temperature to be calculated

c. ensure that the materials being handled will not detonate or

deflagrate and that the process does not involve a violently

exothermic reaction. The initial screen can involve:

i. an examination of the chemical structure of the molecules

involved. Groups such as aromatic, nitro, nitrate ester and

nitramine are closely linked with explosibility and azo,

azide, nitroso, peroxide and acetylenic groups can also form

part of explosive structures

ii. calculation of the oxygen balance. Almost all of the

recognised explosives have balances between -100 and + 4 0 , but

any balance more positive than -200 should be regarded as a

potential high risk

iii. use of a computer program, such as CHETAH [7 ]. This allows

the estimation of the heat of reaction, thermodynamic

properties of individual substances and the prediction of

whether the compound or mixture has the tendency to propagate

a deflagration or detonation.

Other calculations may also be useful. Craven [ 8] described how the

approximate exothermicity of a reaction or decomposition can be predicted

from the atomisation energies of the reactants and the assumed products.

Atomisation energies can be determined from the summation of average bond

energies given in the literature [9]-

At this stage, it is also necessary to carry out some initial screening

tests (see Section 3.1) to answer specific questions on the exothermicity

of the proposed reaction. The main questions are:

a. What are the normal rates and quantities of heat and gas evolution?

b.

At what temperature will runaway commence?

c. What are the consequences of runaway in terms of heat and gas

evolution rates?

Therefore, any sequence of initial screening tests must be able to

provide the following basic information:

a. temperature for onset of thermal decomposition

b. quantity and rate of heat release

c. rate of gas evolution as decomposition proceeds

d. catalytic effects caused by potential materials of construction of

the envisaged plant

e.

autocatalytic effects

f. induction time effects



394

g. decomposition rate, including any secondary decompositions.

2.2.

Pilot Plant

Following successful laboratory development, pilot plant scale operations

should be carried out. Under the normal, human supervision associated

with pilot plant scale work, it is necessary to demonstrate that the

process can be operated safely both as defined and with the individual

company's accepted normal variations which could occur in practice. The

experience of the company and of the individuals running the plant will

play an important role at this stage.

The basis of safety, i.e. use of preventative and/or protective measures,

requires the consideration of the reaction hazards and the influence of

the plant and its operation on those identified hazards. Ideally, a

formal hazard assessment will call for a clear definition of the process

prior to scaling-up in a pilot plant. This definition will include data

on the process

a. as written with fixed parameters

b.

with acceptable variations found in manufacture

c. with faults known to occur in normal processing, e.g. charging errors

d. with all potential faults.

Essential data at this stage, prior to pilot scale operation is given in

Table 2.

TABLE 2. Data for Reaction Hazard Evaluation

Heat of reaction

Heat capacity

Rate of heat production

Rate of heat removal

Heat transfer properties of reaction mass

Kinetics with regard to accumulation of

reactants/heat

Temperature range and nature of any

decompositions

Factors which affect accumulation

Effects of mischarging, impurities, errors

and those caused by materials of construction

of plant

Kinetics (autocatalysis) of decomposition

reactions

Rate and quantity of gas evolution

The prime objective of supporting calorimetric laboratory studies (see

Section 3.2) is to obtain information that can be evaluated in relation

to the conditions which occur in the plant. The design of preventative

and protective measures will require details of the deviations which may



395

occur from the normal process definition. The information required to

characterise a runaway or decomposition is:

a. the onset temperature for the specific plant system being studied

b.

rate of heat evolution at runaway

c. rate of gas evolution at runaway

d. maximum pressure developed in a closed vessel when runaway occurs.

2.3. Manufacturing Scale Operations

Following bench scale and pilot plant operations, a number of further

decisions need to be made. The assessments carried out at the two

previous stages will need to be re-evaluated and some further testing

may be required to relate the data to the specific plant and operating

conditions.

The manufacturing scale plant can be:

a. an existing reactor

b.

a multi-purpose reactor, with possibly some modification to

accommodate the process

c. a new purpose-designed and built reactor.

The effect of scale of operation is a very significant factor, although

it is not always fully appreciated. Many incidents occur when processes

are scaled up, some having been performed successfully for years on a

slightly smaller scale. The reasons are clear when the following are

considered:

a. the rate of heat generation increases exponentially with temperature

b.

the total heat generated is proportional to the batch volume (a cubic

term)

c. the rate of cooling is proportional to the surface area (a squared

term).

Any increase in batch size will substantially increase the total heat

generated. Unless the cooling capacity is increased accordingly then

the reaction temperature will rise. This leads to an increase in the

reaction rate and the reaction can go out of control.

The required cooling area for batch operation can be calculated by a

number of methods. The method described by Hugo [10] requires data on

the rate of reaction and the adiabatic temperature rise. Depending on

the reactor size, 2 - 5 m m can be installed in reaction vessels with

only jacket cooling and 4 - 8 m m if the vessel is also provided with

an internal cooling

coil.

The determination of the required cooling area

may mean taking the decision about moving from batch to semi-batch

operation. The latter allows the option of feed control to minimise

potential runaway conditions.

Any available safety system must be adequate for all situations, which

may arise. The bench scale studies can define the most suitable

agitator, the inside film heat transfer coefficient for use in scale-up

correlations and the design of normal operating and emergency relief

systems. The materials of construction of any plant needs careful

consideration, since it may catalyse undesired side or secondary



396

reactions. Laboratory scale tests may include samples of the materials

of construction or their decomposition products, e.g. rust.

The design of a reactor and the chosen operational procedures should be

accompanied by a series of formal hazard assessments. The easiest

technique for the non-specialist is the use of HAZOP [11]. The Hazard

and Operability study can be carried out at various stages of the process

development. More quantitative techniques, e.g. the application of fault

tree analysis [12], require some specialist knowledge.

The manufacturing scale also raises the possibility of designing for

inherent safety; however, where this is not possible then reliance must

be placed on process control and associated safety back up systems, where

necessary. The basis of process control is set by the experimental

results from calorimetric investigations. These include the definition

of onset of exotherm temperature, the safety margins, amount of cooling

required, the temperature limit to prevent accumulation of unreacted

material and the effect of loss of agitation.

2.4. Modified Processes

Many incidents follow modifications to plant and/or process. Any

assessment procedure must cater for on-going changes in the running of

processes and plants. If a hazard assessment of the plant and process

is available and the modification does not invalidate the basis for safe

operation then the formal recording of this decision and the reasons for

it are all that is required. Alternatively a detailed evaluation and

possibly alternative or additional recommendations to ensure safe

operation of the modified process or plant may be necessary. It is

essential that for any suggested modification, checks must be made on the

chemical and operational hazards and the basis of safety clearly re- ■

defined.

There is currently no standard procedure or no one test for the assess-

ment of reaction hazards; however, the type of data required, calls for

the use of calorimetric instrumentation.

3. CALORIMETRIC AND OTHER INSTRUMENTATION

Calorimeter is the generic term for a range of instruments used for

gaining thermodynamic, kinetic and heat transfer data to aid process and

plant design and operation. Calorimetry ranges in complexity from basic

heating tests to the sophistication of simulating an entire, as written,

process in a model bench-scale, computer-controlled batch or semi-batch

reactor. The main types of equipment, which can be used, after the

preliminary calculations and any necessary explosibility screening tests

are:

a. basic screening tests - These are used primarily at the laboratory

scale development stage and prior to any studies outside the

laboratory environment.

b. isothermal calorimetry - This is used to gain data on the normal,



397

desired reactions, in terms of kinetics, thermodynamics and heat

transfer.

c. adiabatic calorimetry - This is used to gain data on the runaway

potential of reactions and individual compounds.

d. reactor venting instrumentation - This is used to gain data to enable

the calculation of emergency vent sizes, but they also provide some

thermal data.

3.1. Basic Screening Tests

These tests tend to use small samples and hence can be used during the

laboratory scale development programme. They can be used to examine the

effects on stability of the presence of materials of construction and

their decomposition products, e.g. rust and any ageing effects caused by

the reaction mass being held for prolonged periods at elevated

temperatures. From some of the tests, it is possible to gain ideas on

the initial exotherm temperature, adiabatic self-heating rate,

activation energy for decomposition, adiabatic temperature increase,

overall energy release during decomposition, adiabatic induction time,

estimates of the initial exotherm temperature for a larger size of

reaction mass and the volume of gas evolved on decomposition.

Many test methods have been developed "in-house" and are described in the

literature

[13,14].

Particularly useful test methods employ gramme size

quantities. Some companies use commercial DSC/DTA as a screening tool

employing milligramme quantities. For reaction hazard evaluation it is

recommended that use is made of:

a. sealed pressure resistant capsules

b.

heating rates of 1 to 5 C min

c. sample mass of 5 to 10 mg

d. temperature range of 30 3 to 623 K

when using conventional DSC/DTA.

The unfortunate "100 Degree Rule" is often misused in the evaluation of

reaction hazards. The rule basically states that if the operating

temperature of a process is 100 C higher than the detectable exotherm

found in a small scale test, then the process operation will not

experience this thermal event [ 15]. Based on experience, it is known

that many factors influence the temperature dependent rates of heat

generation as detected by screening test methods [16 ]. These include the

physical aspects of the test procedure, such as heating rate, sample size,

thermal inertia, sensitivity for the particular type of substances

involved, the agitation and the activation energy. The sensitivity of

the small scale test needs to be viewed in relation to the large scale

operation. Safety margins should only be used as guides and not for

defining a basis for safety.

Recently a number of commercial, relatively low cost screening tests have

become available. These include the Radex [17] and the RSST (Reactive

System Screening Tool) [ 18 ]. The latter also provides data for the



398

sizing of emergency relief vents. The advent of commercial equipment

will aid the individuals/companies who are unable to develop their own

instrumentation, due to lack of workshop facilities or internal working

practices. However, the literature contains some very detailed

descriptions of easy to construct and use equipment, which can provide

the fundamental data on thermal stability and this includes onset

temperature, magnitude of an exotherm and its induction time. From such

data the size of the potential problem and the time available to correct

it can be estimated.

When expensive commercial instrumentation, such as the Seteram C-8 0,

Thermometries Thermal Activity Monitor, Columbia Scientific Industries

Accelerating Rate Calorimeter, is available some companies use them as

basic screening tests, although they are usually more expensive to run

and can take longer to provide the preliminary data. Although, of course,

they also provide additional data to that obtainable from the other

cheaper tests and instrumentation.

3.2. Reaction Calorimeters

Numerous commercial and "in-house" reaction calorimeters exist and the

choice of one particular instrument over another very much depends on the

type of data required (and the money available). Nearly all reaction

calorimeters can be said to operate in a number of modes, e.g. isothermal

and adiabatic. However, despite claims by some instrument manufacturers

their actual suitability for use in one or more modes can only be defined

for each specific study undertaken. Many of the instruments have common

features,

although the method of gaining the calorimetric data may vary

slightly.

Dewar-based calorimeters are easy and cheap to construct [19]. Due to

their basic construction they can simulate the thermal characteristics

of the plant and measure the heat output of the reaction by measuring the

changes in the batch temperature. Experiments to determine the cooling

rates of large reaction vessels [20] have shown that the rate of heat

losses from 0.5 to 2.5 m vessels correspond to those from 250 ml and

500 ml Dewar flasks. Hence, measurements of the temperature rise when

reactants are charged to Dewar flasks at known rates enables the rate and

quantity of heat evolved in large scale plant to be found.

In the simple isoperibol calorimeter, the heat transfer medium in the

jacket is held at a constant temperature and the heat flow measured by

the change in reactant mass temperature. Unfortunately, it is usually

non-linear at high power outputs and both reaction kinetics and heat

capacity are affected by allowing the temperature to rise. The results

are only approximate. Power compensation calorimeters [21,22] are

relatively easy to design, construct and operate. The temperature of the

heat transfer medium in the reactor jacket is set below the desired

reaction temperature which is maintained by a heater in the reactants or

base.

Any change in heat flow is compensated by a corresponding change

in the electrical power to the heater, which provides a direct measure of



399

the heat flow caused by the reaction.

Heat flow calorimeters monitor the temperature difference between a

rapidly moving heat transfer medium, e.g. silicone oil, in the reactor

jacket and the reaction

mass.

The heat (power) output of the reaction

is quantified by measuring the flow of heat between the batch and the

heating/cooling system. Heat balance calorimeters monitor the

temperature difference between the inlet and outlet points of the heat

transfer medium, which is flowing at a measured slow rate in the jacket.

All the above types of reaction calorimeters are ideal for studying

desired, normal reactions. They can provide temperature-time curves for

reactions,

provide evidence of self-heating and can provide the data for

calculating heats of reaction and heat capacities. If assumptions can

be made about the reaction mechanisms, then it is possible to gain some

thermokinetic data on the reaction. The simplest type of analysis

assumes that the rate of reaction is proportional to the power output or

rate of temperature rise and is based on dimensionless rates and

concentrations. They can also be used to model semi-batch operation.

The heat flow calorimeter is an ideal instrument for gaining data on the

inside film convective heat transfer coefficient, which can be used as a

basis for scale up, in the standard heat transfer correlations in stirred,

jacketed vessels [23,24]. Geometric factors for the different types of

agitators can also be obtained from experiments using heat flow calori

meters [ 24 ]. However, it must be remembered that this is only possible

with reasonably mobile systems; too viscous materials cause a breakdown

of the necessary heat transfer paths between reactant-reactor wall-heat

transfer medium.

Reaction calorimeters can also be used to examine the problems of

accumulated heat, inhibition of the desired reaction and delayed

initiation. They are increasingly used for process development and

optimisation. It is possible to examine reactions under reflux

conditions with the addition of further equipment [25]. Reactions, which

generate limited amounts of gas can also be studied. Gas evolution

during a normal, desired reaction can be measured using an upturned

measuring cylinder filled with a suitable collecting fluid. Timing the

rate of gas collection can provide a quick assessment of the evolution

rate. An automated gas burette has been developed by staff at ICI pic

[26].

Lambert and Amery [27] have described the use of a thermal mass

flowmeter for measuring the gas evolved in both reaction calorimeters and

on full scale plant.

Commercial reaction calorimeters include the Toledo-Mettler Reaction

Calorimeter RC 1, the Thermometries Reaction Monitor RM 1 and the

Columbia Scientific Industries QRC (Quantitative Reaction

Calorimeter).

However, numerous individuals and companies have designed and use their own

reaction calorimeters to great effect. These incorporate reflux

facilities [25] and the use of pressure vessels to extend the range of

reactions which can be studied [28 ]. Steele et al [24 ] has converted a



400

-3 3

675 x 10

m

computer-controlled pilot plant reactor to operate as a

heat flow calorimeter.

3.2.1. Adiabatic Calorimeters

Uncontrolled reactions can originate from:

a. the desired reaction going out of control

b.

a secondary reaction

c. a decomposition

The screening tests give some indication when runaway occurs but because

of the low heat loss conditions on industrial plant the accurate deter

mination of the minimum temperature at which self-heating will start on

the plant requires the use of adiabatic calorimeters. While a number of

calorimeters can operate under an adiabatic mode, some specialist

instruments are available for examining the runaway condition.

Test methods can fail to detect the onset of an exotherm due to heat loss

from:

a. the sample to its surroundings

b.

the sample to the test

cell.

The latter is particularly important when the thermal capacity of the

test cell is large compared with that of the sample. A parameter, 0 is

used to characterise the effect and is termed the thermal inertia

0

w h e r e M

1

=

+ M C

c vc

M C

s vs

mass (

C = specific heat at constant volume

v

subscripts s and c relate to the sample and container respectively

An analysis of the importance of the thermal inertia term is given by

Townsend and Tou [29].

Techniques operating under adiabatic mode for the study of runaway

conditions include the use of stainless steel Dewars, fitted with

pressure-tight lids [ 3 0 ]. The large sample size and the low heat

capacity of the Dewar means that a low value of the thermal inertia is

obtained. The sensitivity can be further increased, by placing the

Dewar in an adiabatic environment, i.e. in an oven, in which the

temperature follows that recorded in the sample.

The bench-mark, commercial adiabatic calorimeter is the accelerating rate

calorimeter from Columbia Scientific Industries. A 10 g spherical sample

container is suspended within a copper vessel containing heaters and the

whole assembly is enclosed in a steel safety casing. The instrument is

normally operated in an isothermal mode or in a step-wise temperature

regime, the heat-wait-search sequence. At each temperature step, the

A.R.C.

is programmed to detect any self-heating above a specified



401

threshold, now down to 0.01 C min , i.e. any thermal excursion above

this threshold is recognised as an exotherm. The instrument is then

maintained under adiabatic conditions and temperature-pressure-time data

under runaway conditions is obtained. The data can be manipulated to

provide pseudo-kinetic information [29] as well as all the data offered

by the basic screening tests. Mores [31] has used ARC data, in

combination with self heat models, to gain self accelerating decomposition

temperatures [32] and for the modelling of sequential and parallel

reactions.

A number of other commercial instruments can provide similar data to the

ARC,

e.g. Sikarex. The latter instrument can be operated under both

adiabatic and isothermal modes of operation. Pressure-temperature-time

data can also be obtained from instruments, which have been primarily

designed for the acquisition of information needed to size emergency

relief vents using the DIERS methodology [33,34]. Considerable attention

must be paid to the sensitivity of instruments over their defined range

of application and in terms of the type of substances investigated.

3.3. Instrumentation for Emergency Vent Sizing

The AIChE sponsored Design Institute for Emergency Relief Systems

produced a calorimeter, which uses a pressure equalisation system and a

weak test cell, with a low thermal inertia. The original Vent Sizing

Package (VSP) [33] uses a 120 ml heated test cell with a pressure control

system which balances the internal and external cell pressure and hence

the integrity of the test cell is maintained. The cell can operate in a

closed or open mode, the latter using a vent pipe into an outer contain

ment vessel. Temperature-pressure-time data can be obtained, together

with the flow behaviour of the discharging runaway reaction masses. The

experimental data is combined with data from the actual plant (i.e.

ullage,

total reactor volume and relief set pressure) and physical

properties of the reaction

mass,

i.e. density, to allow the calculation

of the size of the emergency vent. It is possible to simulate the

presence of an external fire on a reactor.

A similar device is the Phi-tech from Hazard Evaluation Laboratory Ltd.

Fauske and Associates, the originators of the VSP have now developed the

RSST [ 18 ]. This is a relatively cheap instrument, which operates in a

quasi-adiabatic mode. It is necessary to use some modified equations

from the DIERS programme for vent sizing. The vast majority of the

original VSP users have carried out substantial development work to

create improved instrumentation, yet retain the basic concept of

pressure equalisation to maintain the integrity of thin walled containers.

Whether a low thermal inertia factor results from this technique is

debatable. Some very sophisticated instruments now exist in the

specialist laboratories of industrial companies and academic establish

ments. Most developments are readily made available to others wishing

to modify existing equipment or to build their own vent sizing equipment.



402

A. BASIS OF SAFETY

The data from calorimetric experiments and the adoption of formal hazard

assessment procedures permit decisions relating to the safe design and

operation of the process and plant. Safe operation can be achieved by

preventative and protective measures. In order to select such measures,

it is necessary to define the worst case condition. The possible

measures include:

a. process control

b.

process control + containment

c. process control + emergency venting

d. process control + inhibition of runaway reactions

A reactor can be designed to withstand the maximum pressure produced in

the runaway situation or alternatively a normal reactor can be installed

in a concrete and steel bunker. Since the products of a runaway can be

toxic, flammable, corrosive or foul smelling, containment offers the

possibility of restricting their release into the environment. Venting

is a normal operation in the course of chemical manufacture. Relief

vents sized to cope with gas pressure and/or fire engulfment are rarely

if ever adequate to provide protection against uncontrolled runaway.

The sizing of relief vents for worst case conditions has been covered by

the DIERS programme, although it is becoming increasingly important to

consider alternatives to emergency relief venting, due to economics, the

containing/disposing of the relief discharge and the problems of dealing

with the rate of rise in pressure found with some reactions. Inhibition

can take several forms. Quenching and dumping are common methods. The

sizing of dump tanks has been addressed by Grossel [3 5] . Occasionally,

it is possible to use reagents to remove free radicals from the reaction

mass.

In any considerations relating to the definition of the basis of safety,

it is necessary to always consider the reliability of the operators and

the instrumentation.

Process control can employ hard-wired instrumentation and micro

processors. Duplication of sensors monitoring key parameters is usually

recommended. The correct level of protection can be defined by the use

of Hazan [3 6 ].

5. ESTABLISHING A REACTION HAZARD EVALUATION LABORATORY

With the ever increasing legislation requirements and the quest for

better manufacturing routes to both old and new products, there is a

great need to support such developments with appropriate data on the

potential hazards and to provide information for the specification of

the design and safe operation of processes and plants. However, it is

easy to recognise that a need exists but it is a problem to actually

satisfy that need. It is important to establish "in-house" testing,

primarily because the individual company should know its processes

better than any external consultants and because the use of a hazard



403

assessment schedule also requires the incorporation of local process and

plant experience. Simultaneously, such testing may provide opportunities

for process development and optimisation. The initial steps are always

the most difficult because they involve the identification of the

problems of the individual company concerned. The literature and the

advertisements for commercial equipment can be confusing to the novice

in the field. Once the problems of the company have been identified,

the next stage is normally to seek advice from others, who have already

started such work. They will normally suggest the use of simple, cheap

methods presented in the literature or in specific publications e.g. the

ABPI Guidelines for Chemical Reaction Hazard Evaluation. Some of

Europe's major companies have their own "in-house" test methods and all

are prepared to give advice on tests, their results, the limitations and

their interpretation with respect to company activities in general terms.

The construction and use of cheap but effective methods for reaction

hazard screening will give confidence to the staff in an embryonic

hazard evaluation laboratory and it will be possible to see how the

measured data relates to past process and plant operating experience.

It is also possible to "calibrate" the obtained data by comparing the

results obtained on well defined materials with those given in the

literature for the same materials but found using more sophisticated

equipment. Based on experience, conversations with specialists and

comparative studies the level of confidence in the application and inter

pretation of data should grow.

At this stage, a decision must be made as to whether further equipment

and methods are needed. If developments are required, then the choice

of either purchasing commercial equipment or designing specific

instrumentation must be made. The work at the South Bank Polytechnic,

in London and its associated reaction hazard specialists based in

industrial companies has shown that it is possible to design, construct

and successfully use every type of calorimeter, including the next

generation of all-purpose calorimeters. Obviously, the development of

"in-house" instrumentation takes resources but they can be specifically

designed to solve particular problems. The purchase of commercial

equipment reduces the instrument development time but they all require

time for training of operators and for gaining sufficient experience to

apply the manufacturers operating instructions to specific industrial

reactions. An "in-house" instrument is usually easier to maintain and

modify. It must be stressed that in order to solve particular industrial

problems it may be necessary to operate commercial instruments in a

variety of configurations, other than that described in the manual of

operation. User forums certainly help the beginner to appreciate the

variations of operation and interpretations of data which are possible.

Gradually, the beginner is accepted as a specialist and user of

particular methods and a number of groupings have established themselves

for the free exchange of information. The European DIERS group meets to

discuss the uses of equipment, methods, data and designs. It is open to

industrialists and academics with practical experience. It is not



404

involved in training or in the promotion, marketing, sales of

commercial equipment. However, the people involved in reaction hazard

evaluation tend to meet regularly and exchange their experiences. They

have an open policy to welcome and guide new people into the subject area.

Experience of the very latest commercial equipment or some new idea to

permit the measurement of say, the rate of gas evolution is readily

discussed. The basic steps of setting up a reaction hazard evaluation

laboratory are given in Table 3.

TABLE 3. Setting-up a Reaction Hazard Laboratory

i. identify the problems in the company. There

is no need to build or buy a reaction

calorimeter if all the problems relate to

the storage of thermally instable products

ii. discuss what methods are available to solve

the identified problems with some specialists

iii. gain some experience with easy to construct

and use equipment

iv. relate the acquired data to past experience

of processes and plant

v. integrate the methods and results into an

assessment programme, involving personnel

from other parts of the company

vi. assess the accuracy of the data obtained and

question whether it needs to be improved to

define the basis of safety

vii. define the need or otherwise for more

sophisticated equipment

viii.

decide whether commercial equipment can

provide a reasonably ready answer or on the

need to design and construct "in-house"

equipment which will provide the means to

gaining data of a level of acceptability

defined by the company

ix.

always keep records of the methods employed

and the resulting data and where possible

carry out calculations to check that the

values found bear some relation to that

expected, say for heats of reaction given

the fact that the extent of the particular

reaction studied can be found by chemical

analysis of the product (i.e. employ good

laboratory practice)

x. relate all the available test methods,

their results and the interpretation in the

reaction hazard evaluation laboratory to

process and plant experience to decide on

the most suitable methods of assessment for

each stage of the process development



405

6. CONCLUSIONS

Reaction hazard evaluation must be considered at each stage of

development and scale of operation of a process. The details relating

to potential hazards need continuous expansion and re-definition. A

considerable number of methods and associated calorimeters exist and

their selective use can gain data, which can either directly, or when

used in appropriate formulae define a basis of safety for the

manufacturing scale plant.

The results from reaction hazard evaluation need to be combined with the

findings of formal hazard assessment procedures, e.g. HAZOP, FTA and

HAZAN, to define the worst case condition and the level of protective

measures required.

The basic steps of setting up a reaction hazard evaluation laboratory

include the identification of manufacturing problems and the acquisition

of raw and manipulated data. Confidence in the use of such data to

design and operate new plant and processes can be established on the

basis of relating laboratory-generated data to the past experience of

plant and process operations of the manufacturing company.

7.

REFERENCES

1. Barton J. A. and Nolan P. F. (1984). Runaway reactions in batch

reactors. IChemE Symposium Series No. 8 5. The Protection of

Exothermic Reactors and Pressurised Storage Vessels.

2. Nolan P. F. and Barton J. A. (1987). Some lessons from thermal

runaway incidents. J. Hazardous Materials 14 , 233 - 239-

3. Gibson N. (1987). Hazard evaluation and process design. IBC

Conference on Techniques for the Control and Prevention of Runaway

Chemical Reaction Hazards. London.

4. Bretherick L. (1990). Handbook of Reactive Chemical Hazards.

Butterworth-Heinemann. Oxford.

5. National Fire Protection Association

(1975).

Manual of Hazardous

Chemical Reactions. Boston.

6. Austin G. T. (1982). Hazards of commercial chemical operations in

Safety and Accident Prevention in Chemical Operations (editors

H. H. Fawcett and W. S.

Wood).

Interscience.

7. Frurip D. J., Freedman E. and Hertel G. R. (1989). A new release of

the ASTM CHETAH program for hazard evaluation: versions of mainframe

and personal computer. AIChE/IChemE International Symposium on

Runaway Reactions. AIChE Center for Chemical Process Safety

3 9 - 5 1 .



406

8. Craven A. D.

(1987).

A simple method of estimating exothermicity by

average bond energy summation. IChemE Symposium Series No. 102.

Hazards from Pressure, Manchester.

9. Sanderson R. T.

(1971).

Chemical Bond and Bond Energy. Academic

Press.

New York.

10. Hugo P. (1980). Chem. Ing. Techn. 52, 712 and Hugo P., Konczalla M.

and Mauser H. (1980). Chem. Ing. Techn. 52, 761 included in

Westerterps K. Ft., van Swaaij W. P. M. and Beenackers A. A. C. M.

(1984). Chemical Reactor Design and Operation. Wiley. Chichester.

11.

Kletz T. A.

(1984).

Hazop and Hazan - notes on the identification

and assessment of hazards. IChemE (Loss Prevention). Rugby.

12. Thomson J. R.

(1987).

Engineering Safety Assessment. Longman.

Harlow.

13.

Cronin J. L. and Nolan P. F.

(1987).

Laboratory techniques for the

quantitative study of thermal decompositions. Plant/Operations

Progress 6, 2, 89 - 97.

14. Association of the British Pharmaceutical Industry (1990).

Guidance Notes on Chemical Reaction Hazard Analysis.

ABPI.

London.

15.

Lambert P. G. and Amery G.

(1989).

The use of DSC as a screening

tool in chemical reaction hazard analysis. IChemE Symposium Series

No.

115. Hazards X Process Safety in Fine and Speciality Chemical

Plants.

Manchester.

16.

Cronin J. L. and Nolan P. F.

(1987).

The comparative sensitivity of

test methods for determining initial exotherm temperatures in thermal

decompositions of single substances. J. Hazardous Materials 14, 293 -

307.

17. Hub L. (1986). Experiences with the TSC 500 and Radex Calorimeter.

IBC Conference on Control and Prevention of Runaway Chemical

Reaction Hazards. Amsterdam.

18. Fauske H. K., Clare G. H. and Creed M. J. (1989). Laboratory tool

for characterising chemical systems. AIChE/IChemE International

Symposium on Runaway Reactions, Cambridge, Boston.

19- Harris M. T. G. (1991). Adiabatic Dewar calorimetry. PhD CNAA South

Bank Polytechnic, London.

20 . Wright T. K. and Rogers R. L. (1986). Adiabatic Dewar calorimetry.

IChemE Symposium Series No. 97. Hazards IX Hazards in the Process

Industries, Manchester.



407

21. Wright T. K. and Butterworth C. W. (1987). Isothermal heat flow

calorimeter. IChemE Symposium Series No. 102. Hazards from Pressure.

Manchester.

22. Blitz J. L.

(1989).

The design and construction of a power

compensation heat flow calorimeter for the study of fermentation

processes. PhD CNAA South Bank Polytechnic, London.

23 . Chapman F. S. and F. A. Holland (1965). Heat transfer correlations

for agitated liquids in process vessels. Chemical Engineering 1,

153 - 158.

24 . Steele C. H. (1988). Calorimetric techniques for reflux analysis

and scale-up for the design and operation of batch reactors. PhD

CNAA South Bank Polytechnic, London.

25. Steele C. H. and Nolan P. F. The design and operation of a reflux

heat flow calorimeter for studying reactions at boiling.

26 .

G ibson N., Maddison N., Rogers R. L.

(1987).

Case studies in the

application of DIERS venting methods to fine chemical batch and

semi-batch reactors. IChemE Symposium Series No. 102. Hazards from

Pressure. Manchester. Pergamon Press.

27. Lambert P. G. and Amery G.

(1989).

Assessment of chemical reaction

hazards in batch processing. AIChE/IChemE International Symposium on

Runaway Reactions. AIChE Center for Chemical Process Safety,

Cambridge, Boston, MA.

28 .

Tee D. G.

(1991).

Heat flow calorimetric studies of ethylene oxide

reactions.

PhD CNAA South Bank Polytechnic, London.

29.

Townsend D. I. and Tou J. C.

(1980).

Thermal hazard evaluation by

an accelerating rate calorimeter. Thermochimica Acta 37, 1 - 3 0 .

30. Rogers R. L. (1989). The use of Dewar calorimetry in the assessment

of chemical reaction hazards. IChemE Symposium Series No. 115.

Hazards X Process Safety in Fine and Speciality Chemical Plants.

Manchester. Pergamon Press.

31. Mores S. (1991). Enhanced control and data evaluation for

accelerating rate calorimetry. PhD CNAA South Bank Polytechnic,

London.

32. Mores S. and Nolan P. F.

(1991).

Determination of SADT from thermal

stability data generated using accelerating rate calorimetry.

Submitted to Journal of Loss Prevention in the Process Industries.

33. Fauske H. K. and Leung J. L. (1985). New experimental techniques

for characterising runaway chemical reactions. Chemical Engineering

Progress 8 1, 8, 39 - 4 6.



408

34. Fisher H. G. (1985). DIERS research program on emergency relief

systems.

Chemical Engineering Progress 81, 8, 33 - 3 6.

35.

Grossel S. S.

(1990).

An overview of equipment for containment and

disposal of emergency relief system effluents. Journal of Loss

Prevention in the Process Industries 3, 1, 112 - 124 .

36. Lees F. P. (1980). Loss Prevention in the Process Industries.

Butterworth-Heinemann. Oxford.



O U T L I N E O F T H E M O D E L L I N G A C T I V I T I E S I N V E N T I N G

A. N. SKOULOUDIS

Process Engineering Division, JRC Jspra,

Commission of the European Com munities

21020 Ispra. (VA), Italy.

A B S T R A C T . The present work describes various aspects of modelling the loss of containment and

covers several problems which could be encountered in the theoretical calculations with several numerical

models (codes). The key features of four different codes which are suitable for the analysis of venting

transients are illustrated and the parameters which characterise the emergency relief of the reactor vessel

are identified. Six practical venting problems are analysed and comparisons are made with the data

calculated by the relevant codes.

1 . G e n e r a l A i m s

T h e c o n t a i n m e n t o f m u l t i c o m p o n e n t m i x t u r e s in v e ss el s u n d e r h ig h t e m p e r a t u r e a n d

pressure has been a lways an impor t an t sub jec t fo r t he sa fe ty o f Chemica l Indus t r i e s .

The re a re seve ra l p rocesses occur r ing dur ing the emergency ven t ing o f vesse l s which

a re d i rec t ly r e l a t ed wi th t he in i t i a l cond i t i ons which a re f r equen t ly c lose to sa tu ra t ion .

Thus, a f te r the opening of a re l ie f device the contents of reac tor vesse l a re empt ied

unde r mul t iphase f low cond i t i ons . The fo l lowing a re t yp ica l p rocesses i den t i f i ed dur

ing top ven t ing t r ans i en t s (1 ,2 ,3 ) . As soon a s t he re l i e f va lve opens vapour con ta ined

in the f reeboard volume of the pressure vesse l wi l l be re leased and the pressure fa l l s

rap id ly . Th e l i qu id pha se can no t fol low th i s r ap id chang e o f p re s sure wi th a p ro m pt

c h a n g e in t e m p e r a t u r e a n d t h e l iq u i d b e c o m e s s u p e r h e a t e d . T h i s l e a d s t o t h e r m o

dy nam ic d i sequ i l i b r ium b e tween th e pha ses which i s r e -e s t ab l i she d a f t e r a sho r t t im e

by v igoro us re -eva pora t io n o f t h e l i qu id . D ur in g th i s pe r iod the h igh de pres sur i sa t ion

ra t e i s r edu ced . Th en a ma rke d p re ss ure r ecove ry m igh t occur wh en the vap ou r vo l

ume produced by evapora t ion exceeds the vo lume of t he mix tu re which f lows ou t o f

th e vesse l. Th i s r ecove ry is ve ry p ro nou nced if a l a rge an d s t ee p p re ss ure decay has

occu r red a t t h e fir st s t ages o f t h e t r an s i en t . Va pou r is s t il l d i scha rged th ro ug h the

ven t - l i ne t oge the r wi th some drop le t s en t ra ined f rom the in t e r face sepa ra t ing the p re

dominan t ly l i qu id and the p redominan t ly vapour r eg ions o f t he vesse l . As soon a s t h i s

l eve l r eaches t he ven t - l i ne a d i s t i nc t two-phase mix tu re wi l l be d i scha rged wi th l a rge

l iq u i d c o n t e n t . N e v e r t h e l e s s , t h e e v a p o r a t i o n p r o c e s s e s c o n t i n u e a n d t h e t h e r m o d y

nam ic d i sequ i l i b r ium i s r edu ced . Th e in t e r face level is g ra du a l ly co l l aps ing so th a t t he

ven t - l i ne wil l be no longe r b locked . Th en a p re do m inan t ly vap ou r mix tu re wil l aga in

l eave the vesse l wi th seve ra l l i qu id d rop le t s en t ra ined . Dur ing th i s p rocess t he p re ssure

in the vesse l fa l l s cont inuously unt i l a new sta te of equi l ibr ium has been establ i shed

w i t h t h e s u r r o u n d i n g s .

409

A. Benuzzi and J. M. Zaldivarfeds.), Sa fely of Chemical Batch Reactors a nd Storage Tanks, 409—429.

© 1991

ECSC,

EEC.

EAEC. Brussels a nd Luxembourg. Printed in the Netherlands.



410

T h e m a g n i t u d e a n d t h e i n t e r a c t i o n o f t h e p r o c e s s e s m e n t i o n e d a b o v e d e p e n d o n

a n u m b e r of g e o m e t r i c a l , o p e r a t i o n a l a n d p h y si c o -c h e m i c al p a r a m e t e r s . T h e s e p a r a m

e te r s a re i den ti fi ed in s ix exam ples which a l so de m on s t r a t e t he i r im po r t a nc e . Th e

exper imenta l da ta repor ted here have been obta ined a t four tes t s i tes in f ive di f fe r

ent vesse ls . T h e wo rking f luids have been e i ther w ate r or re f r igera nt R 114 and the

ope ra t ing p re ssure a re up to 7 .2 MPa . The theore t i ca l ca l cu l a t ions have been ca r r i ed

o u t w i t h t h e c o d e s R E L A P , S A F I R E , R E L I E F a n d D E E R S . D e t a i l s a b o u t t h e i n p u t

op t ions used by each code a re desc r ibed ind iv idua l ly i n each example .

2 .

I n t r o d u c t i o n t o t h e N u m e r i c a l C o d e s

Al l the codes tha t wi l l be used in ana lysing the vent ing examples which fol low have

been dev elope d for d i f ferent typ es of ap pl ic a t io ns and a l tho ug h in pr inc iple solve s im

i la r se t s o f conse rva t ion equ a t ion s fo r t he ma ss , m om en tu m an d ene rgy th ey a ll have

signi f icant ly di f fe rent fea tures for desc r ibing th e ph en om eno log y of th e t ra ns ien t . Here

a t t h e J .R .C . w e h a v e a v a i l a b l e t h e A m e r i c a n c o d e s R E L A P, SA FI R E a n d D E E R S

toge the r wi th t he code RELIEF (o r ig ina l ly ca l l ed VESSEL) which has been deve loped

loca lly . The ore t i ca l ca l cu l a t ions f rom a l l o f t he s e codes a re dem on s t r a t e d in t he n ex t

sec t ion however , i t i s useful to descr ibe here the key fea tures of these codes and to

iden t ify t he i r mo de l l i ng capab i l i t i e s fo r t he emergen cy ven t in g of chem ica l r e ac to r s .

The ma in code fea tu re s a s used in t he Benchmark Exe rc i se s (5 ) a re shown in Tab le 1 .

TA BL E 1 : The ma in fea tu re s o f t h e codes

N a m e

of the

C O D E

R E L A P 5

S A F I R E

R E L I E F

D E E R S

N o d e s

in the

Vessel

Severa l

1

Severa l

Severa l

N o d e s

in the

Vent- l ine

Severa l

8 or 50

1

Severa l

No of

C h e m i c a l

R e a c t i o n s

-

10

10

4

No of

C o m p o

n e n t s

1

10

10

6

E x t e r n a l

H e a t

F l u x e s

Yes

Yes

Yes

Yes

T w o - p h a s e

Flow

M o d e l s

Accord ing to

Flow Reg ime

Two Dr i f t -

f lux models

Drift-f lux

Dri f t - f lux

Al l t he abov e men t ioned codes employ d if fe ren t t yp es of tw o- ph as e flow mod e l s .

Th i s i s a c losure r e l a t i onsh ip which depends on the f l ow pa t t e rn o f t he l i qu id -vapour

m i x t u r e a n d c o r r e l a t e s t h e t w o - p h a s e p a r a m e t e r s i n t h e m a s s , m o m e n t u m a n d e n e r g y

conse rva t ion equa t ions . In p r inc ip l e , fo r t he two-phase f low a long a channe l wi th o r

wi thou t ex t e rna l hea t i npu t t he fo l lowing re l a t i onsh ip i s app l i cab le

(Pa

1

—

x ot u> 1

—

a

1



411

This i s d i rec t ly der ived f rom the def ini t ion of the qual i ty , x, a s t he ra t i o of vap ou r t o

the to ta l mass-f low-ra te and f rom the def ini t ion of the void f rac t ion, a, as the ra t io of

a re a occup ied by the vap ou r t o t h e t o t a l f low a rea . I t is usua l ly poss ib l e t o express

x

as a funct ion of the loca l spec i f ic entha lpy f rom the energy conserva t ion equat ion

t o g e t h e r w i t h t h e a s s u m p t i o n of t h e r m o d y n a m i c e q u i l i b r i u m b e t w e e n t h e tw o p h a s e s .

W h a t i s s t i ll necessa ry in de t e rm in in g the o th e r pa r am e te r s inc lud ed in equ a t ion 1

i s e i t he r a r e l a t i onsh ip be tween x a n d a, o r a r e l a t i o nsh ip be twee n the vo id f rac t ion

an d th e ra t io of th e va po ur to l iquid average ve loc i t ies . T he re is a wh ole ran ge of

such re l a t i onsh ips which a re e i t he r o f pure empi r i ca l o r ig in o r o the r more soph i s t i ca t ed

re l a t ionsh ips which a re based on the de t a i l ed phenomenology o f t he f l ow.

Most o f t he codes p re sen ted be low, use a pure ly empi r i ca l r e l a t i onsh ip fo r t he

veloc i ty di f fe rence be twe en the va po ur and l iquid phas es (dr i ft - f lux mod el ) or they

employ a typica l dr i f t - f lux corre la t ion. In the dr i f t - f lux te rminology the re la t ive ve loc i ty

be tween the two phases i s d i rec t ly r e l a t ed to t he cor re spond ing d r i f t ve loc i t i e s u

gj

- and

u/_j

accord ing to

Ug-U l = U gj - U(,j . [2]

For each phase the re la t ive dr i f t - f luxes a re expressed as :

jgl = a Ugj [3]

jig = (1 - a) u

t

j [4]

which mus t obey the fo l lowing con t inu i ty equa t ion

kg + jgl = 0 • [5]

Th i s equa t ion s t a t e s t ha t t he re i s no ne t d r i f t t h rough a p l ane moving wi th t he to t a l

superf ic ia l ve loc i ty of the two phases . From equat ions 2 to 5 i t fo l lows tha t :

• , 1 1 ^

Ug-U

t

= Jgl { - + ) 6

a 1 — a

There a re severa l dr i f t - f lux models (10) which re la te the vapour dr i f t - f lux to the loca l

vo id f rac t ion . However , t he se a re aga in empi r i ca l co r re l a t i ons which mus t be deduced

from exper iments carr ied out wi th di f fe rent f lu ids under var ious f low regimes wi th

s t e a d y s t a t e o p e r a t i n g c o n d i t i o n s .

O t h e r p a r a m e t e r s d i r e c t l y r e l a t e d w i t h t h e v e n t i n g c a l c u l a t i o n s a r e t h e n u m b e r o f

con t ro l vo lum es (nodes) em ployed and the s ize o f t h e t im e s t ep used . I t i s r equ i re d th a t

the numer i ca l so lu t ions a re i ndependen t bo th f rom the number o f nodes and f rom the

size of th e t ime s te p. T he la t te r i s easi ly achieved in m os t of th e codes by in tern a l ly

a d j u s t i n g t h e t i m e s t e p b e tw e e n p re - sp e ci fi ed m a x i m u m a n d m i n i m u m v a l u e s . T h e

former can be solved only w i th conse cut ive ru ns wi th gr ids of red uc ed s ize .

2.1.

THE RELAP5-EUR/MF CODE

T h i s c o d e o r i g i n a t e s f ro m t h e N u c l e a r I n d u s t r y , a n d t h e v e r s io n R E L A P 5 - E U R / M F

has been subs t an t i a l l y modi f i ed a t t he J .R .C . I sp ra i n o rde r t o improve i t s pe r fo rmance

and fo r us ing f lu ids di ffe ren t f rom wa te r . I t de sc r ibes t r ans i en t s in g le - an d tw o- ph as e

flows in com plex ne twork s on the bas i s o f a one -d im ens ion a l app roa ch . I t ha s been

or ig ina l ly deve loped fo r t he p red ic t ion o f t r ans i en t s i n t he coo lan t sys t em of p re ssur i zed

wa te r r eac to r s w i th t yp ica l p re ssur e va lues i n t he range be tween 16 M P a > p > 1 M Pa .



412

There fore , mos t o f t he code a sse ssment work has been concen t ra t ed on sepa ra t e e f fec t s

and in t egra l t e s t da t a i n t he h igh p re ssure r eg ion .

T w o - p h a s e f l o w c o n d i t i o n s i n R E L A P a r e t r e a t e d u s i n g s e p a r a t e m a s s a n d m o

m e n t u m e q u a t i o n s f o r t h e i n d i v i d u a l p h a s e s ( t w o - f l u i d s m o d e l ) . D u e t o t h e a s s u m p t i o n

th a t t he l ea s t mass ive phase is a lways sa tu ra t ed on ly one ene rgy equa t io n i s needed

for t he two -pha se m ix tu re . Th e app roac h se lec t ed can desc r ibe cond i t i on s o f non-

ho m og en eou s f low (di ffe rent ph ase ve loc i t ies) , an d the rm al dise qu i l ibr iu m effec ts d ur

i n g t h e p h a s e t r a n s i t i o n ( e v a p o r a t i o n , c o n d e n s a t i o n ) . M a s s , m o m e n t u m a n d e n e r g y

exchange be tween the two phases a re ca l cu l a t ed by cor re l a t i ons which a re f l ow reg ime

de pe nd an t . Speci fic mo dels exis t for th e pred ic t ion of c r i t ica l f low co nd i t io ns (choking)

bas ed on th e sonic ve loc i ty in th e s ingle or two-p has e f lu id .

T h e R E L A P 5 - E U R / M F c o d e i n cl u de s t h e d es c r ip t io n of o n e - d i m e n s i o n a l h e a t

conduct ion in the vesse l wal l and the hea t t ransfer be tween the sol id vesse l wal l and

th e flu id . T he hea t t r ans fe r i s ca l cu l a t ed u s ing the t em pe ra tu re d if fe rence be tw een the

wal l and the f lu id and a hea t t ransfer coeff ic ient based on the concept of a "boi l ing

curve" . The l a t t e r i nc ludes cor re l a t i ons fo r s ing le phase na tu ra l and fo rced convec t ion ,

subcoo led and sa tu ra t ed nuc lea t e bo i l i ng , c r i t i c a l hea t - f lux , t r ans i t i on bo i l i ng , min i

mum hea t - f lux , annu la r and d i spe r sed f i lm bo i l i ng . The hea t t r ans fe r co r re l a t i ons a re

au toma t i ca l ly se l ec t ed based on loca l f l ow pa rame te r s and wa l l su r face t empera tu re s .

Also, the loss coeff ic ient due to abrupt a rea change a t the exi t of the vesse l i s ca lcula ted

inte rna l ly by th e cod e . T he sam e i s t r ue for th e f r ic tion be tw een f lu id an d wal l an d

the f r i c t i on be tween the phases .

The physica l model l ing of the code resul t s in a system of f i rs t -order par t ia l d i f fe r

ent ia l equat ions which are solved numerica l ly by an eff ic ient semi- impl ic i t numerica l

t echn ique . The concep t o f f r ee noda l i sa t ion g ives t o t he code the capab i l i t y t o desc r ibe

a la rge var ie ty of sys tem s w i th di ffe rent degre es of geo me tr ica l de ta i l and m ake s i t

cap ab le of han d l ing whole p l an t ca l cu l a t ions . How ever , a t t he mom en t it does no t

a l low for chemica l reac t ions dur ing the vent ing process; thus i t s d i rec t re levance to the

ana lys i s of chemica l r eac to r s t r ans i en t s is r a t he r l imi t ed .

2.2.

T H E S A F I R E C O D E

Th e ma in fea tu re o f S A F IR E i s i t s ab i l i ty t o hand le u p to t en s im ul t an eou s chem ica l

reac t ions wi th t en com po nen t s . Th i s code can on ly desc r ibe re l a t ive ly s imple vessel

geome t r i e s wi th nozz l e s o r l ong p ipes se rv ing a s ven t ing dev ices and which can be

a t t a ch ed e i the r a t t he t op o r a t t h e bo t to m of t h e reac to r vesse l. S A FI R E so lves t he

o n e - d i m e n s i o n a l m a s s , m o m e n t u m , a n d e n e r g y c o n s e r v a t io n e q u a t i o n s in t h e v e n t - l in e

but uses a s ingle cont rol volume for descr ibing the vesse l .

T h e flow regime inside th e vesse l is chosen by the user an d on ce spec i fied i t does

no t a l t e r t h ro ug ho ut t h e du ra t ion of t he t r ans i e n t . Th e use r m ay op t for e i t he r no

vapour / l i qu id d i sengagement coup led in t he ven t - l i ne wi th e i t he r an homogeneous f low

reg ime o r wi th a cons t an t p re spec i f i ed ex i t mass qua l i t y . Al t e rna t ive ly , t he use r may

se l ec t t he pa r t i a l vapour / l i qu id d i sengagement op t ion wi th a "churn" o r "bubb le" f l ow

regim e. T he se regim es are bo th typica l dr i f t- f lux mo dels in wh ich th e va po ur dr i f t -f lux

and the bubble r i se ve loc i ty a re descr ibed by :



413

Bubbly f low

_ u

a

( 1 - Q )

2

f 7

,

Jg i

~ °° ( i _

a

3 ) l

7

J

U

OQ

= 1.18 [

g g

^ - ^ ] ° -

2 5

[8]

P«*

C h u r n t u r b u l e n t

Jgt

U

0

U

ao

= 1.53 [

g < 7 ( P

V

P g )

]

0

'

2 5

[10]

Ra dia l va r ia t ion s of ve loc i ty and void f rac t ion a re tak en in to acco un t v ia an em pir ica l

d i s t r i b u t i o n p a r a m e t e r C

0

. If C

0

i s se t to 1 th ere i s no t var ia t io n ass um ed in th e ra dia l

d i rec t ion . Va lues be tw een 1 and 2 shou ld be se t a t t he code in pu t . Th e use r has

a lso the possibi l i ty for se t t ing the two-phase f r ic t ion fac tor for the vent - l ine by e i ther

se l ec t ing a va lue which i s kep t cons t an t dur ing the t r ans i en t pe r iod o r by ac t iva t ing

an op t ion which ca l cu l a t e s t he f r ic t ion fac to r au tom a t i ca l ly . W he n a tw o- ph as e flow

m ix tur e is expe c t ed in t h e ven t - l i ne t hen th i s f r ic t ion fac to r i s ca l cu l a t ed p r ima r i ly

f rom s ing le -phase f low re l a t i onsh ips based on ly on the l i qu id phase v i scos i ty .

The phys i ca l p rope r t i e s mus t be p rov ided by the use r i n t he i npu t da t a i n t e rms

of t he coe f f i c i en t s co r re spond ing to t he cor re l a t i ons i nc luded in SAFIRE. A cons t an t

t im e s t e p i s a l so requ i red a t t he i np u t which i s kep t cons t an t dur in g the t r an s i e n t . Th e

size of th is t ime s tep must be spec i f ied a t the input .

To a ce r t a in degree the use o f seve ra l i npu t op t ions i n cha rac t e r i s ing the ven t ing

process m akes the code user de pe nd an t . For t h i s r ea son in t h e exam ples des c r ibed

be low, two ca l cu l a t ions f rom the SAFIRE code has been inc luded which a re con t r ibu ted

by di f ferent u sers (11 ,12 ) . B ot h ca lcu la t ion s a re s ti l l firmly bas ed on th e or igina l

ve r s ion o f SAFIRE g iven to t he J .R .C I sp ra , howeve r , i n SAFIRE-2 ca l cu l a t ions t he re

a r e i n c l u d e d s o m e s t r u c t u r a l a l t e r a t i o n s . T h e s e a l t e r a t i o n s a r e m a i n l y a d d r e s s i n g t h e

conve rgence p rob lems enco un te red wh en the f r ic t ion fac to r is ca l cu l a t e d au t om a t i ca l ly

by the code . In these cases there a re some di f fe rences in the way the coupl ing equat ion

be tween the vesse l and the ven t - l i ne se l ec t s t he r i gh t ex i t -qua l i t y when more than two

numer i ca l so lu t ions a re found by the code .

The ma in comment s which re f l ec t our expe r i ence f rom the use o f SAFIRE a re

tha t some a l t e ra t ions migh t be necessa ry fo r t he numer i ca l scheme to t he code (12 ) . A

tw o- ph as e v i scos i ty shou ld be used ins t ead o f t h e li qu id v i scos i ty which h as been used

in the or igina l vers ion of the code (even i f the mixture in the vent - l ine was conta ining

vapour up to 98%) . However , i t mus t be po in t ed ou t t ha t t h i s code has been deve l

oped pr imari ly for vent -s iz ing ca lcula t ions and has been a lso used successful ly for the

in t e rp r e t a t i o n of t h e re su l t s f rom the D IE R S pro j ec t w i th chemica l ly r eac t in g flu ids.

2.3.

THE J.R.C. CODE "RELIEF"

T h e c o d e R E L I E F i s u n d e r d e v e l o p m e n t a t t h e J .R .C . I s p r a . A s u s e d fo r t h e B e n c h

m ark E xe rc i se s (5 ) i t ha s employed th e opp os i t e appro ach t o SA F IR E . I t ve ssel was

discre t i sed in severa l cont rol volumes but a s ingle cont rol volume was used for the



414

ven t - l i ne . The c o d e has the capab i l i t y to hand le chemica l r eac t ions of a r b i t r a r y o r d e r

a n d can desc r ibe the v e n t l i ne h y d r o d y n a m i c s if it is t h o u g h t n e ce s s ar y . E x t e r n a l h e a t

t r a n s f e r t h r o u g h

the

vessel

and the

ven t l ine

can be

a l so inc luded .

T h e m o d e l l i n g in R E L I E F is b a s e d on the fol lowing pr inc ip les and a s s u m p t i o n s

as desc r ibed

by

Friz

G. (13) and

Duffield

et al (14).

T h e r m o d y n a m i c e q u i li b r iu m

has

b e e n a s s u m e d b e t w e e n the p h a s e s . The p r e s s u r e d r o p in the vesse l due to frict ion,

and acce l e ra t ion fo rces

is

a s s u m e d

to be

negligible

and a

dr i f t - f lux m ode l

has

been

used as a c losure r e l a t i onsh ip . The kine t ic en ergy and a x i a l c o n d u c t i o n t e r m s in the

e n e r g y e q u a t i o n

are

a l so a s s u m e d

to be

negl igible .

For the

num er i ca l so lu t ion

of the

c o n s e r v a t i o n e q u a t i o n s a modi f ied "donor -ce l l " t echn iq ue which cons ide r s c on t inu i ty

waves

is

a d o p t e d .

The dr i f t - f lux model

is

d r a f t e d

in

t e r m s

of

t h e re l a t i ve ve loc i ty be twee n

the

p h a s e s

s u c h t h a t ,

a

m

( l - a )

n

. .

U

°-

U

> =

U

>°°> « J » ( 1 - «

M

) » M

w h e r e otM is the void f rac t ion wh ich gives to the t e r m a

m

( l — a)

n

its m a x i m u m v a l ue .

T h e d e n o m i n a t o r

is a

sca l ing fac to r which ensure s t h a t

the

m a x i m u m v a l u e

of the

slip

is given by U

poo

i i r r e spec t ive of the va lue of void f rac t ion at which it o c c u r s . The

coefficients m and n desc r ibe bu bb ly f low and drople t f low respec t ive ly and have been

fitted to exp e r im enta l da t a .

U

poo

i can be

t h o u g h t

as a

cha r ac t e r i s t i c b ub b le ve loc i ty

w h i c h is c lose ly re la te d to the t e rm ina l ve loc i ty of the l a r g e s t b u b b l e in the s y s t e m and

c o n t a i n s the p h y s i ca l p r o p e r t y g r o u p [goAp/pi)

1

'

4

.

In the B e n c h m a r k e x e rc i se s the mass flow in the ven t - l i ne was m o d e l l e d in a

s impli f ied ma nn e r t ak ing in to accou n t b lowdow n expe r im ent s pe r fo rmed

at the

J . R . C .

T h e r e the mass f low in b o t h the supe r -c r i t i c a l and sub-c r i t i c a l r eg ion is ca l cu l a t ed in

a s imi lar way as in the gas d y n a m i c t h e o r y u s i n g the u p s t r e a m s t a g n a t i o n p r e s s u re

a n d

the

m i x t u r e d e n s i ty .

The

frict ion

at the

en t r anc e reg ion

and

a long

the

ve nt l ine

is

cons ide red and the c r i t i c a l p re ssu re r a t i o , used for the t r a n s i t i o n to sub-cr i t ica l f low, is

t aken f rom the i dea l gas r e l a t i o n s h i p . W i t h the a s s u m p t i o n of h o m o g e n e o u s c o n d i t i o n s

a t

the

e n t r a n c e

of the

ven t - l i ne

the

vo lum etr ic f low

is

ob ta ine d f rom

the

m ass f low

us ing the m i x t u r e d e n s i t y t a k e n f ro m the ce ll which adjo ins the ven t - l i ne .

2.4.

THE

D EERS CO D E

T h e D e s i g n and E v a l u a t i o n of Em erge ncy Re l ie f Sy s t em s code (D EE R S) so lves the

o n e - d i m e n s i o n a l m a s s , m o m e n t u m and e n e r g y c o n s e r v a t i o n e q u a t i o n s as d e s c r i b e d by

Klein (15). T h e s e e q u a t i o n s are solved in the axia l d i rec t ion of the flow for the vessel

a n d

for

va r ious conf igura t ions

of the

ven t - l i ne

all the way up to the end of the

ca tch

t a n k .

I t

can

h a n d l e

up to

four chemica l r eac t ions w i th

six

co m po ne n t s . Di f fe ren t t em

p e r a t u r e , p r e s s u r e

and

c o n c e n t r a t i o n

of

t h e s e c o m p o n e n t s

are

a l lowed a long

the

axis

of

the

flow. Along

the

vessel

the

fluids

are

a l lowed

to

exis t

in

d i ffe ren t com bin a t ion s

of liquid

and

v a p o u r m i x t u r e s

and

chemica l r eac t ions

can

occur e i t he r

in the

l iquid

o r / a n d

in the

v a p o u r p h a s e

of the

v a r i o u s c o m p o n e n t s .

Nozzles

or

d i ffe ren t c om bina t ions

of

long pipes

can be

t a k e n i n t o a c c o u n t

in the

ven t - l i ne which can be at the top a n d / o r at the b o t t o m of the rea c t io n vesse l and can



415

be ve r t i ca l o r i nc l ined to t he hor i zon ta l . In add i t i on to t hese va r ious rup tu re d i sks can

be placed a t any cont rol volume a long the reac tor vesse l .

The two-phase mode l employed by th i s code re l a t e s t he vo id f rac t ion to t he re l a t i ve

ve loc i ty be tween the two phases accord ing to :

u

t

= sj 10 A

d

[ ap

g

+ (1 - a)pi ] a

[121

where the empi r i ca l f ac to r Aj, is referred to as the interface sl ip coefficient and has

d im ens io ns o f m K g s . Th i s coef fi ci en t has been t e s t e d aga ins t exp e r im enta l

d a t a from th e M P M C te s t fac il it y o f t h e J .R .C . I sp ra (7 ) for s imple non - reac t ing flu ids

and the fo l lowing va lues were p roposed :

A

d

= 8.0 X 1 0 ~

4

(Non -foamy l iquids)

Aj. = 1.5 X l 0

- 5

(Foam y l iquids)

A j = 0 .0 ( H o m o g e n e o u s m i x t u r e ) .

S imi l a r t o t he SAFIRE and the RELIEF codes th i s mode l i s no t a l l owed to a l t e r

th roughout t he dura t ion o f t he t r ans i en t and has been used fo r vo id f rac t ions f rom

0 to 1 i r r e spec t ive of t h e flow reg imes . Co mp ar i so ns have been m ad e (16 ,17) wi th

seve ra l expe r imenta l da t a ob ta ined unde r s t eady s t a t e cond i t i ons i n o rde r t o t e s t t he

accu racy o f t h i s mod e l . For vo id f rac t ions be tw een 2 5% and 70% i t ha s been found to

be accura t e enough fo r seve ra l t ypes o f two-phase mix tu re s .

Heat conduct ion in the sol id vesse l wal l and hea t t ransfer be tween the wal l and

th e vessel con ten t s can be a l so t aken in to acco un t . Va r iou s ex t e rna l hea t fluxes a re

a l lowed a long the ax i s f l ow thus , ven t ing t r ans i en t s unde r complex hea t ing o r coo l ing

con d i t i on s can be ana ly sed . Th e two -p ha se f r ic t ion fac to r an d th e loss coe ff ic ien ts du e

to an ab ru p t a re a chan ge in t h e ven t - l i ne a re ca l cu l a t ed in t e rna l ly by th e code . In

add i t i on to t h i s , t h e use r has t he poss ib i li t y t o supp ly ex t e rna l ly d i f feren t h ea t t r ans fe r

coeff ic ients and di f fe rent wal l roughness fac tors in the var ious cont rol volumes.

DEERS i s a gene ra l purpose code which can be used in t he ven t ing o f a l a rge

va r i e ty of sys t em s . How ever , t he use o f a s ing le tw o- ph as e mode l t h ro ug ho ut t he w hole

t ran s i en t r e s t r i c t s t he accuracy of i t s p red ic t ions . A no the r d i s adv an ta ge of t h i s code

i s t h a t i t r equ i re s seve ra l hou rs o f C P U t ime in an o rd ina r y Pe rso na l C om pu te r . B o th

these have been modi f i ed a t t he Jo in t Resea rch Cen t re by conve r t ing and t r ansfe r r ing

t h e c o d e t o m a i n f r a m e c o m p u t e r s a n d b y i n t r o d u c i n g s e v e r a l t w o - p h a s e f l o w m o d e l s

in to the code .

3 .

V e n t i n g E x a m p l e s

T h e p u r p o s e o f t h e e x a m p l e s s h o w n h e r e d e s c r i b e t h e p h e n o m e n a a n d d e m o n s t r a t e t h e

i m p o r t a n c e of s o m e of t h e p a r a m e t e r s r e l a t e d w i t h v e n t i n g . B a s i s of t h e E x a m p l e s a r e

t w o e x p e r i m e n t s c a r r ie d o u t a t t h e M u l t i p h a s e M u l t i c o m p o n e n t ( M PM C ) t e s t f a ci li ty

of t he Jo in t Resea rch Cen t re t oge the r wi th two t e s t ca se s wi th re f r ige ran t R114 which

have been k ind ly con t r ib u te d by Ho echs t AG (8) . T he inp u t cond i t i o ns o f t he s e t e s t s

a re se l ec t ed so a s t o be in l i ne wi th two more depressur i sa t ion expe r iment s r epor t ed in

th e in t e rna t ion a l l i t e ra tu re (18 ,19 ) . T he d imens io ns of t h e vesse l, t h e wo rk ing flu ids,



416

t h e s t a r t i n g c o n d i t i o n s , t h e t y p e a n d t h e d i m e n s i o n s o f t h e v e n t - l i n e a r e s u m m a r i s e d

in Table 2.

The same pa rame te r s have been moni to red fo r a l l t he examples p re sen ted be low

however , more emphas i s i s g iven to compar i sons where expe r imenta l da t a a re ava i l ab l e .

T h e p a r a m e t e r s m o n i t o r e d a r e t h e p r e s s u r e , t h e v o i d - fr a c ti o n a n d t h e l i q u i d / v a p o u r

interface in the reac tor vesse l . At the exi t of the vesse l the mass-f lux and the s ta t ic

ex i t -qu a l i t y a re a l so ca l cu l a t ed . Th e l a t t e r i s de f ined a s t h e ra t i o of t h e vapo ur mas s

to the to ta l mass exi t ing the vesse l a t a par t icular t ime s tep. In the f i rs t two examples

wi th a l ong ven t ing p ipe a t t ached a t t he t op o f t he vesse l t he p re ssure h i s to ry a t a

pa r t i cu l a r l oca t ion i s a l so ca l cu l a t ed by the pa r t i c ipa t ing co des .

Not a l l o f t he above ment ioned pa rame te r s cou ld be ca l cu l a t ed fo r each example

d u e t o t h e m o d e l l i n g a s s u m p t i o n s t a k e n b y e a c h c o d e . Fo r e x a m p l e , w i t h t h e SA FI R E

code i t i sn ' t possible to ca lcula te the in terface leve l -swel l in the vesse l due to the

ass um pt io n th a t t he vesse l i s mode l l ed wi th a s ing le nod e . S imi l a r ly , RE L IE F d id

not provide any da ta for the pressure and s ta t ic qual i ty in spec i f ic loca t ions a long the

ven t -p ipe because the whole ven t -p ipe was cons ide red a s a s ing le node .

E x a m p l e

No.

1

2

3

4

5

6

Vessel

V o l u m e

K )

5 0 x l 0

- 3

5 0 x l 0 ~

3

6 . 3 2 X 1 0

- 3

4 .53

1 4 . 6 X 1 0

- 3

105 x l O

- 3

Vessel

D i a m .

( m )

0.40

0.40

0.178

1.19

0.216

0.40

T y p e

of

Vent

L / D = 9 0

L / D = 9 0

Nozzle

B o t t o m

Nozzle

L / D = 7 9

Orifice

L / D = 7 9

Vent

D i a m .

(cm)

2.0

2.0

1.27

5.4

1.9

1.5

1.9

Work ing

Flu id

W a t e r

W a t e r

W a t e r

W a t e r

Freon 114

Freon 114

In i t .

P r e s s u r e

(Pa )

2 . 5 x 1 0

s

2 . 5 X 1 0

5

2 . 9 x 1 0

s

7.2 x 1 0

s

7 . 0 x 1 0

s

8 . 3 x 1 0

s

Ini t .

Void

(%)

2

3 5

2

46

15

15

TABLE 2. The venting examples considered for different vessels and different fluids;

L/D refers to long pipes with the specified Length/Diameter ratio.

The codes used here do not inc lude a leve l t racking model for the in te rface in the

vesse l be tween the p redominan t ly l i qu id and the p redominan t ly vapour r eg ions . For

t h i s r e a s o n R E L A P u s e s a r a t h e r s i m p l e m o d e l w h i c h a s s u m e s t h a t t h e m i x t u r e l e v e l

ex i s t ed in t he h ighes t vo lume wi th in a ve r t i ca l channe l whe re the l i qu id vo lume f rac t ion

exceeds the va lue of 0 .05 . The exac t loca t ion of the leve l i s then found according to :

au - a

level

H + dh

13

w h e r e

H

i s t he b o t to m e l eva t ion of t he vo lum e iden t i fi ed ,

dh

i s the he ight of th is volume,

a i s th e void f rac t ion ,

OCT,

and a y are the va lues for th e void f rac t ion in th e vo lum e be low



417

o r a b o v e r e s p e c t i v e l y . Fo r t h e c o d e s R E L I E F a n d D E E R S t h e l i q u i d / v a p o u r i n t e r f a c e

is a ss um ed t o be a t t h e p l ace w here the vo id f rac t ion g rad ien t ge t s i t s m ax im um va lue

a long the vesse l length .

Di f fe ren t noda l i sa t ion approaches have been fo l lowed in t he va r ious codes wi thou t

a n y a t t e m p t t o o p t i m i s e t h e s iz e a n d / o r t h e n u m b e r of c o n t r o l v o l u m e s u s e d . I n R E L A P

the vesse l is sub d iv ide d in to 10 vo lum es wi th t he ex cep t ion o f Ex am ple - 4 wh ere 12

volumes were used in order to a l low the correc t posi t ion of the discharge l ine , and the

cor rec t vesse l geome t ry . In t he ca ses wi th a l ong ven t -p ipe RELAP used on ly 2 con t ro l

v o l u m e s . I n t h e c a l c u l a t i o n s w i t h t h e t w o SA FI R E s t h e v e n t - l i n e w a s r e p r e s e n t e d w i t h

8 c o n t r o l v o l u m e s ( SA FI R E - 1 ) a n d w i t h 5 0 c o n t r o l v o l u m e s ( SA FI R E - 2 ) . R E L I E F in

a l l th e cases used 100 con t rol volu me s for th e vesse l . As i s a l re ad y show n in Tab le 1

SAFIRE and RELIEF used a s ing le con t ro l vo lume in t he vesse l and in t he ven t - l i ne

re spec t ive ly . In a l l t he ca l cu l a t ions shown he re wi th t he DEERS code the vesse l and

the ven t - l i ne have been mod e l l ed w i th 18 and 15 con t ro l vo lum es re spec t ive ly .

3 .1 .

E X A M P L E - 1 ; T O P V E N T I N G , L OW P R E - R E L I E F V O ID

Th i s is a w a te r b lowdo wn case which ha s been ca r r i ed ou t in t h e Mu l t i -p has e M ul t i -

co m po nen t t e s t fac il it y o f t he J .R .C . I sp ra wi th a long ven t ing p ipe a t t a ch ed a t t h e t o p

of a cyl indr ica l vesse l . In th is example the contents of a near ly ful l vesse l under low

sta r t i ng p re ssure ( com pared to t he am bien t p re ssure ) a re ven ted in a ca t ch t an k . Th e

expe r imenta l da t a ava i l ab l e fo r t h i s exe rc i se a re shown in F ig . l t oge the r wi th o the r

p a r a m e t e r s w h i c h a r e c a l c u l a t e d b y t h e p a r t i c i p a t i n g c o d e s .

The d r iv ing mechan i sm i s t he l imi t ed vapour p roduc t ion in t he vesse l which ho lds

the p re ssure c lose to t he s t a r t i ng va lue whi l e a p redominan t ly l i qu id mix tu re i s expe l l ed

un de r h igh mass- f luxes . Th e who le p rocess m a in t a in s t h e vesse l p re s sure h igh (F ig . l )

for a re la t ive ly longer per iod than in the corresponding case wi th lower in i t ia l f i l l ing

(Ex am ple - 2 ) . Th e p re ssu re osc i l l at i ons wi ll con t inu e un t i l enou gh va po ur has been

produced and the l i qu id -vapour i n t e r face has f a l l en be low the en t rance o f t he ven t - l i ne .

The d i f fe rences be tween the two SAFIRE ca l cu la t ions a re due to t he empi r i ca l

d r i f t - f l u x d i s t r i b u t i o n p a r a m e t e r C

0

for the void f rac t ion and due to the di f fe rent ways

by wh ich the two-ph ase fr i ct ion fac to r i s ca l cu l a t ed in t he ven t - l i ne . In SA FI R E- 1 t he

C

0

has been t ak en a s 1.5 t oge th e r wi th a con s t an t two-p has e f r ic t ion fac to r w he r eas ,

i n S A F I R E - 2 C

0

was equa l t o 1 and th e two -pha se fr i c ti on fac to r ha s been ca l cu l a t ed

in t e rna l ly accord ing to t he loca l cond i t i ons i n each node a long the ven t - l i ne . In bo th

codes the f l ow reg ime in t he vesse l has been a ssumed a s churn tu rbu len t wi th pa r t i a l

l i qu id /v ap ou r d i sengag em ent . Th e flow in t h e ven t ing p ipe has been mode l l ed in

b o t h SA FI R E c a l c u l a t i o n s a s a h o m o g e n e o u s m i x t u r e . D e t a i l s a b o u t t h e tw o ty p e s of

ca l cu l a t ions wi th SAFIRE can be found in (11 ) and (5 ,12 ) r e spec t ive ly .

Al l codes reproduce rea sonab ly we l l t he p re ssure curve ins ide the vesse l wi th a

ra t he r sm oo th pa rabo l i c t yp e o f cu rve . Th e h ighe r mass- f lux p red ic t ed by the code

R E L IE F du r ing the f ir st 6 seconds of t h e t r an s i en t me ans th a t enoug h l iqu id is expe ll ed

from th e vesse l so th a t bulk evap ora t io n wi ll begin ear l ie r th an for th e oth er cod es.

Th is is a l so re f lec ted in th e void -f rac t ion s co m pa riso ns ( Fi g . l ) a t least in th e f irs t few

secon ds o f t he t r ans i e n t . Th ese vo id - f rac t ions i n t he vessel a re t hen t r an s l a t ed in to

h i g h e r e x i t - q u a l i t i e s . C o n t r a r y t o t h i s t h e c a l c u l a t i o n s b y R E L A P a n d D E E R S s h o w a



418

EXAMPLE 1 PRESSURE IN THE VESSEL.

LU 1.80

<n 1.60

1.00

l ' ' ' ' l

i

T I M E

(SEC)

EXAM. 1 PRESSURE AT 1.37 m ALONG THE VENT PIPE

FIG. la. Top Venting, 2.5 bar pre-relief pressure , 2% initial void [ or (x) Experiment;

RELAP; SAFIRE-1; SAFIRE-2; RELIEF; DEERS j .



419

EXAMPLE 1 MASS - FLUX AT THE EXIT OF THE VESSEL

£

1500.

EXAMPLE 1 QUALITY AT THE EXIT OF THE VESSEL

T

I M E

( S E C

FIG. lb. Top Venting, 2.5 bar

pre-relief pressure,

2% initiai void [ or fxj Exp eriment;

RELAP; SAFIRE-1; SAFIRE-2; RELIEF; DEERS

j .



420

EXAMPLE 1 NORMALISED LEVEL SWELL IN THE VESSEL

EXAMPLE 1 VOLUMETRIC VOID-FRACTION IN THE VESSEL

0 .45

0 . 4 0

0 . 3 5

0 . 3 0

0 . 2 5

0 . 2 0

0 . 1 5

0 . 1 0

0 .05

0 .00

V /

/

/<

1

-

-

X

;

:

•j

:

:

■

40.0 60.0

T I M E SEC)

FIG. lc . Top Venting 2.5 bar pre-relief pressure, 2% initial void [ or (x ) Experiment;




421

pe rio d of ma ss-flu x fluctuations w hile th e exit qu ali t y re m ai ns ve ry close to al l- l iquid

f low. During th is per iod the pressure in the vesse l i s mainta ined a t h igh leve ls ; the la t te r

exp la ins to a cer ta in exte nt th e pre ssu re f luctua tions obs erved in th e ven t - l ine . Th e

p h e n o m e n o l o g i c a l d i f f e r e n c e s b e t w e e n t h e R E L I E F , R E L A P a n d t h e D E E R S c o d e s a r e

a lso found in the comparisons of the exi t -qual i t ies ca lcula ted dur ing the f i rs t 40 seconds

wh en the m ass flux i s r a th e r uns t ab l e . Th e two SA F IR E ca l cu la t ions a re s imi l a r t o

t h o s e o f R E L A P.

The exi t -qual i t ies shown in Fig . l a re in l ine wi th the ca lcula t ions for the leve l swel l

wh ich i s a f ic ti tious in te rface be twe en th e pr ed om ina nt l y l iquid an d th e pr ed om in an t ly

vapour regions in the vesse l . For the RELIEF code th is leve l swel l causes th is in te rface

to be ful l contac t wi th the top of the vesse l dur ing the f i rs t 58 seconds of the t ransient .

A simi lar leve l swel l curve i s a l so shown in the same f igure for the RELAP and for

th e DE E R S codes . Th e d i ffe rences be tween thes e codes re f lec t t he va r i a t i o ns of t he

ex i t -qua l i t i e s ca l cu l a t ed a l though i t mus t be a l so t aken in to accoun t t ha t t he l eve l - swe l l

i s ca lc ula ted di f fe rent ly in RE L A P .

3 . 2. EX A M P LE - 2 ; TO P V EN TI N G , LA RG E P RE- RE LI EF V O I D

Th i s is a s imi l a r ca se a s in Exa m ple - 1 bu t a t t he b eg inn ing o f t h e t r ans i en t on ly

6 5 %

o f t he vesse l vo lum e was filled wi th w a te r . Th i s chan ged co mp le t e ly t h e ve n t ing

mechan i sms and the vapour p roduced in t he vesse l was no t su f f i c i en t t o ma in t a in a

high pressure for very long (Fig .2) . For th is reason the pressure curve in the vesse l i s

no t of t h e sam e pa rab o l i c sha pe a s i n F ig . l . Th e am pl i tud e o f t h e p re ssu re osc i l l a t i ons

observed in the corresponding f igures for the previous case a re s igni f icant ly reduced as

is sho wn in Fig .2 and t he pr ess ure in th e vesse l fa ll s ra th er fast in th e f irst 15 seco nds

of the t ransient . Also, the de lay in boi l ing dur ing the f i rs t few seconds of the t ransient

has a much more profound effec t in th is case ra ther than in f i rs t example where the

vessel was pract ical ly ful l .

Al l ca l cu l a t ions ca r r i ed ou t seem to reproduce ra the r we l l t he expe r imenta l da t a

for the pressure in the vesse l . The ca lcula t ions for the pressure in the vent - l ine a re in

good ag reem ent exp e r im enta l va lues a f t e r t he fir st 10 secon ds o f t he t r an s i e n t . In t h i s

e x a m p l e t h e t w o SA FI R E c u r v e s h a v e b e e n c a lc u l a t e d w i t h t h e s a m e i n p u t o p t i o n s a s

t h o s e u s e d i n E x a m p l e - 1 .

T h e p r e s s u r e c u r v e s c o r r e s p o n d i n g t o t h e t w o SA FI R E s a r e s t r o n g l y i n f l u e n c e d

f rom the way the two -phas e fr ic t ion fac to r was ca l cu l a t ed in t he ven t - l i ne . Th i s t o ge t he r

wi th the di f fe rences in the C

0

va lue a re t he ma in rea sons fo r t he va r i a t i ons obse rved

in F ig .2 am on g th e ca l cu l a t ed va lues of t he mass- f lux a t t h e ex i t o f t h e vesse l . W ha t

i s a l so wo r th ob se rv ing f rom the sa me f igure is t h a t t h e pe r iod o f p red ic t ed two -pha se

f low in t he ven t -p ipe i s r a the r shor t .

Al l ca l cu l a t ions p re sen ted in F ig .2 fo r t he ex i t -qua l i t y demons t ra t e t ha t a f t e r a

cer ta in t ime the f low in the vent - l ine becomes a l l -vapour f low unt i l the end of the

t ran s i e n t . Th i s t ime is sho r t e r for R E L A P and longe r for t h e R E L IE F code . In

th e same figure i t is shown t ha t D E E R S s ti l l p red ic t s osc i ll a t i ons for t he ex i t -qu a l i t y

an d th e mass- f lux fo r t he f ir st 30 second s o f t he t r an s i e n t . Co n t r a ry to t he p rev iou s

example , the ca lcula ted leve l swel l does not reach the vesse l top as i s shown in Fig .2 .

T h e R E L I E F a n d t h e D E E R S co d e s , p r e d i c t e d v e n t i n g o f a t w o - p h a s e m i x t u r e d u r i n g



422


S 2.00

r > 1.60 .

L0

20.0 40.0 60.0 80.0

T I M E (SEC) .

EXAM. 2 PRESSURE AT 1.37 m ALONG THE VENT PIPE

FIG. 2a. Top Venting, 2.5 bar pie-relief pressure, 35% initial void [ or (x) Experiment;




423


40.0 60.0

T I M E SEC) .


1.00

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20

t i l l I

T

-.« , .

:

i i /

H i

/

i l l

I i l U j i / >

■

i l

i

H I ?

i ;

F » |iih * in

t i l l

I K l U

I

1

I I M

O K \

ii y

i

n v

T I M E

( S E C )

FIG.

2b .

Top

Venting,

2.5

bar

pre-relief

pressure,

35%

initiai void

[

or

(x)

Experiment;




424


1.20

i.O 20.0 40.0 EO.O 80 .0

T I M E (SEC) .


FIG. 2c. Top Venting, 2.5

bar

pre-relief pressure, 35% initial void [ or (x) E xperiment;

RELAP; SAFIRE-1; SAFIRE-2; RELIEF; DE ERS j .



425

t he fir st 38 secon ds . Th i s i s p ro bab ly due to t he me tho d u sed in ca l cu l a t ing the m ix tu re

leve l which a l lows the loca l void f rac t ion above th is leve l to be di f fe rent f rom one .

On the o the r ha nd , R E L A P does no t show any con t ac t of t he ca l cu l a t ed in t e r face

w i th the vesse l to p , th er e a re not any mass-f lux f luctua tions th i s t im e an d af te r a

sh or t per io d of mas s-f lux increa se the flux fol lows an expo ne nt ia l dec reas e . Th is is in

agreement wi th t he ca l cu l a t ed ex i t -qua l i t y which i s p rac t i ca l ly one (a l l -vapour f l ow)

du r in g the wh ole t rans ien t . A s for th e void-f rac t ion in th e vesse l , a l l cod es seem to

agree on the shape of the curve ca lcula ted wi th smal l var ia t ions for the f ina l vesse l void

frac t ion.

Th e gene ra l conc lus ion d ra w n f rom th i s exam ple i s t h a t whe n th e vesse l i s no t

ful l , the depressur isa t ion las t s for a shor te r per iod and the vesse l pressure fa l l s ra ther

qu ick ly in t h e beg inn ing o f t he t r an s i en t . Th e vap ou r p ro du c t io n does no t m a in t a in

the in i t ia l pressure in the vesse l , the per iod of two-phase f low in the vent - l ine las t s

sho r t e r and th e ca l cu l a t ed m ass- f lux is sma l l e r t ha n in Ex am pl e -1 . Al so , t h e p re ssu re

his tor ies in the vesse l and in the vent - l ine a re f ree f rom the high f requency osc i l la t ions

found in t he p rev ious example .

3.3.

EXA MPLE-3; TOP VENTING THROUGH A NOZZLE

Th is i s a w ate r b lowd ow n exerc ise carr ied ou t a t th e Th ay er School of En gin eer ing (18)

in a sma l l ve sse l wi th a nozz l e r a the r t han a l ong ven t -p ipe a t t ached a t t he t op o f t he

vesse l . The inpu t cond i t i ons a re s imi l a r t o t hose o f Example -1 thus , we can iden t i fy i f

t he phenomena desc r ibed in t he f i r s t example a re i ndependen t o f t he ven t t ype and o f

th e s ize o f t h e reac to r vesse l. Th e expe r im enta l da t a ava i l ab l e for t h i s exe rc i se a re t h e

pressure his tory a t the bot tom of the vesse l , the f ina l void f rac t ion in the vesse l and

the in terface leve l -swel l da ta measured by an e lec t r ica l c i rcui t be tween the nozz le and

the water in the vesse l .

The expe r imenta l p re ssure i n t he vesse l i s shown wi th the con t inuous l i ne i n

F ig . 3 .

T h e high f requency pre ssu re f luctua tions a re presen t for ab o u t 8 sec ond s an d th e de lay

in boi l ing is of th e sa m e m ag ni tu de as th e f luctua tions in th e pre ssu re cur ve . Sim i lar to

the f i r s t example , bu lk vapour p roduc t ion does no t s t a r t immedia t e ly and the vapour

produced in the vesse l mainta ins the pressure in the vesse l a t re la t ive ly high leve ls .

Th i s l a s t s un t i l enou gh vo id is c rea t e d in t he vessel and du r ing th i s pe r iod th e in t e r face

level is up to the top as is shown in

F i g . 3 .

T h en , th e interf ace level f luctuates up to

the to p o f t he vesse l i nd i ca t ing t ha t t h e ex i t -qua l i t y i s va ry ing d ur in g th i s pe r iod of

instabi l i ty . This a l so a ffec ts the ca lcula ted mass-f lux and the pressure in the vesse l .

A pa r t from the pa rabo l i c sha pe of t h e p re ss ure curve , t he ca l cu l a t ions wi th RE -

L A P a n d D E E R S s h o w n i n F i g . 3 , g ive a be t t e r i ns igh t t o t he phenomena invo lved

by bei ng th e only co de s wh ich ac co un t for th e fluctuations in th e inte rfac e level-swell .

Th es e f luctuat ions a re pr ob ab ly th e resu l t of th e va r ia t ion s obs erved in th e m ass-f lux

and the s t a t i c qua l i t y a t t he ex i t o f t he vesse l . In t he two SAFIRE ca l cu la t ions t he same

equ i l ibr iu m ra t e m ode l i s used to desc r ibe th e f low th ro ug h nozzles . T h e di f fe rences

be tween those ca l cu l a t ions a re due to t he empi r i ca l d r i f t - f l ux d i s t r i bu t ion pa rame te r

C

0

for t he vo id f rac t ion . Co n t r a ry to t he Ex am ples 1 and 2 , t he mass- f luxes ca l cu l a t ed

f r o m SA FI R E 1 a n d 2 a r e c o m p a r a b l e . T h u s , fo r t h e SA FI R E c o d e , t h e m a s s - fl u x is

more sens i t i ve t o t he two-phase f r i c t i on fac to r t han to t he va lue o f C

0

.



426


UJ 1.50

w 1.00

T I M E (SEC) .


w 6000.

o 5000.

•:-*•--

FIG. 3 a. To p Venting, 2.9 ba r pre-relief pressure, 2% initial void [ Experiment; -




427


T I M E (SEC)


T I M E ( S E C ) .

FIG. 3b. Top Venting, 2.9 bar pre-reJief pressure, 2% initial void [ Exper imen t ;

RELAP; SAFIRE-1; SAFIRE-2; RELIEF; DEERS ,



428

The exi t -qual i t ies shown in Fig .3 a re in l ine wi th the ca lcula t ions for the in terface

leve l swel l . T he leve l-swell ca lcula ted by th e RE L IE F cod e (Fig .3) i s in ful l co nta c t

w i th th e top of th e vesse l du r in g the f irs t 18 seco nd s. A fter th i s per iod th is in te rface

level fa ll s be low the top of th e vesse l an d a l l -vapo ur f low st a r t s . T he co rre sp on din g

i n t e r f a c e c a l c u l a t i o n s f r o m t h e c o d e s R E L A P, R E L I E F a n d D E E R S a r e s h o w n i n t h e

same f igure and a re i n good agreement wi th t he expe r imenta l da t a .

3 .4 . E X A M P L E - 4 ; B O T T O M V E N T I N G

This i s a bot tom vent ing exerc ise carr ied out in the la rge vesse l of Genera l Elec t r ic

(19 ) .

Th is vesse l i s 1 .19 m in dia m ete r , 4 .07 m in he ight and th e ven t ing nozzle

has been p l aced 0 .7 m f rom the bo t tom of t he vesse l . The the s t a r t i ng p re ssure was

72 ba r t hus , t he capab i l i t i e s of t he codes a re t e s t ed und e r h igh ope ra t ing p re ssu re s

tog e the r wi th t he i r ab i l it i e s for sca l ing up from l abo ra to ry s i ze vesse ls . Th e pa ram e te r s

measured in t h i s example a re shown in F ig .4 . These pa rame te r s a re t he p re ssure and

the l iquid/vapour in te rface in the vesse l , as wel l as the mass-f lux and the s ta t ic qual i ty

at the exit of the vessel .

As i s shown in Fig .4 , the pressure in the vesse l decreases s lowly dur ing the f i rs t 20

seconds of the t ransient th is i s then fol lowed by a per iod of rapid pressure reduct ion

un t i l a new s t a t e of equ i l i b r ium is r eache d . Du r ing th e f ir s t 20 secon ds the v apo ur

produced in t he vesse l ho lds up the p re ssure i n t he vesse l whi l s t a p redominan t ly

l iquid mix tu re i s expel led f rom th e vesse l . Th is i s conf i rme d a lso by th e low exi t -

qua l i t y dur in g th e f ir s t 16 seconds of t he t r ans i en t u n t i l t h e l i q u id /va po ur i n t e r face

reaches t he ven t ing nozz l e . Then , two-phase mix tu re i s expe l l ed f rom the vesse l and

dur ing th is per iod the pressure in the vesse l fa l l s rapidly .

In t he two SA F IR E ca l cu la t ion s t he rad i a l va r i a t i on o f t h e vo id f rac t ion was

d e a c t i v a t e d (C

0

— 1) and a churn turbulent f low regime in the vesse l has been assumed

wi th no pa r t i a l l i qu id /v apo ur d i seng agem ent . Th e qua l i t y a t t he en t ran ce o f t he ven t in g

nozzle in both codes i s assumed to be the average qual i ty of the vesse l . However , in

SAFIRE-1 the Equ i l i b r ium ra t e mode l has been employed fo r t he two-phase nozz l e f l ow

w h e r e a s , i n SA FI R E - 2 t h e H o m o g e n e o u s E q u i l i b r i u m M o d e l ( H E M ) . T h e d i f f e r e n c e s i n

the f low model a re not very s igni f icant for the pressure and the mass-f lux but a f fec ted

th e ca lc ula ted exi t -q ual i t ies espec ia l ly c lose to th e end of th e t ra ns ien t . I t m us t be

po in t ed ou t t ha t i n SAFIRE the pos i t i on o f t he ven t ing nozz l e can be on ly p l aced

at th e bo t t o m of th e vesse l (due to the fac t th a t the vesse l i s mo del led w i th a s ingle

con t ro l vo lum e) . The re fo re in S A F IR E the t r ans i en t i s t e r m ina ted w i th 100% vo id in

the vesse l . This was not the case for the other codes which discre t i sed the vesse l wi th

seve ra l con t ro l vo lumes .

B e t t e r r e p r e s e n t a t i o n h a s b e e n a c h i e v e d w i t h t h e R E L I E F a n d R E L A P c o d e s

which model led the vesse l wi th severa l nodes. In fac t the shape of the pressure curve

ca l cu la t e d by RE L A P i s ve ry s imi l a r t o t he Ex pe r im ent a l cu rve even wi th a sma l l n um

ber of nodes in the vesse l . Close to the end of the t ransient , due to l iquid ent ra inment

in t he ven t t he measured mass- f lux i s h ighe r t han the va lue p red ic t ed by RELIEF and

RELAP. These sma l l d i f fe rences i n t he mass- f lux a re t r ans l a t ed in to l a rge dev ia t ions

f rom the measured ex i t -qua l i t i e s due to two-d imens iona l e f fec t s which cou ld no t be

t a k e n i n t o a c c o u n t i n o n e - d i m e n s i o n a l c o d e s . T h e c a l c u l a t i o n s w i t h t h e D E E R S c o d e



429


>

■

■

i

£

50.0


35000 .

1

J

1 5 0 0 0 .

FIG.

4a. Bottom

Venting 72

bar

6

initial void [ or (x) Experiment;

SAFIRE-1; SAFIRE-2; RELIEF; DEERS j .

RELAP;



430

EXAMPLE 4 STATIC QUALITY AT THE EXIT OF THE VESSEL


0. so

0 .4 0

0 .3 0

0 .2 0

0 .10

0 .00

: \

-

-

•

—\

\

\ \

i . . .

\

\

NN.

~\

j

J

i

L _

. . . i . .

-

•

:

-

i i i i i i

T I M E (SE C )

FIG. 4b. Bottom Venting, 72 bar, 46% initial void [ or (x) Experiment;

SAFIRE-1; SAFIRE-2; RELIEF; DEERS j .

RELAP;



431

a re a l so in exce l len t ag re em ent wi th t he exp e r im enta l d a t a for t h e ex i t -qua l i t y . Th e

shape o f t he o the r cu rves i s r ep roduced equa l ly we l l howeve r wi th some s ign i f i can t

differences for the vessel pressure and for the interface level swell . These differences

are due to the in terface s l ip coeff ic ient used in the ca lcula t ions. The va lue sui table for

non-foamy l iquids has been se lec ted which was the same as in a l l the other top vent ing

cases wi th no a t t empt t o op t imi se i t fo r bo t tom ven t ing .

T h e v e n t i n g m e c h a n i s m n o t i c e d f ro m t h i s b o t t o m v e n t i n g e x a m p l e is t h a t t h e

va po ur p rod uced d ur in g the f ir s t pa r t of t he t r ans i en t ca nn o t ea si ly e scap e f rom t he

vent . This process las t s unt i l the leve l swel l in the vesse l drops s igni f icant ly and unt i l

two-phase f low s t a r t s . Then the change o f t he f l ow reg ime c rea t e s a sha rp reduc t ion o f

the pressure in the vesse l . In rea l i ty th is change i s not so sharp due to two—dimensional

effec ts . B et te r repre se nta t io n i s achieved wh en th e vesse l i s ana lyse d wi t h severa l node s.

3.5.

EXAMPLE-5; TOP VENTING, SMALL VESSEL

Th i s exam ple i s a dep re ssu r i sa t ion exe rc ise which has been ca r r i ed o u t a t Ho echs t

wi th re fr igerant R114 as the working f lu id . The vent ing pipe inc ludes an or i f ice which

has been p l aced 0.70 m from the ex it o f t h e vesse l. Th e pa ra m e te r s me asu red du r ing

th i s example a re shown in F i g . 5 . For reas ons of s im pl ic i ty only one ca lc ula t i on f rom

S A F IR E i s p re sen ted he re . Th i s ca l cu l a t ion has been ca r r i ed ou t w i th churn tu r bu len t

f low, pa r t i a l l i qu id /vapour d i sengagement , and wi th t he d r i f t - f l ux d i s t r i bu t ion pa ram

e t e r C

0

equa l t o 1. Th e or if ice p l a t e wa s neg lec t ed in SA F IR E and t he d i am e te r of t he

ven t ing p ipe was t aken a s 1 .9 cm. RELAP and DEERS have mode l l ed the o r i f i ce by

su i t ab ly ad jus t ing the f l ow a rea be tween two con t ro l vo lumes used fo r t he ven t -p ipe .

In t h e R E L IE F code the d i scha rge f low-ra te mo de l has been ad jus t ed acc ord ing to t h e

phys i ca l p rop e r t i e s of t he re f r ige ran t R114 . H ea t - t r an sfe r p he no m en a f rom the vessel

wa l l have been t aken in to accoun t i n RELAP.

W h a t i s s ign if i can t ly d i ffe ren t i n th i s examp le in comp ar i son w i th Ex am ple -2 ,

i s th a t th e de lay in boi l ing dur i ng th e f i rs t second wh ich does no t seem to affec t th e

pre ss ure curve so much a s i n t he o the r ven t ing ca ses . Th e p red ic t ions wi th t h e R E L IE F

code a re i n exce l l en t ag reem ent wi th t he m easu red va lues . As is shown in

F i g . 5 ,

all

codes seem to ove rpred ic t t he mass- f lux even though the ca l cu l a t ed qua l i t i e s a t t he

exi t of th e vesse l a re in re la t ive ly good agr eem en t wi th m ea su red v a lues . I t sho uld be

m ent io ned he re t h a t bo th the mass- f lux an d the s t a t i c ven t -qua l i t y have been m easu red

1.5 m downst ream from the exi t of the vesse l .

The s ta t ic qual i ty for re f r igerant R114 seems to fa l l rapidly to low values (c lose

to a l l - l iquid f low) fol lowed soon af te rwards wi th a sharp increase to a l l -vapour vent ing.

T h e e x i t - q u a l i t i e s c a l c u l a t e d b y t h e R E L I E F a n d t h e D E E R S c o d e s s h o w e d t h a t a l l -

va po ur flow ha s been even tua l ly achieved af te r th e f i rs t 30 seco nds . T he ca lcu la t io ns for

th e void-f rac t ion in th e vesse l (Fig .5) re f lec t the dif fe rences be tw een t he ca lcu la ted and

measured mass- f luxes so the ac tua l vo ids a re much lower t han the ca l cu l a t ed va lues .

3.6. EXAMPLE-6; TOP VENTING, LARGE VESSEL

In the p re sen t ven t ing exa mp le the d im ens ions o f t he cy l indr i ca l ve sse l has been nea r ly

do ub led so th a t th e vesse l vo lum e is now 105 l i t res inste ad of th e 14.6 l i t res used in



432


UJ 4.00

<n 3.00

■

2.

00

'.

K

\ \*

: \ V

\ V \

\

\

\ \ x

: \ \

N

^ x

\ \ \

\ \ \

N

: \ \ >

\ ^

; \ \

\

T » i i ? I i i i i 1 i

•

X *

0

s

\

X

x

^ , \ * x

~^C^-

x

*

5T.

]

•

■

.

;

-

■

■

X w

- * » < x

10.0

20.0

30.0

10

T I M E SEC .


'■

\

m

h

\

\ \

f c £

f

x

x x

x

«

:

X

*

x

- > - ^ x X X

• • ■ 1 ' - ' ^

X

. . 1

^ x ^ T x

;

-

■

■

■

;

;

20 . 0

T I M E I SEC)

FIG. 5a . Top Venting-, 7 bar pre-relief pressure, 15% initial void [ or (x) Experiment;

RELAP; SAFIRE; RELIEF; DEERS j .



433



'

0 . 0 2 0 . 0

T I M E

FIG. 5b. Top

Venting,

7 bar pie-relief pressure, 15% initial void [ or (x) Experiment;

RELAP; SAFIRE; RELIEF; DEER S }.



434


» 3.00

— J — I — I — I — T — J —

0.00 L .

0.0

_ 1_

10.0 20.0 30.0

T I M E SEC) .


- / ••. -

• ; \

: / \

i

\

LI V N

:

«

\

x

N

1

\

\

\

I \ \ x ■

■ >

N l

^ • ^ ^ ■ . - . . :

j t V *

K,

* »%

w

«„ ■

„ [ ^ H

2 0 . 0 30 . 0

T I M E

I

SEC)

.

FIG. 6a . Top Venting, 8.3 ba r pre-relief pressure, 15% initial void [

or (x) Experiment;




435



a 0.30

FIG. 6b. Top Venting, 8.3 bar pre-relief pressure, 15% initial void [ or (x) Experiment;




436

t h e p rev ious examp le . Th e d im ens ion s o f t he ven t ing p ipe which is aga in a t t ach ed a t

the top o f t he vesse l a re t he same a s i n Example -5 . However , con t ra ry to t he p rev ious

example no o r i f i ce was p re sen t and the s t a r t i ng p re ssure was now 8 .3 i ns t ead o f 7 ba r .

The expe r imenta l da t a ava i l ab l e f rom Hoechs t AG a re t he p re ssure i n t he vesse l ,

th e mas s-f lux and th e qua l i ty 1 .5 m from the exi t of th e vesse l (Fig .6) . T hu s, the

measurements must be inf luenced both by the change in the s ize of the vesse l as wel l as

f rom th e chan ge in the typ e of ven t used . T h e sh ap e of th e pre ssu re curv e in th e vessel

sho wn in Fig .6 , i s s igni f icant ly di ffe rent f rom th e co rre sp on din g case in F i g . 5 . T h e

t rans i en t now l a s t s much longe r due to t he l a rge r amount o f l i qu id in i t i a l l y con ta ined

in the vesse l . The pressure does not fa l l as fast as in the previous example and the in i t ia l

de l ay in bo i l i ng wi th t he p re ssure r ecove ry a f t e rwards no t a s l a rge a s i n Example -5 o r

a s in s i m i la r w a t e r d e p r e s s u r i s a t i o n s . T e m p e r a t u r e m e a s u r e m e n t s b e f o re t h e o p e n i n g

of t he va lve has conf i rmed tha t t he l i qu id was a t sa tu ra t ion a t 74 °C . The pe r iod ove r

which th is de lay in boi l ing takes place i s mu ch longer th a n in th e smal le r vesse ls . Th is

i s probably due to the la rger amount of l iquid conta ined in the vesse l pr ior to in i t ia t ion

of t he t r ans i e n t . T he bes t ag re em ent in t he p re ssure curve i s p red ic t e d by R E L IE F

after the first 10 seconds.

S imi l a r t o t he p rev ious example on ly one SAFIRE ca l cu la t ion i s p re sen ted in

Fig.6 wi th the same input opt ions for the f low regime in the vesse l and in the vent - l ine .

Hea t - t r ansfe r phenomena f rom the vesse l wa l l have been a l so t aken in to accoun t i n t he

c a l c u l a t i o n s b y R E L A P.

For a l l codes the mass-f lux ca lcula ted a t the exi t of the vesse l i s much lower than

the ac tu a l va lues me asur ed 1.5 m dow ns t rea m in the ven t - l i ne . Th e ca l cu l a t ion s f rom

R E L I E F a r e in c lo s er a g r e e m e n t w i t h t h e e x p e r i m e n t a l d a t a sh o w n in F i g .6 . T h e

maximum va lue o f t he mass- f lux measured in t h i s exe rc i se i s s l i gh t ly l ower t han the

corresponding va lue in Fig .5 when an or i f ice was reducing the f low area of the vent -

pipe by 38%. These di f fe rences in the mass-f lux are expected to be a lso present in the

ex i t -qua l i t y . Th i s is no t t he case tho ug h a s i s shown in F ig .6 . Th e exp e r im enta l d a t a

in t h i s f i gure cor re spond to t he s t a t i c -qua l i t y measured 1 .5 m downs t ream in the ven t -

l ine and could be compared wi th the ca lcula ted qual i ty a t the exi t of the vesse l only

wh en th e li qu id en t ra ined in t he ven t - l i ne is a ssu me d n o t t o evap ora t e i n t h i s l eng th .

The ex i t -qua l i t i e s ca l cu l a t ed wi th t he SAFIRE and the DEERS codes a re i n exce l l en t

a g r e e m e n t w i t h t h e e x p e r i m e n t a l v a l u e s w i t h t h e c o r r e s p o n d i n g R E L A P c a l c u l a t io n s

a l so rea sonab ly c lose . A compar i son be tween the ex i t -qua l i t i e s measured in Examples

5 and 6 show s th a t t he qua l i t y of t he mix tu r e is abov e 50% an d a l l -vapo ur - f lo w s t a r t s

l a t e r t han when the re was an o r i f i ce (F ig .5 ) . In t he l a t t e r ca se t he ex i t -qua l i t y ge t s

close to al l- l iquid flow but for a shorter period of t ime.

T h i s e x a m p l e d e m o n s t r a t e d t h a t t h e e v a p o r a t i o n p r o c e s s d e p e n d s o n t h e s i z e o f

th e vesse l even if th e in i t ia l void-f rac t ion i s th e sa m e. O n th e oth er h an d, th e size of the

ven t employed changes the dura t ion o f t he two-phase re l ea se a s we l l a s t he compos i t i on

of t he two phase mix tu re . These two pa rame te r s migh t have cance l l i ng e f fec t s which

cannot be easi ly ident i f ied when only the pressure in the vesse l i s moni tored.



437


The p re sen t work focuses on the phenomenology o f t he depre ssur i sa t ion o f r eac to r

vessel s t h r ou gh s ix exp e r im enta l exam ples pe r fo rmed in d i ffe ren t t e s t f ac i li t ie s . The se

examples have been ana lysed in o rde r t o demons t ra t e t he impor t ance o f t he geome t r i ca l

a n d o p e r a t io n a l p a r a m e t e r s .

The depressur isa t ion processes depend on the s ize of the vesse l and on the s ize of

the vent used. For example , the leve l swel l osc i l la t ions observed in smal l reac tor vesse ls

does no t necessa r i l y mean tha t t hey wi l l r ema in the same when the d imens ions o f t he

vesse l and the ven t - l i ne a re i nc reased . Al so , t he pos i t i on o f t he ven t can cause changes

i n t h e d e p r e s s u r i s a t i o n p r o c e s s e s . T h u s , d u r i n g b o t t o m v e n t i n g , t h e l i q u i d d i s c h a r g e

causes a r a the r sma l l depre ssur i sa t ion ra t e dur ing the f i r s t seconds o f t he t r ans i en t ;

th is ra te i s s igni f icant ly in creased la te r whe n two-p has e f low sta r t s .

Compar i sons be tween d i f fe ren t t op-ven t ing examples ca r r i ed ou t wi th a nea r ly

ful l vesse l an d whe n the vesse l wa s ha l f -e mp ty revea led tw o di f fe rent de pre ssu r isa t ion

proc esses dep en din g on th e in i t ia l f il lings. T he f i rs t pro cess occu rs in an a lm os t full

vesse l du r ing th e f irs t seconds o f t h e t r an s i en t and i s cha r ac t e r i se d by va po ur p ro du c t ion

tog e th e r wi th an expu l s ion o f a p red om inan t ly l iqu id m ix tu r e un de r va ry ing m ass-

fluxes. In t he second p rocess a p red om inan t ly va pou r mix tu re is expe l l ed wi th l a rge r

dep ressu r i sa t ion ra t e t ha n in t h e f irs t p rocess .

The cha rac t e r i s t i c de l ay in bo i l i ng which occurs dur ing the top ven t ing ca ses a f t e r

the ven t ing va lve has been opened , i s p rac t i ca l ly shadowed by the p re ssure osc i l l a t i ons

w he n th e vesse l has been in i t ia l ly full . Di fferences in th e im po rta nc e of th e de lay

in boi l ing have been a lso observed in the la rger vesse ls even wi th s imi lar pre-re l ie f

cond i t i ons . These d i f fe rences have been a t t r i bu ted to t he l a rge mass o f l i qu id con ta ined

in the large size vessels.

Four very di f fe rent numerica l codes have been used for the theore t ica l ca lcula t ions.

These codes have been e i the r one -d imens iona l i n t he vesse l (RELIEF) o r i n t he ven t -

l i ne (SAFIRE) o r bo th in t he vesse l and in t he ven t - l i ne (RELAP & DEERS) . I t ha s

been ev iden t i n a ll t he exam ples t h a t for rea l i st i c r epre se n ta t io n o f t h e t h e h ydr od y-

namic p rocesses , a t l e a s t t he vesse l shou ld be mode l l ed wi th seve ra l con t ro l vo lumes .

B e t t e r r ep re se n ta t io n o f t he pa r am e te r s r e fe r r ing to t h e ven t - l i ne has been ach ieved

f rom one -d imens iona l ca l cu l a t ions which , i n add i t i on to t he vesse l , d i sc re t i sed a l so the

ven t - l i ne i n t he ax i a l d i rec t ion . Th i s unfor tuna te ly i nc reases t he computa t iona l t ime

and t he com plex i ty o f t h e code . Th us , t he answer t o t h e d i l e m ma of emp loy ing a

d e t a i l e d o n e - d i m e n s i o n a l c o d e w h i c h u s e s g r e a t e r c o m p u t a t i o n a l t i m e , a g a i n s t t h e u s e

of a f a st and s im ple code wi th a ce r t a in n um ber o f a ss um pt i on s , li es on how acc ura t e

o n e n e e d s t o r e p r e s e n t t h e p h e n o m e n a o c c u r r i n g d u r i n g a n e m e r g e n c y

relief.

Al t hou gh good repre s en ta t ion o f t he depre s sur i sa t ion p rocesses in t he vessel has

been ach ieved wi th t he one -d imens iona l ca l cu l a t ions shown he re , t he use o f t he same

two-phase f low model for the vesse l as wel l as for the vent - l ine and for the whole range

of void fract ions from 0 (al l l iquid flow) to 1 (al l vapour flow) may not always be a

good approach . The re su l t s i n t he bo t tom ven t ing example a s we l l a s fo r f l u ids o the r

t h a n w a t e r d e m o n s t r a t e d t h a t a m o r e p h e n o n o m e n o l o g i c a l r e p r e s e n t a t i o n o f t h e f lo w

migh t be necessa ry . Unfor tuna te ly , t he se mode l s have the d i sadvan tage o f i n t roduc ing

emp i r i ca l pa ram e te r s which then requ i re a ce r t a in degree o f t un in g . Eve n tua l ly , t h i s



438

makes the numer i ca l mode ] use r -dependan t and the ove ra l l p red ic t ive capab i l i t i e s o f

the code wi l l a lways rema in doub t fu l .

F ina l ly , f rom the examples shown he re i t c an be conc luded tha t by measur ing on ly

the p re ssure and the rema in ing mass i n t he vesse l , no t a l l o f t he occur r ing phenomena

can be iden ti f ied . Th e mass- f lux and th e ven t - l i ne qua l i t y d i sclose som e im po r t a n t

in fo rma t ion wheneve r a de t a i l ed unde rs t and ing o f t he depre ssur i sa t ion p rocesses i s

necessary . This de ta i led understanding seems to be necessary for sca l ing to la rger s ize

un i t s and for an accu ra t e i npu t ( source t e rm ) to p rob lem s o f a tm osp he r i c d i sp e r s ion .

ACKNO WLEDGEMENTS

T he au th or t h an ks M essr s . A.B enuzz i , S .Duf fi eld, G.F ranche l lo , G.Fr i z , H.S taed tke

a n d K .B e l l w h o p r o v i d e d t h e c a l c u l a t i o n s w i t h R E L A P, SA FI R E a n d R E L I E F a n d

con t r ibu ted s ign i f i can t ly t o t he eva lua t ions o f t he p re sen t examples .

REFERENCES

1 M ayinge r F . , " Tw o-ph ase flow ph en om en a w i th dep re ssu r i sa t ion-c ons eque nces for

th e des ign and l ayou t of sa fety and p re ssu re r el ie f va lves" , Ch em . E ng . Pro gres s ,

1988,

23 , pp 1-11.

2 Fr i ede l L . , Wehm eie r G. " M ode l l i ng o f t he ven ted m e th an o l / ac e t i c -an hy dr i de

r u n a w a y r e a c t i o n w i t h SA FI R E p r o g r a m " , P r o c . E u r o t h e r m Se m i n a r 1 4 o n H e a t

Transfe r an d M ajor Techno log ica l H aza rds , Un iv . Ca tho l iqu e de Lou va in , May

1990,

Vol.1,

pp 12 .1-12 .15 .

3 Skou loud i s A.N . , Ko t tow sk i H.M . , Be l l K. I . , O s t e r R . ,

u

Towards the p red ic t ion

o f v e n t i n g c h a r a c t e r i s t i c s w i t h t h e c o d e s SA FI R E a n d D E E R S " , I n t . Sy m p . o n

R u n a w a y R e a c t i o n s , C C PS A I C h E , C a m b r i d g e M a s s a c h u s e t t s , 1 9 8 9 , p p 2 4 7 - 2 6 3 .

4 D ux b ur y H.A . , W ilday A .J . , " Eff ic ient design of rea c to r re lie f sy ste m s " , In t .

S y m p . o n R u n a w a y R e a c t i o n s , C C P S A I C h E , C a m b r i d g e M a s s a c h u s e t t s , 1 98 9,

pp 372 -394 .

5 Skou loud i s A.N . , " F i f teen Be nch ma rk exe rc ise s on vesse l dep re ssu r i sa t ion w i th

n o n - r e a c t i n g flu id s; h y d r o d y n a m i c c o n s i d e r a t i o n s " , C E C - J R C I s p r a , E U R - R e p

12602 E N , Nov . 1989.

6 Os te r R . , Be l l K. I . , Ko t tow sk i H.M . , " H yd rod yn am ic con s ide ra t ions o f ven t ing

wi th h igh v i scos i ty non- reac t ing f lu ids " , J .Loss Prev . Process Ind . , 3 (1 ) , 1990 ,

pp 50-52 .

7 Skou loud i s A.N . , Be l l K. I . , Ko t tow sk i H.M . , " Ven t ing o f vessel s con ta in ing reac t

i n g flu id s; a p a r a m e t r i c s t u d y w i t h SA FI R E a n d D E E R S " , J .L o s s P r e v . P r o c e s s

Ind. , 3 (1) , 1990, pp 13-16.

8 Fr i edel L . , " Tw o-p hase the r mo hy dra u l i c s in s to r age vessel s an d d i scha rg e l ine s

d u r i n g t o p v e n t i n g " , P r o c . I B C / H S E E u r . Se m i n a r o n t h e P r e s s u r i s e d S t o r a g e

of F l ammable L iqu ids , London , 1988 .

9 Re id R .C . , Pr au sn i t z J .M . , She rw ood T .K . , " Th e Pr op e r t i e s o f gases and l iqu id s" ,

M cG raw H i ll Book C om pany , 1977 , 3d ed i t i on .

10 H e w i t t G .F . , " L i q u i d - G a s Sy s t e m s " , H a n d b o o k of M u l t i p h a s e Sy s t e m s , H e m i

sph e re Pu b l i s h in g Cor po ra t io n , ed i t ed by G.H e t s ron i , 1982 , pp 2 .44-2 .94 .



439

11 Benuzz i A, " SA FI R E Ca lcu la t ion Resu l t s o f t he Vesse l B low dow n B enc hm ark

Exerc i se s " , Techn ica l No te N. 1 .89 .01 , C E C -J R C I sp ra , ( Ja nu a ry 1989) .

12 O s te r R ., Be l l K. I . , " SA FI R E as a des ign too l ; com par i so n w i th exp e r im enta l

d a t a f r o m t h e M PM C r i g " , C E C - J R C I s p r a , T e c h n i c a l N o t e

1.89.120,

Nov .1989 .

13 Fr iz G. , " Level Swell an d Void D ist r ib ut i on in a Dis cha rgin g Ve r t ica l Vesse l " ,

E u r o p e a n T w o - Ph a s e F l o w G r o u p M e e t i n g , ( 1 9 8 7 ) .

14 Duff ie ld J .S . , Fr iz G. , M ehr K. , Ni js ing R. , " O ut l in e of mo del de ve lop m en t for

emerg ency ven t ing o f chemica l r eac to r s " , Pr oc . E ur o t he rm S em ina r 14 on H ea t

Transfe r and Major Techno log ica l H aza rds , Un iv . Ca tho l iqu e de Lou va in , May

1990,

Vol.1,

p p I L 11 .1 -11 .10 .

15 Kle in H.H . , " Va l ida t ion of a tool for s iz ing em erge ncy rel ie f sy ste m s for ru naw ay

chemica l r eac t io ns" , P l an t Op . Pro g , 1986 , pp 1 -10.

16 Skou loud i s A.N . , Ko t towsk i H.M . , " O ne - d im ens ion a l ana lys i s o f five depre ssur i -

sa t ion ca ses fo r vesse l s wi th t op o r bo t tom ven t - l i ne s " , Proc . Euro the rm Semina r

14 on H ea t T ransfe r and Major Techno log ica l H aza rds , Un iv . Ca tho l iqu e de Lou

vain , May 1990, Vol . I , pp 3 .1-3 .11 .

17 Skou loud i s A.N . , Ko t tows k i H.M . , " H yd rod yn am ic a sp ec t s o f ven t ing for vesse l s

con ta in in g v i scous flu ids, Pro c . o f t he 24 th Loss Pre ven t ion S ym po s iu m , A IC hE ,

A u g .1 9 9 0 .

18 H ard y P .G . , R ich te r H.J . , " Pre ssu re t r an s i en t and two -pha se swe l li ng du e to a

sma l l t op b reak " , Nuc lea r Eng inee r ing and Des ign , 95 , 1986 , pp 207-220 .

19 H e w i t t G .F . , " Ph y s i c a l B e n c h m a r k E x e r c i s es , E x p e r i m e n t a l d a t a s e t s f or ev a l u a

t i on of mo de l l i ng m e th od s " , Ha rwe l l La bor a to r y , Ju n e 1986 .

void f rac t ion

dynamic v i scos i ty (Pa s )

dens i ty (Kg m

- 3

)

surface tension (N m

_ 1

)

S u b / S u p e r s c r i p t

v a p o u r p h a s e

dr i f t quan t i t y

No de be low cur ren t no de

l iquid phase

M a x i m u m v a l u e

0 .4 eqn . [ l l ]

0 . 3 e q n . j l l ]

N o d e a b o v e c u r r e n t n o d e

two phase

A

d

D

dh

f

H

9

J

Re

C/oo

U pool

U

X

N o m e n c l a t u r e

interf ace sl ip coefficient (m

5

K g

- 1

s

- 2

)

d i a m e t e r ( m )

Cont ro l vo lume he igh t (m)

fr ic t ion fac tor (m)

E leva t ion f rom vesse l bo t tom (m)

grav i t a t i ona l acce l e ra t ion (m s

- 2

)

drift flux (m s

_ 1

)

R e y n o l d s n u m b e r

bu bb le r i se ve loc i ty (m s

_ 1

)

bub b le ve loc i ty eq n . [ l l ] (m s

- 1

)

aver age ve loc i ty (m s

_ 1

)

qual i ty

a

p

a

9

J

L

t

M

m

n

U

2p











