A65 Abhijit Styrene CES 2005

Chemical Engineering Science 60 (2005) 347363

www.elsevier.com/locate/ces

Multiobjective optimization of an industrial styrene monomermanufacturing process

A. Tarafder, G.P. Rangaiah, Ajay K. Ray

Department of Chemical and Biomolecular Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore

Received 6 February 2004; received in revised form 6 July 2004; accepted 27 July 2004Available online 30 September 2004

Abstract

Multi-objective optimization of the operation and design of a styrene manufacturing process has been studied with the elitist non-dominated sorting genetic algorithm (NSGA-II). In the first part, the study focused on bi-objective optimization and comparative analysis ofthree different styrene reactor designsthe single-bed, the steam-injected and the double-bed reactors. The objectives were to simultaneouslymaximize styrene flow rate and styrene selectivity. In the second part, on the other hand, a tri-objective optimization study was performedinvolving the entire manufacturing process consisting of the reactor, heat-exchangers and separation units. Only the double-bed reactorwas considered in this study for maximizing the styrene flow rate and selectivity and minimizing the total heat duty required by themanufacturing process. Results are presented and discussed in detail. 2004 Elsevier Ltd. All rights reserved.

Keywords:Styrene; Modelling; Simulation; Multiobjective; Optimization; Pareto set; NSGA; Chemical reactors; Process systems engineering; Reactionengineering; Industrial process

1. Introduction

Styrene is one of the most manufactured monomer inthe world with an annual turnover of 60 billion USD[www.styreneforum.org] comprising thousands of compa-nies and facilities. It is the raw material for the production ofpolystyrene, acrylonitrilebutadienestyrene resins (ABS)and a variety of miscellaneous polymers, which are the ba-sic materials of the plastic revolution. Surely, even a smallimprovement in the plant operation will have a significantimpact on the revenue of the industries, which in turn willbenefit the consumers as well.

In a continuing effort to improve the performance ofstyrene manufacturing process, researchers have carried outseveral modelling and optimization studies for the last fewdecades with the latest analytical tools available. An ac-count of these studies is available in our recent publication

Corresponding author. Tel.: +65-6874-8049; fax: +65-6779-1936.E-mail address:[email protected](A.K. Ray).

0009-2509/$ - see front matter 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2004.07.120

(Yee et al., 2003), where an effort was made to optimize astyrene reactor unit, maximizing the styrene flow, yield andselectivity, using a genetic algorithm, the non-dominatedsorting genetic algorithm (NSGA) (Srinivas and Deb, 1995),developed for multi-objective optimization. Encouraged bythe outcome of this effort, we have carried out an opti-mization study on a styrene manufacturing process, with amore recent algorithmthe elitist non-dominated sortinggenetic algorithm or NSGA-II (Deb et al., 2002). AlthoughNSGA was successfully applied to many multi-objectiveoptimization problems (Yee et al., 2003; Rajesh et al., 2001;Bhaskar et al., 2000), Deb et al. (2002)reported that itscomputational complexity can be drastically reduced and byapplying elitism, a method of preserving good solutions, itsperformance can be still increased. This revision in NSGAresulted in NSGA-II which was shown to be able to achievebetter convergence near the true Pareto-optimal front andfind much better spread of Pareto-optimal solutions (Debet al., 2002). Recent publications (Kasat and Gupta, 2003;Mitra and Gopinath, 2004) which used NSGA-II, as well as

http://www.elsevier.com/locate/ceshttp://www.styreneforum.orgmailto:[email protected]

348 A. Tarafder et al. / Chemical Engineering Science 60 (2005) 347363

our experience with both NSGA and NSGA-II, endorse theclaim of Deb et al.

The styrene manufacturing process, used in the currentoptimization study, contains styrene monomer reactor alongwith heat-exchangers and separation units. Reactors withthree different designs have been used for the study, withthe goal of maximizing styrene flow rate and selectivity andminimizing the overall heat duty required by the manufac-turing process. The next section contains a detailed descrip-tion of the process.

2. Process description

Fig. 1 shows the schematic diagram of a typical styrenemonomer (SM) manufacturing process consisting of a reac-tor unit, where dehydrogenation of ethylbenzene (EB) takesplace, followed by reactor effluent cooling units (HE1, HE2and PC) and separation units (S1S3), where the SM is sep-arated from un-reacted EB and other by-products. The reac-tion is carried out in vapour phase with steam, over a catalystconsisting primarily of iron oxide. Fresh EB feed (F 0EB atT 0EB) and recycled EB are mixed with low pressure saturatedsteam (F 0stm at T

0stm) in a mixer and preheated to a tem-

perature ofTC2 with reactor effluent in HE1. This stream isfurther heated up to the reaction temperature, generally over875 K (Clough and Ramirez, 1976), by superheated steamfrom a fired heater before being passed into the fixed bedcatalytic reactor. In most of the modern plant designs (seeFig. 2), the reactor unit consists of two or three reactors inseries (Lee and Hubbell, 1982), which is to provide reheat-ing to the reactants (as the main reaction is endothermic) andhence boosting forward reaction. The most popular methodof adding heat is to indirectly warm up the reactants between

HE1 HE2

PCReactor

Steam superheater

Benzene-tolueneSplitter

EB recycle Column

Benzene

Toluene

StyreneRecycle EB

Saturated steamfeed (Fostm, T

ostm)

Fostm

(1-)Fostm

Fresh feed(FoEB, TEB,Pin)

TC2Tmix1

TH1

TH2

(1- ) Fostm

(1- )(1- )Fostm L

TC1

S1

S2

S3

Mixer

Fig. 1. Schematic diagram of Styrene plant. (HE: heat-exchanger, S: Separator, PC: partial condenser). Letters inbold and italics represent decisionvariables.

the beds, although, in some other plant designs, steam isdirectly injected at the entrances of the reactor beds to pro-vide reheat for the subsequent section(s). Although steam isadded mainly to provide the heat of reaction, there are otherreasons for its use; a detailed discussion of which can befound in our previous publication (Yee et al., 2003). Usu-ally, a steam to EB ratio (SOR) of 15:1 is maintained at thereactor inlet.

The six main reactions occurring in the styrene reactorare (Sheel and Crowe, 1969):

C6H5CH2CH3 C6H5CHCH2 + H2, (1)C6H5CH2CH3 C6H6 + C2H4, (2)C6H5CH2CH3 C6H5CH3 + CH4, (3)2H2O+ C2H4 2CO+ 4H2, (4)H2O+ CH4 CO+ 3H2, (5)H2O+ CO CO2 + H2. (6)

The main reaction in the styrene reactor is the reversible,endothermic conversion of EB to styrene and hydrogen (Eq.(1)). This reaction proceeds thermally with low yield andcatalytically with high yield. As it is a reversible reaction,producing two moles of product to one mole of reactant, lowpressure and high temperature favour the forward reaction(Le Chatelliers principle). Although the dehydrogenation ofEB is both kinetically and thermodynamically favoured byhigh temperature, by-products like benzene and toluene areproduced by thermal cracking at higher temperatures (Eqs.(2) and (3)), reducing the styrene selectivity. Hence, oper-ating temperature should be chosen compromising betweenthe conversion of EB and styrene selectivity. In addition,special catalyst is used to promote higher production of

A. Tarafder et al. / Chemical Engineering Science 60 (2005) 347363 349

(1- )(1- )F0stm

(1- )F 0stm

Fresh feed, recycled EBand steam Steam

Superheater

ReactorBed 1

ReactorBed 2

(b)

Tmix2

Tmix1

(1- )F 0stmFresh feed, recycled EBand steam Steam Superheater

Reactor Bed

(a)

Tmix1

Saturated Steam Saturated Steam

Saturated Steam

(1- )F 0stm

(1- )F 0stm Fresh feed, recycled EBand steam

Steam Superheater ReactorBed 1

ReactorBed 2

(c)

Tmix,2

Tmix1

Fig. 2. Schematic diagram of (a) Single Bed (SB) reactor, (b) Steam-injected (SI) reactor and (c) Double Bed (DB) reactor. Letters inbold and italicsrepresent decision variables.

styrene at lower temperature while minimizing the side re-actions.

The effluent from the reactor unit is cooled in the coolingsection consisting of heat exchangers (HE1 and HE2) andpartial condenser (PC). The condensed, crude styrene, to-gether with the main by-products (toluene and benzene) andun-reacted EB, separates from water and non-condensablegases like H2 in a settling drum (not shown in the figure). Thecrude styrene is then taken to the distillation units (S1S3)for the recovery of styrene. The purity requirement of styrenein industry is circa 99.7 wt%.

3. Mathematical modelling and simulation of thestyrene plant

In the present study, a pseudo-homogeneous model sug-gested bySheel and Crowe (1969)was used for styrene reac-tor. The model assumes lumped catalytic effects in the bulkfluid phase inside the reactor, so the mass and heat transferwithin the catalyst pellet are assumed to be negligible. Adetailed account of this model is available in our previouswork (Yee et al., 2003) as well as other literature (Sheel andCrowe, 1969; Elnashaie and Elshishini, 1994).

In the present study, the same reactor model is used tosimulate three different configurations of the styrene reac-

tor unit, based on different EB and steam supply schemesto the reactor. The first one is the single bed (SB), wherethere is no intermediate heating and the entire superheatedsteam is mixed with the EB-steam mixture and injected atthe reactor entrance (Fig. 2(a)). In the second configuration(Fig. 2(b)), only a portion of the total available superheatedsteam is mixed with the EB-steam mixture at the reactorentrance, whereas, the rest of the steam is injected at an-other suitable place. It will be called a steam-injected (SI)reactor and is modelled as two SB reactors in series, witha superheated steam flow, mixing directly with the effluentfrom the first part, before entering the second. The third andthe last configuration (Fig. 2(c)), which is the most popularin the industries, is modelled as two SB reactors operatingin series. Here, superheated steam flow, unlike the SI reac-tor, indirectly heats up the effluent from the first bed insidea heat exchanger. Subsequently, the steam is again super-heated, taken to the reactor inlet, mixed with the EB-steammixture and fed to the reactor.

3.1. Distillation columns

Other than the reactor system, the distillation columnsthat separate the unconverted EB from styrene is the mostimportant and expensive equipment in a styrene plant. It is


Table 1Specifications for the three columns

Column Light key Heavy key fiDa fjB

b

Benzenetoluene Column Toluene Ethylbenzene DV DVBenzenetoluene Splitter Benzene Toluene 0.999 0.999Ethylbenzene recycle Column Ethylbenzene Styrene DV 0.997

afiD is the fractional recovery of the light key in distillate.bfjB is the fractional recovery of the heavy key in bottoms.

expensive because close boiling points of EB and styrenerequire a large number of distillation stages (70100) (Denisand Castor, 1992). As styrene is one of the few monomersthat auto-polymerizes, the styrene purification has to be car-ried out in low temperature vacuum distillation columnsto minimize polymerization. In this study, three distillationcolumns each operating at 0.1 bar are utilized, where the sep-aration scheme is a simplified version of the standard schemeused in Fina/Badger process (Lee and Hubbell, 1982). Thebenzene and toluene are separated from EB and styrene inthe first column, where the overhead, consisting of benzeneand toluene, is sent to a benzenetoluene splitter to recoverbenzene and toluene. The bottoms stream, on the other hand,is sent to the EB recycle column, where EB is separated fromstyrene and recycled back to the dehydrogenation reactor.

The product distribution, actual number of theoreticalstages, reflux ratio, condenser and reboiler duties are deter-mined by employing shortcut methods, commonly knownas FenskeUnderwoodGilliland (FUG) method (Khoury,1999). We have used the Molkanovs equation to repre-sent the Gilliland correlation curve. The assumptions madeto simplify the model were: (a) styrene, EB, benzene andtoluene are the only components entering the distillationcolumns, (b) the solution is ideal, thus Daltons law andRaoults law are valid, (c) constant molar overflow and neg-ligible pressure drop in the columns, (d) overall stage effi-ciency is 1.0, (e) the relative volatilities are constant through-out the columns, and (f) the columns use total condenserand partial reboiler.

The components in increasing order of volatility arestyrene, EB, toluene and benzene. Based on the specifica-tions of the key components and their recoveries shown inTable 1, the product distribution is determined. InTable 1,the DVs are the decision variables whose values are to besupplied by the optimizer (discussed in the next section).Based on the above assumptions and product distributionsknown, the column was modelled; the complete set of equa-tions is available in related books (Khoury, 1999; Seider,2004).

3.2. Heat exchangers

The effluent heat exchangers are an integral part of thestyrene plant as they recover waste heat from the reactor ef-fluent and heats up the EB feed, hence reducing the overall

energy consumption. While modelling heat-exchangers forthis study, only the energy balance equations were consid-ered, as it was assumed that no chemical reactions are oc-curring inside, and the pressure-drops, to the fluid streamsinvolved, are also negligible. The other assumptions madewere (a) temperature varies only in axial direction, (b) heattransfer coefficient and flow rates of the hot and cold fluidsare constant throughout the exchanger length, (c) no energyloss to the environment and heat gained by the cold stream isequal to heat lost by the hot stream, and (d) counter-currentflow of fluids inside the heat exchanger. The governing equa-tions are:

Qcold =M(( TB

TC1

Cp,LdT

)+ Hvap

+( TC2

TB

Cp,V dT

)), (7)

Qhot =Qcold, (8)

m

TH2TH1

cpdT =Qhot, (9)

A= QcoldU

(T

)ln

. (10)

For the present study the value ofU was taken= 55 kJ/h/m2/K (Saunders, 1988).

Two heat exchangers are used in the model, one for EB-steam pre-heater (HE1) and the other for recycled EB pre-heater (HE2). While HE1 considers no phase change occur-ring in any of its streams, HE2 considers a phase change inits cold fluid flow. The recycled EB from EB recycle col-umn (S3) enters HE2 in a sub-cooled liquid state, reachesits boiling point inside HE2, and leaves as vapour hav-ing a temperature equal to the fresh EB inlet temperatureTEB. To determine the hot stream outlet temperature fromEq. (9), an iterative calculation was used using the subrou-tine DNEQNF of the IMSL FORTRAN library.

3.3. Partial condenser

The vapour entering the partial condenser is a multi-component mixture, consisting of non-condensable gaseslike, H2, CO, CO2, C2H4 and CH4, steam condensate andwater immiscible organic compounds, like C6H6, C6H5CH3,C6H5CHCH2 and C6H5CH2CH3. The exit temperature ofcondenser was set at 333 K in order to condense most of thesteam and water-immiscible compounds. As pressure dropin heat exchangers was considered negligible, the pressureassigned to the condenser is equal to exit pressure of thereactor, which is usually less than 2 bar. It was assumedthat the inlet mixture behaves ideally, obeying Daltons lawand Raoults law since the vapour mixture is mostly steam(greater than 85% on a molar basis) and a low pressureis maintained inside the condenser. The solubility of non-condensable gases in the organic phase was also considered


negligible. Based on these assumptions, vapourliquid equi-librium constant K for each componenti, was defined as

Ki = yixi

= Psati

Pcond(11)

and the moles of liquid condensed for each componenti (Li)is determined from

L=

Li = Yi

1+Ki(V/L), (12)

whereYi is the original number of moles of componenti invapour, andV andL are the total moles of vapour remainingand the total moles of liquid formed respectively. To deter-mine the amount of vapour condensed at the condenser tem-perature, first a value for (V/L) is assumed and the numberof moles of liquid formed is calculated from Eq. (12). Sub-sequently,V is calculated from the difference of(

Yi) and

L, and if the new value of(V/L) ratio does not agree withits assumed value, another value is assumed and the itera-tion proceeds until convergence. With the amount of vapourcondensed known, the sensible heat of vapour, sensible heatof liquid and latent heat of condensation for each compo-nent is calculated and the condenser duty is calculated asthe summation of enthalpy changes for all the components.

4. Formulation of the optimization problem

The complete process of styrene production involves cat-alytic reaction, cooling and separation. Although all the stepsare equally important, the catalytic conversion of EB tostyrene is the most critical because at this step the ultimatestyrene production, volume of by-products and volume ofrecycled EB to be handledare all decided. Seeing the im-portance of the reactor unit, the present study has been di-vided into two partsthe first part studies only the reactorunit and the EB pre-heater (HE1), which is taken as it af-fects the reactor performance significantly. The second part,on the other hand, involves a study of the entire styrene pro-duction unit (seeFig. 1) including the styrene reactor, heatexchangers, condenser and separation columns.

As the purpose of operation is to produce styrene and it isthe most costly product, the first objective of the optimiza-tion study was determined as maximization of styrene pro-duction. Added to that, minimization of the unwanted by-products, toluene and benzene, is also important as it causesraw material loss. To minimize the toluene and benzene pro-duction in the reactor, the selectivity of styrene should beincreased. The above findings are summarized in the follow-ing equations, which are the objective functions for the firstpart of the present optimization study:

Maximize : J1 = Fst, (13)

Maximize : J2 = Sst = Fst F0st

F 0EB FEB. (14)

Second part of the optimization study involves the entiremanufacturing process (seeFig. 1). The main operating costfor the process, other than the raw material, involves waterand the fuel to the steam boilers. Hence, while optimizing theentire styrene manufacturing process, the objective, whichwas included with the previous two, was minimization of thetotal heat duty. Heat duty minimization indirectly reducesthe emission of gases e.g. COx , SOx and NOx to the envi-ronment, as well. These gases are produced in steam boilerby burning fuel and causes major environmental pollution.

Minimize : J3 = Q, (15)whereQ is the total heat duty, expressed in GJ/h, suppliedas superheated and saturated steam flow to the reaction pro-cess as well as to the separation unit reboilers. Temperaturesof saturated steam for initial heating-up of EB, superheatedsteam and steam used for the column reboilers are fixed at405, 1025 and 373 K, respectively.

The optimization routine, real variable NSGA-II requiresthe objective functions to be described as minimization type.For maximizingJ1 andJ2 (Eqs. (13) and (14)), the actualobjective functions were written as the following, which isone of the popular approaches for inversion (Deb, 2001),

I =[

1

1+ J]. (16)

4.1. Decision variables and constraints

For the optimization of styrene plant, the decision vari-ables were chosen from the operating variables of existingplants and from key design variables of the reactor (Sheeland Crowe, 1969; Elnashaie and Elshishini, 1994). For thisstudy, the catalyst data were taken as fixed. The followingdecision variables and corresponding bounds were chosenfor optimizing the styrene reactorEBpre-heater unit (seeFig. 1):

1.4


And, three additional decision variables for DB type reactor(seeFig. 2) are:

700


80

84

88

92

96

100

0 5 10 15 20 25 30

Fst (kmol/hr)

Sst

(%)

Single Bed (SB)

Steam Injected (SI)

Double Bed (DB)

Industrial data

Fig. 3. Pareto optimal set obtained from the simultaneous maximization of styrene flow rate and styrene selectivity.

former as it converged faster in some cases and could pro-duce better Paretos than the binary-code NSGA-II. A moredetailed report of this comparative performance analysis canbe found in one of our recent publications (Tarafder et al.,2003). The program requires a set of parameters to carry outthe study. Like any GA based algorithm, it needs a seed forrandom number generations (Rs), to start with, and crossoverprobability (pc) and mutation probability (pm), to decidewhether the crossover and the mutation operations would beperformed or not. Besides, real-coded NSGA-II needs valuesof the distribution indices for simulated crossover operation(c) and simulated mutation operation (m). They are used todefine probability distributions, which ultimately determinethe location of resultant or child solution with respect to theparent solutions (Deb and Agrawal, 1995). For the presentstudy, we used:Rs=0.857,pc=0.7,pm=0.05,c=10 andm = 20, which were obtained after experimentation with arange of values, to generate the best Pareto. NSGA-II usesa tournament selection based, constrained non-dominatedsorting method for constraint handling. The process is veryefficient and better than the penalty function based meth-ods, which we used in our earlier study (Yee et al., 2003).Average computational time taken for all the optimizationstudies in this work, i.e. for all the reactor types and for thereactor computation as well as computation for entire man-ufacturing system, was 6 min. in a 2.4 GHz P4 computerwith 512 MB of SDRAM.

5.1. Optimization of styrene reactorEB preheater unit

Styrene reactorEB pre-heater unit was first optimizedfor maximizing the styrene flow rate and selectivity (case 1).The Pareto optimal solutions, for the three different reactorbed designs (Fig. 3), clearly show that the performance ofdouble bed (DB) reactor is the best, followed by the steam-injected (SI) and the SB reactors respectively. Although to-

wards very high selectivity (above 96%) the styrene flowrates are similar for the three reactor types, the differencein Fst increases significantly at lowerSst. The highestFstgenerated by the double-bed reactor is 6 kmol/h greaterthan its single-bed counterpart at the sameSst.

Figs. 4and 5 show the values of the decision variablescorresponding to every point of the Pareto sets inFig. 3,plotted againstFst. All the decision variables directly or in-directly contribute to a set of general factors, which actuallycontrols the reactor performance. These factors are: the EBand steam flow rates to the reactor, reaction temperature andpressure, reactor dimension and the catalyst performance.In different combinations, these factors decide EB conver-sion and styrene selectivity during the reaction process. Therole of EB and the steam flow rate is supportive to maxi-mizing both the objectives,Fst andSst. This is obvious, asthe most important precondition for generating highFst andSst is an availability of high EB flow rate. The same can besaid of the steam flow rate, with all its contribution to thereaction discussed before. The role of the reactor tempera-ture, on the other hand, is different for the two objectives.While a high reactor temperature facilitates higher EB con-version, and hence higher styrene flow rate, but at the sametime it decreases the styrene selectivity. A low reaction pres-sure increases the EB conversion and the styrene selectivitysimultaneously. The effect of the reactor dimensions on theobjectives is not monotonic; it reaches an extremum afterwhich it starts behaving in an opposite way. A high reactordiameter, which lowers the space velocity, increases con-version as well as theSst, if the reactor inlet temperatureis kept unaltered. But, a diameter value higher than a criti-cal one increases the reverse reaction and production of by-products thus reduces the performance. On the other hand,if the reactor diameter is lowered, it increases the space ve-locity and requires a higher inlet temperature to retain theEB conversion rate. So, the reactor diameter can be a factor


700

750

800

850

900

0 5 10 15 20 25 30

TC

2(K

)

SB

SI

DB

1.4

1.6

1.8

2

2.2

2.4

2.6

0 5 10 15 20 25 30

Pin

(bar

)

SB

SI

DB

Ind

7

9

11

13

15

17

19

0 5 10 15 20 25 30

SO

R

SB

SI

DB

Ind

26

31

36

41

0 5 10 15 20 25 30

Fst (kmol/hr)Fst (kmol/hr)Fst (kmol/hr)

Fst (kmol/hr) Fst (kmol/hr)

Fst (kmol/hr)Fst (kmol/hr)

Fst (kmol/hr)

Fo

EB

(km

ol/h

r)

SB

SI

DB

Ind

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30

D1(

m)

SB

SI

DB

Ind

0.7

0.9

1.1

1.3

1.5

0 5 10 15 20 25 30

(L/D

)SB

SI

DB

Ind

0.1

0.4

0.7

1

0 5 10 15 20 25 30

SB

SI

DB

450

460

470

480

490

500

0 5 10 15 20 25 30

TE

B(K

)

SB

SI

DB

(a) (b) (c)

(d) (e) (f)

(g) (h)

Fig. 4. (a)(h) Decision variables corresponding to the pareto optimal set inFig. 3. SBsingle bed; SIsteam-fed; DBdouble bed; Indindustrial data.

0.1

0.4

0.7

1

0 5 10 15 20 25 30


Fst (kmol/hr)Fst (kmol/hr)

Fst (kmol/hr)

SI

0.1

0.4

0.7

1

0 5 10 15 20 25 30

SI

700

750

800

850

900

950

0 5 10 15 20 25 30

Tm

ix2(

K)

SI

DB

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30

D2(

m)

DB

0.7

0.9

1.1

1.3

1.5

0 5 10 15 20 25 30

(L/D

) 2

DB

(a) (b) (c)

(e)(d)

Fig. 5. (a)(e) Additional decision variables for SI and DB reactors corresponding to the pareto set inFig. 3. SIsteam-injected; DBdouble bed.

for controlling theFst andSst to some extent, when the reac-tor temperature is kept invariant. The length of the reactor,for a given reactor diameter, determines the total residence

time of the reactantproduct mixture. While smaller reactorlength leads to unfinished reaction with low EB conversionand styrene production, a larger length decreases the selec-


tivity through reverse reaction and by-product generation.The catalyst performance is taken as uniform in the presentstudy and hence it is not considered as a variable. Indus-trially, to compensate the losses in catalyst activity, the in-let temperature to the reactor must be increased (Lee andHubbell, 1982).

After identifying the role of the contributing factors in de-termining the reactor performance, it is required to identifytheir relations with the decision variables, so that a generalestimate regarding the results of the decision variables canbe made. A glance at the list shows that the following de-cision variablesinlet pressure, SOR, EB flow, reactor di-ameter and reactor length, are the set of factors, which di-rectly control the reaction. The other decision variables, onthe other hand, have a combined effect on the reaction tem-perature, the most important factor that controls the reactionprocess. An approximate estimate can be made out of thisrelation that as the Pareto fronts generated by all the reac-tor types vary smoothly with theFst, the factors which aredirectly used as decision variables vary smoothly with theFst as well. It can be envisaged that the decision variableswhose combined effect determines the reaction temperaturemay scatter as more than one combination of these variables(degrees of freedom) can create the same thermal effect in-side the reactor. We can see fromFigs. 4ac that the valuesof the inlet pressure, SOR and EB flow are almost invariantwith respect toFst, as perceived by the general understand-ing of the reaction process. On the other hand, values of thedecision variables which are related to the reactor tempera-ture, i.e. the EB pre-heater outlet temperature (TC2), the re-actor length fraction () and superheated steam fraction (for SI reactor), the saturated steam fraction () and the re-actor intermediate temperature (Tmix2 for DB reactor)alldisplay noticeable variation and scatter with respect to theFst. Scattering of similar magnitude was noted even whentried with different values of NSGA-II parameters, and evenwith other optimization routines (Tarafder et al., 2003). Aswe have discussed elsewhere (Tarafder et al., 2004), thatscatterings of decision variables increase with the increasein the degrees of freedom (decision variables), and a sys-tematic approach should be devised to lessen it. This maydrastically increase the acceptability of the multi-objectiveoptimization results to the plant operators and designers, byoffering more acceptable and achievable choices.

The decision variables related to the reactor dimension,i.e. the reactor diameter(s) (Figs. 4d and5d) and length(s)(Figs. 4e and5e), although scattered, have an overall trendto reach uniformity. The trend of the temperature relateddecision variable values is expected as it affects theFst andSst in opposite way and the reason for the scattering canbe understood from the previous argument. The scatter inthe reactor dimension decision variables, on the other hand,is related to the scatter in the temperature related decisionvariables, as both the factors, the reactor diameter as wellas the temperature, can independently affect a change in theFst and Sst. If closely scrutinized, it can be seen that any

change in the reactor diameter has been reciprocated by achange in the reactor temperature.

A comparative analysis between the decision variables ofdifferent reactor types is necessary to understand the rea-sons behind their performance difference. Before going fur-ther into the comparative analysis, note that in all the figuresrepresenting the decision variables (Figs. 4and5), changesin decision variables up toFst equal to 10 kmol/h are veryrandom in general. This is possibly because up to this pointthe overall conversion of EB is lower than 20% (Fig. 6c) andit is expected that a wide range of decision variable combi-nations can result in such meager conversion leading to thisgeneral scattering. In the remaining part, any trend of deci-sion variables below thisFst mark would not be discussedto avoid repetition of similar arguments.

Starting with the reactor inlet pressure, it can be observedthat the values are mostly invariant and are close to 1.4 bar,the minimum pressure constraint. It can be also observedthat the DB reactor requires the maximum pressure followedby the SB and the steam injected respectively. It is expected,as the DB with shorter reactor diameters (Figs. 4d and5d)and longer reactor lengths (Figs. 4e and5e) offers the max-imum resistance to flow, whereas the steam injected of-fers least resistance as only a portion (Fig. 5b) of the totalthroughput covers the entire reactor length. For the EB andthe steam flow rates, it can be seen that all the decision vari-able values are almost equal to the highest possible, boundby their upper limits (40.56 kmol/h for EB) and steam flowconstraint (453.59 kmol/h), respectively. An abrupt variationof few EB flow points representing the DB reactor can benoted. A close observation shows that the lower EB flow iscompensated by a combined effect of a sudden rise in thereactor temperatures (Figs. 6a and6b) and the reactor di-ameters (Figs. 4d and5d) to produce a smooth Pareto. In alater part it will be shown that with compensation from re-actor temperature and reactor diameter, a far lower EB flowrate is sufficient to generate similarFstSst Pareto as inFig.3 up to moderately highFst. However, to produce very highFst, maximum possible EB flow is absolutely necessary.

The effect of all the temperature related decision vari-ables are combined into the reactor inlet temperature(Fig. 6a) and the reactor intermediate temperature (Fig. 5c).It can be seen that whatever way the contributing decisionvariables might have varied, both the temperatures increasealmost monotonically towards higherFst, as required by thereaction chemistry. Towards lowerFst, however, the reactordiameter controlled the performance and temperatures didnot vary. The reactor inlet temperature (Tmix1) is controlledby the pre-heater exit temperature (TC2) and the superheatedsteam flow rate[(1 )F 0stm] at the reactor inlet. Valuesof the pre-heater exit temperature (Fig. 4h) vary close tothe lower bound except for the SB and SI type where thevalues changed suddenly towards higherFst. Reason forthe generally low pre-heater temperature is the constraint(Eq. (33)) that the reactor outlet temperature (seeFig. 6b)should be at least 10 K higher than the pre-heater outlet


650

750

850

950

0 5 10 15 20 25 30

Tm

ix1(

K)

SB

SI

DB

0

20

40

60

80

80 85 90 95 100

Sst(%)

EB

Co

nve

rsio

n (

%)

SB

SI

DB

DB-inter

ST-inter

15

20

25

30

35

0 5 10 15 20 25 30

Hea

t-d

uty

(G

J/h

r)

SB

SI

DB

0

10

20

30

0 5 10 15 20 25 30

Rea

cto

r vo

lum

e (m

3 )

SB

SI

DB-Total

0

2

4

6

8

0 5 10 15 20 25 30

Rea

cto

r le

ng

th (

m)

SB

SI

DB

650

750

850

950

0 5 10 15 20 25 30

Fst(kmol/hr)Fst(kmol/hr)

Fst(kmol/hr) Fst(kmol/hr)Fst(kmol/hr)

TH

1(K

)

SB

SI

DB

(a) (b) (c)

(d) (e) (f)

Fig. 6. (a)(f) Calculated values of some variables corresponding to the pareto set inFig. 3. SBsingle bed; SIsteam-injected; DBdouble bed;DB-interoutlet to the first bed of DB reactor; SI-interSI reactor point just before intermediate steam mixing; DB-totalAdding both the beds of DBreactor.

temperature (TC2). To satisfy this, the optimizer opted forlower pre-heater temperature, so that higher temperaturedrop, resulting higher conversion across the reactor, cantake place. The steady increase of the reactor inlet tempera-ture, on the other hand, is supported by the increasing flowof superheated steam, which is evident from the values ofsaturated steam fraction (Fig. 4g), decreasing steadily withFst. For the SB and SI reactor,TC2 increases towards theend because even maximum superheated steam flow wasnot sufficient to raise the temperature to the required level toproducing highFst. It can be observed that only after the netsuperheated steam flow to the reactor reached its maximum(indicated by the lowest values inFig. 4g), the optimizerstarted selecting higherTC2 values (Fig. 4h). However, withhigher pre-heater temperatures, lower superheated steamflows (higher) were selected again, which gradually in-creased to reach the maximumFst point of the SI reactor.Similar phenomenoncan be observed for the SB reactor aswell. The intermediate temperature of the SI reactor is con-trolled by the reactor length fraction () (Fig. 5a) and thesuperheated steam fraction () (Fig. 5b), whereas for theDB reactor, its the superheated steam flow (at 1025 K) thatindirectly heats the outlet flow of the first bed. It can be no-ticed that the DB intermediate temperatures are higher thanthe inlet temperatures as the first bed outlet temperaturesare higher than the temperatures of the pre-heater outletflow. For the SI reactor, the and values were chosenas to boost the reaction temperature at a suitable interme-diate point so that increased objective values are achieved.Cross-referring the values of the SI reactor diameter and theinlet and intermediate reactor temperatures can perform ananalysis of the pattern of changes in and. Fig. 5a showsthat decreases towards higherFst making the second part

of the reactor longer and the first part shorter. The reasonbehind this trend will be addressed later in the analysis ofSI reactor dimensions.Fig. 5b shows that the value cho-sen is 0.37 over a wide range ofFst values, and this isprobably the best way to distribute the steam.

A comparative analysis of the reactor inlet (Tmix1) andthe intermediate (Tmix2) temperatures is necessary to under-stand the reason behind the performance difference betweenthe different types of reactors.Fig. 6a shows that the inlettemperature of SB reactor is higher than both the SI and DBtype. As EB conversion is directly dependent on the reactortemperature and the reaction process decreases the reactortemperature along its length, only a very high inlet tempera-ture for SB reactor can ensure sufficiently high temperaturethroughout the reactor length to achieve the required conver-sion. It can be seen fromFig. 6a that the inlet temperature ofSB reactor reached the maximum limit to produce the max-imum Fst. However, in the process of increasing theFst, ithas to largely compromise with theSst, and made its over-all performance worse than the other reactor types. On theother hand, for both the SI and DB type reactors there areintermediate supplies of energy to boost the reactor temper-atures and so its inlet temperatures are not chosen as high asthat of SB. Obviously this was done to keep theSst valueshigh for them.

The diameter selection of all types of reactors is verymuch dependent on their temperature selection. It can beobserved that although almost uniform diameter is selectedby all the reactor types at the highest respectiveFst, sig-nificant scattering is there in between. The diameters at therespective highestFst may be the best for the reactor inletor intermediate temperatures having upper limit at 925 K.A comparative observation of the entire range of values of


the reactor diameters (Figs. 4d and5d) and reactor inlet andintermediate temperatures (Figs. 6a and5c) shows that allthe values are often abruptly, but complementarily chosen tomaintain a smooth Pareto of the objective values. However,most distinctively, the DB type reactor has chosen muchlower diameters than its counterparts. Starting with the SBreactor, it is understandable that an absence of any interme-diate heating has forced it to maintain a high reactor diam-eter, as well as high reactor inlet temperature to maximizetheFst, by maximizing EB conversion. At lower inlet tem-peratures it could retain highSst value comparable to otherreactors, however, as the inlet temperature is increased,Sstdecreased sharply. The final diameter chosen by the SB re-actor is probably the best to produce the highestFst withthe minimum sacrifice in theSst. The DB reactor, on theother hand, has the option of distributing the reaction pro-cess in two separate beds to maximize the objectives. Thelower reactor diameter (Fig. 4d) and lower inlet temperature(Fig. 4h) chosen by the DB for its first bed is to convertthe EB, keeping theSst as high as possible (Fig. 6c). Thesecond bed, however, converts the EB aggressively to max-imize theFst, which is evident from the high inlet temper-ature (Fig. 5c) and higher diameter (Fig. 5d) of the secondbed. This reduces theSst values significantly in the secondbed, but the overallSst can be maintained high enough tak-ing theFst value far higher than other two reactors (Fig. 3).Anobvious comparison comes between the performances ofthe DB reactor and the SI reactor, as the operational strategyof SI is very close to the former type.Figs. 6a and5c showthat both the inlet (Tmix1) and intermediate (Tmix2) temper-atures of SI reactor can be higher than the DB type, alongwith that, the optimizer could have chosen any reactor di-mensions to make the SI reactor performance comparable tothat of DB. But this could not happen, as the real differencein their performance is made in the first part of the SI re-actor. The first part, having less than half the volume of thetotal steam, results in much higher partial pressures of thereactants compared to the first bed of DB. This high reac-tion pressure significantly reduces the EB conversion in thefirst bed (Fig. 6c) even at high temperatures and large diam-eters. It can be seen that the initial conversion as well as theinitial Fst from the first part of SI reactor is far lower thanthe DB first bed outlet. Though the second part of SI showsa comparable, even better, performance than the second bedof DB, the overall performance could not be matched. Thehigher reactor diameter chosen by SI is to boost the low EBconversion in the first part. Regarding the reactor lengths,althoughL/D ratios show lots of scattering, the actual re-actor lengths (Fig. 6d) are well defined.Fig. 6d shows thatthe total length of both the SB and SI type reactors reacha uniform value circa 3 m, while the length of the DB typeincreases with theFst with values almost twice as the othertypes. To keep the total reactor volume comparable, the to-tal reactor length of DB is chosen higher than the other twotypes, as diameters of both the DB reactor beds are lowerthan the others. It can be observed that the reactor length

of DB increases towards the highestFst. This is to increasethe total reactor volume, for more EB conversion, keepingthe diameters fixed. The decreasing value of in SI reactorcan be explained with similar argument. As the performanceof the first part of SI reactor could not be better, the opti-mizer increased the length of the second part to boost theperformance to the maximum achievable level. Selection ofthe EB inlet temperature (Fig. 4f) by the optimizer is influ-enced by the pre-heater temperature difference constraints(Eqs. (33) and (34)), values of the saturated steam fraction(Fig. 4g) and the pre-heater outlet temperature(Fig. 4h). Inthe optimization study, it has little role in evaluation of theobjectives.

The optimization results bring out some revealing factsregarding the reactor volume and the heat duty required bythe reactors. Intuitively, it may look that the total reactorvolume of DB type must be much higher than the other twotypes and the heat duty required by it should be far higher.But from Fig. 6e it is clear that the total reactor volumeof DB is comparable to the other types and the heat duty(Fig. 6f) required, in actuality, is marginally lower than theSB type and almost equal to the SI type reactor. The totalvolume is comparable as the diameters of both the beds werechosen far lower than the other types. Regarding the heatduty, it can be seen fromFig. 4g, that the total steam-flowfor superheating in DB is far lower than the others and forthis reason the total heat carried by the steam to DB reactoris the same or even lower.

The styrene flow and styrene selectivity were chosen asthe objectives of this optimization study as these are themain factors of the styrene reactor which ensures maximumstyrene production. The results generated by the optimiza-tion, however, show that a bi-objective optimization ofFstandSst computes the maximum possibleFst values, but itdoes not ensure the maximum profitable situation. For ex-ample, even to produce low styrene flows (at highSst), theoptimizer had chosen highest possible EB flow and the othercontributing factors accordingly. We have argued earlier thatfar lesser EB flow rates could have been chosen at this sit-uation, along with appropriate reactor dimensions and tem-peratures. As this lowers plant running cost, this may createa big difference in the plant economics. In industries un-reacted EB is recycled to the process, but the separation ofun-reacted EB from styrene is very costly. So, usage of min-imal EB flow or maximum conversion of EB ensures loweroperating cost. This fact leaves space for a look into the EBconversion aspect as well. It was perceived that the perfor-mance of the SM reactor cannot be fully understood unlessit is optimized along with the conversion of EB as well.

The DB type reactor was chosen for a tri-objective opti-mization study by maximizing theFst, Sst and EB conver-sion (case 2). The results generated by this study were com-pared to the bi-objective optimization results of DB reactor.Fig. 7 plots EB conversion as well asSst againstFst forboth the bi- and tri-objective optimization study. The figureshows that theFstSst trade-off is better in the bi-objective


0

20

40

60

80

100

0 5 10 15 20 25 30Fst (kmol/hr)

EB

Co

nve

rsio

n (

%)

80

84

88

92

96

100

Sst

(%

)

Fig. 7. Comparison of the performances of DB type reactor plotted as (a)Fst versus EB conversion and (b)Fst versusSst, from (1) Pareto obtainedfrom tri-objective optimization ofFst, Sst and EB conversion [() for (a) and () for (b)]; and (2) bi-objective optimization ofFst andSst [() for (a)and () for (b)].

study than the tri-objective; particularly at highFst values.However, corresponding EB conversion of the bi-objectiveprocess is much lower than that suggested by the tri-objectiveprocess. Higher conversion means handling lower volume ofun-reacted EB in the EBstyrene separation unit, resultingin lower steam cost for the distillation column reboiler. Onthe other hand, lower selectivity means higher conversion ofEB to benzene and toluene, and as the market price of boththe benzene and toluene is lower than EB, lower selectivitymeans raw material degradation. A comparison of the bene-fits from the above schemes can be made. It should be notedthat the amount of heat duty required in the EBstyrene sep-arator is significantly high because of high latent heat of EBand the close boiling points of styrene and EB, requiringhigh reflux ratio. If the price of toluene and benzene is muchlower than EB, selectivity should be the main criterion forselecting a suitable operating point. On the other hand, iftoluene and benzene price comes closer to the EB price butsteam cost is on the higher side, conversion of EB shouldbe taken into foremost consideration. Another basis of com-parison is the styrene price. If the styrene price rises signifi-cantly, then the objective should focus on production of thehighest styrene possible, even at the cost of lower selectiv-ity or lower conversion. As the international market price ofstyrene varies widely, this type of comparison carries usefulinsight. From a comparative study of these results (Fig. 7),it can also be said that under the stated operational limita-tions, if the required selectivity is greater than 93%, the de-cision variables suggested by the tri-objective optimizationprocess is more economical. For a requirement of maximumFst within the operational limits, however, the variables sug-gested by bi-objective optimization process are better.

A comparison of decision variables of the DB reactor,generated through bi- and tri-objective optimization (Fig. 8),brings out the reason for the difference in their respectiveperformances. It can be seen fromFig. 8b that much lowerEB flow is required for tri-objective case, accompanied byan elevated SOR (Fig. 8a) as well as reactor intermediatetemperature (Tmix2) (Fig. 8d). The reactor diameter of thefirst bed (Fig. 8c), on the other hand, is higher for the tri-

objective case. The higher inlet temperature and higher di-ameter requirement for the tri-objective case is understand-able as both these factors lead to high EB conversion. As roleof the other decision variables has been already discussedand as they dont change significantly in the tri-objectivecase, no further discussion of the other decision variables ismade.

5.2. Optimization of styrene manufacturing process

From the study of the styrene reactor-EB pre-heater op-timization, it was evident that conversion of EB is a cru-cial factor in the reaction, affecting the required heat dutywhile separating the downstream components. For studyingthe effect of the reaction process on the heat requirement atthe separation units, the next phase of the study includes thecooling as well as the separation units along with the reactorunit. The main source of energy for the reaction and for thedistillation is saturated as well as superheated steam. Thestudy on the entire manufacturing process focuses on reduc-tion of total steam (heat duty) used along with the increasein styrene flow rate and selectivity. The study is carried outonly on the DB type reactor as this has been identified asthe best reactor configuration in the previous section.

Fig. 9plots the Pareto optimal set of the tri-objective opti-mization of styrene manufacturing process for maximizationof Fst andSst and minimization of the total heat duty (Q) re-quired (case 3). The results are plotted asSst andQ againstFst. The Fst vs. Sst Pareto optimal set of the bi-objectiveoptimization of DB reactor (case 1) has also been plottedon the same figure for comparison. AlthoughFig. 9 showsthat theFstSst Pareto optimal set of the tri-objective op-timization problem is scattered and performing worse thanthe FstSst set of bi-objective one, this compromise wasmade to minimize the total heat duty requirement of the en-tire plant. In the bi-objective optimization section, a generalanalysis of the decision variables and their effects on theFst and theSst values has already been done. This sectionrequires a general understanding of the third objective, theheat duty (Q) minimization. The heat duty requirement to


7

9

11

13

15

17

19

0 5 10 15 20 25 30

SO

R

Tri-DB

Bi-DB

Ind

27.56

29.56

31.56

33.56

35.56

37.56

39.56

0 5 10 15 20 25 30Fst (kmol/hr)Fst (kmol/hr)


Fo E

B(k

mo

l/h

r)

Tri-DB

Bi-DB

Ind

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30

D1

(m)

Tri-DB

Bi-DB

700

750

800

850

900

950

0 5 10 15 20 25 30

Tm

ix2

(K)

Tri-DB

Bi-DB

(a) (b)

(c) (d)

Fig. 8. (a)(d) Some decision variables corresponding to the pareto sets referred inFig. 7. TriDBresults from tri-objective and Bi-DBresults frombi-objective optimization of double bed reactor; IndIndustrial data.

80

84

88

92

96

100

0 5 10 15 20 25 30Fst (kmol/hr)

Sst

(%

)

0

10

20

30

40

Q (

GJ/

hr)

Case 1(Sst)

Case 3 (Sst)

Case 3 (Q)

Fig. 9. Comparison of the performance of: Case 1bi-objective optimization ofFst andSst; and Case 3tri-objective optimization ofFst, Sst and heatduty (Q). [-]: pareto set ofFst vs. Sst; [] Fst vs. Sst plot; [] Fst vs. heat duty (Q).

a styrene manufacturing process can be divided under twomajor heads. One part, which is calculated here by the SORand the EB flow rate, enters the reactor as saturated or su-perheated steam, pre-heats and inter-heats the EB feed, ul-timately fed to the reactor as a reactant to the process. Theother part, on the other hand, is used as an indirect supplierof heat to the reboiler units of the distillation columns. Iflesser steam is supplied to the reactor, resulting in un-reactedEB, the reboiler heat duty at the EBstyrene separation unitwill increase drastically to separate the increased un-reactedEB. The process will act vice-versa. Thus the total heat dutyminimization (duty to the reactor plus duty to the separa-tion units) acts counteractively in generating the best set ofresults. From this observation, it can be predicted that theminimization attempt of the total heat duty in the processmay generate scattered objectives because of the counter-acting effects.

The inlet pressure,Pin, selected by tri-objective optimiza-tion study is slightly higher than the bi-objective one; al-

though it likely maintained the lowest pressure possible sat-isfying all other constraints. The main reason for choos-ing slightly higher pressure is because of the lower reac-tor diameter, which will be discussed later. Both the SOR(Fig. 10a) and the EB flow rate (Fig. 10b) of the tri-objectiveoptimization study is scattered in nature. This was specu-lated, for the counteracting effect of the heat duty (Q) min-imization objective on the reactor steam flow rate. The EBflow rate is also scattered for another counteracting effect.In the bi-objective optimization study, we have seen that theFst and theSst maximization requires the highest possibleEB flow. On the other hand, the heat duty minimization,which requires minimum handling of un-reacted EB in theseparation unit, will try to ensure the minimum required EBflow to the reactor. For these counteracting requirements, theEB flow rates chosen are scattered in nature as well. A plotof the total flow (EB plus saturated and superheated steam)shows that the total flow of the tri-objective optimizationstudy is far lower than that of the bi-objective (Fig. 11a).


700

750

800

850

900

0 5 10 15 20 25 30

TC

2(K

)

Case 1

Case 3

1.4

1.6

1.8

2

2.2

2.4

2.6

0 5 10 15 20 25 30Fst (kmol/hr) Fst (kmol/hr) Fst (kmol/hr)

FE

B (k

mo

l/hr)

Fst(kmol/hr) Fst(kmol/hr) Fst(kmol/hr)



Fst(kmol/hr) Fst(kmol/hr)

Pin

(ba

r)

Case 1

Case 3

7

9

11

13

15

17

19

0 5 10 15 20 25 30

SO

R

Case 1

Case 3

26

31

36

41

0 5 10 15 20 25 30

o

Case 1

Case 3

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30

D1

(m)

Case 1

Case 3

0.7

0.9

1.1

1.3

1.5

0 5 10 15 20 25 30

(L/D

)Case 1

Case 3

0.1

0.3

0.5

0.7

0.9

0 5 10 15 20 25 30

Case 1

Case 3

450

460

470

480

490

500

0 5 10 15 20 25 30

TE

B (K

)

Case 1

Case 3

700

750

800

850

900

950

0 5 10 15 20 25 30

Tm

ix2

(K)

Case 1

Case 3

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30

D2

(m)

Case 1

Case 3

0.7

0.9

1.1

1.3

1.5

0 5 10 15 20 25 30

(L/D

) 2

Case 1

Case 3

0.96

0.97

0.98

0.99

0 5 10 15 20 25 30

LK

S1

Case 3

0.96

0.97

0.98

0.99

0 5 10 15 20 25 30

HK

S1

Case 3

0.97

0.98

0.99

0 5 10 15 20 25 30

LK

S3

Case 3

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)

(m) (n) (c)

Fig. 10. (a)(n) Decision variables corresponding to the bi- and tri-objective optimization referred inFig. 9. Case 1results from double-bed bi-objectiveoptimization ofFst andSst; Case 3results from double-bed tri-objective optimization ofFst, Sst and heat duty.

Figs.11b and10g show that both the inlet (Tmix1) as wellas the intermediate (Tmix2) temperatures from tri-objectiveoptimization, are higher than their bi-objective counterparts.These selections were aimed at increasing the EB conversionin the reactor so thatFst is maximized as well as minimizingun-reacted EB moving to the separator. The two contribut-ing decision variables to the values ofTmix1 andTmix2, thesaturated steam fraction () and the pre-heater outlet tem-perature (TC2); both these support increment ofTmix1 andTmix2 (Figs. 10e and f). The values for both the decision vari-

ables have been chosen to ensure higher heat flow than theirbi-objective counterparts. Although the fraction of super-heated steam flow is higher for tri-objective case (lower seeFig. 10e), the overall heat duty supplied to the reaction pro-cess (Fig. 11c) is still lower due to lower EB flow and SOR.

The reactor diameters chosen by the tri-objective study forits first bed is almost half as those chosen by the bi-objective(Fig. 10c), whereas for the second bed (Fig. 10h), the val-ues are comparable, even higher at certain points. While dis-cussing the bi-objective results, we have analysed the reason


650

750

850

950

0 5 10 15 20 25 30

Tm

ix1

(K)

Case 1

Case 3

0

10

20

30

40

0 5 10 15 20 25 30

Fst

(kmol/hr)Fst

(kmol/hr)Fst

(kmol/hr)

Hea

t d

uty

(G

J/h

r)

Case 1

Case 3

150

250

350

450

550

0 5 10 15 20 25 30

To

tal F

low

(km

ol/h

r)

Case 1

Case 3

(a) (b) (c)

Fig. 11. (a)(c) Calculated values of some variables corresponding to the bi- and tri-objective optimization referred inFig. 9. In Fig. 11c, Case 1comprises heat-duty to the reactor only, whereas Case 3 comprises heat-duty to the reactor as well as the separation unit reboilers. Case 1results fromdouble-bed bi-objective optimization ofFst andSst; Case 3results from DB tri-objective optimization ofFst, Sst and heat duty (Q). Note: In Fig. 11c,the heat duty referred to Case 1 is for the reactor unit only, whereas for Case 3 its for the entire manufacturing process.

behind the choice of lower reactor diameters. The first beddiameter was chosen lower to keep theSst high while try-ing to increase the EB conversion. Tri-objective optimiza-tion has chosen still smaller diameters because of higher in-let temperatures than the bi-objective. Additionally, the lowtotal flow rate handled by the tri-objective case makes thediameter still lower. For the second bed, however, in an at-tempt to attain the highestFst the diameters are made higherto maximize the EB conversion. The lengths of both thereactor beds (Figs. 10d and i) are chosen lower than theirbi-objective counterparts as the tri-objective study handleslower total flow of EB and steam.

An analysis of the three more decision variables used inthe tri-objective study shows that the first two variables, thelight key and the heavy key fractions of the first distilla-tion column have selected moderate values (Figs. 10j andk). This shows that the optimizer tried to push more EB inwith the benzene-toluene flow and more benzene with theEBstyrene flow. This attempt, most likely, was made to de-crease the total flow rate of EB to the reactor by replacing itwith toluene impurities. Values of the last decision variable,the light key fraction at the EBstyrene column (Fig. 10l)also shows similar trend, where maximum impurities weretried to mix with the EB flow to keep the heat-load lower atthe condenser.

6. Conclusions

A multiobjective optimization study of an industrialstyrene reactor unit as well as the entire styrene manufac-turing process was carried out with elitist NSGA or NSGA-II. The objectives were to maximize the styrene flow andthe styrene selectivity for the first part and styrene flow,styrene selectivity and total heat duty for the second part.Pareto optimal sets were successfully obtained for all thecases. The trend of the decision variables generated couldbe explained qualitatively, which shows the reliability ofthe results. In the first part of the optimization study, threevariations of styrene reactor were used for a comparativeanalysis of their respective performances at the optimized

condition. It was observed that although at higher selectivitythe performances of all the reactor types are comparable,the double bed (DB) reactor is far more efficient than theother types in producing high styrene flow from equivalentEB flow input. The optimization brought out certain factsregarding the reactor volume and the heat duty required bythe reactors, which are counter intuitive. Initially it maylook that the total reactor volume of DB reactor must behigher than the other two types and the heat duty requiredby it should be far greater. But it was observed that the totalDB reactor volume is comparable to the volumes of othertypes and the heat duty required is actually lower than thesingle bed type and almost equal to the steam-injected typereactor. The optimization of the entire styrene manufactur-ing process suggested different operating points to run theplant at different levels of by-product formation, EB recyclehandling and total heat duty minimization.

The optimization routine, NSGA-II, used in the presentstudy proved to be relatively more efficient than the NSGAroutine used in our previous study (Yee et al., 2003). WithNSGA-II, we could always reach the final solution faster andwith a better distributed and wider spread Pareto. It was alsonoticed that the constraint domination criteria of NSGA-IIworked better than the penalty function approach of con-straint handling in NSGA, which was used earlier (Yee etal., 2003). While NSGA-II could take all the solutions tothe feasible region within first few generations, NSGA gen-erated infeasible solutions till close to the last generation. Itwas speculated that NSGA couldnt generate a wider Paretolike NSGA-II, because the large dummy values, awarded tothe objectives of infeasible solutions, kept nearby potentialfeasible solutions out of the search space.

Notation

A surface area, m2, (also) frequency factorC molar concentration, kmol/m3, (also) num-

ber of componentscp molar heat capacity for hot fluid, kJ/kmol/K


Cp molar heat capacity for cold fluid, kJ/kmol/KD diameter, m, (also) distillate, kmol/hF molar flow rate, kmol/h, (also) distillation

column feed, kmol/hH enthalpy, kJ/kmolHE1 EB feed pre-heaterHE2 recycled EB heaterJ maximization equationK vapour liquid equilibrium constantL total length of reactor, m, (also) liquid flow,

kmol/hL/D reactor length to diameter ratiom molar flow rate of hot stream, kmol/hM molar flow rate of cold stream, kmol/hp partial pressure, (also) probabilityP pressure, barQ rate of heat transfer, kJ/hR universal gas constant, 8.314 kJ/kmol/KRs seed for random numberS selectivity, %, (also) separatorSOR steam to reactant (ethylbenzene) molar ratioT temperature, KU overall heat transfer coefficient, kJ/h/m2/KV vapour flow, kmol/hx liquid mole fractionX conversion, %y vapour mole fractionY yield, %

Greek letters

saturated steam fraction, (also) relativevolatility

superheated steam fraction (only for SI typereactor)

differenceH heat of reaction, kJ/kmol distribution index reactor bed fraction for steam injection (only

for SI type reactor)

Superscripts

0 initialsat saturated

Subscripts

0 initialB boiling point, (also) bottombz benzeneC1 cold stream inletC2 cold stream outletCO carbon monoxideCO2 carbon dioxidec cross-over

cold cold streamcond condenserD distillateEB EthylbenzeneEth Ethyleneexit exit conditionF feedGen GenerationH1 hot stream inletH2 hot stream inletH2 Hydrogenhot hot streami componenti, (also) light key componentin inletL liquidln log-meanm mutation, (also) meanmix1 entry condition at the 1st bed of DB, or 1st

part of SI reactormix2 entry condition at the 2nd bed of DB, or 2nd

part of SI reactorst Styrenestm Steamtol toluenevap VapourizationV Vapour

Acknowledgements

The authors acknowledge the contribution of Ms LeeLee Tang Jaimie for writing the initial structure of thesimulation program. Special thanks to Prof KalyanmoyDeb for making the NSGA-II code available on the net(www.iitk.ac.in/kangal/soft.htm).

References

Bhaskar, V., et al., 2000. Applications of multi-objective optimization inchemical engineering. Reviews in Chemical Engineering 16, 1.

Clough, D.E., Ramirez, W.F., 1976. Mathematical modeling andoptimization of the dehydrogenation of ethylbenzene to form styrene.A.l.Ch.E. Journal 22, 10971105.

Deb, K., 2001. Multi-objective Optimization using EvolutionaryAlgorithms, Wiley, Chichester, UK.

Deb, K., Agrawal, R.B., 1995. Simulated binary crossover for continuoussearch space. Complex Systems 9, 115.

Deb, K., et al., 2002. Fast and elitist multiobjective genetic algorithm:NSGA-II. IEEE Transactions of Evolutionary Computing 6, 182197.

Denis, H.J., Castor, W.M., 1992. In: Elvers, B. et al. (Ed.), Styrenein Ullmanns Encyclopedia of Industrial Chemistry, vol. A25. Wiley,New York, pp. 325335.

Elnashaie, S.S.E.H., Elshishini, S.S., 1994. Modelling, Simulation andOptimization of Industrial Fixed Bed Catalytic Reactors. Gordon andBreach Science Publisher, London, pp. 364379.

Kasat, R.B., Gupta, S.K., 2003. Multi-objective optimization of anindustrial fluidized-bed catalytic cracking unit (FCCU) using geneticalgorithm (GA) with the jumping genes operator. Computers andChemical Engineering 27, 17851800.

http://www.iitk.ac.in/kangal/soft.htm


Khoury, F.M., 1999. Predicting the Performance of Multistage SeparationProcesses, CRC Press, LLC.

Lee, C.H., Hubbell, O.S., 1982. In: McKettam, J., Wesmantel, G.E. (Eds.),Styrene in Encyclopaedia of Chemical Processing and Design, vol.55. Wiley, New York, pp. 197217.

Mitra, K., Gopinath, R., 2004. Multiobjective optimization of an industrialgrinding operation using elitist nondominated sorting genetic algorithm.Chemical Engineering Science 59, 385396.

Rajesh, J.K., et al., 2001. Multi-objective optimization of industrialhydrogen plants. Chemical Engineering Science 56, 999.

Saunders, E.A.D., 1988. Heat Exchangers: Selection, Design andConstruction. Longman Scientific and Technical, New York, pp.528529.

Seider, W.D., et al., 2004. Product and Process Design Principles:Synthesis, Analysis, and Evaluation. Wiley Text Books, 2nd. Wiley,New York, pp. 445446.

Sheel, J.G.P., Crowe, C.M., 1969. Simulation and optimization of anexisting ethylbenzene dehydrogenation reactor. Canadian Journal ofChemical Engineering 47, 183187.

Srinivas, N., Deb, K., 1995. Multi-objective function optimization usingnon-dominated sorting genetic algorithms. Evolutionary Computation2, 221.

Tarafder, A., et al., 2003. Applications of non-dominated sortinggenetic algorithms for multiobjective optimization of an industrialstyrene reactor. Proceedings of Second International Conferenceon Computational Intelligence, Robotics and Autonomous Systems(CIRAS 2003), Singapore.

Tarafder, A. et al., 2004. Multi-objective optimization of an industrialethylene reactor using a non-dominated sorting genetic algorithm.Industrial and Engineering Chemistry Research, revised manuscriptsubmitted to Industrial and Engineering Chemistry Research, 2004.

Yee, A.K.Y., et al., 2003. Multiobjective optimization of an industrialstyrene reactor. Computers and Chemical Engineering 27, 111130.

Multiobjective optimization of an industrial styrene monomer manufacturing processIntroductionProcess descriptionMathematical modelling and simulation of the styrene plantDistillation columnsHeat exchangersPartial condenser

Formulation of the optimization problemDecision variables and constraints

Results and discussionOptimization of styrene reactor---EB preheater unitOptimization of styrene manufacturing process

ConclusionsAcknowledgementsReferences

A65 Abhijit Styrene CES 2005

Documents

Transcript of A65 Abhijit Styrene CES 2005