[Computer Aided Chemical Engineering] Integrated Design and Simulation of Chemical Processes Volume 35 || Case Studies

CHAPTER

CASE STUDIES 2121.1 INTRODUCTIONThe three case studies that follow illustrate key issues developed in this book. The first one deals with

the design and simulation of a process for the thermal hydrodealkylation (THDA) of toluene to ben-

zene. This typical petrochemical process has been used in several chapters of this book, particularly in

developing the hierarchical approach of process synthesis. Although relatively simple, this case study is

very helpful for teaching the key aspects of conceptual process design. In this chapter, we will put to-

gether different aspects developed so far with respect to process synthesis and energy integration, com-

plete the steady-state and dynamic simulation with process control implementation and finally discuss

the quality of design from the perspective of flexibility in operation.

The second case study deals with the product and process design. The object is glycerol tert-butylether (GTBE), a combustion enhancer of motor fuels, which adds more value to a low cost by-product

available today in large amounts from biodiesel industries.

The third case study handles an advanced subject in process intensification, the production of bio-

diesel by the esterification of fatty acids with methanol in a reactive divided-wall column (R-DWC).

The above cases are supported by computer simulation in both steady-state and dynamic modes.

21.2 DESIGN AND SIMULATION OF A HDA PLANTBenzene is a valuable base chemical product. A major source is the dealkylation of aromatic feedstock,

namely of toluene, available in large amounts by reforming processes.

The main reaction is the transformation of toluene to benzene in the presence of hydrogen:

Toluene Tð Þ +Hydrogen Hð Þ!Benzene Bð Þ+Methane Mð Þ (21.1)

The reaction is moderately exothermic. At 25 �C, 1 bar and gas-phase reaction, the thermal effect is

�9.98 kcal/mol, while at 35 bar and 630 �C, this raises to�12.1 kcal/mol. The reaction can take place

by a purely thermal (THDA) mechanism or in the presence of suitable catalysts, such as chromium,

molybdenum and platinum catalysts supported on silica or aluminium oxides. The following equation

describes the kinetics of a thermal process (Douglas, 1988):

r1¼ 6:3�1010exp �52,000=RTð ÞcTc1=2H (21.2)

Computer Aided Chemical Engineering. Volume 35. ISSN 1570-7946. http://dx.doi.org/10.1016/B978-0-444-62700-1.00021-8

© 2014 Elsevier B.V. All rights reserved.789

http://dx.doi.org/10.1016/B978-0-444-62700-1.00021-8

By-products appear too, such as diphenyl, naphthalene and other heavy hydrocarbons. Here, we con-

sider only diphenyl formation by the reversible reaction:

Benzene$Diphenyl + 2Hydrogen (21.3)

In order to cope with the dynamic simulation requirements, we introduce the following overall rate

equation that fits the selectivity data presented in Chapter 7:

r2¼ 3:0�109exp �52,000=RTð Þc2B (21.4)

The reaction rates above are expressed in kmol/m3/s and the concentrations in kmol/m3.

The conditions of the THDA process are temperature 620–700 �C and pressure 30–35 bar. With

catalyst, the temperature may be reduced with 50–60 �C. The technology requires high H2 excess at

the reactor inlet at constant molar ratio hydrogen/toluene of 5/1 to prevent coke formation.

In a first approach, the raw materials are pure toluene and hydrogen with 5% methane.

The purity of the benzene product should be over 99.5%. The study is done for a nominal capacity

of 125 kmol/h toluene, which is equivalent to 11,500 kg/h or to 93,725 tonnes/year for 8150

production hours.

21.2.1 PROCESS SYNTHESISFigure 21.1 presents a simplified flowsheet, as developed in Chapter 7. Fresh rawmaterials, mixed with

recycled toluene and hydrogen, are heated up to the reaction temperature via a feed effluent heat ex-

changer (FEHE) and a furnace. The reaction takes place in an adiabatic plug flow reactor. After heat

exchange with the incoming stream, the outlet mixture is cooled finally at a temperature suitable for

separating gas and liquid streams by a simple flash, usually between 30 and 33 �C. Note that a bypasscold liquid flow is used for quenching the reactor outlet.

The gaseous stream containing hydrogen and methane with traces of benzene and toluene is

recycled to the reaction section. The accumulation of methane in recycle is prevented by using a purge.

This is also the place of eliminating the secondary product, methane, but simultaneously, hydrogen is

eliminated too. The excess of hydrogen in the fresh feed above the stoichiometric requirements and the

loss in purge are linked through the material balance. In addition, the recycle of hydrogen must ensure a

constant ratio hydrogen/hydrocarbon at the reactor inlet. This feature has important consequences on

both design and control of the whole plant.

The liquid stream contains benzene and toluene, as well as heavy impurities, mainly diphenyl, with

traces of dissolved gases. The gaseous components are removed as lights at the top of a stabiliser col-

umn C-1. This is followed by the separation of the benzene product in the distillation column C-2. The

final column C-3 separates on top the unreacted toluene for recycling and, in bottoms, the heavies,

namely, diphenyl.

Note that the separation of the liquid mixture can equally be done in a sequence of two columns,

stabiliser plus benzene top distillation with side stream for toluene recycling and heavies in bottoms.

The existence of two recycles sets an optimum for toluene conversion. Higher conversion decreases

the gas recycle cost but increases the cost of separations due to more by-products and impurities.

A previous optimisation study indicated that the optimal conversion should be around 70%

(Dimian, 2003).

790 CHAPTER 21 CASE STUDIES

21.2.2 DESIGN AND SIMULATIONIn preliminary design, the analysis can focus on the material balance only.

21.2.2.1 Reaction sectionThe reaction rate becomes commercially interesting above 620 �C. Because the adiabatic temperature

rise is about 70 �C, the maximum inlet temperature is considered 640 �C. In Chapter 7, we demonstrate

that using a reasonable large reactor is recommended in order to cope with stability and flexibility in

operation. In this case, a reactor larger than 110 m3 is necessary for toluene feed of 125 kmol/h, con-

version around 70% and gas recycle at 2000 kmol/h. In order to ensure adequate flexibility, we consider

a somewhat larger reactor with the dimensions D¼3 m and L¼20 m and a volume of 141.3 m3.

21.2.2.2 SeparationsThe stabiliser can be simulated as a distillation column with vapour distillate and feed near the top.

Since the distillate amount is very low, setting a small constant reflux flow instead of reflux ratio is

recommended. For the benzene/toluene and toluene/diphenyl separations, the Fenske-Underwood-

Gilliland shortcut method can be used for pre-design. Note that the use of designmode instead of ratingmodelling in preliminary simulation makes the recycles converge easier.

FIGURE 21.1

Simplified flow sheet for the HDA process.

79121.2 DESIGN AND SIMULATION OF A HDA PLANT

21.2.2.3 SimulationThis case study has been simulated with Aspen Plus and Aspen Dynamics version 8.4, but the approach

remains valid for other software. A first issue is the thermodynamic modelling. An equation-of-state

option is appropriate for the whole process, for example, Peng–Robinson or Soave–Redlich–Kwong.

The quench cooling has been simulated by a design specification that keeps the temperature at 620 �Cby manipulating the flow rate of a bypass after the cooler. A pressure drop of 2 bar is assumed for the

whole gas line.

The liquid separation section may be simulated initially as a black box, which allows focusing the

analysis on the reaction section. Rigorous units can be considered after closing the recycles.

An important feature in simulation is that the material balance must be adapted to fulfil the con-

straint of a given ratio hydrogen/toluene at the reactor inlet. This has been done bymeans of a controller

(design specification), where the manipulated variable is the fresh feed of hydrogen.

A debatable point is the specification of purge. Setting purge flow rate or composition is not fea-

sible, because of incompatibility with the overall material balance (see Chapter 3). On the contrary,

setting the split ratio or keeping constant the flow rate of the gas recycle leads always to convergence.

This solution was chosen here for technical reason too, because the compressor is an expensive equip-

ment that should preferably operate at a constant flow rate close to the maximum capacity.

21.2.2.4 ResultsThe objective of the preliminary simulation is getting a good operation point from the material balance

viewpoint. Table 21.1 presents the main streams, while Table 21.3 shows the results for the distillation

columns. The reactor-inlet temperature is at 633 �C, and the gas recycle is at 2000 kmol/h. It can be

seen that due to a large recycle, the reactor-outlet temperature is kept well below 700 �C. The residencetime of 95 s gives a superficial gas velocity of 0.21 m/s. The constraint of a hydrogen/toluene ratio at 5

results in a make-up hydrogen flow of 196.4 kmol/h. The toluene conversion is (173.5�50.5)/

173.5¼0.708. The above hydrogen excess results in a molar fraction of hydrogen in purge of 0.34.

From Table 21.1, it can be seen that the overall yield of benzene product with respect to toluene is

(119.5/123)�100¼95.6%molar but only 81.8%mass. The yield could rise to 96.8%molar if all losses

of benzene in outputs would be recovered. A further increase to about 97.8% can be obtained by re-

ducing the toluene lost in heavies with 1 kmol/h. The rest of yield loss of about 2% is due to the trans-

formation of benzene in diphenyl. Thus, getting a higher overall yield can be achieved by preventing

losses in outputs and working slightly below 70% conversion.

21.2.3 ENERGY INTEGRATIONThe maximum energy saving can be obtained by applying pinch point analysis taking the whole pop-

ulation of streams and heat sources/sinks. This approach followed by Douglas (1988) resulted in the

flow sheet presented in Figure 7.2. In this approach, the reaction and separation systems are tightly

integrated. Thus, the hot reactor-outlet stream is used to drive the reboilers of the distillation columns.

However, this solution raises questions about operability and controllability of the plant. For this rea-

son, we consider another solution, the local energy integration of sections, respectively, reaction and

separations. The excess of heat generated in the reactor can be exported to the utility network and

re-imported for the needs of the distillation section at adequate pressure levels. Moreover, supplemen-

tary low-cost energy can be injected in the reactor heat-integrated loop and recovered to be used as

utility elsewhere.


Table 21.1 Preliminary Material Balance

Feed H Feed T Rec. H Rec. T Rin Rout Product Heavies Purge Gas

Temp. (�C) 25 25 31.5 118.4 633.0 670.2 85.9 149.1 30.0 59.1

Pres. (bar) 35.0 35.0 35.0 35.0 34.4 34.0 1.2 1.3 33.0 11.0

Flow (kmol/h) 196.4 125 2000.0 48.2 2369.6 2369.6 119.5 2.5 188.5 10.9

Toluene 0.0 125 1.5 47.0 173.5 50.5 0.6 1.3 0.1 0.0

Hydrogen 186.5 0.0 680.9 0.0 867.5 745.8 Trace 0.0 64.2 0.7

Benzene 0.0 0.0 10.9 1.2 12.1 132.5 118.9 0.0 1.0 0.5

Methane 9.8 0.0 1306.8 0.0 1316.6 1439.6 Trace 0.0 123.2 9.6

Diphenyl 0.0 0.0 <0.001 <0.001 <0.001 1.3 Trace 1.3 Trace Trace

Firstly, we examine the heat balance around the reactor by disregarding the quench. By simulation,

we find that the enthalpy for heating up the reaction mixture from the mixer (40 �C) to reactor inlet

(633 �C) is Qcold¼23.3 MW. On the hot side, the enthalpy difference from the reactor exit

(670 �C) to flash separation (30 �C) is Qhot¼24.9 MW. The amount Qex¼Qcold�Qhot¼1.6MW rep-

resents the excess of energy, mainly due to the exothermic chemical reaction.

Figure 21.2 describes the heat integration around the adiabatic chemical reactor. The initial mixture

enters a FEHE, where heat exchange with the hot outlet stream from reactor takes place. Further, the

stream goes to a furnace, being heated up to the temperature at which the reaction starts. Note that

installing a heat exchanger for setting the temperature at the inlet of the adiabatic reactor is compulsory

because of dynamic stability reasons, as it can be demonstrated theoretically. From energy balance

viewpoint, the duties of the FEHE and furnace are linked by the relation

Q FEHEð Þ+Q furnaceð Þ¼Qcold (21.5)

The repartition of duties between the two items can be set by technological reasons. Thus, one can

operate with a large FEHE and a smaller furnace, or the opposite (Luyben et al., 1999; Bildea and

Dimian, 1998). In the first case, energy saving is favoured, and in the second one, the process dynamics.

The furnace can be also used to put value on available low-value fuel.

On the hot side, we can install a heat exchanger for recovering high-temperature energy by steam

generation (SG), the FEHE and a cooler for completing the heat balance. The three items are linked by

the relation

Q SGð Þ +Q FEHEð Þ+Q coolerð Þ¼Qhot (21.6)

It can be seen that the sum of duties of steam generator and cooler is determined by the furnace:

Q SGð Þ+Q coolerð Þ¼Q furnaceð Þ+Qex (21.7)

In addition, the heat exchangers must respect the condition of a minimum temperature difference

between hot and cold streams.

FIGURE 21.2

Heat integration around the adiabatic HDA reactor.


The above relations make possible a number of alternatives. Without SG, the excess of energy in

furnace generated by reaction is lost in the cooler. Note that the direct analysis by simulation of the

above heat-integrated loop is possible in Aspen Plus by using the two-stream block HeatX. The

short-cut option can be used in design or rating mode. Easy convergence is obtained when specifying

the duty.

The above scheme was studied theoretically by Bildea and Dimian, (1998) from the viewpoint of

integrating design and control. They considered as disturbances the reactor input flow, SG duty and

overall heat transfer coefficient of FEHE because of fouling. It was found that the best alternative

was with moderate furnace, small steam generator and high-efficiency FEHE.

Table 21.2 presents the characteristics of heat exchangers implied in simulation. Note that relatively

high overall heat transfer coefficients can be assigned because of the high conductivity of the gas mix-

ture (methane and hydrogen) and higher pressure.

Next, we examine the heat integration of the distillation section. Table 21.3 presents some charac-

teristics of the three columns. It can be seen that thermal coupling of (C-2) and (C-3) would be possible

by raising the pressure in the last. A saving of about 30% in energy could be achieved, but the disad-

vantages are higher reboiler temperature and change in utilities’ profile. A much better solution is

assembling them in a single side-stream column, as mentioned earlier.

Table 21.2 Characteristics of Heat Exchangers Around the Heat-Integrated HDA Reactor

Heat Exchanger Duty (MW) Temperature (�C) LMTD (�C) U (W/m2K) Area

a(m

2)

FEHE 16.5 81 523

40!474

45 150 2500

Furnace 5.0 522!633 250 50 500

Steam generator

Steam 40 bar

6.5 671!523

250!251

110 50 1000

Cooler 2.0 81!30

40 20

22 200 500

aRounded to modules.

Table 21.3 Simulation Results for the Separation Section

C-1 C-2 C-3

Nstages 7 27 7

R/D R¼500 kg/h 1.3 0.6

Pc (bar) 11 1.2 1.1

Tc (�C) 50 85.9 113.5

Tr (�C) 194 123.9 149

Qc (kW) �76 �2150 �710Qr (kW) 1460 2150 710


21.2.4 PLANTWIDE CONTROLFigure 21.3 illustrates the flowsheet of the HDA plant with control implementation. The assigned

plantwide control objectives and suitable control loops are as follows:

1. Production: in a first approach, toluene feed is set on flow control (self-regulation). This is

the simplest solution, which is expected to work because the plant was designed for high

toluene conversion, XTol¼0.7, which is achieved by means of a large reactor. Alternatively, the

toluene may be fed as make-up in a buffer vessel (e.g. the reflux drum of the recycle column), from

where a constant flow rate is sent to the reactor (Bildea et al., 2004). This solution may

accommodate large-throughput variations, but the production is set indirectly by modifying the set

point of the recycle.

2. Hydrogen make-up: hydrogen/toluene ratio kept on setpoint with the fresh hydrogen feed.

3. Reaction system: reactor-inlet temperature with the furnace duty.

4. Gas recycle: keep constant the recycle flow rate close to the maximum compressor capacity.

5. Gas loop pressure: keep constant the gas pressure after flash by manipulating the vapour flow.

Reactor

Flash

Purge

FEHE Furnace

Steam generator

Quench

Compressor

Sta

bilis

er

(FT)

(FH)

(1)

(22)

(D)

(P)

(RH)

Cooler

TC

LC

PC

LC

TC

LC FC

LC

TC

LC FC

LC

(B)

(M)

TCLC

PC

TC

TC

FC

Pro

duct

col

umn

Rec

ycle

col

umn

H2/T

FC

Production(2)

(3) (4)

(5)

(6)

(7)(8)

(20)

(10)

(23)

(24)

(26)

(27)

(RT)

x

(11)

PC

PC

FIGURE 21.3

Process control implementation of the HDA plant.


The control of units may follow the standard control structures applicable for stand-alone units.

The HDA plant has been decomposed in several parts for an easier control implementation in Aspen

Dynamics™ as follows:

1. Heat-integrated reaction loop

2. Separation section

3. Make-up of reactants

21.2.4.1 Control of the heat-integrated reaction loopThe following controllers can be considered:

• TC1: reactor-inlet temperature with furnace duty

• TC2: reactor-outlet temperature with quench flow

21.2.4.2 Control of the separation sectionThe control of the separation section is developed unit by unit by applying standard control schemes.

Stabiliser. The control objective is the stripping of gases from liquid but with minimum loss of

benzene. A suitable control structure is as follows:

• Reboiler level with bottom product

• Reflux drum level with reflux flow rate

• Column pressure with vapour distillate

• Composition (inferential control) with reboiler duty

Benzene column. The purity of distillate has to be over 99.5%. One-point control of purity gives good

results if the reflux flow rate is high enough. Setting the reflux ratio allows good behaviour at large

variations in throughput. The control configuration is as follows:

• Level in reflux drum with distillate

• Level in reboiler with bottoms

• Condenser pressure with cooling water

• Constant reflux ratio

• One-point quality control: inferential concentration measurement (sensitive temperature in the

rectifying section) with reboiler duty

Recycle column. This column operates more as stripping. One-point quality control is sufficient:

• Level in reflux drum with distillate

• Level in reboiler with bottom product

• Condenser pressure with cooling water

• One-point quality control: inferential concentration measurement (sensitive temperature in the

rectifying section) with reboiler duty

21.2.4.3 ResultsIn this exercise, the toluene feed is set on flow control, giving a direct measure of the achievable pro-

duction. Hydrogen is on make-up control to keep constant hydrogen/toluene ratio at the reactor inlet.

The purge flow is let free. The proposed control structure is of self-regulation type.


Figure 21.4 presents the flexibility of the plant, in terms of benzene production rate and product

purity, for a nominal toluene feed rate of 125 kmol/h with increase/decrease of 25 kmol/h (20%),

keeping the same parameters for controllers. The reactor-inlet temperature was increased from 633 to

640 �C. It may be seen that the plant reacts smoothly at these large variations. The benzene production

increases/decreases proportionally. At higher production, the product purity increases slightly, while by

decreasing the throughput, the opposite happens. When the reactor-inlet temperature was 633 �C, themaximum increase in the production rate was only 8% but still important, demonstrating that the reactor

volume alone ensures already a good flexibility in operation by self-regulation. However, acting on

reaction temperature allows getting a much stronger effect, as reported also by Luyben et al. (1999).

21.2.5 SUGGESTIONS FOR FOLLOW-UP PROJECTS1. Examine solutions ensuring better efficiency of raw materials, such as the use of membranes for

recovering methane as a valuable by-product.

2. Examine the process for simultaneous production of benzene and xylenes by toluene

disproportionation.

3. Examine other dealkylation processes for benzene production, namely, by the catalytic conversion

of aromatic streams.

4. Study the production of BTX from low-value refinery streams with recent technologies.

21.3 DESIGN AND ROBUST OPTIMISATION OF A PROCESS FOR GTBEMANUFACTURING21.3.1 INTRODUCTIONIn Chapter 12, GTBEs were identified as valuable fuel additives. Based on literature data, the reaction

of glycerol with isobutene catalysed by p-toluene sulphonic acid appeared as a promising process. The

reaction leads to a mixture of mono-, di- and tri-tert-butyl glycerol ethers (ME,DE and TE), fromwhich

ME is recycled, DE and TE being the process products:

0.99

0.992

0.994

0.996

0.998

1

100

110

120

130

140

150

160

0 1 2 3 4 5

Pur

ity

Flo

w r

ate

(km

ol/h

)

Time (h)

Flow rate

Purity

0.99

0.992

0.994

0.996

0.998

1

80

90

100

110

120

130

0 1 2 3 4 5

Pur

ity

Flo

w r

ate

(km

ol/h

)

Time (h)

Flow rate

Purity

FIGURE 21.4

Dynamic response of the product flow rate and purity to the increase and decrease of fresh toluene feed rate.


G+ i-B$MEME+ i-B$DEDE+ i-B$ TE

(21.8)

Several alternative processes for the production of GTBE were presented in Figure 12.14. The reaction

takes place at moderate pressure, using p-toluene sulphonic acid as homogeneous catalyst or Amberlyst

15 as heterogeneous catalyst. Isobutene is separated from the reaction mixture as vapour in a flash or a

striping column. Unreacted glycerol and ME are separated from DE and TE mixture by extraction with

glycerol and recycled. Final purification of high ethers is achieved by vacuum distillation.

The important drawback of the processes described in Chapter 12 is the use of high-purity iso-

butene as a raw material, which is expensive and therefore seldom available as feedstock for glyc-

erol etherification process. Therefore, the design of the GTBE plant must take into account the

variability of this raw material. A key unit of the etherification plant is the extraction column, where

glycerol is used for ME separation by extraction. However, the binary interaction parameters of the

liquid activity model used to calculate the liquid–liquid equilibria are usually affected by experimen-

tal errors. Another uncertainty is related to the kinetic data used for designing the reactor, which

may be affected by modelling assumptions, experimental errors and catalyst deactivation. Last

but not least, the plant must process variable amounts of glycerol, as delivered by the biodiesel pro-

duction plant.

All GTBE production processes involve a reaction unit followed by a separation section and

two recycle streams containing isobutene and glycerol–ME mixture, respectively. Such reaction–

separation–recycle systems exhibit a non-linear behaviour (Bildea et al., 2000). In particular, small

changes of the feed rate, reaction kinetics or separation performance can lead to very large increase

in the recycle flow rate (snowball effect, Luyben, 1994). Therefore, the operating conditions must

be chosen and the plantwide control must be designed such that robustness with respect to disturbances

or uncertain design parameters is ensured.

This chapter will present the design and optimisation of the glycerol etherification plant taking into

account robustness with respect to the following disturbances and uncertain design parameters

(Table 21.4):

– Glycerol feed rate. The plant must be able to process variable amounts of glycerol, as delivered by an

upstream biodiesel production plant.

Table 21.4 Uncertain Parameters and Their Range of Variation

Parameter Nominal Value, p(0) Maximum Change, Dp

Glycerol feed rate, FG,0 (kmol/h) 2.25 0.5

Butane fraction in feed, yB,0 0.1 0.1

Catalyst activity, ’ 1 0.5

Reaction temperature, T (K) 363 10

Fraction of DE recovered in the extract stream, a 0.15 0.05

Fraction of TE recovered in the extract stream, b 0.15 0.05

79921.3 DESIGN AND ROBUST OPTIMISATION OF A PROCESS

– Raw material purity. High-purity isobutene is expensive and therefore seldom available as feedstock

for glycerol etherification process. The design of the GTBE plant should take into account the

presence of inert species (modelled here as isobutane) and therefore the uncertainty regarding the

purity of the raw material.

– Kinetic data used for designing the reactor, which may be affected by modelling assumptions,

experimental errors and catalyst deactivation.

– Reaction temperature.

– Errors affecting the binary interaction parameters, which lead to uncertainty of the calculated phase

equilibria (in particular, the fraction of DE and TE recovered in the extract stream of the extraction

column).

21.3.2 PLANT DESIGNA nominal capacity of 2.25 kmol/h processed glycerol, assumed to be the by-product of a

15,000 tonnes/year biodiesel plant, is considered. The raw materials are pure glycerol and isobutene

with significant amounts of an inert of similar volatility (10% isobutane, the raw material for isobutene

production).

The process flowsheet is presented in Figure 21.5 combines ideas taken from the previous works.

The reaction takes place in a CSTR. The reaction temperature and pressure are set to 363 K and

Reactor

EX

i-Butene

Glycerol

i-Butene / inert recycle

Glycerol, ethers and catalyst

0

1b

2

3c

Di-etherTri-ether

MIX-IB

C1 C2

0

4a

4b

Purge

1a

3a 3b

3d

FC

x

FC

r1

LC

2a

YCyB,4

Catalystmake-up

FIGURE 21.5

Flowsheet of the glycerol etherification plant (Vlad et al., 2013).


1.4 MPa, respectively, when the reaction mixture is liquid. The immiscibility of high ethers in glycerol

is exploited for separating the reactants from products, by using the fresh glycerol as an extraction sol-

vent (column EX). The raffinate stream ‘2a’ contains isobutene, inert,DE, TE and small quantities ofGandME and is sent to separation. Column C1 separates the isobutene and the isobutane. The column has

a total condenser and is operated at 0.5 MPa in order to keep the isobutene as liquid. This avoids the

disadvantage of using a compressor for recycling purpose. The entire amount of isobutene and isobu-

tane present in column feed is recovered in stream ‘3c’. A purge (stream ‘4b’) is necessary to remove

the inert from the plant. The stream ‘3d’ is mixed with fresh isobutene and fed to the reactor. Column

C2 separatesDE and TE from glycerol andME. The column has a total condenser and is operated under

vacuum (0.02 MPa) to avoid high temperature in the bottom of the column. The distillate ‘4a’ is the

plant product. The bottom stream ‘3b’, containing mainly G and ME, is mixed with the glycerol-rich

phase from the extraction column and fed to the reactor.

The plant was simulated using Aspen Plus. The properties of glycerol, isobutene and butane are

available from Aspen Plus database. The ethers’ properties were estimated by group contribution

methods. The behaviour of the liquid phase was described by the NRTL activity model. The interaction

parameters of pairs involving ethers and glycerol or isobutene were taken from Behr and Obendorf

(2003). The other interaction parameters were estimated using UNIFAC–Dortmund modified method.

The kinetic expressions used to calculate the reaction rates are presented in Table 21.5.

The economics of the process was investigated by generating several design alternatives, a selection

being presented in Table 21.6. The reactor volume V and the ratio between the reactor-inlet flow rates

r1¼F1b/F1a were considered as design decisions. The glycerol feed rate, which determines the plant

throughput, was fixed to 2.25 kmol/h. The purge composition was set to yB,4¼0.5. After setting these

values, the plant was designed using common heuristic rules, such as 99.5% recoveries in separation

units, R¼1.2 Rmin and N¼2 Nmin.

The capital cost includes the costs of reactor, extraction and distillation columns and heat ex-

changers, calculated by well-known relationships (Dimian, 2003). An M&S index of 1476.7 (year

2010) and a payback period of 3 years were considered. The utilities cost includes costs of cooling

water and steam. It should be remarked that the etherification plant can be integrated with a plant per-

forming the dehydrogenation of isobutane to isobutene. Because a typical dehydrogenation plant has

Table 21.5 Kinetic Parameters for Etherification of Glycerol with Isobutene Catalysed

by p-Toluene sulphonic Acid (Behr and Obendorf, 2003)

Reaction Pre-exponential Factors Activation Energies (kJ/kmol)

G + i-B��! ��k1

k�1ME k0,1¼3.04�108 L/min/mol 74.04

r1¼k1 �CG �Ci-B�k�1 �CME k0,�1¼3.69�1013 min�1 111.78

ME + i-B��! ��k2

k�2DE k0,2¼1.70�1011 L/min/mol 92.80

r2¼k2 �CME �Ci-B�k�2 �CDE k0,�1¼8.54�1014 min�1 118.06

DE+ i-B��! ��k3

k�3TE k0,3¼2.26�1010 L/min/mol 92.56

r3¼k3 �CDE �Ci-B�k�3 �CTE k0,�3¼6.35�1015 min�1 125.13


Table 21.6 Economic Evaluation of Several Design Alternatives

Design (1)

(2) (Base

Case) (3) (4) (5) (6) (7)

Design decisions

Reactor volume (m3) 2 4 4 10 10 15 15

r1¼F1b/F1a 1.01 0.6 2.12 0.76 1.94 0.59 1.90

Design results

Feed streams

Glycerol, FG,0 (kmol/h) 2.25 2.25 2.25 2.25 2.25 2.25 2.25

i-Butene (90% purity), FIB,0

(kmol/h)

5.91 6.09 6.12 6 6.2 5.98 6.22

Product (D+T)

Flow rate (kmol/h) 2.25 2.25 2.25 2.25 2.25 2.25 2.25

xDE 0.89 0.831 0.815 0.865 0.785 0.873 0.781

xTE 0.10 0.161 0.176 0.13 0.207 0.122 0.212

xME (103) 1 1 1 1 1 1 1

xG (103) 1.71 1.49 1.96 1.14 2.8 1.3 2.8

Purge

Flow rate (kmol/h) 1.17 1.18 1.22 1.2 1.2 1.2 1.24

Reactor

Installed cost (103 US$) 99.43 153.1 153.1 270.7 270.7 348.4 348.4

Extraction column (two trays)

Tray volume (m3) 0.473 0.44 0.20 0.37 0.32 0.42 0.3


C1

Number of trays 10 10 9 10 10 10 10

Reflux ratio 0.17 0.13 0.09 0.28 0.14 0.2 0.15

Diameter (m) 0.17 0.11 0.14 0.16 0.11 0.13 0.10

Reboiler duty (kW) 105.6 96.44 112.46 98.8 104.76 97.88 104.05

Condenser duty (kW) 34.5 17.23 39.43 15.26 24.09 12.97 21.84


C2

Number of trays 16 16 13 16 16 17 17

Reflux ratio 4.1 3.9 4.8 3.1 3.2 4.04 3.2

Diameter (m) 0.44 0.47 0.55 0.45 0.46 0.49 0.46

Reboiler duty (kW) 119.75 147.17 221.6 124.23 127.3 167.37 125.8

Condenser duty (kW) 190.73 214.13 298.4 192.9 199.8 236.18 198.15


Utilities’ cost (103 US$/

year)

70.43 75.41 104.64 68.82 72.04 81.93 71.25

TAC (103 US$/year) 238.07 259.36 304.39 284.95 287.45 336.63 311.89


large capacity (e.g. 300,000 tonnes/year in CATOFIN process), the cost of processing the purge stream

does not have an important contribution to the economy of the overall process (etherification+dehy-

drogenation). For this reason, the cost of the fresh C4 stream was not included in the total annual cost

(TAC), and the influence of the purge composition (which was set to 0.5) was neglected.

The smallest TAC (238.07�103 US$/year) was obtained for a base case employing a 2 m3 reactor,

two-stage extraction column and the ratio between reactor-inlet streams (r1¼F1b/F1a, related to

reactants ratio) set to r1¼1.01, the cost of utilities and vacuum distillation column C2 having the main

contributions. Decreasing the concentration of inert in the purge leads to a slightly smaller TAC.

However, this is achieved at the expense of a larger purge. The TAC increases for larger reactors,

because the more costly reactor is not compensated by a cheaper separation. However, the following

section will show that the design alternatives with small reactors have high sensitivity of the recycle

streams with respect to disturbances and uncertain parameters. This issue should be included in the

optimisation problem.

Although Aspen Plus offers facilities for solving constrained-optimisation problems, the construc-

tive non-linear dynamics technique that will be used as solution method is computationally intensive

and requires Jacobian matrices that are difficult to obtain from the Aspen Plus simulation. Therefore,

the following steps were taken:

– Derive a simple cost model to be used as objective function.

– Derive a simple reactor–separation–recycle model that can be easily solved in Matlab. This model

will be used to evaluate the recycle sensitivity with respect to operating conditions and design

parameter uncertainty.

– Formulate the constrained-optimisation problem.

– Use the constructive non-linear dynamics technique to find the optimal values of the design

decisions (solution of the optimisation problem).

– Develop rigorous steady-state simulation (Aspen Plus) for economic evaluation.

– Use rigorous dynamic simulation (Aspen Dynamics) to prove the robustness in the worst-case

scenario.

21.3.3 ROBUST OPTIMISATION21.3.3.1 The objective functionAs first step in solving the optimisation problem, the dependence of the TAC versus the design param-

eters V and r1 was correlated by the following objective function:

TAC 105US$� �¼ 2:42 + 1:79�10�3�V2 + 0:28�r21�0:04�V�r1 + 0:067�V�0:306�r1 (21.9)

The parity plot is presented in Figure 21.6. Each point represents one design alternative obtained for

certain values of the design parameters (V, r1). The TAC model agrees very well with the values

obtained by detailed calculations.

The results presented in Figure 21.6, together with the TAC cost model, indicate that from an eco-

nomic point of view, plants built around small reactors and low isobutene/glycerol ratio are better.

However, as we will show in this section, they have limited flexibility due to high sensitivity of the

internal flow rates with respect to production rate or uncertain parameters.


21.3.3.2 Reactor–separation–recycle modelThe notation used in this section will follow Figure 21.5. Fk, j will denote the molar flow rate of spe-

cies k in stream j, while 0, 1, 2, 3 and 4 will refer to fresh feed, reactor-inlet, reactor-outlet, and re-

cycle and product streams, respectively. For example, FG,1 stands for the flow rate of glycerol at the

reactor inlet.

The model of the plant considers a CSTR operated at a fixed temperature (90 ºC). The reactions

described earlier were considered, while the formation of isobutene oligomers and glycerol decompo-

sition were neglected because these reactions were not observed in homogeneous catalysis (Behr and

Obendorf, 2003). It is assumed that isobutene, glycerol and ME are recovered from the reactor-outlet

stream and recycled. Parameters a and b in the next equations account for the fractions of DE and

TE from the reactor outlet, which are found in the extract stream ‘3a’ and recycled. V, n and g are

the reaction volume, the matrix of stoichiometric coefficients and the purge fraction, respectively.

The factor ’ multiplying the reaction rates was introduced to account for uncertainty in the kinetic

parameters that can arise due to experimental errors or due to catalyst deactivation:

Fk,2� Fk,1 +V�Xi¼1,3

uk, i�’�ri !

¼ 0, k¼G, i-B,B,ME,DE,TE (21.10)

FG,1� FG,0 +FG,2ð Þ¼ 0, FG,4¼ 0 (21.11)

Fi-B,1� Fi-B,0 + 1� gð Þ�Fi-B,2ð Þ¼ 0, Fi-B,4� g�Fi-B,2¼ 0 (21.12)

2

2.5

3

3.5

2 2.5 3 3.5

TAC (105 $/year)

TA

C_m

od

el

(10

5 $

/ye

ar)

(2, 0.66)

(2, 1.01)

(3.71, 1.41)(4, 1.60)

(10, 1.35)

(4, 0.88)

(4, 0.61)

(6, 0.62)

(10, 0.76)

(10, 1.94)(4, 2.12)

(15, 1.90)(15, 1.20)

(15, 0.59)

(16.1, 1.49)

FIGURE 21.6

Parity plot of the TAC model (Vlad et al., 2013).


FB,1� FB,0 + 1� gð Þ�FB,2ð Þ¼ 0, FB,4� g�FB,2¼ 0 (21.13)

FME,1�FME,2¼ 0, FME,4¼ 0 (21.14)

FDE,1�a�FDE,2¼ 0, FDE,4� 1�að Þ�FDE,2¼ 0 (21.15)

FTE,1�b�FDE,2¼ 0, FTE,4� 1�bð Þ�FTE,2¼ 0 (21.16)

Fi-B,0

FB,0¼ 1�yB,0� �

yB,0(21.17)

FB,4�yB,4 Fi-B,4 +FB,4ð Þ¼ 0 (21.18)

Fi-B,1 +FB,1ð Þ� r1� FG,1 +FME,1 +FDE,1 +FTE,1ð Þ¼ 0 (21.19)

The concentrations necessary to calculate the reaction rates are obtained assuming ideal mixing:

ck,2¼ Fk,2XkVm,k�Fk,2

, k¼G, i-B,ME,DE,TE,B (21.20)

The values used for the molar volume Vm of glycerol, isobutene, ME, DE, TE and butane are (in m3/

kmol) 0.072, 0.094, 0.155, 0.143, 0.18 and 0.094, respectively.

The model of the glycerol etherification plant consists of 21 equations. After specifying the reactor

volume V, the feed composition yB,0 and the separation performance a and b, there are 24 model vari-

ables: 21 species flow rates, the purge composition yB,4, the purge fraction g and the ratio between

reactor-inlet flow rates r1. Therefore, three additional specifications are needed. The control structurepresented in Figure 21.5 fixes the glycerol feed rate FG,0, the purge composition yB,4 and the ratio r1.

21.3.3.3 Problem formulationReaction–separation–recycle systems can show high sensitivity of recycle flow rate with respect to

changes of the feed rate, reaction kinetics or separation performance (snowball effect; Luyben, 1994).

Figure 21.7 presents the dependence of recycle flow rates F3c and F1a (Figure 21.5) versus the glycerol

feed rate FG,0, obtained from the simplified model, for different values of the kinetic uncertainty ’ and

fixed values of the reactor volume, flow rates ratio and purge composition (V¼4 m3, r1¼1 and

yB,4¼0.5).

At the nominal operating point (FG,0¼2.25 kmol/h, ’¼1), the recycle flow rates are

F3c¼4.0 kmol/h and F1a¼6.5 kmol/h. These values were used to size the distillation column C-1

(reboiler and condenser duties, diameter, trays type, etc.) and the extraction column EX (stage

hold-up). The equipment has a limited flexibility, being able to withstand flow rate variations within

certain limits. For example, we assume that the capacities of the distillation column C-1 and extraction

column EX are limited to F3cmax¼10 kmol/h distillate and F1a

max¼10 kmol/h extract, respectively. These

feasibility limits should not be exceeded during operation, even if there are disturbances or the design

parameters are uncertain:


F3c�Fmax3c (21.21)

F1a�Fmax1a (21.22)

Results from Figure 21.7 show that the distillation column C1 easily withstands a 50% kinetic uncer-

tainty or a 0.5 kmol/h increase of the glycerol feed rate, when F3c<F3cmax. However, the combination of

these disturbances cannot be tolerated. The situation is worse when the glycerol–ether recycle F1a is

considered (Figure 21.7, right), as the operational limit is reached when only one disturbance (’¼0.5)

or a combination of smaller disturbances (’¼0.75, FG,0¼2.75 kmol/h) is introduced.

In the following, we will address the problem of finding the optimal design (minimum TAC) for

which the feasibility conditions are fulfilled even when the plant is disturbed or the design parameters

are uncertain.

The following short notation is introduced. The next equations represent the process model, and the

feasibility constraints, where x, p and q are the unknowns, the uncertain and the design parameters,

respectively. The uncertain parameters p are presented in Table 21.4. The reactor volume and the ratio

of reactor-inlet flows are chosen as decision variables q¼ (V, r1). The uncertain parameters p are de-

fined in terms of their nominal value p(0), the maximum expected change Dp and the scaled change d.The optimisation problem aims to find the optimal design defined by the objective function chosen as

the TAC relationship, achieving feasibility that is robust with respect to disturbances and uncertain

parameters:

f x, p, qð Þ¼ 0 (21.23)

~f x, p, qð Þ� 0 (21.24)

p¼ p 0ð Þ +Dp�d, d2 �1,1ð Þ (21.25)

minq

h x, p, qð Þ (21.26)

0

5

10

15

20

0.75

1.0

V = 4 m3

r1 = 1yB,4 = 0.5

0

5

10

15

20

1.75 2 2.25 2.5 2.75 3 1.75 2 2.25 2.5 2.75 3

FG,0 (kmol/h)FG,0 (kmol/h)

F3

c (

km

ol/

h)

F1

a (

km

ol/

h)

j = 0.5j = 0.5

0.75

1.0

V = 4 m3

r1 = 1yB,4 = 0.5

FIGURE 21.7

Dependence of recycle flow rates versus the glycerol feed rate.


21.3.3.4 Solution methodThe constructive non-linear dynamics method (Monnigmann and Marquardt, 2003; Marquardt and

Monnigmann, 2005) allows finding the economical optimum while ensuring that the feasibility bound-

ary is not crossed when design parameters change or are uncertain. By solving the extended system

together with the additional relationships, the method calculates the shortest distance r from the nom-

inal operating conditions d(0)¼0 to the feasibility constraint and the direction u along which this dis-

tance is measured:

f Tx~fT

x

h i�v¼ 0 (21.27)

u� f Td~fT

d

h i�v¼ 0 (21.28)

vTv�1¼ 0 (21.29)

d 0ð Þ � d +r� u

uj jj j� �

¼ 0 (21.30)

In these equations, f x, ~f x are Jacobian matrices with respect to unknowns x, f d, ~f d are Jacobian

matrices with respect to uncertain parameters d and v is an auxiliary vector having the same dimension

as x.The uncertainty is overestimated by a ball of radius

ffiffiffiffiffinpp

, where np is the number of uncertain pa-

rameters. Regardless of the actual values of the uncertain parameters in the robustness box, the fulfil-

ment of the feasibility constraint is guaranteed by enforcing the distance r to be larger than the radius ofthe ball:

r� ffiffiffiffiffinpp

(21.31)

The above equations define the mathematical formulation of the robust optimisation problem.

21.3.4 RESULTS21.3.4.1 Robust, optimal designTaking into account the uncertainties presented in Table 21.4, the result of the robust optimisation

is V¼16.1 m3, r1¼1.49. Compared to the base case, the reactor is four times larger and requires a higher

excess of co-reactant. The final design has a TAC of 3.21 �105 US$/year, which is almost 50% more ex-

pensive than the cheapest alternative from Table 21.6. This is the price that has to be paid to achieve

robustness.

At the optimum, both constraints were active. Using these specifications, the full plant was designed

and simulated in Aspen Plus. Details are given in Table 21.7, while Table 21.8 presents the stream

report. Relaxing the constraint on F1a to F1amax¼12.5 kmol/h, it becomes inactive, the optimal design

being V¼15.0 m3, r1¼1.2, for a TAC of 3.14 �105 US$/year.We emphasise the effectiveness of using a simple reactor–separation–recycle model of the plant

during the robust optimisation procedure. Application of the method to a rigorous model of a whole


chemical plant (such as glycerol etherification) is very computationally demanding, due to the large

number of equations involved. However, although the separation units are the origin of most equations

(mass and energy balance and physical properties), their input–output behaviour is much simpler be-

cause they comply with the given performance specifications. In this context, using the simple reactor–

separation–recycle model and replacing the cost calculation by a cost model are very effective, allow-

ing solution of the optimisation problem in a short time.

21.3.4.2 Dynamics and controlFor a rigorous check of the optimal process robustness, a dynamic model was developed using Aspen

Dynamics. Figure 21.8 shows the full flowsheet, together with the control structure (Vlad

et al., 2013).

Figure 21.9 presents results of dynamic simulation (Vlad et al., 2013). The simulation starts from

the nominal steady state, which is maintained for the first 2 h. Then, large disturbances were intro-

duced. At time t¼2 h, the glycerol feed rate was increased from 2.25 to 2.75 kmol/h. The reactor-inlet

Table 21.7 Economic Evaluation of the Optimal, Robust Design

Design Optimal, Robust Design

Reactor volume (m3) 16.1

r1¼F1b/F1a 1.49

Reactor

Installed cost (103 US$) 364.13

Extraction column (two trays)

Tray volume (m3) 0.3


C1

Number of trays 10

Reflux ratio 0.18

Diameter (m) 0.12

Reboiler duty (kW) 100.95

Condenser duty (kW) 17.58


C2

Number of trays 17

Reflux ratio 3.4

Diameter (m) 0.47

Reboiler duty (kW) 136.3

Condenser duty (kW) 207.02


Utilities’ cost (103 US$/year) 73.95

TAC (103 US$/year) 321.01


Table 21.8 Stream Report

Stream Name G0 IB0 1a 1b 2 2a 3a 3b 3c 4a 4b

Flow (kmol/h) 2.25 6.15 5.22 7.78 8.08 5.52 4.81 0.40 2.85 2.25 1.23

Flow (kg/h) 207.5 346.8 598.8 439.6 1038.4 697.4 548.5 50.3 163.0 481.7 70.3

Temp. (K) 363 293 377.5 297.2 363 346.1 375.8 479.9 312.6 431 312.6

Pressure (MPa) 1.4 1.4 1.4 1.4 1.4 0.55 1.4 0.02 0.5 0.02 0.5

Flow (kmol/h)

G 2.25 0 2.99 Trace 0.74 0.19 2.80 0.19 Trace 0.005 Trace

IB 0 5.5 0.12 6.35 1.55 1.43 0.12 Trace 1.42 0.004 0.61

B 0 0.61 0.12 1.43 1.55 1.43 0.12 Trace 1.42 Trace 0.61

ME 0 0 1.74 Trace 1.74 0.21 1.53 0.20 Trace 0.002 Trace

DE 0 0 0.19 Trace 2.02 1.83 0.18 0.009 Trace 1.82 Trace

TE 0 0 0.04 0 0.46 0.42 0.04 Trace Trace 0.42 Trace

LC

i-Butene

FC

LCLC

Glycerol

IB0

1b

Glycerol and ethers recycle

FC

x r1

FG,0

TC

i-Butene recycle

CC

FC

PC

TC

LC

TC

PC

LC

4a

LC

TC

4b3d

3c

G0

3a

1a

Purge

GTBE

EX C1C2

3b

2a

2

FIGURE 21.8

Plant-wide control structure.

flow rate F1a increases, more isobutene is withdrawn from the vessel V to keep reactants ratio at the

specified value r1¼1.49, and more fresh isobutene is fed to the process (FIB,0). Because the dynamics

of the plant throughput is slow, the theoretical value F4a¼2.75 kmol/h ethers is reached after 10 h of

operation. A new steady state is established. At time t¼20 h, the reaction temperature is decreased

from 90 to 80 ºC. After a short transient period, a new steady state is reached. A rather big disturbance

is introduced at time t¼40 h, when all the pre-exponential factors in kinetic expression are reduced to

half, to simulate the reduction of the catalyst activity. The flow rates F3c (C1 distillate) and F1a (fresh

glycerol+ recycled glycerol and ethers) settle to higher values. The concentrations of glycerol andMEin the product stream 4a increase, but the control system is able to bring them to the specified values.

Finally, at t¼60 h, the concentration of inert in feed is increased from yB,0¼0.1 to yB,0¼0.2. This is

compensated by larger feed and purge (FIB,0 and F4b, respectively) with small influence on other pro-

cess variables. We note that the fraction of DE and TE in the extract stream drop from the initial values

of �0.15 to around 0.1, which has a favourable effect on robustness. Therefore, during the entire sim-

ulation, the recycle streams F3c and F1a stay well below the specified feasibility boundaries.

From the study presented in this section, we conclude that the plant achieves stable operation both at

the nominal operating point and when large disturbances are introduced. The concentration of glycerol

in the product streams is less than 0.3%mol, corresponding to 0.15%wt. This means that when 5%wt.

GTBE mixture is added to biodiesel, the final glycerol contents is below the 0.02% specification of the

ASTM 6571 standard.

21.3.5 CONCLUSIONSThis section presented the optimal design of glycerol etherification plant. The considered plant has a

processing capacity of 2.25 kmol/h glycerol and uses isobutene with large amounts of inert impurity

(10% molar) as raw material. Compared to the base case, the optimal solution requires a much larger

reaction volume and higher isobutene/glycerol reactor-inlet ratio to ensure robust feasibility with re-

spect to uncertainties. Based on the experience gained by solving this case study, we recommend the

following efficient procedure for robust, optimal design of complex chemical plants:

0

2

4

6

8

10

t (h) t (h)

F (

km

ol/h

)

F4b

F4a

F3c

FIB,0

F1a

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 0 10 20 30 40 50 60 70 80

x

0

0.001

0.002

0.003

0.004

0.005

x

xD,4a

xT,4a

yB,4b

xG,4a

xM,4a

FIGURE 21.9

Dynamic simulation results.


1. Starting from the plant flowsheet, recognise the design decisions and generate several design

alternatives.

2a. Identify the feasibility constraints, uncertain design and operating parameters.

2b. Perform the economic evaluation of the alternatives and develop a simple model relating the

economic objective to the design decisions.

2c. Develop a simplified reactor–separation–recycle model of the plant.

3. Apply a robust optimisation method (e.g. constructive non-linear dynamics) using the models 2a,

2b and 2c.

4. Check the robustness by rigorous dynamic simulation.

21.3.6 SUGGESTIONS FOR FOLLOW-UP PROJECTS1. Assess the feasibility of glycerol (G) etherification with tert-butyl alcohol (TBA) as a co-reactant

and ion-exchange resins as catalyst, according to the following reactions (the kinetic constants are

given in Table 21.9):

Main reactions:

G+TBA$ME +H2O

ME+ TBA$DE+H2O

DE+ TBA$TE+H2O

Secondary reaction (dehydration of TBA to i-butene):

TBA! i-B +H2O

2. Assess the feasibility of glycerol (G) etherification with isobutene and TBA as a co-reactant, using

catalytic distillation as process intensification technique.

21.4 DESIGN AND SIMULATION OF A REACTIVE DWC FOR BIODIESELPRODUCTIONProcess intensification technologies for biodiesel production play an important role in the quest of

driving the investment and operating costs to lower values. Among them, reactive separations and

dividing-wall column (DWC) technology stand out as very promising technologies to achieve these

Table 21.9 Equilibrium Constants and Rate Constants (Kiatkittipong et al., 2011)

Equilibrium Constant Rate Constant (mol/s/kg)

Keq1¼exp(2.581�754.8/T) k1¼exp(17,342�6835/T)

Keq2¼exp(1.228�942.1/T) k2¼exp(26,953�10,382/T)

Keq3¼exp(1.779�2212/T) k3¼exp(26,953�10,382/T)

– k4¼exp(23.358�12,480/T)


goals (Kiss, 2013, 2014a,b). Moreover, the cost margin of biodiesel (a mixture of fatty esters) can be

much improved when low-cost rawmaterials (e.g. waste vegetable oil or animal fat) with high free fatty

acid (FFA) content are used instead of virgin oils. The following case study briefly illustrates the op-

timal design and simulation of an R-DWC for biodiesel production.

Conventional biodiesel processes are plagued by the drawbacks of using homogeneous catalysts

and the high-energy requirements. Reactive separation processes such as reactive distillation and re-

active absorption were proposed for the biodiesel production (Kiss and Bildea, 2012). Most of these

processes make use of solid acid/base catalysts, thus eliminating all conventional catalyst-related op-

erations, improving efficiency and reducing the energy requirements for the biodiesel production. The

problem of these reactive separation systems is that a stoichiometric ratio of reactants is required in

order to allow complete conversion of the fatty raw materials and production of two high-purity prod-

ucts (e.g. water by-product as top distillate and FAME as bottom product). However, maintaining the

stoichiometric ratio in practice can be difficult especially when the composition of the fatty acids feed

is not continuously monitored or not known. To solve this problem and still maintain all the advantages

of RD, we developed a novel design based on a reactive dividing-wall column (R-DWC). This allows

the use of a slight excess of methanol (�15% or higher) while still delivering pure products – methanol

as top distillate that can be recycled, water by-product as side stream and FAME as bottom product.

21.4.1 PROCESS OPTIMISATION STRATEGYSimulated annealing (SA) is used hereafter as an optimisation strategy, but othermethods are also possible.

SA mimics the thermodynamic process of cooling of molten metals to attain the lowest free energy state.

Starting with an initial solution, the algorithm performs a stochastic partial search of the space defined for

decision variables. In minimisation problems, uphill moves are occasionally accepted with a probability

controlled by the parameter called annealing temperature (TSA). The probability of acceptance of uphill

moves decreases as TSA decreases. At high TSA, the search is almost random, while at low TSA, the searchbecomes selective where good moves are favoured. The core of this algorithm is the Metropolis criterion

that is used to accept or reject uphill movements with an acceptance probability given by

M TSAð Þ¼ min 1,exp�DfTSA

� �� (21.32)

where Df is the change in objective function value from the current point to the new point.

The objective function is evaluated at the trial point, and its value is compared to the objective value

at the starting/current point. The Metropolis criterion is used to accept or reject the trial point. If this

trial point is accepted, the algorithm continues the search using that point. Otherwise, another trial point

is generated within the neighbourhood of the starting/current point. A fall in TSA is imposed upon the

system using a proper cooling schedule. Thus, as TSA declines, uphill moves are less likely to be ac-

cepted and SA focuses on the most promising area for optimisation. These iterative steps are performed

until the specified stopping criterion is satisfied. The random numbers can be uniformly distributed in

the interval [0, 1]. If the condition rand<M(TSA) is fulfilled, then the trial point is being accepted. Oth-erwise, the starting/current point is used to start the next step. The temperature TSA can be considered acontrol parameter. The initial temperature (Ti) is related to the standard deviation of the random per-

turbation, and the final temperature (Tf) with the order of magnitude of the desired accuracy gives the

location of the optimum.

81321.4 DESIGN AND SIMULATION OF A REACTIVE DWC

In order to optimise the complex R-DWC, we use the SA implementation in Matlab. The SA pa-

rameters were tuned using several short tests in order to improve the efficiency of the stochastic

method, while the initial point of SA was created randomly in the feasible region. The values of

the key parameters used in the SA are annealing function (Boltzmann), re-annealing interval (100),

temperature update (linear) and initial temperature (100).

Specifically, for process design of complex separation schemes, the minimisation of the heat duty of

the distillation column is the optimisation target – since up to 80% of the TACs are associated with

energy requirements even for complex distillation columns. Consequently, the use of the heat duty

is always a good approximation of the TAC. In the R-DWC, the optimisation problem for the mini-

misation of the reboiler heat duty is defined as

Min Qð Þ¼ f T,NR,NDWC,D,FSIDESTR,V,NSIDESTR,NRECYCLE,rV,rLð Þsubject to y

!m� x

!m

(21.33)

where T is the temperature in the FFA heater, NR is the number of reactive stages, NDWC is the total

number of stages in the DWC,D is the distillate rate, FSIDESTR is the side-stream product flow rate, V is

the boilup ratio, NSIDESTR and NRECYCLE are the side-stream product and recycle location, rL and rV are

the liquid and vapour split, while ym and xm are vectors of obtained and required purities for the mproducts, respectively.

The optimal design of the R-DWC was found by using SA as an optimisation method implemented

in Matlab and coupled with Aspen Plus simulations. Figure 21.10 shows the connection of MathWorks

Matlab with AspenTech Aspen Plus via MS Excel, including the flow of data between these programs

(Kiss et al., 2012). During the evolution of the SA, the vector values of decision variables (Vx) are sent

from Matlab to Microsoft Excel using DDE (dynamic data exchange) by COM technology. These

values are attributed in Excel to the corresponding process variables (Vp) and then sent to Aspen Plus

by a similar interface. Note that using the COM technology, it is possible to add code such that the

applications behave as an Object Linking and Embedding (OLE) automation server. After running

the rigorous simulation, Aspen Plus returns toMS Excel the vector of results (Vr). Finally, Excel returns

the objective function (FOB) value to Matlab for the SA procedure.

21.4.2 OPTIMAL PROCESS DESIGNThe integrated RD process was designed according to the process synthesis methods for reactive sep-

arations, as described in specialised monographs (Sundmacher and Kienle, 2003; Schmidt-Traub and

Gorak, 2006; Luyben and Yu, 2008). Rigorous simulations embedding experimental results were

performed using Aspen Plus. The RD column was simulated using the rigorous RADFRAC unit

Vx

FOB

Vp

Vr

Microsoft ExcelMathWorks Matlab

Optimization Toolbox (SA)AspenTech Aspen Plus

FIGURE 21.10

Connection of MathWorks Matlab with AspenTech Aspen Plus via MS Excel.


and explicitly considering three-phase balances. Phase splitting must be accounted for, as free water

phase can deactivate the solid acid catalyst. Nevertheless, as later revealed by the composition profiles,

the molar fraction of water in the liquid phase does not exceed 0.1 on the reactive stages – so catalyst

deactivation does not occur here, under these process conditions.

The physical properties required for the simulation and the binary interaction parameters for the

methanol–water and acid–ester pairs were available in the Aspen Plus database of pure components,

while the other interaction parameters were estimated using the UNIFAC–Dortmund modified group

contribution method. Similar results are obtained using other state-of-the-art estimation methods, such

as UNIFAC andUNIFAC–Lyngbymodified. The fatty components were conveniently lumped into one

fatty acid and its fatty ester according to R-COOH+CH3OH$R-COO-CH3+H2O. Dodecanoic (lau-

ric) acid/ester was selected as lumped component due to the availability of experimental results and

VLLE parameters for this system (Kiss and Bildea, 2012). The assumption of lumping components is

very reasonable since fatty acids and their corresponding fatty esters have similar properties. In this

work, sulphated zirconia is considered as solid acid catalyst, since kinetic data for the esterification with

methanol are also available from previous work.

Figure 21.11 shows the proposed flowsheet (Kiss et al., 2012). The conceptual design of the process

is based on an R-DWC that integrates the reaction and separation steps into a single operating unit. By

combining reaction and separation, one can shift the reaction equilibrium towards products formation

by continuous removal of reaction products, instead of using an excess of reactant. Since methanol and

water are much more volatile than the fatty ester and acid, these will separate easily as top distillate and

side stream. High conversion of the reactants is achieved, with the productivity of the RD unit exceed-

ing 20 kg fatty ester/kg catalyst/h and the purity specifications over 99.9%wt for the final biodiesel

product (FAME stream).

ACID F-ACID

ALCO1

F-ALCO

SIDESTR

WATER

RECYCLE

BTM FAME

TOPALC

ALCO

HEX1

HEX2

DEC

COOLER

DWC

B2

NL

NV rV

rL

NR

N

N-1

1

2 MeOH >90%wt

>99.0%wt

>99.9%wt1250 kg/h

MeOH >97%wtH2O <3% wt

MeOH : Acid ratio > 1.15

MIX

FIGURE 21.11

Flow sheet and topology of reactive DWC for FAME production: N, number of stages; NR, number of reactive

stages; NL, liquid split stage; NV, vapour split stage.


Figure 21.12 shows the liquid–vapour composition, as well as the temperature profile along the

R-DWC (Kiss et al., 2012). Similar profiles were obtained also for the alternative designs. The con-

centration of the fatty acid and methanol is high at the top of the column, while the fatty ester concen-

tration increases from the top to bottom. Therefore, the water accumulated in the middle zone is

removed as side stream, while FAME is delivered as high-purity bottom product.

The tray arrangements and the most important design variables for the base case and the optimal

R-DWC structures are given in Table 21.10 (Kiss et al., 2012). Remarkably, energy savings of up to

25% can be achieved, just by properly tuning the design of the R-DWC. It can be seen that the total

number of stages in the optimised DWCs is higher in comparison to the base case, and consequently,

the number of reactive stages is increased. An important point is that the optimised designs also comply

with all the restrictions on the purities and recoveries of the products. Consequently, an important issue

is reviewing the feasibility to obtain the purity of 99.9%wt for FAME in all these reactive schemes. The

results shown in Table 21.10 clearly indicate that it is indeed feasible to obtain biodiesel of very high

purity in all schemes.

The improved alternatives (S2–S7) were generated by the SA algorithm previously described. The

SAmethod is stochastically by nature, so it has twowell-known advantages: It can be readily connected

to highly sophisticated simulators – such as Aspen Plus – and it converges towards a global optimum as

computing time approaches infinity. In practice, it finds the global optimality very efficiently. The evo-

lution course of the best function value for the SA is conveniently shown in Figure 21.13, while

Table 21.10 provides the best solution (S7) along with other five configurations (S2–S6) evaluated

every 1000 iterations. It can be seen that a great number of the function values are jumped off as

the optimisation method reduces the best function value.

Notably, the design with the greatest savings in energy requirements (Case S7) shows the largest

total number of stages and reactive stages as compared to the base case. It can be seen that the total

number of stages and reactive stages are 140% and 162.5% higher than those of the base case (Case S1).

These results are used to conduct a study on the total annual cost of operating these systems in order to

see the impact of the equipment cost and utilities’ cost on the total annual cost. In this way, the designer

could make decisions about the potential energy savings that the equipment can have, without a high

increment in the total annual cost due to the increase in the number of stages.

0

4

8

12

16

X (-) Y (-)

Tra

y

MeOH

MeOH

Acid H2O

FAME

FAME

0

4

8

12

16

Tra

y

MeOHH2O

Acid FAME

MeOH

H2O

0

4

8

12

160 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 300 350 400 450 500 550 600

Temperature (K)

Tra

y Main column side

RD side

FIGURE 21.12

L–V molar composition and temperature profiles along the R-DWC (base case).


Table 21.10 Design Parameters for the Reactive DWC: Base Case Versus Designs Found by SA

S1 S2 S3 S4 S5 S6 S7

Column topology

Number of stages, N 15 20 39 33 34 35 36

Number of reactive stages, NR 8 11 24 20 21 19 21

Liquid split stage, NL 3 5 8 7 7 8 8

Vapour split stage, NV 12 16 32 27 28 27 29

Side-draw stage, N1 8 12 30 18 18 17 13

Organic phase-return stage, N2 3 9 28 7 25 25 26

Feed streams

Acid flow rate (kmol/h) 5.83 5.83 5.83 5.83 5.83 5.83 5.83

Temperature HEX1 (K) 418.1 385.6 373.2 410.4 428.1 423.2 418.9

ALCO flow rate (kmol/h) 6.8 6.997 6.997 6.997 6.997 6.997 6.997

Temperature HEX2 (K) 340.6 338.7 338.7 338.7 338.7 338.7 338.7

Specifications

Distillate rate (kg/h) 33 35.34 39.06 34.71 37.12 37.45 37.12

Boilup ratio (kg/kg) 5 4.85 4.89 4.43 3.96 3.75 3.39

Side-draw flow rate (kg/h) 107 118.23 107.63 113.49 122.74 120.15 122.04

Liquid flow rate, L1 (kmol/h) 2.6 3.14 2.23 1.32 1.37 1.50 1.29

Vapour flow rate, V1 (kmol/h) 2.6 3.25 3.96 1.53 1.90 1.94 2.14

Product streams

Water flow rate (kmol/h) 5.70 5.82 5.66 5.82 5.75 5.70 5.67

Water purity (%wt) 99.10 97.96 98.68 97.34 98.34 97.73 96.99

FAME flow rate (kmol/h) 5.83 5.83 5.83 5.83 5.83 5.83 5.83

FAME purity (%wt) 100.00 100.00 100.00 99.97 99.94 99.96 99.96

Recycle stream

TOPALC flow rate (kmol/h) 1.10 1.10 1.12 1.08 1.12 1.10 1.07

TOPALC purity (%wt) 94.00 99.65 92.28 99.69 96.36 93.73 92.39

Continued

Table 21.10 Design Parameters for the Reactive DWC: Base Case Versus Designs Found by SA—cont’d

S1 S2 S3 S4 S5 S6 S7

Energy requirements

HEX1 duty (kW) 95.30 68.27 58.34 88.66 103.84 99.57 95.88

HEX2 duty (kW) 9.69 9.54 9.54 9.54 9.54 9.54 9.54

Reboiler duty (kW) 405.59 396.48 399.20 361.64 323.39 306.23 277.20

Condenser duty (kW) �278.11 �246.60 �239.43 �232.21 �209.11 �187.79 �155.18Cooler duty (kW) �205.57 �200.71 �200.71 �200.72 �200.72 �200.72 �200.72Total heating duty (kW) 510.58 474.29 467.08 459.84 436.77 415.34 382.62

Total cooling duty (kW) �483.68 �447.31 �440.14 �432.93 �409.84 �388.51 �355.89Key performance indicators

Energy requirements (kw h/tonne FAME) 408.46 379.43 373.67 367.87 349.42 332.27 306.10

Energy savings (%) 0.00 7.11 8.52 9.94 14.46 18.65 25.06

Total CO2 emission (tonnes/year) 1405 1291 1277 1238 1165 1105 1012

Economic evaluation

Annual operating cost (k$/year) 149.79 147.85 136.61 135.04 123.38 117.24 107.71

Capital cost (k$) 171.60 214.17 395.36 303.21 331.79 324.52 357.06

Total annual cost (k$/year) 184.11 190.68 215.68 195.68 189.74 182.15 179.12

Note: S1, base case design; S2–S6, intermediate designs found by SA; S7, optimal design.

21.4.3 RE-OPTIMISED PROCESS DESIGNSignificant savings in the operating and capital investment cost can be achieved by combining RD and

DWC technologies, but the high degree of integration can raise more difficulties in process control.

Therefore, having an optimal design is not always sufficient since the problem of dynamics and process

control is just as important as the optimal process design. At a first glance, the control of an R-DWC

may not appear to be an issue as several efficient control structures are available for DWC (Kiss, 2013).

Nonetheless, DWC units are designed for ternary separations, and, therefore, the already proposed con-

trol structures are applicable to multi-component separations without reaction. Moreover, in case of

reactive distillation, the performance of the control structure strongly depends on the process design

and on the type of chemical reactions that occur in the column.

The R-DWC unit studied here is designed for a quaternary system – two products and two reactants,

with one of the reactants in excess. A critical aspect of the process is to ensure the full conversion of the

FFA by having an excess of methanol and, therefore, avoiding that unreacted FFA becomes an impurity

in the bottom stream. However, the excess methanol can become an impurity in the side stream. The

reason is that the prefractionator of the R-DWC is operated with multiple feeds (with lightest compo-

nent fed at the lower part) and therefore unable to perform the sharp split between the light and the

heavy components of the system like as is typically the case in a standard DWC.

Rigorous dynamic simulations were performed in order to understand the dynamic behaviour of the

process. The initial results of the dynamic simulations pointed out that under different scenarios, the

excess methanol becomes an impurity in the side stream. This problem arises from the fact that meth-

anol is the light key component of the system and, moreover, is fed at the bottom of the column pre-

fractionator. An effective solution to overcome this problem is to feed the alcohol stream as vapour

instead of saturated liquid and to increase the acid inlet temperature. Therefore, the design is

re-optimised and an efficient control strategy is proposed.

200

250

300

350

400

450

500

550

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10,000

Number of iterations

DW

C h

eat d

uty

(kW

)

S2 S3 S4 S5 S6 S7

FIGURE 21.13

Evolution of best function value during the course of SA optimisation.


Figure 21.14 (left) shows the updated R-DWC design, where FAME is produced as pure bottom

product and water as side stream, while the methanol excess is recovered as top distillate and recycled

(Ignat and Kiss, 2013). The alcohol-to-acid ratio plays a crucial role in the design and operation of the

integrated R-DWC unit. All products can be obtained at high purity only in a narrow optimal range of

the alcohol-to-acid ratio. At smaller ratio, methanol is fully converted but the excess of FFA becomes

an impurity in the FAME stream, while at high ratio, the FFA are fully converted and the excess of

methanol becomes an impurity in the side stream (Kiss and Bildea, 2012).

The initial optimal R-DWC design was modified and optimised in terms of minimal energy require-

ments, this time using the sequential quadratic programming (SQP) method from Aspen Plus. Based on

a solid theoretical and computational foundation, the SQP method has become the most successful

method for solving non-linearly constrained-optimisation problems. The SQP optimisation method

and the effective sensitivity analysis tool from Aspen Plus were employed in the R-DWC optimisation

procedure illustrated in Figure 21.14 (right) (Ignat and Kiss, 2013). The objective of the optimisation is

to minimise the total reboiler duty required, as follows:

Min Qð Þ¼ f TFFA,NT,NRT,NF,NSS,FSS,NDWS,NDWC,RxR,V,RR,rV,rLð Þsubject to y

!m� x

!m

(21.34)

Methanol

Water

F-ACID

rL

rV

1

1 7

18

22

19

6

FAME

(biodiesel)

4

12

RD

CDWC

16

DEC

Recycle-ACID

Side stream

ACID

F-ALCOALCO

R-DWC

9

InitialisationTFFA, NT, NRT, NF, NSS, FSS, NDWS, NDWC

NT, NRT, NF, NSS, NDWC/DWS, V, RR, RxR

V, RR, RxR, rL, rV

Change

Optimal designConverged R-DWC profiles

and stage requirements

No

Adjust rL and rV

min QR

min N(RR+1)

Yes

No

Yes

FIGURE 21.14

Reactive DWC used for the FAME synthesis from free fatty acids and methanol (left). Procedure for the optimal

design of a reactive (DWC) (right).


where the optimisation parameters used here are temperature of the inlet FFA stream (TFFA), totalnumber of stages (NT), total number of reactive stages (NRT), feed location (NF) of each reactant,

side-stream product flow rate (FSS), side-draw stage (NSS), wall size (NDWS) and location (NDWC),

alcohol-to-acid reactants ratio (RxR), boilup rate (V), reflux ratio (RR) and liquid and vapour split

(rL and rV), while ym and xm are the vectors of the obtained and required purities for the m products.

Note that in order to determine the optimal ratio between the energy cost and the number of stages, an

additional objective function was used, Min NT (RR+1), which approximates very well the minimum

of the TAC of a conventional distillation column (Ignat and Kiss, 2013).

Figure 21.15 plots the temperature and composition profiles along the R-DWC unit, while the key

parameters of the optimal design are presented in Table 21.11 and the mass balance is provided

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Stage (-)

Stage (-)

Mas

s fr

actio

n (-

)

FAME

Water

FFA

Methanol

40

60

80

100

120

140

160

180

200

220

240

260

280

0 2 4 6 8 10 12 14 16 18 20 22

0 2 4 6 8 10 12 14 16 18 20 22

Tem

pera

ture

(�C

)

Prefractionator (PF)

Main column

FIGURE 21.15

Temperature and composition profiles along the reactive DWC.


in Table 21.12 (Ignat and Kiss, 2013). Compared to the optimal design by SA presented earlier, there

are some key differences in the optimal R-DWC design that must be noted. In addition to the change

of the feed streams’ thermal state, a key finding of this study is that it is imperative to use a vapour feed

of alcohol in order to reach the product specifications. Moreover, while requiring a 39% fewer number

of stages and 57% fewer reactive stages, water and methanol are obtained as high-purity products

(99.8%), with just a minor trade-off – only a 1.5% increase in the total heat duty.

21.4.4 DYNAMICS AND PROCESS CONTROLThe economic benefits predicted by the optimal design should also be achievable in the practical oper-

ation of the plant. Therefore, the controllability of the process is just as important as the savings in the

capital and operating costs. As composition analysers are rather expensive and require more mainte-

nance, their use should be minimal or avoided altogether. In practice, inferential temperature measure-

ments are preferred over direct composition measurements. For the selection of the trays to control the

Table 21.11 Design Parameters of an Optimal Reactive (DWC)

Design Parameters Value Unit

Flow rate of acid feed stream 1168.2 kg/h

Flow rate of ALCO feed stream 198.1 kg/h

Temperature of acid feed stream 160 �CTemperature of ALCO feed stream 69 �CPressure of feed stream 1.2 bar

Operating pressure 1 bar

Column diameter 1.1 m

Number of stages prefractionator side 12 –

Number of reactive stages prefractionator side 9 –

Total number of stages DWC 22 –

Acid feed stage prefractionator 4 –

ALCO feed stage prefractionator 9 –

Side-stream withdrawal stage 16 –

Organic phase-return stage 7 –

Wall position (from/to stage) 7–18 –

Liquid split ratio (rL) 0.07 kg/kg

Vapour split ratio (rV) 0.26 kg/kg

Methanol product purity 99.80/99.60 %wt/%mol

Water product purity 99.80/99.90 %wt/%mol

FAME product purity 99.99/99.99 %wt/%mol

HEX 1 duty 108 kW

HEX 2 duty 69 kW

Reboiler duty 212 kW

Condenser duty �154 kW

Total heating duty 389 kW


temperature, several methods based on steady-state calculations are available – namely, the slope cri-

terion, invariant temperature criterion, sensitivity criterion and singular value decomposition (SVD)

method. Hereafter, the sensitivity analysis and SVD criteria were used. The steady-state gain matrix

(Kp) is expressed (decomposed) as a product of three matrices: a U matrix, a diagonal matrix s and a

VTmatrix. The highest value in each column of theUmatrix indicates the tray on which the temperature

should be controlled:

Kp¼UsVT (21.35)

A small change is made in one of the manipulated variables (V, L, S and RxR) while keeping the othersconstant. The steady-state gains for each tray are calculated by dividing the change in each tray tem-

perature by the change in the manipulated variable. For a DWC, there are two steady-state gain ma-

trices, one for the main column and one for the prefractionator. Each matrix is then decomposed using

the SVD function available in Matlab, and the U vectors are plotted against tray number:

U, S, V½ ¼ SVD x, 0ð Þ (21.36)

Table 21.12 Mass Balance of a 10 ktpy Biodiesel Process Based on Reactive DWC

FAME

F-

ACID

F-

ALCO

Recycle-

ACID

Side

Stream Methanol Water

Temperature

(�C)275.21 160.00 68.90 103.34 103.34 64.25 103.34

Mass flow (kg/h)

Methanol Trace 0.00 198.10 Trace 0.21 11.03 0.21

Acid <0.001 1168.20 0.00 Trace Trace Trace Trace

Water Trace 0.00 0.00 0.12 105.15 0.02 105.04

Ester-M 1249.8 0.00 0.00 15.63 15.63 Trace Trace

Mass fraction

Methanol Trace 0.0000 1.0000 168 ppm 0.0018 0.9980 0.0020

Acid 300 ppb 1.0000 0.0000 125 ppm 6 ppm Trace 116 ppb

Water Trace 0.0000 0.0000 0.0074 0.8690 0.0020 0.9980

Ester-M 1.0000 0.0000 0.0000 0.9924 0.1292 Trace 26 ppm

Mole flow (kmol/h)

Methanol Trace 0.00 6.18 Trace 0.01 0.34 0.01

Acid Trace 5.83 0.00 Trace Trace Trace Trace

Water Trace 0.00 0.00 0.01 5.84 0.001 5.83

Ester-M 5.83 0.00 0.00 0.07 0.07 Trace Trace

Mole fraction

Methanol Trace 0.0000 1.0000 0.0010 0.0011 0.9964 0.0011

Acid 381 ppb 1.0000 0.0000 124 ppm 581 ppb Trace 10 ppb

Water Trace 0.0000 0.0000 0.0815 0.9865 0.0036 0.9989

Ester-M 1.0000 0.0000 0.0000 0.9175 0.0123 Trace 2 ppm


Figure 21.16 provides the results of the SVD analysis, clearly showing that the most sensitive stages

are 11, 13 and 17 of the main column, for changes in the reflux rate, side-stream rate and reboiler heat

duty (Ignat and Kiss, 2013). However, stages 11 and 13 are too close to be independent – and such

situation can lead to a less effective dynamic response of the control structure. For the change in

reflux rate, a smaller peak can be observed at stage 7. Therefore, the temperature on stage 7 will

be controlled by manipulating the reflux rate. Note that the results for the SVD analysis are presented

only for the main column without taking into consideration the prefractionator side (the steady-state

gain matrix for the prefractionator). Since the inlet feed stream temperature is fixed and the liquid

split is not used as a manipulated variable, there are no more variables available that can be effec-

tively used as manipulated variables to control at least one of the temperatures in the prefractionator

side of the column.

In order to limit the amount of excess methanol that may pass below the partition wall of the main

column and therefore become an impurity in the side stream, an extra composition controller that

–0.8–0.6–0.4–0.2

00.20.40.60.8

11.21.41.6

0 2 4 8 10 12 14 16 18 20 22Stage

Gai

ns

DT/DSS

DT/DQR

DT/DRR

–1

–0.8

–0.6

–0.4

–0.2

0

0.2

0.4

0 2 4 86 10 12 14 16 18 20 22

Stage

U

U3 U1

U20.6

6

FIGURE 21.16

Results of the SVD analysis: plots of the steady-state gains and U vectors.


measures the methanol mass fraction in the water stream is added to set the alcohol-to-acid ratio.

Figure 21.17 illustrates the final proposed control structure, while Table 21.13 gives the tuning param-

eters of the PID controllers – where the control loops were tuned by a simple version of the direct syn-

thesis method (Ignat and Kiss, 2013).

The level of the reflux drum, the reboiler and the decanter can be controlled by the following ma-

nipulated variables: D (distillate), B (bottoms), S (side stream) and Rec (recycle stream). The compo-

sition of the free product streams is controlled by the remaining variables: L (liquid reflux), S (side

stream) and V (vapour boilup). An extra control loop is needed in order to set the alcohol-to-acid ratio

(RxR). The proposed control structure is somewhat similar to the DB/LSV control structure that was

reported as the best option for a DWC, in previous studies (Kiss, 2013). However, there are some key

differences such as the inability to use the additional optimisation loop that manipulates the liquid split

to control the heavy component composition at the top of prefractionator and implicitly achieve mini-

misation of the energy requirements.

In the case of standard DWC, any heavy component going out the top of the wall will appear also in

the liquid flowing down in the main column, thereby affecting the purity of the side stream (S). How-

ever, this is not the case here, since the water by-product is removed as a side stream and separated in a

Water

F-ACID

rL

rV

1

1 7

18

22

19

6

4

12

RD

C

DWC

16

DEC

Recycle-ACID

Side stream

ACID

F-ALCOALCO

RC

Methanol

LC

TC

LC

TCFAME

CC

9

17

TC13

LC

LC

FIGURE 21.17

Control structure of the R-DWC unit, based on level control (4�), inferential temperature control (3�),composition (1�) and reactants ratio (1�) control.


decanter from which the organic phase (heavy component of the system) is recycled back to the col-

umn. Therefore, the liquid split is not effective as a manipulated variable for controlling the heavy

impurity at the top of the prefractionator. Actually, in this study, the situation is the other way around.

Any light component going down below the bottom of the dividing wall will become an impurity in the

side stream since the prefractionator is not operated at the preferred split between the light and heavy

key components like in the case of a standard DWC. Since the side stream is collected as a liquid prod-

uct, it means that any small amounts of light impurity in the vapour phase will become an impurity in

the side stream. Because the location of the wall fixes how the vapour flow splits between the two sides

of the column, the vapour split (rV) variable is not adjustable during operation for control purposes

(Kiss, 2013). Therefore, the vapour split ratio is not used as a manipulated variable in the dynamic

simulations presented hereafter.

Figures 21.18 and 21.19 present the results of the dynamic simulations for industrially relevant dis-

turbances such as production rate changes and modifications in the vapour split ratio (Ignat and Kiss,

2013). Remarkably, the mass fractions of all components are returning to their set point within reason-

able short times and low overshooting, thus proving that the system can successfully reject the distur-

bances. As the methanol stream is fed as vapour – and thus ensures most of the vapour amount required

on the prefractionator side of the column – the vapour split ratio has in this case only a weak influence

on the purities of the products. Note that no disturbances are expected in the liquid split (rL) since thisvariable is set (manipulated) in open loop.

The performance of the control system was also tested for a deactivating catalyst. The investigated

scenario assumed a decrease of the pre-exponential factor from 250 (at t<2 h) to only 200 kmol �m3/

(kg2 � s) (at time t¼10 h). The control system succeeds to keep the throughput and product quality

unchanged. Figure 21.20 presents the temperature profiles, while Figure 21.21 shows the composition

profiles in the column for different catalyst activities at different times: t¼1 h and t¼10 h (Ignat and

Kiss, 2013). As one can notice, the lower catalyst activity is compensated by a slight increase of the

temperature, while the product purities are kept at the desired values. In other words, the control system

compensates the lower catalyst activity by a higher temperature inside the column, with the result of

maintaining a similar reaction rate.

Table 21.13 Tuning Parameters of the PID Controllers

Controlled

Variable

Manipulated

Variable

Gain, P(%/%)

Int. Time, I(min)

Drv. Time, D(min)

Control

Direction

T7_DWC L 0.4 30 0 +

T13_DWC S 1 20 0 +

T17_DWC V 1 20 0 –

xmethanol rL 0.6 40 0 –

DWC_TankLevel D 1 60 0 +

DWC_ReboilerLevel B 1 60 0 +

Dec_OrganicPhaseLevel Rec 1 60 0 +

Dec_AquaPhaseLevel Water 1 60 0 +


This case study illustrated how to tackle the optimal design, dynamics and control of an inte-

grated R-DWC for biodiesel synthesis from FFAs and methanol. As the first optimal design had

poor dynamic performance, a key finding was that it is imperative to use a vapour feed of alcohol

in order to reach the product specifications. The re-optimised design proved to work well also in

transient (dynamic) regime. SVD was effectively used to find the sensitive trays for inferential tem-

perature control. The control structure proposed for a two-reactant and two-product RD system suc-

cessfully demonstrates the excellent performance of the system in the case of industrially relevant

disturbances such as production rate changes and catalyst deactivation. However, in case of differ-

ent types of reactions (e.g. two reactants and one product), other control structures have to be

considered.

0.9965

0.9970

0.9975

0.9980

0.9985

0.9990

0.9995

1.0000

0 1 2 3 4 5 6 7 8 9 10Time (h)

Mass

fra

ctio

n (

–)

+10% Production rate change

FAME

Water

Methanol

0.9965

0.9970

0.9975

0.9980

0.9985

0.9990

0.9995

1.0000

0 1 2 3 4 5 6 7 8 9 10

Time (h)

Mass

fra

ctio

n (

–)

–10% Production rate change

FAME

Water

Methanol

FIGURE 21.18

Results of the dynamic simulations at production rate changes of 10%.


0.9965

0.9970

0.9975

0.9980

0.9985

0.9990

0.9995

1.0000

0 1 2 3 4 5 6 7 8 9 10Time (h)

Mas

s fr

actio

n (–

)

+10% Vapour split ratio disturbance

FAME

Water

Methanol

0.9965

0.9970

0.9975

0.9980

0.9985

0.9990

0.9995

1.0000

0 1 2 3 4 5 6 7 8 9 10

Time (h)

Mas

s fr

actio

n (–

)

–10% Vapour split ratio disturbance

FAME

Water

Methanol

FIGURE 21.19

Results of the dynamic simulations at vapour split ratio disturbance of 10%.

406080

100120140160180200220240260280

0 2 4 6 8 10 12 14 16 18 20 22

Stage (–)

Tem

pera

ture

(°C

)

Prefractionator (PF)

Main column

FIGURE 21.20

Change of the temperature profile during catalyst deactivation.

21.4.5 SUGGESTIONS FOR FOLLOW-UP PROJECTS1. Design an optimal intensified process for bioethanol dehydration based on extractive distillation

taking place in a single (DWC).

2. Design a bioethanol dehydration process based on azeotropic distillation in a DWC, and examine

the differences compared to the extractive DWC alternative.

3. Design an optimal reactive distillation or R-DWC for other types of equilibrium-limited reactions

(esterification, etherification, condensation, alkylation, etc.).

REFERENCESBehr, A., Obendorf, L., 2003. Development of a process for acid-catalyzed etherification of glycerine and isobu-

tene forming glycerine tertiary butyl ethers. Eng. Life Sci. 2, 185–189.

Bildea, C.S., Dimian, A.C., 1998. Stability and multiplicity approach to the design of heat-integrated PFR.

AIChE J. 44, 703–2712.

Bildea, C.S., Dimian, A.C., Iedema, P.D., 2000. Nonlinear behavior of reactor-separator-recycle systems. Comput.

Chem. Eng. 24, 209–215.

Bildea, C.S., Cruz, S., Dimian, A.C., Iedema, P., 2004. Design of tubular reactors in recycle systems. Comput.

Chem. Eng. 28, 63–72.

Dimian, A.C., 2003. Integrated Design and Simulation of Chemical Processes. Elsevier, Amsterdam.

Douglas, J.M., 1988. Conceptual Design of Chemical Processes. McGraw-Hill.

Ignat, R.M., Kiss, A.A., 2013. Optimal design, dynamics and control of a reactive DWC for biodiesel production.

Chem. Eng. Res. Des. 91, 1760–1767.

Kiatkittipong, W., Intaracharoen, P., Laosiripojana, N., Chaisuk, C., Praserthdam, P., Assabumrungrat, S., 2011.

Glycerol ethers synthesis from glycerol etherification with tert-butyl alcohol in reactive distillation. Comput.

Chem. Eng. 35, 2034–2043.

Kiss, A.A., 2013. Advanced Distillation Technologies – Design, Control and Applications. Wiley.

Kiss, A.A., 2014a. Process Intensification Technologies for Biodiesel Production – Reactive Separation Processes.

Springer.

Kiss, A.A., 2014b. Distillation technology – still young and full of breakthrough opportunities. J. Chem. Technol.

Biotechnol. 89, 479–498.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 2 4 6 8 10 12 14 16 18 20 22

Mol

e fr

actio

n (–

)

FAMEWater

FFA

Methanol

t = 10 h

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 2 4 6 8 10 12 14 16 18 20 22

Stage (–) Stage (–)

Mol

e fr

actio

n (–

)

FAME

Water

FFA

Methanol

t = 1 h

FIGURE 21.21

Change of the composition profile during catalyst deactivation.

829REFERENCES

Kiss, A.A., Bildea, C.S., 2012. A review on biodiesel production by integrated reactive separation technologies.

J. Chem. Technol. Biotechnol. 87, 861–879.

Kiss, A.A., Segovia-Hernandez, J.G., Bildea, C.S., Miranda-Galindo, E.Y., Hernandez, S., 2012. Reactive DWC

leading the way to FAME and fortune. Fuel 95, 352–359.

Luyben, W.L., 1994. Snowball effects in reactor-separator processes with recycle. Ind. Eng. Chem. Res.

33, 299–305.

Luyben, W.L., Yu, C.C., 2008. Reactive Distillation Design and Control. Wiley-AIChE.

Luyben, W.L., Tyreus, B.D., Luyben, M.L., 1999. Plantwide Process Control. McGraw-Hill.

Marquardt, W., Monnigmann, M., 2005. Constructive nonlinear dynamics in process systems engineering. Com-

put. Chem. Eng. 29, 1265–1275.

Monnigmann, M., Marquardt, W., 2003. Steady-state process optimization with guaranteed robust stability and

feasibility. AIChE J. 49, 3110–3126.

Schmidt-Traub, H., Gorak, A., 2006. Integrated Reaction and Separation Operations. Springer.

Sundmacher, K., Kienle, A., 2003. Reactive Distillation: Status and Future Directions. Wiley-VCH.

Vlad, E., Bildea, C.S., Bozga, G., 2013. Robust, optimal design of glycerol etherification process. Chem. Eng.

Technol. 36 (2), 251–258.


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[Computer Aided Chemical Engineering] Integrated Design and Simulation of Chemical Processes Volume 35 || Case Studies