rxnes acetato de butilo

8/13/2019 Rxnes Acetato de Butilo

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A Novel Distillate Policy for Batch Reactive Distillation with

Application to the Production of Butyl Acetate

Ganesh Venimadhavan, Michael F. Malone, and Michael F. Doherty*

Departm ent of Chemi cal En gin eeri ng, Un iversity of M assachusetts, Amh erst, M assachusetts 01003-3110

Co n sid e rin g th e lo n g stan d in g im p o rtan ce o f b atch d ist i l lat io n in ch e m ical p ro d u ctio n , i t is

surprising th a t t he utility of man ipulat ing operat ing policies wa s not underst ood unt il the 1970s.This is par tly due to the ma thema tical difficulty of f inding the t ime-optima l policy. P erha ps themost elegan t a nd effective treat ment of this problem is found in t he work of Mayur a nd J ackson(Chem. Eng. J.1971,2, 150-163). They used Pontryagins maximum principle to find the optimalreflux policy for t he bat ch distillat ion of ideal mult icomponent m ixtures. In t his paper, motiva tedby Ma yur a nd J acksons classic treat ment, w e exam ine a novel distillat e policy a nd a conventionalcolumn configuration for batch distillation with chemical reaction. This distillate policy leads toa new explicit reflux policy for t he special cla ss of equimolar reactions. For th e part icular caseof butyl acetate production, it is shown that this leads to complete conversion of ingredientsa n d h i gh -p ur i t y p r od u ct s , w h i ch a r e u n a t t a i n a b le b y t h e t r a d i t i on a l a p p roa c h , i n a s in g leoperation.

Introduction

Batch processes have always been used in the chemi-cal indust ry, especially for development a nd for season-al, un certa in, or low-capacity production. Ba tch rea ctorsand batch distillations are very common. Their combi-nation in react ive dist illat ion is a process alternativethat has the potential to lower process costs and reduceenvironmenta l emissions, a dvant ages w hich ha ve beendemonstrated in continuous processing.2-6 B a t c h re a c-t ive dist illat ion is often used for equilibrium-limitedreactions, but systema tic design methods for bat ch reac-t ive dist illat ion ar e scarce. Typically, a l iquid-phasereaction takes place in the reboiler, and a product isremoved using a batch rect if ier placed above the st ill.This configuration has the potential for essentially com-plete conversion of the limiting r eacta nt. F or az eotropic

mixtures, however, it m a y not be possible to reach com-plete conversion d ue t o the pr esence of low-boiling a zeo-tropes containing one or more reactants. In such cases,novel opera ting stra tegies a nd/or equipment configura -t ions may be advantageous. This is the case for butylacetat e production, which we use a s a n example in thiswork.

B utyl a ceta te is an important solvent in t he chemicalin du s t ry . I t is u s e d p rima ri ly in c o a t in g s , wh e re i t ss o lv e n t p o we r a n d i t s lo w re la t iv e v o la t i l i t y ma k e i tuseful for adjustment of evaporation rate and viscosity.It is particularly useful as a solvent for acrylic polymers,vinyl resins, etc. I t is also used as a react ion mediumfor a dhesives, as a solvent for leath er dressings, an d a

process solvent in various applications and in cosmeticformulations. The equilibrium constant favors the pro-

duction of butyl acetate, but acceptable product purityrequires further purification.

Ea rlier work on bat ch reactive distillat ion focused ondeveloping detailed models, e.g. , Cuille and Reklaitis 7

or on optimizing operations, e.g. , Mayur and J ackson,1

Egly et al .8 and Quintero-Marm ol and Luyben.9 We a re

interested in developing a simplified model to capturethe essence of the process and to provide insight forexploring process alternatives. With such a model, wes h ow h ow a n ov el op er a t i n g s t r a t e g y c a n l ea d t o asimplified process with higher productivity than thatof a conventiona l stra tegy.

Simplified Batch Reactive Distillation Model

The schematic of a batch reactive distillation systemis given in F igure 1. We develop a s implified model wit hthe following assumptions:

This pa per is dedicated t o Pr ofessor Roy J ackson in honorof hi s m any out st and i ng c ont r i b ut i ons t o t he m at he m at i c alan alysis of chemical engineering systems.

* To whom correspondence should be addressed at Depart-ment of Chemical E ngineering, 154B G oessma nn La boratory,686 North Pleasant Street, Amherst, MA 01003-3110. Tele-phone: (413) 577-0132. Fa x: (413) 545-1133. E-ma il: mdoher ty @ecs.umass.edu.

P r e se nt ad d r e ss: UO P L L C , P . O . B ox 5017, De s P l ai ns,IL 60017-5017.

Figure 1. Schematic of a batch r eact ive dist illa t ion process.

714 I nd. Eng. Chem. Res.1999, 38 , 7 14-722

10.1021/ie9804273 CC C: $18.00 1999 American C hemical SocietyP ubl ish ed on Web 02/04/1999


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a s p ect s of t h e s y s t em by s pe cify in g t h e n u mber ofstages, N, t h e r ef lu x r a t i o, R, a n d t h e D a mk oh le rnumber,D a. The simplified model considers the case R) , in w hich case eq 9 reduces to yn-1 )xn.

Reaction Kinetics

We study the esterificat ion of acetic acid with buta nolto produce butyl acetat e.

Kinetic data for a sulfuric acid catalyst were obtainedfrom Leyes and Othmer.12 They report concentration vst ime data at various temperat ures and cata lyst concen-tra t ions. They a lso gave values for th e a pparent (con-centra tion-based) equilibrium consta nt at different tem-peratures (this quantity is also a function of compositionfor nonideal liquid mixtures). Using a U NIQU AC modelto estima te t he a ctivity coefficients (see Table 1 for t hethermodynamic dat a), we calculated the thermodyna micequilibrium consta nt Keqat each temperature. We foundthat the equilibrium constant did not vary strongly withtemperat ure (it var ied from 15.1 to 11.3 over a temper-ature range of 100-120 C). Because there is a lot ofscat ter in t he values of Keq between the values of 11.3e Keqe 15.1 (Venimadhavan 13), we used a m ean va lueof 12.57 for all further calculations. This correspondsto a Gibbs free energy of react ion G0 ) -1.87 kcal/mol, which is rea sonable for esterificat ion reactions. Thekinetic data were regressed to get the forwa rd rea ct ion

ra te consta nt for the a ct ivity-based h omogeneous rat eexpression

wh e re r is the react ion rate per mole of mixture, kf isthe forward reaction rate constant, and aiare th e liquid-phase a ct ivit ies. B oth r a nd kf have units of reciprocalhours.

Figure 2 shows a typical f it of the experimental dat aand the predict ion of eq 14. Figure 3 shows the loga-rithm of the forw ar d reaction rate consta nt a s a functionof reciprocal t emperat ure. A least-squa res f it of thepoints in Figure 3 gives the following Arrhenius expres-sion:

wherekfis the forw ar d reaction ra te constant w ith unitsof reciprocal hours a nd T is in kelvin. The activationenergy ba sed on th is ra te expression is 13.66 kcal/mol.

Vapor-Liquid-Liquid Equilibrium

I n t h e re a c t ion mixt u re , t h e re a re t h re e min imum-boiling binary azeotropes (butanol and butyl acetate,w a t e r a n d b ut a n o l, w a t e r a n d b u t y l a c et a t e ) a n d o n eternary azeotrope (water, butanol, and butyl acetate).While the azeotrope between buta nol and butyl a ceta te

Table 1. Thermodynamic Data for the Butyl Acetate System

Antoine Parameters and the Area and Volume Parameters for the UNIQUAC Equation

component A B C r q

w a t er (1) 23.2256 -3835.18 -45.343 0.92 1.4but a n ol (2) 21.9783 -3080.66 -96.150 3.4543 3.052a cet ic a cid (3) 22.1001 -3654.62 -45.392 2.2024 2.072but y l a cet a te (4) 21.07637 -3151.09 -69.150 4.8274 4.196

Bina ry Int eract ion Pa ram eters for the U NIQUAC Eq uation (cal/mol)a

U11

)

0.0 U

21)

68.0083 (a) U

31) -

343.593 (b) U

41)

685.71 (c)U12 ) 581.1471 (a) U22 ) 0.0 U32 ) -131.7686 (d) U42 ) 24.6386 (e)U13 ) 527.9269 (b) U23 ) 148.2833 (d) U33 ) 0.0 U43 ) 712.2349 (f)U14 ) 461.4747 (c) U24 ) 82.5336 (e) U34 ) -298.4344 (f) U44 ) 0.0

Antoine Equa tion

ln (Psa t) ) A +

B

T + C, P

sa t [Pa], T [K ]

U N I Q U A C Eq u a t ion b

ln i ) ln iC

+ ln iR

ln iC

) lni

xi+

z

2qil n

i

i+ li -

i

xi

j

xjlj

ln iR ) qi

[1 - ln (j)1

m

jji) -j)1

m ji j

k)1

m

kkj]li )

z

2(ri - qi) - (ri - 1) z ) 10

a All interact ion parameters, Uij, a r e t a k e n f r om t h e V a p or-Liquid Equilibrium Data Collect ion of the D E C H E M A C h em i s t r y D a t a Seriesedited by J . Gmehling a nd U . Onken. The volume and pa ge numbers ar e as follows: (a) Vol. 1, Pa rt 1b, p 254; (b) Vol. 1, P art 1,p 106; (c) Vol. 1, P ar t 1b, p 338; (d) Vol. 1, P ar t 2d, p 157; (e) Vol. 1, P a rt 2b, p 197; (f) Vol. 1, P a rt 5, p 147. b zis the coordinat ion number;ji ) exp[- (uji - uii)/RT],ii ) jj ) 1; iis t he dimensionless volume fraction of component idefined as rixi/jrjxj; a n d iis th e dimensionlessarea fract ion of component i defined as qixi/jqjxj.

r ) kf(aHOAcaBu O H -aBuOAcaH 2O

Keq) (14)

kf ) ex p(22.17 - 6873.9T ) (15)

HOAc + n-BuOH S n-B uOAc + H 2O (13)

716 Ind. Eng. Chem. R es. , Vol. 38, No. 3, 1999


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is homogeneous, the others are heterogeneous. Thereis some uncertaint y a bout the r elat ive boiling t emper-a tur e of the tw o light est a zeotropes. Some sources reportt h a t t h e l ig h t e st boi le r is t h e h e t erog en e ou s t e rn a rya ze o t ro p e be t we e n wa t e r , bu t a n o l , a n d bu t y l a c e t a t e(McKetta 14), wh ile others r eport tha t t he heterogeneousbinary a zeotrope between wa ter a nd butyl a cetate is thelightest (Karpilovskiy et al.15). Experimental values ofthe norma l boiling points of these a zeotr opes var y overan interval of 2 C and overlap (pp 1194 and 1693 inG m e h li ng e t a l .16). The boiling point of the ternar ya ze o t ro p e ra n g e s f ro m 89. 40 t o 90. 60 C, wh ile t h eb oi li n g p oi n t of t h e w a t e r -bu t y l a c et a t e a ze ot ro peranges from 90.20 to 91.04 C. I t is crit ical to knowwhich is actually the lightest boiler because even though

their boiling points are quite close their compositionsare not (see Table 2).

I f the binary azeotrope is the lightest boiler (whichcomes off as the overhea d va por t o the condenser), thent h e d e s i g n w o u l d b e q u i t e e a s y . B e c a u s e t h i s i s a nazeotrope between the react ion products, i ts removalallows for complete conversion of the limiting reactantin the still. In addition, the overhead product separatesin th e condenser/decan ter into t wo liquid pha ses: ana q u e o u s p h a s e o f n e a r l y p u r e w a t e r a n d a n o r g a n i cphase which contains 83 mol %butyl acetate a nd 17mol % wa t e r . Th e w a t e r p h a s e is re mov ed f rom t h eprocess, and butyl acetate is purified in a stripper (the

overhea d va por from th e stripper can be recycled to thedecant er). On the other ha nd, if the terna ry a zeotropeis t h e l ig h t e s t bo i le r , t h e s e c o n d l iq u id p h a s e in t h econdenser/decant er ha s a composition of 56 mo l %butyl acetate, 23 mol %wa ter, and 20 mol %buta nol.In this case, the design w ould be very different .

B e c a u s e t h e re is n o a c e t ic a c id in e i t h e r o f t h e s ea ze ot ro pe s , o ur u n ce rt a in t y is c on f in e d t o a t e rn a rymixt u re c on t a in in g w a t e r , bu t a n ol , a n d bu t y l a ce t a t e .For ternary systems, Doherty and Perkins17 and Doher-t y 18 developed rules for the structure of residue curvema ps ba sed on t opology. The global result is expressedin terms of a relat ionship between the different typesof singular points in t he system:

wh e reNdenotes a node (sta ble or unst a ble), Sdenotesa saddle, and the subscripts represent the number ofcomponents in that singular point ( i .e. , 1 indicates apure component, 2 indicates a binary azeotrope, and 3indicates a ternary azeotrope). In addit ion to the twoazeotropes in question, there are f ive other singularpoints in t his terna ry mixtur e. These are the t hree purecomponents (wat er, butanol, and but yl a ceta te; all sta blen o de s ) a n d t h e t wo bin a ry a ze o t ro p e s ( o n e be t we e nwa t e r a n d bu t a n o l a n d t h e o t h er be t we e n bu t a n ol a n dbutyl a ceta te; both of w hich ar e sa ddles). (See Table 3for the boiling points and stabilities.) The stabilities of

Figure 2. Comparison of the m odel predict ion vs experimenta ldata from Leyes and Othm er12 for butyl acetate kinetics; dat a from

experimental run O (T ) 110 C , cata lyst concentrat ion ) 0.0322w t % H 2S O4).

Figure 3. Forward react ion rate constant vs reciprocal temper-ature for the butyl acetate react ion.

Table 2. Mole Fractions of the Two HeterogeneousAzeotropes Containing Water and Butyl Acetate

componentoverall

compositionaqueous

phaseorganicp h a s e

Terna ry Azeotropew a t er 0.712 0.995 0.232B uOH 0.085 0.004 0.206B uOAc 0.203 0.001 0.562

Bina ry Azeotropew a t er 0.7228 0.9988 0.1694

B uOAc 0.2772 0.0012 0.8309

Table 3. Boiling Points and Stabilities of All of the PureComponents and Azeotropes in a Ternary Mixture ofWater, Butanol, and Butyl Acetate at 1 atm Pressure

pure componentsand azeotropes

normal boilingt e m pe ra t u r e ( C ) s t a b il it y a

w a t e r-butanol-bu ty l a cet a t e 89. 40-90. 60 U N or S A?w a t e r-but y l a cet a t e 90.20-91. 04 S A or U N ?w a t e r-B uOH 92.83 S Aw a t er 100.0 S Nbutanol-but y l a cet a t e 116.94 S Abut a n ol 117.74 S Nbut y l a cet a t e 125.95 S N

a U N in d ic a t e s u n s t a b le n od e, S N in d ic a t e s s t a b le n od e, a n d

SA indicates saddle.

2N3 - 2S3 + N2 - S2 + N1 ) 2 (16)

Ind. Eng . C hem. Res. , Vol. 38, No. 3, 1999 717


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these five singular points ca n be resolved by rules givenby D o h e rt y .18 T h e o n ly s c e n a rio t h a t s a t is f ie s e q 16demands that the ternary azeotrope containing water,bu t a n o l, a n d bu t y l a ce t a t e is t h e u n s t a ble n o de wh ilet h e bin a ry a ze ot ro pe be t we en w a t e r a n d bu t y l a c et a t eis a s a ddle . T h e re f o re , we c o n c lu de t h a t t h e t e rn a ryazeotrope is the lightest boiler and the overhead vaporenterin g t he condenser/decant er ha s a composition closeto this azeotrope.

The phase equilibrium wa s modeled using the UNI -QUAC equation (Table 1) with parameters from datasets tha t a re consistent w ith the a bove result . Figure 4is the residue curve map for a mixture of wa ter, buta nol,and butyl acetate calculated by the model in Table 1.

Column Configuration

The overhea d va por condenses int o a w a ter-rich phasea n d a n o rg a n ic - ric h p h a s e t h a t c o n t a in s 56 mo l %bu t y l a c e t a t e , t h e re s t be in g a mix t u re o f wa t e r a n dbu t a n o l . N o w we n e e d t o p ic k t h e p h a s e t h a t we wil lremove as distillat e. The am ount of tha t pha se removeda s d i s t i l l a t e a n d t h e a m o u n t t h a t i s r e f l u x e d t o t h ecolumn is determined by the reflux rat io. Intuit ively,w e w o ul d l i ke t o r e m ov e t h e m a i n p rod u ct a s t h edistillat e. This implies a configura tion tha t removes theorganic phase as t he dist illate a nd returns th e aqueousphase to th e column a s reflux. Figure 5 shows the modelresults for this configurat ion w ith D a ) 1 , N ) 7, andan init ial molar rat io of butanol to acetic acid of 1:1.These results show that this dist illate policy is poor.First , t he composit ion of the desired product in t hedist illate is never greater than 56 m ol %. Therefor e,we n e ed t o p u ri fy t h e p rodu ct f u rt h er a n d re cov erbutan ol for r ecycle. Second, we a re returning a streamrich in the unw an ted product (wa ter) back to the columnas reflux. The removal of one of the reacta nts (buta nol)in t h e dis t i l la t e a n d t h e bu ildu p o f wa t e r in t h e s t i l l(F i gu r e 5 a ) w i l l l ea d t o a n i ncr ea s e i n t h e r a t e ofbackreaction, leading t o an increase in the overa ll batchtime.

A second an d more common str a tegy is t o remove thea q u e o u s s t re a m a s dis t i l la t e a n d re t u rn t h e o rg a n icphase with the desired product back to the column asreflux, e.g., Keyes,19 Leyes and Othmer,12 and Zhicai eta l. 20 Figure 6 shows t he still a nd distilla te compositionsfor this configurat ion with D a ) 1, N ) 7, and a n init ialmolar rat io of 1:1 butan ol to a cetic a cid. The st ill getsprogressively richer in butyl acetate while the distillateconsists of nearly pure water. The advantages of thisdistillate policy are (1) continuous removal of a nearly

p u re ( u n wa n t e d) p ro du c t f ro m t h e s y s t e m a n d ( 2) ahigher purity of the desired product at the end of therun.

The end of the react ion in the st ill can be detectedfrom a sharp decrease in the water concentration in thedist illate. At this point , butyl acetate can be removeda s t h e dis t i lla t e t o s e p a ra t e i t f rom t h e t ra ce a mo u n t sof the other components in the system. Figure 7 showsthe still and distillate compositions for this second phaseof the operation, which is a nonreactive purification step(n ot e t h a t t h e w a rp e d t ime h a s be e n re s et t o ze ro inthe figures). At t he beginning of this st ep, a mixtu re ofbutan ol, acetic acid, a nd butyl acetat e is produced a s adist illate. After the butanol and acetic acid have been

Figure 4. Nonreact ive residue curve map for a mixture of wat er,butanol, and butyl acetate. The diagram also shows the liquid -liquid-phase boundary.

Figure 5. Batch react ive dist illa t ion of butyl acetate a t infinitereflux and an aqueous reflux policy, N )7 , a n d a n in i t ia l m ola rr a t io of B u O H : H O A c ) 1:1. The composit ion of H OAc in thedist illa te is not shown because it is nearly zero.



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dist illed, there is a pure butyl acetate cut . The inter-mediate slop cut is typically collected and recycled.

A difficulty is tha t t here is a long tail of contam ina tedproduct (Figure 7b). One of the reasons for this is thatthe separat ion of acetic acid and butyl acetate is verydiff icu l t bec a u s e o f a t a n g e n t p in ch bet we e n t h o secomponents in t he vicinity of pure butyl a ceta te. Therea re a ls o v e ry s t r in g en t p u rit y re q u ire men t s on bu t y laceta te (e.g., less tha n 50 ppm acetic acid). This mea nsthat a significant acetic acid concentrat ion in the st illa t t h e e n d o f t h e re a c t io n wil l le a d t o u n a c c e p t a bleproduct purity. One solution is to cha rge the st ill witha s ma ll excess of buta nol to compensa te for the slightlyh ig he r los s in t h e dist i l la t e . Ace t ic a c id is n o w t h elimit ing reactant and is eliminated. The final mixturein t h e s t i l l c on s ist s on ly o f bu t y l a c et a t e a n d a s ma llam ount of butan ol. Figure 8 shows the still and distillat ecompositions for D a ) 1, N ) 7, a n d a n in it ia l c h a rg ethat contains 49 mol %acetic acid and 51 mol %butanol.At t he end of the reaction, the still has 95 mol %butylacetate, 5 mol %butanol, and only trace amounts of theother components.

B u t a n o l a n d bu t y l a c e t a t e f o rm a bin a ry a ze o t ro p ewit h a composition of 79 mol %buta nol an d 21 mol %

butyl a ceta te. Once the reaction reaches completion, th ewater composit ion in the dist illate drops sharply andthe distillate composition reaches a composition closeto the azeotrope until all of the butanol in the systemis removed. Pure butyl acetate then starts coming offthe top the column (Figure 9b). The intermediate cutwith the azeotropic composit ion may be recycled to afresh batch. I t can be seen that the amount of sloppycu t u n der t h e s e con dit ion s is mu ch les s t h a n t h a t inFigure 7b.

To s t u dy t h e e ff ect of t h e n u m be r of s t a g es , w e

increased the number of stages in the column to 20. Theresults of this simulat ion (Venimadhavan 13) s h ow n oqualitative difference from Figure 6. The only differenceis tha t , because a larger num ber of sta ges improves theseparat ion, the cuts are slightly sharper.

A More Rigorous Model

The ma jor adva nta ge of a simplified model is th at itgives a quick est imate of the behavior of the system.To a c ce ss t h e a c cu ra c y of t h e s implif ie d mode l, wedeveloped a more rigorous model in which we relaxedsome of th e simplifying a ssumpt ions. These included theinfinite r eflux a nd the q uasi-steady-sta te a ssumptions.When these assumptions are removed, the system is

Figure 6. Batch react ive dist illa t ion of butyl acetate a t infinitereflux and an organic reflux policy, N ) 7 , a n d a n in i t ia l m ola rratio of BuOH:HOAc ) 1:1. The compositions of BuOAC and HOAcin the dist illa te are not shown as t hey fa ll rapidly to values belowthe composit ion of B uOH.

Figure7. P urificat ion of the butyl acetate in the still at an infinite

reflux, and N ) 7 for the case in Figure 6. The composition of waterin the dist illa te is not shown because it is nearly zero.



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modeled by a set of (N + 1)(c- 1) differential equa tions(c-1 equations for the still and c - 1 equa tions for eacho f t h e N s tages). Without the quasi-steady-state as-s u mp t io n , a s t e a dy - s t a t e ma t e ria l ba la n c e c a n n o t bewr itten for th e envelope in Figure 1 an d, hence, the stillequation is modified t o

whereyS ,iis the vapor phase mole fraction of componenti leaving th e st ill , x1, i is the liquid-phase mole fractionof component ion stage 1, Vis the vapor f low ra te, andL is the liquid f low rate. With the introduction of theD a mk oh le r n u mber a n d wit h u s e o f t h e de cre a s in gdist illate rate policy D / D0 ) (HS /HS ,0) , e q 17 c a n bereduced to a form similar to eq 8.

In this equation, Rrepresents the r eflux ra t io, L / D.

F or a n y s t a g en, i f we assume tha t the holdup (H) onthe sta ge is a consta nt (but not negligible), mat erial ba l-ance yields (stage numbering increases up the column)

This equa tion is rearr an ged to give

The condenser ba lance (eq 10) rema ins th e sam e as tha tfor the simplified model.

This formulat ion introduces two new variables, thereflux r at io, R, a n d t h e ra t io o f t h e h oldup in t h e s t i llto the holdup on a sta ge. For our calculat ions, we set R) 10 a n d t h e h o ldu p in t h e s t i l l t o be 50 t ime s t h eholdup on a stage (in other words, around 12%of thetotal system holdup is on the stages). The number ofs t a g e s N was set to seven as before, and we removedthe a queous pha se as distilla te. Figure 10 gives the still

Figure 8. Batch react ive dist illa t ion of butyl acetate a t infinitereflux and an organic reflux policy, N ) 7 , a n d a n in i t ia l m ola rr a t io of B u O H : H O A c ) 51:49. The compositions of HOAc andB u O Ac in t h e d is t i ll a t e a r e n ot s h ow n b ec a u s e t h e y a r e n e a r lyzero.

Figure 9. P urif icat ion of the butyl aceta te in the st ill a t infinitereflux and N ) 7, beginning with a feed composition produced asthe still composition at the end of the distillation shown in Figure8.

Hd xj, i

d t ) L (xj+1, i - xj, i) + V(yj-1, i - yj, i)

i ) 1, ..., c - 1 (19)

dxj, id

) HS

H [R(xj+1, i - xj, i) + (R + 1)(yj-1, i - yj, i)]

i ) 1, ..., c - 1 (20)

d HS xS ,i

d t ) -V yS , i + L x1, i + iHS r (17)

dxS ,i

d ) (R + 1)(xS ,i - yS , i) + R(x1, i - xS , i) +

D a(i - TxS , i) r

kf,refi ) 1, ..., c - 1 (18)



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and dist illat e composit ions a s a function of the dimen-sionless time w ith r esults similar to Figure 6. The ma indifference is that the response of the rigorous model isa lit t le slower because of the sta ge dyna mics.

This gives us confidence that we can use the simpli-fied model to get a good understanding of the systembehavior. This is desirable because the more detailedcalculat ions a re extremely slow compared to the simpli-fied model. This is due to the r igorous phase sta bilitytest followed by vapor -l iquid equilibrium or vapor -

liquid-liquid equilibrium calculations for the still, ande a ch s t a g e a n d a l iq u id-l iquid f lash calculat ion in t hecondenser for each t ime step. A typical r un t ime for thesimplified model is on th e order of 2-3 h on a DEC 3000AXP while that for the more detailed model is 2 weeks.

Although the simplified model and the detailed cal-culat ion at large reflux agree well, i t is also useful tohave an explicit policy for the reflux to implement theresults.

Distillate and Reflux Policies

For the special case ofT ) 0, the decreasing distillaterate policy , D / D 0 ) HS /HS ,0, leads to an explicit rela-tionship between a n d t(see eq 2) as follow s:

Therefore,

The value of D0

i s s e t by t h e in i t ia l a n d f in a l s ize s oft h e ba t c h HS ,0 a n d HS ,F , respectively, and a choice ofthe total t ime for dist illat ion, tbatch, a ccording t o D0 )(HS ,0/tbatch) ln (HS ,0/HF, 0) . N o rma lly , t h e v a p o r ra t e isma in t a in e d a t a con s t a n t v a lu e n ea r t h e ma x imu m f orflooding. In this case, a material balance for the con-denser leads to

Substitut ing for D(t) and rearra nging give the explicitreflux policy

wh e rer0is the initia l reflux rat io. The va lue of r0is set

by the va por ra te (equipment) and D0according tor0 )V/D0 -1 .

This policy suggests th a t occa siona l mea surements ofthe st ill holdup and comparison to the dist illate f lowcan be used to update the dist illate and reflux rates toma in t a in D / Ha pproximately consta nt a t i ts set point .

Conclusions

We h a v e de ve lop ed a s implif ie d mode l f or ba t c hre a c t iv e dis t i l la t io n a n d u s e d i t t o s t u dy a l t e rn a t iv eoperating strategies for the production of butyl acetate.I n t h i s m i x t ur e, t h er e i s s om e u n ce rt a i n t y i n t h eliterature about the identity of the light boiler. Using arelat ionship based on topology, we ha ve proved conclu-sively that the heterogeneous ternary azeotrope betweenwater, butanol, and butyl acetate is the lightest boilerand hence the composition of the overhead vapor mustbe close to this azeotrope. The azeotrope phase-sepa-rates on condensation into an aqueous phase which ispredomina ntly w a ter (99.5 mol %wa ter) a nd a n organicphase which is a mixture of water, butanol, and butylacetate.

We also describe a n ovel opera ting policy in w hich th edistillat e flow ra te is decreased in proportion to th e stillholdup. We ha ve studied a column configurat ion inwhich the aqueous phase is removed as dist illate andthe organic phase is returned t o the column a s reflux.This constantly removes one of the products from the

re a c t io n , t h u s f o rc in g t h e re a c t io n f o rwa rd, a n d t h isaccumulat es the desired product (butyl a ceta te) in thest ill . Once the react ion is complete, butyl acetate iscollected as a high-purity dist illate. An intermediateslop cut, wh ich is a m ixture of buta nol and butyl a ceta te(with w at er as a t race component and a n immeasurablea mount of a cetic a cid), is first collected a nd r ecycled t oa fresh bat ch. Thus, w e can produce high-purity butylacetate without any addit ional separat ion steps.

Acknowledgment

We ar e gra teful to th e sponsors of the P rocess Designand Control Center, University of Massa chusetts, Am-herst, and especially for helpful comments from BASF,

Figure 10. B atch react ive dist illa t ion of butyl acetate a t a refluxr a t io R ) 10, Hstill/Hs t ag e ) 50, a n organic reflux policy, N ) 7,a n d a n in i t ia l m ola r r a t io of B u O H : H O Ac )1:1.

) (D0

HS ,0)t (21)

HS (t) ) HS ,0e-(D0/HS ,0)t (22)

D(t) ) D0e-(D0/HS ,0)t (23)

V ) (r(t) + 1)D(t) (24)

r(t) ) (r0 + 1)e -(D0/HS, 0)t

- 1 (25)



9/9

AG, and Eastman Chemical Co. Financial support wasprovided by the NSF (G ra nt CTS-9613489).

Notation

ai ) liquid-phase activity of component iA i )component iD ) distilla te flow ra te (mol/tim e)D0 )initia l dist illate flow ra te (mol/time)D a )Da mkohler number, defined a s HS ,0kf,ref/D0G0 ) Gibbs free energ y of rea ction (kca l/mol)H ) liquid holdup on a stage (mol)HS ) liquid holdup in the still (mol)HS ,0 ) initial liquid holdup in the still (mol)Keq ) reaction equilibrium constantkf ) forw ar d rea ction r at e consta nt (1/time)kf,ref ) forward reaction rate constant at reference temper-

a tu re (1/ti me)L ) liquid flow r a te (mol/tim e)N )number of s t a ges in t he columnr ) rea ction r a te (1/tim e)R )ref lux ra t iot ) clock timeV ) vapor flow ra te (mol/tim e)xD ,i ) liquid-phase mole fra ction of component i i n t h e

dis t i l la t e

xn, i ) liquid-phase mole fraction of component ion s t a ge nxS ) vector of mole fractions in the stillxS ,0 ) vector of initial mole fractions in the stillxS ,i ) liquid mole fraction of component i in t he s t i l lyn, i ) vapor pha se mole fra ction of component i on s t a ge n

Greek Symbolsi ) stoichiometric coefficient of component iT )sum of the stoichiometric coefficients ) w a rped t ime va ria ble

Subscripts0 ) init ia lD )dis t i l la t ei )component i1, n - 1 , n, N )s t a ge numbers

S ) st ill

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Received for review J uly 3, 1998Revised ma nu scri pt received November 5, 1998

Accepted November 5, 1998

IE9804273


rxnes acetato de butilo

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