Design Alternatives for the Amyl Acetate Process Coupled Reactor

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Article

Design Alternatives for the Amyl Acetate Process: Coupled Reactor/Column and Reactive Distillation

Sheng-Feng Chiang, Chien-Lin Kuo, Cheng-Ching Yu, and David S. H. WongInd. Eng. Chem. Res. , 2002 , 41 (13), 3233-3246 DOI: 10.1021/ie010358j

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SEPARATIONS

Design Alternatives for the Amyl Acetate Process: Coupled Reactor/Column and Reactive Distillation

Sheng-Feng Chiang, Chien-Lin Kuo, Cheng-Ching Yu,* , and David S. H. Wong

Department of Chemical Engineering, National Taiwan University of Science and Technology,Taipei 106-07, Taiwan, and Department of Chemical Engineering, National Tsing Hua University,Hsinchu 300-13, Taiwan

Recent a dvan ces in reactive distil lat ion h ave led to renewed int erest in the design/redesign ofmany esterification processes. For the esterification of amyl acetate, design alternatives existthat offer a gradual transition from the conventional recycle structure to reactive distil lation.The phase behavior of the quaternary mixture immediately excludes the possibi l i ty of theconvent ional recycle s t ructure , a nd in this work, w e explore the designs of t wo differentconfigura tions, a coupled rea ctor/column a nd rea ctive distilla tion column , for th e amy l aceta teprocess. The t otal a nnua l cost (TAC) is used to evalua te the economic adva nta ges of differentdesigns. S yst ema tic design procedures w ere devised for t he coupled react or/column sy stem, a swell a s for th e reactive distil lat ion process. The results clearly indicat e the economic adva nta geof reactive distillat ion for the amy l aceta te process. Unique char a cteristics of a myl a ceta te processinclude a significant t w o-liquid zone and h igh-purity w a ter from the a queous pha se of a decant er.This leads us to a single-end-composition control problem. However, limit cycles can occur ifthe net react ion rate and product ion rate are not properly balanced or i f the feeds are notstoichiometrically bala nced. Therefore, a second composition loop is used to infer possibleimbalances. Dynamic s imulat ions indicate that reasonable control can be achieved for verycomplex rea ctive distil lation dy na mics.

1. Introduction

Reactive disti llation ha s been employed in industryfor decades, but i t has received renewed attention in

recent yea rs.1,3,6,12,19,21,22

Reactive distillation can reducecapital a nd energy costs in some systems, part icularlywhen the reactions are reversible or when the presenceof azeotropes makes conventional separation expensive.As pointed out by Malone and Doher ty, 19 combiningreaction and separa tion is not alw ays a dvant ageous, an din some cases , i t might not even be feas ible. Mostprocess design begins with the conventional reactor/separator recycle structure 7,18,25 where the reactor i sdesigned f irs t , fol lowed by the separa tors , w i th thedesign t ypically being done in a hierarchical order.7From the process operation perspective, reaction andsepar at ion a re carried out sequentia lly. For reversiblereactions, the coupled reactor/column might be ana t t r ac t ive a l t e rna t ive. I t f ea tu res a r eac tor wi th arectifier a nd/or a str ipper. 27 The principle behind thecoupled rea ctor/column, similar to r eactive d istillat ion,is that i t removes the products continuously from thereaction mixture by distillation, which reduces the effectof the backward reaction. I t also has the advantages of

easy cata lys t replacement , la rge reactor holdup, andreuse of existing equipment. 27 The full-blown versionof the coupled reactor/column is, certa inly, reactivedisti l lation.3,17,19,22 Cla ssical success stories include themethyl acetate process and the production of methyltert -butyl ether (MTBE).

Amyl a ceta te ha s been used in industry a s a solvent,an extra ctant , and a polishing agent, for example. It canbe synthesized from acetic acid and amyl alcohol via anesterification. However, ternary azeotropes were found

* Corresponding a uthor, current ly with Department ofChemical Engineering, National Taiwan University, Taipei106-17, Ta iwa n. F a x: + 886-2-2362-3040. Tel.: + 886-2-3365-1759. E-ma il: [email protected] u.edu.tw .

Nat iona l Taiw an Un iversity of Science and Technology. National Tsing Hua University.

Table 1. Binary Parameters of the NRTL Model a forAcetic Acid (1) + Amyl Alcohol (2) + Amyl Acetate (3) +Water (4) Systems 4,14

(i , j ) Aij (K ) A ji (K) R ij (1,2) - 316.8 178.3 0.1695(1,3) - 37.943 214.55 0.2000(1,4) - 110.57 424.018 0.2987(2,3) - 144.8 320.6521 0.3009(2,4) 100.1 1447.5 0.2980(3,4) 254.47 2221.5 0.2000

a NRTL equation:

ln i )

j ) 1

m

ji G ji x j

k ) 1

m

G ki x k

+ j ) 1

m x j G ij

k ) 1

m

G kj x k [ ij - (r ) 1m

x r r j G r j

k ) 1

m

G kj x k )]G ij ) exp( -R ij ij ), G ji ) exp( -R ij ji )

ij ) A ij /T , ji ) A ji /T , a nd ii ) jj ) 0

.

3233In d. E ng. Chem. Res. 2002, 41 , 3233 - 3246

10.1021/ie010358j CC C: $22.00 2002 American C hemical SocietyP ubl ish ed on Web 06/04/2002


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in the mixture of 1-pentanol - amyl a ceta te- water.4,14,15This might lead t o difficulties in downstrea m separa tionwhen the conventiona l recycle st ructure is employed.The coupled rea ctor/column a nd rea ctive dist illat ioncould be effective in overcoming these difficulties. Toour knowledge, this is the first thorough study of theam yl a ceta te process in the open li teratur e.

The object ive of th is work is to evaluate designalternatives for the amyl acetate esterification process.Rather than going di rect ly to react ive dis t i l la t ion, agradua l t ra nsit ion is considered. D ifferent process de-signs are evaluat ed quant itat ively on the basis of theireconomic potentials. Finally, the dynamics and controlof reactive disti l lation a re studied.

2. Amyl Acetate Process

2.1. Reaction Kinetics. The est erifica tion of a ceticacid w ith am yl a lcohol (1-pentan ol) follows the elemen-

tary reaction

The rea ction is ca ta lyzed by a cidic cation-excha nge resin(Amberlyst 15 from Aldrich C hemical C o. 15 ). From theexperimental data of Lee et al . ,15 for a given catalystden sit y (0.8 g /cm 3) a nd porosity of 30%, the rea ction rat ecan be expressed a ccording to a qua si-homogeneousmodel 26

where r is the reaction rate per unit volume [kg mol/(m 3 s) ] and C represents t he molar densi ty of the

Figure1. B inary VLE for (a) amyl acetate- wa ter, (b) acetic acid - wa ter, (c)a cetic acid- amy l acetat e, (d) 1-pentanol - wa ter, (e)1-pentanol -amyl acetate, a nd (f) acetic acid- 1-pentanol.

C H 3COOH + C5H 11 OH S k b

k fC5H 11 COOCH 3 + H 2O

(1)

r ) k f(C HOAcC AmOH - C AmOAc C H 2OK eq ) (2)

3234 Ind. E ng. C hem. Res., Vol. 41, No. 13, 2002


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corres pondi ng componen t (kg mol/m 3). k f is the forwa rdreaction ra te consta nt given by

with T in kelvin, and K eq is th e equilibrium consta nt

From the kinetics, it is observed tha t th is is a slightlyendothermic reaction with an almost-negligible heateffect . This impl ies that an increase in the react iontemperature will increase the equilibrium conversionb ut b y on ly a v er y s m a ll a m ou nt .15 N ot e t h a t t h eparameters of the concentration-based rate expression(eqs 2 - 4) were obta ined directly from the experiment a ldata via regression and that good agreement betweenthe model predictions and the experimenta l dat a werealso reported. 15 The equilibrium constant was found tobe about 2 for the temperatures of interest (100 - 150 C). The cat a lyst price is ar ound 14 $/lb, an d a cata lystl ife of 1 year is assumed in this study.

2.2. PhaseEquilibria. For the a myl a ceta te process,the normal boi ling points are ranked, in ascendingorder, as follows:

The two reactant s , a cet ic a cid and 1-pentanol , a reintermediate boilers, whereas the products, water andam yl aceta te, are th e low a nd high boilers, respectively.Following L ee and Lia ng,13 Chang ,4 and Lee et al . ,14,15the nonrandom two-liquid (NRTL) activity coefficientmodel 20 was used for the vapor- liquid - liquid equilib-r ium (VLLE) for the quaternary sys tem conta iningacetic acid, 1-pentanol, amyl acetat e, and wa ter. Vapor -l iquid equilibrium (VLE) data are available for all ofthe binary pai rs , a nd l iquid- liquid equilibrium (LLE)dat a for tw o ternary systems (acetic acid- 1-pentanol -wate r and ace t i c ac id- amyl ace ta t e- w a t e r) a n d t h equa te rna ry sys t em can a l so be found in the l i t e r a -ture. 14,16,18 Eight very di fferent se ts of b inary param-eters for the NRTL model were presented in Lee et al., 14

Figure 2. Residue curve maps (solid lines) and liquid - l iquid envelopes (dashed lines) for the t ernary mixtures (a) wat er - acetic acid-amyl acetate, (b) water - acetic acid- 1-penta nol, (c) acetic a cid - 1-pentanol - amyl a ceta te , a nd (d) wat er- 1-pentanol - amyl a ceta te .

k f ) 17 500e- 6223.2/ T (3)

K eq )k fk b

) 13.9e - 777/ T (4)

H 2O100 C

< C H 3OO H118 C

< C5H 11 OH137.8 C

< C5H 11 COOCH 3148.8 C

(5)

Ind. Eng . C hem. R es., Vol. 41, No. 13, 2002 3235


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and even though they gave a good description of theVLE, they were regressed from different combinationsof data sets. As will become clear later, that the ternaryLLE plays an important role in descr ib ing productpurity, so the binary pa ram eters from tw o terna ry LLEdata sets (set 1 of ref 14 and the original set of ref 4)are employed in th is work. Table 1 g ives the b inarypar am eters of the NRTL model. The Ha yden - OConellsecond viria l coefficient model10 with associa t ion pa-rameters was used to account for the dimerization ofa cetic a cid. The Aspen P lus 2 built-in a ssociat ion pa ra m-eters were employed to compute fugacity coefficients.

The quaternary sys tem has two minimum-boi lingbina ry az eotropes (1-penta nol - wa ter and amyl acetate-wa ter) a nd one maximum-boi ling binary azeotrope(acetic acid- 1-penta nol). Whereas the azeotrope be-tw een acetic acid a nd 1-penta nol is h omogeneous, t heother two are heterogeneous azeotropes wi th ra therhigh-purity w at er in the aq ueous phase. Figure 1 showsthe VLE for all six bina ry pairs. There are tw o ternarya zeotropes for a cetic a cid- 1-pentanol - amyl aceta te andwate r - 1-pentanol - amyl aceta t e , and they a re a n un -sta ble node an d a saddle point, respectively, a s shown

in Figure 2. The water - 1-pentanol - amyl aceta te ter-na ry a zeotrope temperat ure is 95.2 C, w hich is in goodagr eement w ith th e experimenta l result, 94.9 C. 11 Notethat a very large liquid- liquid (LL) envelope is observedfor the wa ter- 1-pentanol - amyl acetate system (Figure

Figure 3. Residue curve map for the quaternary system.

Figure 4. Two-liquid zone of the four t ernary systems.

Figure 5. Coupled rea ctor/column .

Figure6. (A) Schema tic description of compositions in the organ icphase and aqueous phase of the decanter and (B) largest allowableacetic acid composition in the feed to achieve 99%water in theaqueous phase for a typical feed wa ter/1-pentanol/amyl acetatera ti o of 0.385/0.385/0.230.



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2d), with one end of the tie lines connected to very high-purity w at er. Moreover, more tha n 50%of th e composi-tion space in Figure 2d is in the LL envelope. Figure 3shows the res idue curve map 3,9,24 for the quaternarymixture. The residue curves sta rt from the minimum-boiling ternary azeotrope (95.2 C in Figure 3) and movetoward three binary azeotropes (95.4, 96.0, and 140.5C) and two pure-component vortexes (100 and 148.8C), as shown in Figure 3. Two branches are of particu-lar interest , one is the residue curves moving towardthe a myl a ceta te vortex (148.8 C ) and t he other is theresidue curves converging to the ma ximum-boilingbina ry a zeotrope (140.5 C) near the 1-penta nol corner.A dist i l la t ion boundary is clear ly observed betweenthese two branches; i t is a surface that starts from the

minimum-boiling ternar y azeotrope (95.2 C), movestoward the amyl a ce ta t e- 1-pentanol - acetic acid sur-face , and then curves down and ends a t 1-pentanolvor tex. Note that the products of the es ter i fica t ionprocess are amyl aceta te and water, which l ie on thetop an d t he lower left corner, r espectively, of Figur e 3.Because three of the four terna ry systems show a n LLenvelope (Figure 2), a two-phase zone persists towardthe a cid-rich portion, a s can be seen in F igure 4, wherea large portion of the ternary composition space l iesinside the two-phase zones. More importantly, movingtoward the acid-lean surface, all of the t ie l ines pointto pure water.

The phase behavior of the amyl acetate process isquite different from tha t of the methyl a ceta te or ethyl

Figure 7. The water corner of the LL envelope for 1-pentanol - amyl ace ta te- wate r.

Table 2. Steady-State Design Parameters and Total Annual Cost (TAC) for the Coupled Reactor/Column

ca se 1 2 3 4 5 6

rea ctor t empera ture ( F) 176 176 176 176 176 176V R (f t3) 7593.0 8122.0 8476.0 8829.0 9182.0 10594.4D R (ft ) 16.91 17.29 17.54 17.78 18.01 18.89

stripping sectiona myl a cet a t e a t t he bot tom (mf) 0.99 0.99 0.99 0.99 0.99 0.99no. of tra ys (N s) 14 14 14 14 14 14B R 2.48 2.46 2.44 2.43 2.41 2.38D C (ft ) 10.29 10.26 10.16 10.17 10.14 10.06Q R (10 7 B tu/h) 2.25 2.23 2.20 2.20 2.19 2.15

rectifying sectionw a ter a t t he t op (mf) 0.99 0.99 0.99 0.99 0.99 0.99no. of tra ys (N R) 60 47 43 40 38 33RR 2.34 2.33 2.33 2.36 2.37 2.42D C (ft ) 13.63 13.58 13.64 13.87 14.03 14.52Q C (10 7 B tu/h) 3.92 3.91 3.91 3.94 3.96 4.01

heat exchanger a reas (ft 2)reboiler 1998.2 1985.1 1959.9 1951.2 1942.7 1911.8condenser 11672.6 11650.5 11640.8 11725.9 11783.2 11946.2hea t er 1138.2 1138.2 1138.2 1138.2 1138.2 1138.2

capital costs ($1000)rea ctor 2,509.4 2,616.8 2,687.3 2,756.4 2,824.5 3,087.7st r ipper 490.2 488.4 483.4 483.8 482.6 478.3st r ipper t ra ys 53.7 53.4 52.6 52.7 52.5 51.8rect ifier 2,124.2 1,740.5 1,627.9 1,563.3 1,519.0 1,407.2rect ifier t ra ys 355.4 277.0 255.1 243.4 235.5 215.7hea t excha ngers 1,797.9 1,794.8 1,791.2 1,795.6 1,798.3 1,805.1

operating costs ($1000)ca t a lyst cost 1,881.3 2,012.4 2,100.1 2,187.6 2,275.0 2,625.0energy cost 1,544.7 1,542.5 1,347.9 1,354.5 1,357.6 1,586.4tot a l a nnua l cost ($1000) 5,869.5 5,878.6 5,747.1 5,840.5 5,936.8 6,560.1



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aceta te process in the order of the boiling points a nd inthe shape of the two-liquid-phase zone. However, it is

quite similar t o the butyl a ceta te process23 where a largeLL envelope is connected to t he a lmost pure wa terregion.

3. Steady-State Design

The production ra te of a myl aceta te is 551 lb mol/h(about the a nnual demand in Taiwa n) wi th a productpurity of 99 mol %and w ith the other stream having aspecification of 99%water. Because a distillation bound-ary exists for the quaternary system, the conventionalrecycle structure, with either a direct or a n indirectsequence, 7 is immediately excluded from further inves-tigation.5

The phase behavior (Figures 3 a nd 4) of the q uat er-na ry sy stem gives a good indicat ion of the configura tionof the react ion/separa t ion process. Fi rs t , the l ightproduct (water) is enclosed by a two-liquid zone, andtherefore, the top product is w ithdra wn from t he aq ue-ous phase of a decanter. Amyl aceta te , the heavies tcomponent , should be taken f rom the bot tom of theprocess unit (i .e. , top section of t he coupled reactor/disti l lat ion column in Figure 5) and the rea ction t akesplace in the middle section. In both designs, the coupledreactor/distilla tion column a nd t he rea ctive distillat ioncolumn, a decant er is installed, and t he aq ueous phaseis taken as the top product (without recycle), while theorganic phase is totally recycled ba ck to th e column.

Because the product specification on the top is 99%water, it is helpful to locate the likely composition spaceof the overhead vapor flow (the feed to t he decanter).Eq ua tion 5 indicates th a t th e boiling point of acetic a cidis next to that of water and that the two-l iquid zoneshrinks gradually toward the acetic-acid-rich region.Therefore, a lar ge a cetic acid concentra tion prevents usfrom achieving high-purity water. Figure 6 shows thema ximum allowable a cid mole fraction a s a function ofcolumn pressure, and at at mospheric pressure, only0.23%acid is allowed in the overhead vapor flow. Thisimplies that most of the acid must be consumed in thereaction zone or that an extremely large number of tra ysis needed in the rectifying section. When the columnpressure i s reduced to 0 .1 a tm, the a l lowable ac idconcentra tion becomes 2.4%. With a sma ll a mount of

acid in the sys tem, we are pract ica l ly looking a t the1-pentanol - amyl acetate- wa ter phase diagram (Figure2d). A closer look at th e wa ter corner of the LL envelope(F igure 7 ) r evea l s t ha t a h igh wa t er pur i ty can beobta ined i f the overhead vapor i s located toward theamyl aceta te- wa ter s ide.

3.1. Coupled Reactor/Column. Yi and Luyben 27s tudied the design and control of var ious coupledrea ctor/column s yst ems w ith d ifferent levels of complex-

ity. A similar a pproach wa s ta ken for t he design of theam yl a ceta te process, but t he design is complicat ed bythe phase-split behavior in the decanter. With a givendecanter and a g iven pressure (0 .1 a tm) , the des ignprocedure for the coupled r eactor/column (Figure 5)consists of the fol lowing s teps : (1) Fix the reactorvolume (V R) an d guess the tra y numbers in the strippingand rectifying sections (N S a nd N R, respectively). (2)Find the minimum number of t rays in the s t r ippingsection (N S,min ) from th e short-cut design 7 with a givenspecifica tion of a myl a ceta te (99%), an d set N S ) 2N S,min .(3) Cha nge the num ber of tra ys in th e rectifying section(N R) such that the top product specification (99%water)is met . (4) Repeat s teps 2 and 3 unt i l N S converges(usually N S does not change m uch for different N Rvalues). (5) Compute t he t otal an nua l cost (TAC; 7,8 seeAppendix A). (6) Cha nge the reactor volume ( V R) suchtha t the TAC is minimized.

Table 2 shows the steady-state design for differentreactor volumes. Case 3, giving the lowest TAC, is theoptima l design a nd corresponds to N R ) 43, N S ) 14,B R ) 2.44 (boilup ra tio), RR (reflux ra tio, wh ich is t heorganic-phase flow ra te divided by the aq ueous-phaseflow rate) ) 2.33, an d 85%of t he equilibr ium conversionin the reactor. Because the conversion in the reactor isclose to the equilibrium conversion, the assumption ofequilibrium conversion can be used as the init ial sta rt-ing point for the design. As mentioned earlier, a verysmal l amount of ac id can be to lera ted in the column

overhead (2.4%a t 0.1 at m), a nd even w ith such a low pressure, a large number of trays in the rectifier is stillrequired to separate acetic acid from water (which isknown to be a difficult separation). Also, note that N Rincreases dra mat ica l ly as the reactor volume dropsbelow a certain value (e.g., case 1) and that the catalystcost play a significant role in the TAC. Figure 8 showsthe distilla tion line of the coupled rea ctor/distilla tioncolumn. I t sta rts from the almost-pure (99%) a mylacetat e and moves towa rd th e 1-pentanol - amyl a cetate-water plane. The l iquid composition on the top tray(labeled N T on the dashed line of Figure 8) is outsidethe two-phase zone, whereas the overhead vapor (feedto the decanter; identified by the solid tr iangle in Figure8) is clearly inside t he LL envelope. The t ie line pointsto 99%w at er in the a queous phase a s the t op product,a nd t he other end corresponds t o the composition of theorganic reflux. Figure 9 shows the composition profileof t he coupled r eactor/distilla tion column. The resultreveals a sha rp increase in th e am yl acetat e compositionat the feed location (around tray 15) and that i t takes43 trays in the rectifier to bring the acid compositiondown to an acceptable level (Figure 9A). It is interestingto note tha t the composition profiles of the t wo hea vycomponents (1-pentanol a nd am yl acetat e) in th e r ec-tifying section behave very different ly from th e profilesin typical disti l lation systems, as they stay relativelyconstant in the rectifier (Figure 9A). The reason for thisi s t ha t t he o rgan ic r e f lux (mos t ly amyl ace ta t e and

Figure 8. Disti l lation l ines and corresponding tie l ines for thecoupled reactor/disti l lation column (dashed lines) a nd reactivedistillation column (solid lines).



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1-penta nol) brings t hese heavy components ba ck to therectifying section as opposed to bringing back only lightcomponents as in conventional distillation.

3.2. Reactive Distillation. Un like conventional dis-t i l lation, detailed design of reactive disti l lation (e.g. ,minimum number tra ys, minimum number of reactivetra ys, feed loca tions, etc.)is less obvious. Sneesby et al.21presented a design procedure for th e E TBE reactivedis t i l la t ion sys tem, Subawal la and Fair22 proposed ageneral procedure for th e design of reactive distillat ion,and Luyben 17 compared design alternatives (neat versusexcess reactant) and studied several design parametersfor ideal reactive distillations. The reactive distillationapparatus for the amyl aceta t e process (Figure 10)differs from the a bove-mentioned designs in t he pha se-spli t beha vior in the decanter. With a given decant er,the des ign procedure is qui te s imi lar to that of thecoupled rea ctor/dist illa tion column, but one ca n choosefrom severa l feed locat ions for the acet ic a cid and

1-pentanol. From the reaction kinetics point of view (keeping the reactant concentrations as high as pos-s ible), the heavy reactant (1-pentanol) i s fed to thecolumn from the top section of the reactive zone, a ndthe light reactant (acetic acid) comes in from the lowersection of the reactive zone (Figure 10). 1 In the simula-tion, a 15-s residence time wa s a ssumed for the rea ctivetrays. Once the feed locations are determined and thecolumn pressure is fixed at 1 at m, th e design procedurebecomes: (1) Fix the number of reactive tra ys ( N Rx n),and guess the numbers of t rays in the s t r ipping andrectifying sections (N S a nd N R, respectively). (2) Findthe minimum number of tra ys of the st ripping section(N S,min ) from the short-cut design with a given speci-fica tion of a myl a ceta te (99%), a nd set N S ) 2N S,min .(3) Increase the number of trays in the rectifying section(N R) until the top product specification (99%water) ismet. (4)Repeat steps 2 and 3 unt il N S converges (usua llyN S does not change much for different N R values). (5)

Figure 9. C omposition profiles for (A) coupled rea ctor/column an d (B) rea ctive distilla tion column.



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Compute t he t otal a nnua l cost (TAC; see Appendix A).(6) Cha nge the num ber of reactive tra ys (N Rx n) so thatthe TAC is minimized.

Table 3 gives the steady-state design for differentnumbers of reactive trays (N Rx n). C a se 2 (Ta ble 3) is theoptima l design, wh ich corresponds t o N Rx n ) 6, N R ) 9,N S ) 12, B R ) 3.0, and RR ) 0.78. I t is important tonote t ha t the TAC is a pproximat ely one-fourth (26%)of tha t for th e coupled r ea ctor/column (ca se 3 of Ta ble2). In other words, reactive distillation is 4 times moreefficient ( in terms of TAC) than the coupled reactor/column for t he a myl a ceta te process.

As in the case of coupled reactor /column, i f thenumber of reactive trays drops below 6, a significant

number of trays is required in the rectifying section.Figure 8 compar es the distillation lines between the tw oalterna tives. The composition profiles of F igure 9Bindicate that this is a much more effective separationin the rect i fy ing sect ion, compared to the coupledrea ctor/dist illa tion column , beca use the a cid compositiondecreases m onotonically towa rd an almost acid-freemixture and only 9 tra ys a re used to reach th e desireda cid level (compa red t o 43 tra ys for t he coupled reactor/disti l lation column). Again, as in the case of coupledreactor/disti l lat ion column, the compositions of tw oheavy components, a myl a ceta te a nd 1-penta nol, rema infairly constant as a result of organic reflux (Figure 9B).

4. Dynamics and Control

Because rea ctive disti l lation ha s a much lower TACtha n t he coupled rea ctor/distilla tion column, t he rea c-tive distillation process was subjected to further study.Despite the economic potential of reactive distillation,only a few papers studying the dynamics and control ofreactive distillation have been published. Al-Arfaj andLuyben 1 gives a review on t he closed-loop control ofreactive disti l lation. For reactive disti l lation with twoproducts, a ll contr ol structur es of Al-Arfa j an d L uyben 1shar e a common featur e: To mainta in stoichiometricamounts of the two fresh feeds, the composition of onereactant in the reactive section is controlled by adjustingthe feed ra tio. For the a myl a ceta te process (Figure 10),the major product i s amyl a ceta te , and w ater i s w i th-drawn from the decanter with the purity set by the t ielines (Figur e 7) w ith rea sonable purity levels. Therefore,only the bottom composition is controlled. Actually, ifall of the aqueous condensate is removed (because ofits relat ively high purit y) and a ll of the organ ic conden-sate i s refluxed, then only one degree of f reedomrema ins (inst ead of tw o in a t ypical column). The contr olstructure becomes: (1) Control t he column pressurewith cooling water flow rate. (2) Maintain the aqueous-

Table 3. Steady-State Design Parameters and Total Annual Cost (TAC) for Reactive Distillation

rea ct ive dist illa t ion column 1 2 3 4

tot a l no. of t ra ys 50 27 26 27no. of trays in stripping section (N S) 12 12 12 12no. of trays in reactive section (N Rxn ) 5 6 7 8no. of trays in rectifying section (N R) 33 9 7 7rea ct ive t ra y 13- 17 13 - 18 139 13 - 20pent a nol feed t ra y 17 18 19 20a cet ic a cid feed t ra y 13 13 13 13feed flow ra t e of pent a nol 5551.15 5551.15 5551.15 5551.15

feed flow ra t e of a cet ic a cid 5551.15 5551.15 5551.15 5551.15top product flow ra t e 551.35 551.33 551.28 551.31bot t om product flow ra te 550.95 550.97 551.02 550.99w a ter a t t he top (mf) 0.99 0.99 0.99 0.99a myl a ceta t e a t t he bot t om (mf) 0.99 0.99 0.99 0.99RR 0.723 0.783 0.795 0.819B R 3.11 3.00 3.01 3.05Q C (10 7 B tu/h) 1.82 1.89 1.91 1.94Q C (10 7 B tu/h) 2.71 2.70 2.71 2.74D C (ft ) 9.19 9.58 9.35 9.38

heat exchanger a reas (ft 2)condenser 1392.15 1447.22 1457.94 1479.11reboiler 2411.98 2397.51 2406.75 2436.16

capital costs ($1000)column 1,205.45 768.83 727.05 752.04column t ra ys 160.73 92.59 85.90 89.66hea t excha ngers 468.01 466.38 467.44 470.77

operating costs ($1000)ca t a lyst cost 161.57 210.75 234.34 269.60energy cost 849.24 844.96 848.29 858.71tot a l a nnua l cost ($1000) 1,622.21 1,498.30 1,509.42 1,565.79

Figure 10. Reactive distillation with light feed on the bottom andheavy feed on th e top of the reaction zone.



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phase level in the deca nter by changing the t op productflow rate. (3) Control the organic-phase level in thedecan te r by man ipu la t ing the r ef lux f low ra t e . (4)Control the ba se level by ma nipulating t he bottoms flow rate. (5) Control the bottoms composition by changingthe va por boilup. (6) Contr ol the tw o feeds a ccording tothe ratio between them.

Figure 10 shows the ba sic control structure; note th at ,a t the present s tage , the feed ra t io i s f ixed a t 1 (i .e .,the feed ra tio is n ot controlled). This control configura -tion is far simpler than alternatives that can be imag-ined. It is a single-input - single-output system, a nd aPI controller is used. From a step increase in t he heatinput, the transfer function between the amyl acetatecomposition and the heat input becomes

Four minutes of ana lyzer dead t ime wa s a ssumed forthe composition measurements, a transmitter span of0.1 mole fraction w as used, and th e valve gain w as setto t wice the nominal steady-sta te value. The composi-tion loop wa s tun ed using Tyreus - Luyben set tings. Thisgave va lues of K c ) 0.3 an d I ) 17 min. Figure 11 showsthe response for a 10%increase in th e feed flow ra te. Itt a k es 30 m in t o r e a ch t h e n e w s t ea d y s t a t e, a n dreasonable control can be obta ined us ing s imple PIcontrol. However, for a 10% step decrease in the feedflows, a l imit-cycle-like behavior is observed with aperiod close t o 80 min (Figure 12). The r eason for th isbehavior i s that the react ive sect ion produces moreacetate than desired, which results in the accumulationof products (acetate and water), which subsequently

slows th e net rea ction (producing less aceta te). However,aft er most of the products ar e removed from the system,the rea ctive section aga in produces more aceta te tha ndesired. The process repeats i tself , which leads to asust a ined osci ll a t ion , a s shown in F igure 12. Oneapproach to overcoming the continuous cycling is toincrease product pur i ty when the product ion ra te i sdecreased. Figure 13 shows the r esponse for the samedisturbance (a 10%decrease in the feed rate) when theset point of th e aceta te is cha nged t o 99.4%. The result sclearly indicate that oscillation disappears and the speedof response is close to th a t of a positive production r a techang e. Another a lterna tive is to use P -only contr ol forthe bottoms composition. Very fast control is obtainedusing t he P -only composition control, as sh own in F igure13. Th is l ea d s t o a P I - P con t rol le r for t he samedisturbance (in different directions). In practice, sucha configura tion can be a ccomplished by ga in scheduling(reset time scheduling to be exact). This should be oflittle problem, because the production rate of reactivedisti l lat ion is set by the opera tors.

The proposed single-loop control seems to be viablefor reactive distilla tion. However, a s pointed out by Al-Arfaj a nd Luyben,1 there is alw ays some inaccura cy inflow measurements, and even the slightest imbalancein the reactant s would lead t o a gra dual buildup of thecomponent . B ecause there i s no w ay for the excessreactant to leave the system except from the productstrea m, one of the product specificat ions ca nnot be metunless t his imba lance is ha ndled via feedback control.Figur e 14 shows how t he single-loop P I control respondsto flow imbala nces. For a 1%a cid excess, the bottomscomposition can be controlled quite well, but for a 1%alcohol excess, again, a limit cycle is observed (dashed

Figure 11. Closed-loop responses for a 10%production rate increase using PI control.

(x B,AmOAcQ R )) 1.09e- 4s

(0.27) 2s 2 + 2(0.27)(0.52) s + 1



11/15

line in Figure 14). The excess heavy reactant, alcohol,results in a less pure bottoms product composition

initia lly, and t he composition contr oller countera cts wit hthe increase in the vapor boi lup. This r estores the

Figure 12. Closed-loop responses for a 10%production rate decrease using PI control.

Figure 13. Closed-loop responses for a 10%production rate decrease using PI control with a set-point change of x B,AmOAcset ) 0.994 (solid

lines) and P-only control (dashed lines).



12/15

bottoms composition temporally and allows the excessalcohol to boil up toward the top. Because the decanteris a natural composition controller, most of the excessa lcohol is recycled back to the column via orga nic reflux.The recycled alcohol cannot increase the net reactionra te further (acid is the limiting reacta nt), an d a gra dualbui ldup of a lcohol in the bot tom again resul ts in adecrease in the bottoms composition. Again, the wholeprocess repeats it self, and a limit cycle is clea rly show n

in Figure 14. Therefore, a second composition loop is,indeed, necessary to prevent the accumulation of excessreactants .1

Because a ceta te a nd a cid (instead of alcohol) ar e themajor components in the stripping section, either onecan be u sed to contr ol the feed ra tio (Figure 10). In thiswork, we chose aceta te to infer the imbalance of thefeeds. Figure 15 shows t he a ceta te composition profilesfor 1% changes in the feed ra t io ( F HAc /F AmOH ). I t i s

Figure 14. Closed-loop responses using PI control for errors in feed ratios ( F HAc /F AmOH ) of 1.01/1 (solid lines) a nd 0.99/1 (da shed lines).

Figure 15. C omposition profile of am yl acetat e for a 1% change in feed ratios (F HAc /F AmOH ).



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Figure 17. C losed-loop responses for err ors in feed ra tios of F HAc /F AmOH ) 1.01/1 (solid lines) a nd 0.99/1 (dash ed lin es) using P I cont rolfor the bottoms composition a nd P-only control for the tra y 12 a myl a cetat e composition.

Figure 16. Closed-loop responses for 10%production rate changes using PI control for the bottoms composition and P-only control forthe tray 12 amyl acetate composition.



14/15

interesting to note tha t cha nges in either direction (acidexcess or alcohol excess) give less pure product composi-tions. In other words, most of the excess reactant (acidor alcohol) ends up in the bott om as a r esult of the VLLEchara cteristics (only very pure w a ter is a llowed t o lea vethe column top, as seen in Figure 7). Only t hree tra ys(trays 11 - 13) in the stripping section can be used toinfer the feed imbala nce, and the a myl a ceta te composi-tion on tr a y 12 wa s chosen to adjust t he feed ra tio. Notethat the selection of the right tray location to infer feedimbalan ce is very importa nt, a s seen in Figure 13. If awrong location (e.g., tray 8) is chosen, a very difficultnonlinear contr ol problem or a n un contr olla ble processmight result. Follow ing Al-Arfa j and L uyben, 1 a P-onlycontroller was employed. From a step test, the transferfunction between th e tra y 12 a ceta te composition andfeed ratio becomes

Again , 4 min of ana lyzer dead t ime wa s a ssumed, andthe tra nsmitter spa ns for the composition and r at io were

1 and 2, respectively. This gave K c )

0.008. Figure 16demonstra tes tha t th is control structure works well, an dtha t i t requires a sl ightly longer t ime, 50 min, to sett le10%production ra te cha nges. The ina ccura cy in th e flow measurements can also be handled easily as shown inFigure 17.

5. Conclusion

In this work, the acidic cation-exchange resin cata-lyzed amy l aceta te process wa s studied thoroughly. Twodesign a lterna tives, coupled rea ctor/distilla tion columnand reactive disti l lation column, were evaluated. Thephase equilibria of the quaternary system revealed that

a significant two-liquid region exists, and more impor-tantly, that the t ie l ines are all pointed to high-puritywater for the aqueous phase. Therefore, a decanter wasplaced on top of the column, w here high-purity w at erwas withdrawn from the aqueous phase, and the organicphase was totally refluxed. Systematic design proce-dures w ere proposed for t hese two a lterna tives. Results,in terms of the total annual cost, indicated that reactivedisti l lat ion is 4 t imes m ore efficient t ha n the coupledreactor/separ at or for the am yl acetat e process. Thedyna mics of reactive distillation with a decant er is muchmore complicated than expected. Limit cycles can occurif the control structure is not properly designed. Theimbalance in feed must be ta ken in to account in a nyrealistic process operation.

This often leads to a t least tw o composition loops (ortwo inferential variables). Despite the complex dynam-ics, simulat ion results show th at reasona ble control canbe achieved with the proposed control system.

Appendix A. Formula for the Computation of the Total Annual Cost

The equipment cost estima tion follows the procedureof Douglas,7 and the specific equations of Elliott andLuyben 8 were used. The annual equipment cos t wasassumed to be one-th i rd of the capi ta l cos t (3-yearpayback). The energy costs were calculated as

The cooling water cost was computed from

For the cat alyst , a 1-year cat alyst lifetime was a ssumed,giving the following expression for the cost

Acknowledgment

This work was suppor ted by the China Pet roleumCorporation of Taiwan under Grant NSC88-CPC-E011-017. Insightful discussions with professors M. J . Lee,H. M. Lin, and Y. S. Chou are gra tefully a cknowledged.

Nomenclature

B R ) boilup ra tio (vapor boilup/bott oms flow )C AmOH ) molar concentra tion of 1-penta nol (amyl

a lcohol, kg mol/m 3)C AmOAc ) molar concentration of amyl acetate (kg mol/

m 3)C HOAc ) molar concentration of acetic acid (kg mol/

m 3)C H 2O ) molar concentra tion of w a ter (kg m ol/m 3)D C ) column diameterF AmOH ) 1-penta nol feed flow ra te (lb m ol/h)F H Ac ) a cetic a cid feed flow ra te (lb m ol/h)N F ) feed tra y for coupled rea ctor/columnN F1 ) lower feed t ra y for reactive disti l lat ionN F2 ) upper feed tra y for r eactive disti llationN R ) number of tra ys in the r ectifying section

N Rx n )

number of tra ys in the rea ctive sectionN S ) number of tra ys in the str ipping sectionN S,min ) minimum number of trays in the stripping

sectionN T ) to ta l number of t ra ysk b ) backward ra te constant for the es ter i f ica t ion

reactionK eq ) equil ibr ium constant for the ester if ica t ion

reactionk f ) forwa rd ra te constant for the es ter i fica t ion

reactionQ C ) heat removed from t he condenser (Btu /h)Q R ) heat input to t he reboiler (B tu/h)r ) react ion ra te per unit volume [kg mol/(m 3 s)]R i ) reaction rate on the i th tr a y (kg mol/s)R or ) orga nic reflux flow ra teR to ta l ) total rea ction r a te in the column (kg m ol/s)RR ) reflux ra tio (organic reflux/top product flow)TAC ) to ta l a nnual cos tV R ) reactor volumex B,AmOAc ) amyl acetate mole fraction at the bottomx B,AmOAc

set ) set point of amyl acetate composition atthe bottom

x D ,H 2O ) water mole fraction at the top

Literature Cited

(1) Al-Arfaj, M.; L uyben, W. L . Comparison of AlternativeControl Structures for an Ideal Two-Product Reactive DistillationColumn. Ind. Eng. Chem. Res. 2000 , 3 9 , 3298.

( x 12,AmOAcF H Ac/F AmOH)) 38e- 4s

(0.12) 2s 2 + 2(0.12)(0.72) s + 1

stea m cost ( $year)) $0.0306 Q R

cooling water cost [ $year]) $0.000977 Q C

catalyst cost ($) ) catalyst weight (lb)

14.1875 ($lb)



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Received for review April 24, 2001Revised manuscript received March 13, 2002

Accepted April 9, 2002

IE010358J


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