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Volume 4, Issue 1 2009 Article 14

Chemical Product and ProcessModeling

Modelling and Optimisation of an IndustrialEthylene Oxide Reactor

Shahla Aryana, The University of SydneyMitra Ahmadi, The University of Sydney

Vincent G. Gomes, The University of SydneyJose A. Romagnoli, The University of Sydney

Kian Ngian, Huntsman Corporation, Australia

Recommended Citation:Aryana, Shahla; Ahmadi, Mitra; Gomes, Vincent G.; Romagnoli, Jose A.; and Ngian, Kian(2009) "Modelling and Optimisation of an Industrial Ethylene Oxide Reactor," ChemicalProduct and Process Modeling: Vol. 4: Iss. 1, Article 14.DOI: 10.2202/1934-2659.1231Available at: http://www.bepress.com/cppm/vol4/iss1/14

©2009 Berkeley Electronic Press. All rights reserved.

Modelling and Optimisation of an IndustrialEthylene Oxide Reactor

Shahla Aryana, Mitra Ahmadi, Vincent G. Gomes, Jose A. Romagnoli, and KianNgian

Abstract

A dynamic model of an industrial packed-bed multi-tubular reactor was developed toinvestigate performance of an industrial ethylene oxide (EO) reactor, conducting epoxidation ofethylene over a silver-based catalyst. The set of nonlinear kinetic rate equations for the catalyticoxidation process in the presence of ethylene dichloride (EDC) as a moderator was coupled withthe governing heat and mass transfer equations along the packed bed. Catalyst deactivation wasmodelled as a nonlinear function of operating time and the equation was benchmarked againstplant data for the period of operation. Our process model was compared with experimental dataobtained from an industrial EO reactor. The model predictions were found to agree well with theplant data. The influences of operating parameters such as EDC level, reactant concentrations,reactor pressure, coolant temperature and the feed temperature on reactor performance wereinvestigated. The variables having significant impact on work rate and selectivity were identified.The model was used to optimise the performance of ethylene oxide reactor for maximising workrate and selectivity.

KEYWORDS: ethylene oxide, oxidation reactor, ethylene dichloride, optimisation, selectivity

Introduction

Ethylene oxide (EO) is a major chemical, and the global demand for ethylene oxide continues to increase because of its importance as an intermediate in producing antifreeze, polyester fibres and other petrochemical products. The production of EO is a critical process because the reactor can generate eleven times as much heat in a runaway condition as under normal operation conditions [Rebsdat 1987; Kishor 2003]. From 0.03 to 1 mole fraction, a mixture of EO in air is explosive at room temperature. As result, EO is normally stored at 5oC under 4.5 kg/cm2 pressure [Rebsdat, 1987]. Therefore, the safety issues for an EO reactor are of paramount importance.

Commercial processes for producing EO are based on direct oxidation of ethylene with pure oxygen. Complete combustion of ethylene, as well as further oxidation of ethylene oxide to carbon dioxide and water, also occurs during the reaction. Silver catalyst, packed in tubes with promoters, is the state-of-the-art catalyst for ethylene oxidation, because of its high activity and selectivity for EO. Organohalide inhibitors such as 1,2-dichloroethane or ethylene dichloride (EDC) are added to control the reaction rate and improve the selectivity of the catalyst and its concentration is usually 1-3 ppm. The complete oxidation of ethylene is inhibited to a great extent by EDC than partial oxidation; hence the selectivity for ethylene oxide is promoted. Thus, EDC is termed an “inhibitor” and a “promoter” due to its promoting effect on selectivity and inhibiting effect on oxidation.

Since the reactions involved are highly exothermic, heat transfer efficiency is critical. Multi-tubular fixed bed reactors are widely used in industrial EO production. Heat is removed by a coolant circulating through the shell side. Failure to remove the heat adequately may lead to thermal runaway. With time, the silver based catalysts for EO production exhibit a continuous loss of activity and selectivity, which is accelerated if the reactor is run at higher than necessary temperatures. Run-away conditions and burn-out of the catalyst and equipment may transpire at elevated temperatures. These considerations are particularly important in industrial EO manufacture, where maximising production and minimising risks under variable conditions are imperative.

Several authors investigated the modelling and simulation of ethylene epoxidation [Azevedo, 1990; Cornelio, 2006; Zhou & Yuan, 2005] however, the published information is insufficient. Zhou and Yuan [2005] studied the steady-state and dynamic optimisation of an ethylene epoxidation process. They investigated the effect of inlet ethylene, O2 and CO2 concentrations, and operating pressure on productivity but did not consider the effect of ethylene oxide oxidation, which has significant consequences. The current work considered all relevant reactions for analysis and optimization of the EO reactor over the period of catalyst life time.

1

Aryana et al.: Modeling and Optimisation: Industrial Ethylene Oxide Reactor

Published by Berkeley Electronic Press, 2009

Reaction Kinetics

The parallel consecutive reaction of ethylene and ethylene oxide is shown in Figure 1. The first reaction is known as partial oxidation or epoxidation of ethylene, while the second reaction involves total oxidation or combustion.

C2H4 C2H4O 2CO2 + 2H2O

The three main reactions in our process are.

OHCOCHCH 42222 .2/1 →+= 151 .1023.1 −×−=Δ kmolkJH (R1)

OHCOOCHCH 22222 22.3 +→+= 16

1 .1030.1 −×−=Δ kmolkJH (R2)

OHCOOOHC 22242 22.25

+→+

161 .1017.1 −×−=Δ kmolkJH (R3)

The overall reaction rate is described by:

ikijii CpTtapTfR ××= ),,(),( Eq.1

where ai and Ci denote deactivation term and correction factor, respectively. Park and Gau [1987] presented a Langmuir-Hinshelwood mechanism for

oxidation and epoxidation of ethylene with surface reaction as the rate-determining step. Petrov et al. [1984] developed a kinetic model of ethylene epoxidation over supported silver catalyst based on a Rideal-Eley type mechanism. They concluded that the gaseous or weakly adsorbed ethylene interacts with chemisorbed oxygen. Westerterp et al. [1984] suggested that with a large excess of ethylene, the rate equations simplify to first order kinetics in oxygen concentration. Borman et al. [1992], proposed a rate expression without any inhibitor. Petrov et al. [1986], considered a rate expression including EDC effects. We tested a number of published rate equations in conjunction with our reactor model. The rate expressions used in the current work, including the three

Figure 1- The parallel consecutive reaction of ethylene and ethylene oxide

(1) ½ O2

3O2

(2)5/2 O2

(3)

2

Chemical Product and Process Modeling, Vol. 4 [2009], Iss. 1, Art. 14

http://www.bepress.com/cppm/vol4/iss1/14DOI: 10.2202/1934-2659.1231

main reactions with effects of EDC as inhibitor, were adapted from elsewhere [Petrov et al., 1984, 1986, 1988, Eliyas et al., 1988] as given below:

catEthxy

kEDCOxyEthOxyEth

PKPKPPPKPPK

f ρ×++

−×−=

605

21

121)1(

13

Eq.2

catEthxy

kEDCOxyEthOxyEth

PKPKPPPKPPK

f ρ×++

−×−=

605

43

13)2(

14

Eq.3

catoxyEOEOoxyxy

kEDCEOEthOxyEO

PPKPKPKPKPPPKPPK

f ρ×++++

−×−= − 25.0

.12115.0

.1009

87

)1(25)3(

15

Eq.4

where Eth, Oxy, EO, and EDC stand for ethylene, oxygen, ethylene oxide and dichloroethane, respectively. The kinetic rate constants k1 –k12 have an Arrhenius dependency on temperature and can be expressed as:

)( ,,087,41

S

iaii RT

EeKK

−=−−=

)( ,,0129,6,5

S

iaii RT

EeKK =−=

The equation parameters are given elsewhere [Petrov et al, 1986]. The

correction factors (Ci) were calculated based on the information provided by the catalyst vendor. The catalyst density of 1260 kg/m3 is calculated from catalyst pellet packing data received from plant.

Process Description

The industrial ethylene oxide reactor [Huntsman, 2005], a multi-tubular reactor (Figure 2) with 7750 tubes, is packed with silver catalyst supported on alumina. MobilTherm "607" flows in the 3.3 m diameter reactor shell to remove the heat generated. The operating temperature of the reactor is 230-260ºC and the pressure varies from 20-25 atm. The oil feed temperature is about 245 ºC and heats the incoming gas in the first part of the reactor before acting as a coolant. The process is oxygen-based and operates in the oxygen lean zone to prevent explosion.

3



Figure 2- Schematic representation of the EO reactor (not to scale)

The product gas from the outlet of the reactor preheats the inlet gas in a

separate heat exchanger. The product gas is then stripped off ethylene oxide in 2 scrubbers. The stripped gas is thereafter de-carbonated before being recycled back to the reactor. The outlet cooling oil is cooled in a kettle boiler to produce saturated steam.

The raw feed materials including pure oxygen and ethylene mixed with recycle gas stream (from the scrubbers), are heated and fed to the reactor. The reactor feed consists of 7 main components including: ethylene, oxygen, ethylene oxide (usually less than 0.01%), carbon dioxide, water (reaction’s by-products), argon (built up in the system by adding oxygen) and nitrogen (used as ballast). Also, a small concentration of 1,2-dichloroethane (EDC) and ethane are intentionally added to the feed to improve reactor selectivity and to moderate the oxidation. A typical reactor feed and product composition is shown in Table 1.

Table 2 shows the reactor typical operating conditions. We note that a difference in oil inlet temperature between start of run (SOR) and end of run (EOR) exists due to catalyst deactivation.

Table 1- Typical reactor feed and product composition (mol %) Composition (mol %) Feed Product

Ethylene 17.5 16 Oxygen 7 5 ethylene oxide 0.01 1.7 Carbon dioxide 5.0 6.1 Water 0.3 1.51 Nitrogen + Argon 70.2 69.7 EDC (ppm) 1-2 1-2

4



Table 2- Reactor operating conditions SOR (@t = 0) EOR (@t = 1000 days) Gas feed flow rate (kg/hr) 163 700 163 700 Pressure (bar) 20.68 20.68 Gas inlet temperature (oC) 204 204 Oil flow (kg/s) 1250 1250 Oil inlet temperature (oC) 235 250

Model Development

In our one-dimensional model, radial variations of concentration and temperature are not considered. The radial dispersion of concentration and temperature within the reactor bed is negligible due to the small radius of the tubes relative to the length (r/L<<1). EO reactor operates below 673 K and a radiation term is negligible [Khanna and Seinfeld, 1987]. The main assumptions for the model are:

• Radial dispersion is negligible compared to axial dispersion; • Mass transfer resistance between gas and catalyst is negligible; • Nitrogen and argon molar flows are constant along the bed; • Alumina support data are taken from Bradshaw et al. [1970]; • Catalyst-gas heat transfer is included; • Convective heat transfer dominates heat effects in an industrial reactor; • Heat transfer coefficient for catalyst pellet is calculated from j-factor

[Bradshaw et al., 1970]; • Heat transfer coefficient on the shell side is given by Bell-Delaware method

[Hewitt et al., 1994]; • Heat transfer coefficient in the gas film adjacent to the tube wall is estimated

from correlations [Drew et al., 1962]; • Pressure drop estimate is based on plant data and literature correlation [Fogler,

1999].

Mass Balance

The species mass balance for the gas phase is given by:

2

2

,31

)( )1()/(ZF

DZF

VeARVt

F jax

jgasTC

iiiBASEjgas

j

∂∂

×+∂∂

×−−××××=∂∂

∑−=

νν Eq.5

5



Ethylene species balance

2

2

,21

4242

42 )1()3/12(

ZF

DZ

FV

eARRVt

F

HCax

HCgas

TCgasHC

∂

∂×+

∂

∂×

−−×××+××=∂

∂

Eq.6

Oxygen species balance:

2

2

,321222 )1()(

ZF

DZ

FVeARRRV

tF O

axO

gasTCgasO

∂

∂×+

∂

∂×−−××++×=

∂

∂ Eq.7

Ethylene oxide species balance:

2

2

,31 )1()5/22(

ZF

D

ZF

VeARRVt

F

EOax

EOgasTCgas

EO

∂∂

×

+∂∂

×−−×××−××−=∂

∂

Eq.8

Carbon dioxide species balance:

2

2

,32

2

22 )1()5/43/2(

ZF

D

ZF

VeARRVt

F

COax

COgasTCgas

CO

∂

∂×

+∂

∂×−−×××+××−=

∂

∂

Eq.9

Water species balance:

2

2

,32

2

22 )1()5/43/2(

ZF

D

ZF

VeARRVt

F

OHax

OHgasTCgas

OH

∂

∂×

+∂

∂×−−×××+××−=

∂

∂

Eq.10

6



Energy balance on catalyst pellet

b

b

iiiiBASEj

catgasVPcatcat

catcat

ee

HR

TTSt

TCp

−×Δ××+

−××=∂∂

××

∑−=

1)/(

)(

31)(νν

αρ Eq.11

Energy balance on gas side

bbgascatVPCat

bgasIwallVIT

gasgasgasgasmol

gasgasgasmol

eeTTS

eTTSZ

TVCp

tT

Cp

)1()(

/)( ,

,,

−×−××

+−××+∂

∂×××−=

∂

∂××

α

α

ρρ

Eq.12

Energy balance on tube wall

The outer tube wall temperature is dependent on the heat transfer to the tube inner surface, characterized by wallα , and the heat transfer of the shell side ( Sα ).

)()()4(

)()()4(

,,22

,22,

IwallOwallIOOwall

OwalloilIOOsOwall

wallwall

TTDDD

TTDDDt

TCp

−×−××−

−×−××=∂

∂××

α

αρ Eq.13

The inner sides of the tube wall exchange heat with the outer side of tube wall as well as the gas, where wallα the tube side heat transfer coefficient is:

)()()4(

)()()4(

,22

,,22,

gasIwallIOIT

IwallOwallIOOwallIwall

wallwall

TTDDD

TTDDDt

TCp

−×−××−

−×−××=∂

∂××

α

αρ Eq.14

Energy balance on cooling oil

The oil temperature is dependent on the heat transfer to the outer surface of the tube wall, which is characterized by Sα , and the heat loss from the shell to the surface.

)()()(

)(

,

,

oilambSlossoilOwall

OTsoil

oiloiloil

ccoiloil

TTDUTT

DNZ

TCpG

tT

ACp

−×××+−×

×××+∂∂

××−=∂∂

×××

π

παρ Eq.15

7



Heat capacity, viscosity and thermal conductivity data [Vargaftik, 1975] were approximated by linear functions of pressure and temperature in the range of the reactor operating conditions.

Catalyst Deactivation

The main mechanisms of catalyst deactivation can be grouped into six types: (i) poisoning, (ii) fouling, (iii) thermal degradation, (iv) 1,2-dichloroethane vapor formation accompanied by transport, (v) vapor–solid and/or solid–solid reactions, and (vi) attrition/crushing [Bartholomew, 2001].

The catalyst deactivation model used in this study is derived from Boskovic et al. [2004a] for a commercial Ag/Ag2O3 catalyst. The equation describes catalyst activity decline as a function of time with a term of steady-state activity, ass, reached at infinite time [Fuentes, 1985]:

dssOd aaPK

dtda )(

2−=− α

Eq.16

Boskovic et al. [2004b] used a power-law giving index of 1 (d=1):

))(exp()1(2

0 tPRTE

Kaaa Oa

dssssα−−−+= Eq.17

The catalyst deactivation is modeled using Eq.17 which is a nonlinear function of operating time and catalyst temperature. Data from the catalyst vendor were used to evaluate the catalyst deactivation parameters (with subscripts ass and kd).

The temporal profiles of a1 and a2, the catalyst deactivation functions, introduced for the partial and complete oxidation reaction rate equations of ethylene, are shown in Figure 3 for a period of three years.

8



0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000Time (day)

Dea

ctiv

atio

nDeact 1

Deact 2

Figure 3- Catalyst deactivation profiles for a period of 3 years operating time

Model Predictions and Industrial Reactor Data

The catalyst temperature has a major effect on the reactor performance, catalyst aging and safety. Since no plant data are available for the catalyst temperature, data for the oil and gas outlet temperature were used to validate our model. Figure 4 and Figure 5 show the oil and gas outlet temperatures of the model predictions against plant data during 3 years of reactor operation. The model predictions are in reasonable agreement with plant operating data. However, some discrepancies exist due to error in measurement related to model input data. We observe that the oil inlet temperature increases with time to compensate for the loss in catalyst activity and maintain desired production rate and selectivity.

9



230

235

240

245

250

255

260

265

270

0 200 400 600 800 1000Time (day)

Tem

p (C

)

Plant DataModel Prediction

Figure 4- Comparison of outlet oil temperature predictions with plant data during

3 years operation

230

235

240

245

250

255

260

265

270

0 200 400 600 800 1000Time (day)

Tem

p (C

)


Figure 5- Comparison of outlet gas temperature predictions with plant data during

3 years operation

The other important parameters are selectivity and work-rate. These two parameters represent the EO reactor efficiency and product rate, respectively. The selectivity (Sel%) and the work-rate (WR) definitions we used are given as follows:

100% ×=consumedethyleneTotal

producedEOSel Eq.18

10



)/( dayTproducedEOWR = Eq.19

Comparisons of the selectivity and the work-rate between the model prediction and the plant data are shown in Figure 6 and Figure 7, respectively. The selectivity is decreasing over the period of catalyst life time due to loss in catalyst activity and the work-rate changes are related to the market demand.

70%

75%

80%

85%

90%

0 200 400 600 800 1000Time (day)

Sele

ctiv

ity (%

)


Figure 6- Comparison of catalyst selectivity predictions with plant data during

3 years operation

Overall, the model predictions for the selectivity and the work-rate against the plant data are satisfactory. Whenever the plant data for the input variables were available, the model predictions were very close to plant data. However, when accurate plant data are unavailable, we noticed disagreements between model predictions and plant data. For example, EDC concentration has significant effect on the selectivity and work-rate; however, accurate data on EDC concentration (ppm levels) were not always available. Despite the uncertainties in plant data and unknown disturbances, our model prediction show reasonable agreement with the plant data.

11



80

100

120

140

160

0 200 400 600 800 1000Time (Day)

Wor

k R

ate

(T/D

ay)


Figure 7- Comparison of work-rate predictions with plant data during

3 years operation

Sensitivity Analysis

Sensitivity analysis was undertaken to check the sensitivity of the reactor performance, using the validated model, to inlet variables such as coolant and feed temperature, EDC level, and reactant concentration.

Coolant and feed temperature

The inlet temperature of oil as coolant is one of the important control variables which could control possible thermal runaways as well as the reactor performance. There is a limitation on the allowable temperature rise of the coolant as it passes through the reactor. On one hand, it is advantageous for the temperature to rise large enough to allow efficient heat transfer in the secondary heat exchanger for steam generation, but there is also strong motivation to minimize this temperature rise in order to reduce thermal shocks in the reactor. Figure 8 shows the effect of step increasing (+5%) the oil inlet temperature (@ t = 0 s) on the temperature profile along the reactor. The disturbance propagates in a linear fashion and the transition time is less than 100 s due to the high gas velocity and fast reactions.

12



190

200

210

220

230

240

250

260

270

280

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5

Gas

Tem

pera

ture

(ºC

) .

Distance along the reactor (m)

Time = 0 Sec

Time = 100 Sec

Figure 8-Temperature profile in reactor with +5% step-change in T-oil-inlet

We note that the first and the last half meter of the 7.35 meter long tubes have no catalyst which means no reaction, so, just heat exchange between the oil and gas take place. During the first half meter of tubes and the last half meter, respectively, the model shows a significant rise and small decline in the gas temperature due to heat exchanger between gas and oil. Figure 9 shows the effect of step increasing (+5%) the oil inlet temperature (@ t = 0 s) on the work-rate and selectivity. With increasing oil temperature, the work-rate increases by about 12% while selectivity decreases by 2.5% as be expected, since the reaction rates of all the three reactions increase with temperature and the work-rate increases with increasing oil temperature. However, a decrease on selectivity is expected due to stronger effect of temperature on the undesired reaction (the total ethylene and EO oxidation) than the desired one (partial oxidation of ethylene).

110

115

120

125

130

0 40 80 120 160 200Time (s)

Wor

k R

ate

(Ton

/day

)

78

78.5

79

79.5

80

80.5

81

81.5

Sele

ctiv

ity (%

)Work-rateSelectivity

Figure 9- Selectivity and work-rate with +5% step-changes in oil inlet temperature

13



For further investigation, the amount of heat transferred between the tube wall and the coolant oil is shown in Figure 10. This graph shows that in the beginning, the amount of transferred heat drops dramatically due to the step increase of shell side temperature (oil inlet temperature) which results in decreasing the temperature difference between the shell side and the gas phase. Consequently, the bedside temperature starts to increase enhancing the reactions thereby increasing the released heat by reactions and the reactor inside temperature. Thus, heat transfer starts to increase. The dramatic decrease in heat transfer rate could lead to a thermal runaway condition and catalyst damage.

234

236

238

240

242

244

246

248

0 10 20 30 40 50 60 70 80 90 100Time (s)

Tem

pera

ture

(C)

0

500

1000

1500

2000

2500

3000

Oil Inlet temp

Heat Transferred

Possible Runaway Condition

Hea

t Rem

oved

(J/s

)

Figure 10- The oil inlet temperature and transferred heat between oil and tube wall in response to a +5% step-change in oil inlet temperature

During industrial operation, use of a linear-change is better suited than a step-change. Figure 11 shows the modification of oil inlet temperature according to a linear increase and the amount of heat removed from tube side. As seen, the heat transferred is increasing smoothly and there is no dramatic change. Figure 12 shows the selectivity and work-rate following a linear-change. In both cases the final outcomes are similar but the reactor performance is expected to be better in case of linear increase. So, to avoid any runaway condition, linear increase is suggested.

14



230

234

238

242

246

250

0 10 20 30 40 50Time (min)

Tem

p. (º

C)

1500

1700

1900

2100

2300

2500

2700

Hea

t Rem

oved

(J/s

)

Oil Inlet Temp

Heat Transferred

Figure 11- Oil inlet temperature and heat transferred between oil and tube wall

with +5% linear change in oil inlet temperature

110

115

120

125

130

0 10 20 30 40 50Time (min)

Wor

k R

ate

(Ton

/day

)

78

78.5

79

79.5

80

80.5

81

81.5

Sele

ctiv

ity (%

)

Work-rateSelectivity

Figure 12- Selectivity and work-rate with +5% linear change

in oil inlet temperature

15



EDC level

The 1,2-dichloroethene (EDC) helps enhance process selectivity by reducing the availability of active sites on the silver/alumina catalyst. Figure 13 shows the effect of EDC level on the selectivity and work-rate, the disturbance propagates in a nonlinear fashion. With the addition of EDC, there is a shift in the rates of reactions, resulting in a relatively smaller decrease in the amount of EO formed. Thus, the selectivity for EO increases, although the work-rate decreases. Figure 14 shows the production rates of ethylene oxide and carbon dioxide decrease with increasing level of EDC which ethylene oxide decreases to a smaller extent (about 28%) compare to carbon dioxide decrease of 10%. This results in a decreased load on the downstream separation units.

85

95

105

115

125

1 1.4 1.8 2.2 2.6 3EDC Level (ppm)

Wor

k R

ate

(Ton

/day

)

787980818283848586878889

Sele

ctiv

ity (%

)


Figure 13- The influence of EDC level on work-rate and selectivity

102030405060708090

100110

1 1.4 1.8 2.2 2.6 3EDC Level (ppm)

Mol

e Fl

ow (m

ol/s

)

EO Mole FlowCO2 Mole Flow

Figure 14- The influence of EDC level on product mole flow (EO and CO2)

16



Reactant

The influences of reactant concentrations were studied by varying oxygen concentration (5-8 mol%) with constant ethylene (17.5 mol%), and by varying ethylene concentration (15-19 mol%) with constant oxygen concentration (6.16 mol%). As shown in Figure 15, with increasing molar concentration of oxygen in the feed, work-rate increases significantly while selectivity decreases about 4%. Also, Figure 16 shows that with ethylene addition in the feed, work-rate increases significantly and selectivity increases slightly.

80

90

100

110

120

130

140

150

5 5.5 6 6.5 7 7.5 8 Oxygen Mole %

Wor

k R

ate

(Ton

/day

)

78

78.5

79

79.5

80

80.5

81

81.5

82

82.5

83

Sele

ctiv

ity (%

)


Figure 15- The influence of inlet oxygen concentration on work-rate and selectivity

80

90

100

110

120

130

140

150

15 16 17 18 19 Ethylene Mole %

Wor

k R

ate

(Ton

/day

)

79.5

79.9

80.3

80.7

81.1

81.5

Sele

ctiv

ity (%

)Work-rateSelectivity

Figure 16- The influence of inlet ethylene concentration on work-rate and selectivity

17



Optimisation

For the EO reactor, higher temperature leads to excessive carbon dioxide and water formation which results in loss of selectivity. Lower temperatures result in lower conversion and loss of productivity. Thus optimisation is to maximise conversion of ethylene to EO (selectivity) within the flammability limit for safe operation. The objective function is defined to maximise selectivity for desired production rate (work rate). Flammability is a major constraint of the EO reactor. The flammability limit gives the proportion of combustible gases in a mixture, between which limits this mixture is flammable. It is known that in actual practice in order to remain outside the flammability limit of the gas mixture the concentration of oxygen has to be lowered as the concentration of ethylene is raised. The actual safe operating ranges depend, along with the gas composition (reactants and balance gases), also on individual plant conditions such as temperature and pressure. Therefore in each individual plant a flammability equation is used to determine the concentration of oxygen which may be used with any given concentration of ethylene. The flammability equation can be expressed via a flammability curve. The flammability limit is calculated based on the maximum allowable oxygen limit using equation provided by industry patent. Based on our sensitivity analysis, the coolant temperature, reactant concentration and EDC level in the feed, which significantly affect the reactor performance, can be manipulated for maximal profit. EO has a significantly negative effect on selectivity and work-rate. In practice, its concentration is kept as low as possible. The inlet feed temperature has insignificant effect on productivity and is unsuited as a manipulated variable. Steady state optimisation was carried out for 2 cases:

Case 1: Low production rate (110 Ton/day EO)

Case 2: High production rate (130 Ton/day EO)

The constraints and the final values for first and second case studies are shown in Tables 3 and 4, respectively.

Table 3- Constraints for low production rate

Constraint Optimum Value

Lower Bound

Upper Bound

Work-rate (Ton/day) 111 110 111 Oil Outlet Temperature (ºC) 237.6 200 280 Gas Outlet Temperature (ºC) 239.8 200 275 Flammability Limit (%) 0.6 0.3 1

18



Table 4- Constraints for high production rate

Constraint Optimum Value

Lower Bound

Upper Bound

Work-rate (Ton/day) 130 129 131 Oil Outlet Temperature (ºC) 242.0 200 280 Gas Outlet Temperature (ºC) 244.0 200 280 Flammability Limit (%) 0.3 0.3 1

The control variables and their optimum values the first and second case studies are shown in Table 5 and 6, respectively. The EDC level, ethylene and oxygen concentration in the feed and oil inlet temperature are chosen as control variables. At the start of the operation, the results show that in both low and high production cases, ethylene and EDC concentrations act as active bounds. Furthermore, in high production rate (second case), the oxygen concentration acts as lower active bound according to the flammability point.

Table 5- Control variables for low production rate

Control Variable Optimum Value

Lower Bound

Upper Bound

Oil Inlet Temperature (ºC) 233.8 230 260 Ethylene Inlet (Mol. Frac. %) 17.5 15 17.5 Oxygen Inlet (Mol. Frac. %) 6.48 5 7.5 EDC Level (ppm) 1.5 1.2 1.5 Optimum (Selectivity %) 81.7%

Table 6- Control variables for high production rate

Control Variable Optimum Value

Lower Bound

Upper Bound

Oil Inlet Temperature (ºC) 234.1 223 260 Ethylene Inlet (Mol. Frac. %) 19 16 19 Oxygen Inlet (Mol. Frac. %) 7.05 5 7.5 EDC Level (ppm) 1.5 1 1.5 Objective Function Value (Selectivity %) 81.0%

In industry, usually oxygen concentration is kept constant at 7% to avoid the flammability limit. In low production case, the required inlet oxygen is less than 7%. As seen in Figure 15, oxygen concentration has a negative effect on

19



selectivity. Also the results show that the optimum selectivity in the first case (low work-rate) is higher than the second case (high work-rate). To increase the work-rate, the oil inlet temperature should be increased to enhance the reactions, although the selectivity would be decreased. Nevertheless, the result shows that the selectivity could be improved by keeping the control variable close to the optimal point.

Dynamic Optimisation

The dynamic optimisation problems can be represented in the following algebraic form: ))((

],0[,),(, fttvtuttzMax

ff ∈ Eq.20

],0[,0)),(),(),(),(( fttvtutytxtxF ∈=& Eq.21

0)),0(),0(),0(),0(( =vuyxxI & Eq.22

maxminfff ttt ≤≤ Eq.23

],0[,)()()( maxminftttututu ∈≤≤ Eq.24

maxmin vvv ≤≤ Eq.25

maxmin )( eifei wtww ≤≤ Eq.26

tgteefee wtw =)( Eq.27

],0[,)()()( maxminfiiii tttwtwtw ∈≤≤ Eq.28

],0[,)()()( maxminftttwtwtw ∈≤≤ Eq.29

Equation 20 indicates that the optimisation (maximisation) is performed considering the variable )( ftz as performance measure or objective function. Without any loss of generality, the objective function is simply the magnitude of a variable )(tz evaluated at the end of the optimisation horizon ftt = . In addition, Equation 20 denotes the fact that the decision variables of the optimisation problem are the time horizon ft (a scalar) and a subset of variables given by the vectors )(tu and v . The former denotes control variables that are allowed to vary

20



according to the functionality )(tu over the span of the time horizon ],0[ ft . The latter indicates parametric variables that are fixed at a value.

Equation 21 denotes the set of differential-algebraic equations (DAEs) representing the process model, while equation 22 symbolises a set of additional equations (initial conditions) that must be satisfied at the beginning of the optimisation horizon. In these equations x and y denote differential and algebraic variables respectively, and indicates the time derivatives of x. Equations 23, 24 and 25 denote lower and upper bounds on the decision variables, indicated by the superscripts min and max, respectively. There are also other types of constraints and importantly those which bound the decision variables and in some cases the time horizon of the process. Further constraints are in the form of interior point constraints, path constraints and end-point constraint. The end product concentration must be greater than 99%, a purity demand. This constraint can be formulated as an inequality where the constrained condition must be less than a desired value (Equation 26), greater than a desired value or within a desired region or may be an equality constraint where the final value must equal a desired value (Equation 27). Equation 28 denotes interior-point constraint variables, which are used to enforce process variables to lie within the defined upper and lower bounds at any other time except the end of the optimisation horizon. By definition, these are inequality constraints. Although the inclusion of these constraints is not strictly essential, research [Vassiliadis et al., 1994] demonstrated that adopting them may increase the robustness and efficiency of algorithms handling inequality constraints. Eq. 29 symbolises the inequality path constraints mentioned above. Two case studies were considered:

Case 1: Optimal coolant temperature profile during 3 years operating time.

Case 2: The optimal profiles for coolant temperature and oxygen inlet concentration with transition between low production (110 Ton/day) and high production rate (127 Ton/day).

Results from steady state optimisation were used as initial conditions for the dynamic optimisation. Since the catalyst decays continuously, the production process is dynamic and a dynamic optimisation strategy was used. However, it is infeasible to simultaneously change all the variables dynamically. Experience shows that the improvement of the optimisation performance with more than one variable in dynamic optimisation is minor over that when only one variable is varied dynamically while others are fixed to constant sub-optimal values [Bonvin, 1998]. The variable that is most sensitive to dynamic behavior is bed temperature, which is responsible for thermal sintering and catalyst decay.Activity losses are attributed to a decrease of the catalyst surface area, by poisoning or sintering, and

21



a monotonic decline in selectivity is implicated as the temperature is increased to obtain a desired total reaction rate (work-rate).

Case 1

Figure 17 shows the oil inlet temperature optimal profile to obtain the desired work-rate (127 Ton/day) over the 3 year operation which maximises selectivity. As observed, the oil inlet temperature needs to be increased by 15 ºC to compensate for catalyst deactivation. By increasing oil inlet temperature, it is expected that the selectivity will decrease gradually. The loss of selectivity according to the optimal condition is shown Figure 17.

235

238

241

244

247

250

0 6 12 18 24 30 36Time (month)

Tem

p (°

C)

79.4

79.6

79.8

80

80.2

80.4

80.6

80.8

81

81.2

Sele

ctiv

ity (%

)

TOil_InSelectivity

Figure 17- Optimal oil inlet and selectivity losses profile for 3 years operating time

Case 2

Oil inlet temperature and oxygen inlet concentration were used as control variables to shift work-rate from 110 (Ton/day) to 127 (Ton/day) and objective function was to maximise selectivity. The ethylene inlet concentration and the EDC levels are kept constant at 17.5 mol% and 1.5 ppm, respectively. It was assumed that the transition operation takes place in 2 hours. To avoid a runaway condition, linear increase was suggested. Therefore, piecewise-linear control was used for the oxygen inlet concentration and oil inlet temperature.

Figure 18 shows the optimal transition profiles for the oil inlet temperature and the optimal transition profiles for the oxygen concentration. The results show that to increase the work-rate from 110 (Ton/day) to 127 (Ton/day), the oil inlet temperature and the oxygen concentration require to increase by 4 ºC and 0.5

T_OilIn

Selectivity

22



mol%, respectively. Also, Figure 18 shows the change in work-rate during the transition period. By increasing oil inlet temperature, the selectivity decreases by 1.2% due to increasing oil inlet temperature.

6

6.2

6.4

6.6

6.8

7

0 2000 4000 6000 8000Time (s)

Wor

k R

ate

(Ton

/day

)

233

234

235

236

237

238

Tem

p (°

C)

O2 Mole FracToil-In

Figure 18- Optimal transition profiles for oil inlet temperature

and oxygen inlet concentration

Conclusions

A one-dimensional heterogeneous dynamic model of the EO reactor was developed. The partial and total ethylene oxidations as well as the EO oxidation are considered with the inhibiting effect of dichloroethane as an inhibitor. Also the process energy balances were developed and included in one model. The set of nonlinear kinetic expressions are coupled with heat and mass conservation equations and variable physical properties along the reactor. The catalyst deactivation kinetics was modeled as a function of time and oil inlet temperature using the catalyst vendor data.

Plant data from Huntsman EO reactor were used to validate the model. The results showed satisfactory agreement between the model predictions and plant data. No fitting parameters were used for the model. The kinetic parameters were obtained from external sources. For sensitivity analysis, the effects of inlet variables such as coolant and feed temperature, EDC level, and reactant were investigated. Using the validated EO reactor model, the effect of the oil and gas inlet temperature, the EDC level, the ethylene and oxygen inlet concentration on the reactor performance were investigated. The results showed that the EDC level and oil inlet temperature have major effects on both selectivity and work-rate and the gas inlet temperature has negligible effect on the reactor. Ethylene and oxygen concentrations in the feed only affect the work-rate and selectivity, respectively.

O2 Mole Percent %

T_OilIn

O

2 Mol

e Pe

rcen

t (%

)

23



By increasing EO concentration in the recycle gas, the selectivity decreases significantly, while it has negligible effect on the work-rate. Steady state optimisation was carried out for two different scenarios: low product (110 Ton/day EO) and high product (130 Ton EO/day). The EDC level, the oil inlet temperature and the ethylene oxygen inlet concentration were used as control variables. The flammability limit, the fundamental constraint in the EO reactor and other constraints were introduced to the system. The objective function in all scenarios was to maximise the selectivity.

The results from steady state optimisation study showed that the ethylene concentration and the EDC level act as active bounds. In high production rate, the oxygen concentration acts as lower active bound according to the flammability point. The outcomes of steady state optimisation were used as initial conditions for the dynamic optimisation. In dynamic optimisation study, firstly, the oil inlet temperature was used as control variable to compensate for catalyst activity losses during 3 years operating time to obtain desired work-rate (127 T/day) to maximise selectivity. The results compared to the vendor data indicated that the selectivity could be improved by more than 2%. Optimal transition profiles for the oil inlet temperature and the oxygen concentration were obtained to shift the work-rate from 110 to 127 T/day to maximise the selectivity.

Nomenclature

ai catalyst deactivation term A area [m2] AC,T empty tube cross sectional inner area [m2] ass catalyst deactivation in steady-state BASE(i) component that the reaction i is based on CP heat capacity [kJ/kmol °C] Dax axial dispersion coefficient [m2/s] DI tube inside diameter [m] DO tube outside diameter [m] Ds reactor shell diameter [m] Ea Activation Energy [kJ/mol] e catalyst bed voidage f i reaction rate [mol O2/kg cat s] Fi mole flow [kmol/hr] G mass gas flow per cross area [kg/m2] k1,3,7 kinetic coefficient [mol/gcat.atm2.hr] k2,4,8 kinetic coefficient [mol/gcat.atm3.hr] k5,6,9,10,11,12 kinetic coefficient [atm-1]

odk sintering rate constant

24



NT number of tubes Pi partial pressure of component i [in bar unless noted otherwise] S and SV specific surface area [m2/m3] Sel Selectivity (%) Ri overall reaction rate [kmol O2/m3 (cat) s] t time [s] T temperature [°C unless noted otherwise] U heat tranfer (overall unless stated) [kW/m2 °C] WR workrate (ton/day) Vgas velocity [m/s] Z length in tube direction

Greek letters

α heat transfer coefficient [kW/m2 °C] υ stoichiometric coefficient ρ density [kg/m3]

Subscripts

0 inlet condition 1 reaction 1 (C2H4 + 1/2O2 ⇒ C2H4O) 2 reaction 2 (C2H4 + 3O2 ⇒ 2CO2 + 2H2O) 3 reaction 3 (C2H40 + 5/2O2 ⇒ 2CO2 + 2H2O) amb ambient b catalyst bed c cross (e.g. area) cat catalyst Eth ethylene EO ethylene oxide Oxy oxygen EDC ethylene Dichloride gas gas phase H2O water I inside tube in inlet Loss heat loss O outside tube oil cooling oil out outlet p particle S shell

25



T tube or total wall tube wall

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