Studies of a membrane reactor: Esterification facilitated by pervaporation

Studies of a membrane reactor: Esterification facilitated by pervaporation

Chemical En#ineerin# Science, Vol. 51, No. 20, pp. 4673-4679, 1996 Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved...

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Chemical En#ineerin# Science, Vol. 51, No. 20, pp. 4673-4679, 1996 Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0009-2509/96 $15.00 + 0.00

Pergamon PII:


STUDIES OF A MEMBRANE REACTOR: ESTERIFICATION FACILITATED BY PERVAPORATION XIANSHE FENG and ROBERT Y. M. HUANG* Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3GI (First received 1 February 1996; revised manuscript received and accepted 24 April 1996) Abstract--This study deals with pervaporation-facilitated esterification. A parametric study was carried out to provide a fundamental understanding of the reactor behavior. A batch reactor integrated with a pervaporation unit was selected as the model system. It was shown by simulation that conversions exceeding equilibrium limits can be achieved by using pervaporation to remove water from the reaction mixtures, and that complete conversion of one reactant is obtainable when the other is in excess. The membrane reactor tolerates the presence of water, which can be either in the reaction medium or as impurity of the reacting reagent. There are upper and lower limits in the performance of reactor facilitation by pervaporation. Membrane permeability, membrane area and the volume of the reaction mixtures to be treated are important operating parameters influencing the reactor behavior. Operating temperature influences reactor performance through its influences on reaction rate and membrane permeability. Copyright © 1996 Elsevier Science Ltd Keywords: Membrane reactor, esterification, pervaporation, parametric study.

INTRODUCTION There has been an engineering effort to combine reaction and separation into a single process unit so as to improve process performance. In recent years membrane technology has emerged as one of the viable unit operations in separation processes. The potential applications of membrane technology in reaction engineering are being recognized. Since separation membranes permit selective permeation of a component from a mixture, membrane reactors can help enhance the conversion of thermodynamically or kinetically limited reactions through controlled removal of one or more reactant or product species from the reaction mixture. The majority of published work on membrane reactor to date is in the field of biotechnology. The membranes used are typically microporous, and the function of the membranes is mainly for immobilizing enzymes, eliminating product inhibition, recycling enzymes and other biocatalysts, and manipulating substrates and nutrients. Recently, extensive studies have been carried out on membrane reactors applied to catalytic dehydrogenation, hydrogenation, and decomposition reactions (Mohan and Govind, 1988; Shu et al., 1991; Itoh and Wu, 1993; Ioannides and Gavalas, 1993; Ziaka et al., 1993a,b; Gao et al., 1993, 1995). However, relatively little work has been done on liquid-phase reversible reactions due to lack of suitable membranes with good permselectivity and solvent resistance. Ultrafiltration membranes are too porous to effect efficient separation of small liquid

*Corresponding author. Fax: (519) 746-4979. E-mail: [email protected],watstar, uwaterloo,ca.

molecules, while reverse osmosis membranes are likely to require an inconveniently high operating pressure due to osmotic pressure of the reaction mixtures. Pervaporation, an emerging membrane process specially used for organic-water and organic-organic separations (Huang, 1991), seems to be an appropriate choice. In this process the mass transport through the membrane is induced by maintaining a low vapor pressure on the downstream side, thereby eliminating the effect of osmotic pressure. The concept of using pervaporation to remove by-product species from reaction mixtures was proposed in the early stage of pervaporation research by Jennings and Binning (1960), but the interest in pervaporation membranereactors was only rekindled recently when pervaporation has proven to be a viable separation technique in the chemical industry. Presently, pervaporation is best applied to dehydration of organic solvents, and the dehydration membranes normally work best when water content in feed mixture is not high. Thus, reversible reactions that produce by-product water are a niche of pervaporation for reaction enhancement. Esterification of carboxylic acids and alcohols is a typical example of an equilibrium-limited reaction that produces by-product water. The conversion is generally low due to limits imposed by thermodynamic equilibrium. To achieve a high ester yield, it is customary to drive the position of the equilibrium to the ester side by either using a large excess of one of the reactants (usually the alcohol) or using reactive distillation to accomplish in situ removal of product(s) (Reid, 1952). The use of a large excess of reactant is accompanied with increased cost for subsequent separation operations, while reactive distillation is only




effective when the difference between the volatility of product species and the volatility of reactant species is sufficiently large. In the cases where the reaction mixtures form an azeotrope, a simple reactive distillation configuration is inadequate. Moreover, in reactive distillation the preferred temperature range of reaction should match that for the distillation (deGarmo et al., 1992). The optimum operating conditions cannot be determined principally by the reaction thermodynamics and/or kinetics, but is, to a large extent, subject to the restraint of the temperature suitable for performing the distillation. In practice, the process performance and energy consumption in reactive distillation are often dominated by distillation operations, as is the case for the manufacture of ethyl acetate and other esters (Reid, 1952). Pervaporationenhanced reactors are expected to provide a promising alternative due to the following considerations: (1) pervaporation is a rate-controlled separation process, and the separation efficiency is not limited by relative volatility as in distillation, (2) in pervaporation only a fraction of feed that is permeated by membrane undergoes the liquid- to vapor-phase change, and thus energy consumption is generally low as compared to distillation, (3) with an appropriate membrane, pervaporation can be operated at a temperature that matches the optimal temperature for reaction. The last feature is particularly important for enzymatic esterifications due to temperature constraints normally imposed by enzyme stability. Pervaporation membrane reactors have been studied for esterification of oleic acid and ethanol (Kita et al., 1988; Okamoto et al., 1993), propionic acid and propanol (David et al., 1991a,b), erucic acid and cetyl alcohol (Nijhuis et al., 1992), tartaric acid and ethanol (Keurentjes et al., 1994), oleic acid and butanol (Kwon et al., 1995) and valeric acid and ethanol (Ni et al., 1995) with various acids or lipases as catalysts. In some cases the membrane itself can be catalytically active (Bagnell et al., 1994). Waldburger et al. (1994) studied heterogeneously catalyzed esterification of acetic acid and ethanol, and cascade arrangements of membrane reactors were proposed for continuous operation. A pilot plant test was conducted and an industrial plant operation has been designed and scheduled; in both cases the commercial poly(vinyl alcohol)-based membranes were used (Bruschke et al., 1995). In this work a parametric study was carried out for esterification facilitated by pervaporation in an attempt to provide a fundamental understanding of the behavior of the membrane reactor. A batch reactor, the simplest of all reactor configurations, integrated with pervaporation, was selected as the model reactor system. The influence of some parameters on the reactor performance was analyzed. An ideal case where the membrane was perfectly permselective to water was investigated to show the maximum improvement in reactor performance achievable by the use of membrane pervaporation. Though the study is aimed at esterification reactions, the results obtained here can

be extended to other reactions with similar features (e.g. condensation reactions) provided that the product species can be removed by pervaporation.

THEORETICAL Consider an esterification reaction of the type RCOOH + R'OH ~ RCOOR' + H 2 0


carried out in a batch reactor equipped with a pervaporation unit, as shown in Fig. 1. Assume isothermal operation and negligible change in catalyst concentration. Applying a material balance on any reactant or product species at any instant yields d(C~V) - dt


r i V




where subscript i denotes species i, C the concentration, and J the permeation flux. r is the rate of disappearance of the species in the reactor due to chemical reaction; for product species, r is the rate of formation and takes negative sign. V and S are the volume of reaction mixtures and the membrane area for permeation, respectively. Since the stoichiometric coefficients for reactants and products are equal, the numerical values of reaction rate expressed with respect to any species i are equal. Suppose the reaction rate can be written as r

= klCACn -- k2CECw = kl(C aC n - - - ~

C~Cw) (3)

where kl and k2 are the rate constants for forward and reverse reactions, respectively, and K e (= kl/k2) is the equilibrium constant. Subscripts A and B refer to the two reactants, and subscripts E and W refer to ester and water, respectively.

~~~Reactor (a) l


I ~actor


Permeate Permeate


Unit Fig. 1. An idealized batchwise membrane reactor (a) and its equivalent that integrate a membrane unit with a batch reactor (b).


Studies of a membrane reactor Table 1. Stoichiometric table showing concentration variation in the reactor A






Concentration No. of moles

Co CoVo

CoOn CoOnVo

CoO~ CoOeVo


No. of moles

CoVo(1- X)

CoVo(On- X)



V°Co(1 - X)

Co(On - X)

VoCo(OE+ X) Vo --~Co(Or+ X)

At t=0


Assuming the volume change of the reaction mixtures in the membrane reactor is given by



die = - ~, dt i Pi

where Mi and pi are molar mass and density of species i, respectively, then eqs (2)-(4) constitute the basic equations describing a batchwise pervaporation membrane reactor. For given initial conditions of concentration and volume, the concentration of the reaction mixture at any instant can be solved provided that the knowledge of reaction rate constants and membrane permselectivity are known. Consider an ideal case where the membrane permeates only water. Take the concentration of the less abundant reactant (designated as species A hereafter), whose initial concentration is Co, as basis, let X be the conversion at any time t, and define 0n, 0E and Ow as the ratios of the initial concentrations of species B, E and W to Co, respectively. One can then proceed to set up Table 1 to show the concentration change with the extent of reaction. Defining

v = V/Vo


Y = Cw/Co


and substituting the appropriate quantities in Table 1 into eqs (2) and (3) yields dXd_-__=t k a C o [ ! l - X ) ( O , - X ) v

(OE+X)Y1K~ 3"


For a 'perfect' water permeable membrane, J a = Jn = JE = 0. Rewriting eq. (4) gives



CoOw CoOwVo CoVo(Ow+ X) - S~JwSdt

For a special case where the membrane permeability is so large that water is removed from the reactor as fast as it is formed, i.e. Cw = 0, then the above differential equations can be solved analytically to give the following relations: 1

In [(1 - X/OB)t -~°B1

k, Co - on- 1 L


(when 0n > 1)


and (1 - ~ ) X


klCot - _--L1 ~ - I- e l n f ~ - - X

(when On = 1)

(!)[dX ~



ydV dt

(S_ff__~Jw1 \VoJ Col .


The initial conditions are Att=0,






e = Co Mw/Pw •


This represents the best performance that can be achieved by membrane pervaporation to facilitate the reaction since no reversal of the reaction occurs. On the other hand, if the membrane permeability is so small that the reactor performance is hardly affected by the membrane, the following equation can easily be derived to relate conversion and reaction time 1 -

X =



2y [[email protected]) + ~ 3

/¢-t~ where

Or + Ow~ fl=klCo(1 +On+~/I ?=ktCo



(16) (17)


From the relations expressing water amount in the reactor, shown in Table 1, the following equation can be obtained dY d---t-=



I// = (f12 __ 4~7)1/2

dt = - Jw


Y o = 0 w . (10)

Thus at a given time the quantities X, v and Y can readily be obtained by solving eqs (7)--(9) numerically.


On- Ke J"


This represents another extreme case of a simple batch reactor. RESULTS AND DISCUSSION

The permeation flux through a pervaporation membrane is usually concentration dependent. For simplicity of analyses water flux is assumed to be proportional to water concentration

Jw = c°Cw








~,(s/v.).h '

~(s/v.). h -t 0

0.8 0.6 0.7 0.6













0.3 0.2 0.2 0.1 0.1 0.0


1'0 2'0 3'0 ,'0 ~'0 ~'0 7'0 8'0 9'0

' 120 ' 130' 140 ' 150 ' 100 118

Time, hr

l 10 20 30 410 510 610 710 80i 910 I00110112011301 1,~-0 150 I

m--'~'---t~ i



Fig. 2. Conversion as a function of reaction time for different ~o(S/Vo) values.

Fig. 3. Variation of water concentration in the membrane reactor vs reaction time.

where ~o is a coefficient characterizing membrane permeability. This assumption is normally true for dehydration membranes when water content is not very high (Kita et al., 1988; David et al., 1991a, b; Okamoto et al., 1993; Bruschke et al., 1995). Therefore, membrane parameter ~o and operating parameters S and Vo in eqs (8) and (9) can be combined as a single variable, i.e. ~o(S/Vo), to measure the capacity of the membrane unit for removing water from the reactor. Figure 2 shows the calculated results of conversion vs reaction time at different ~o(S/Vo) values for the following parameter values: kl = 3 x 10- 5 ma/mol h, Ke = 2, 0s = 1, and 0E = 0w = 0; these numerical values will be used throughout the studies unless specified otherwise. Note that the reaction parameters kl and K e used here are representative of the case of esterification of acetic acid and ethanol at 100°C with hydrochloric acid as catalyst (Smith, 1970). Other parameters used in the calculations are Co = 1000 mol/m 3 and Pw = 950 kg/m 3. Figure 2 shows that the conversion of the membrane reactor can go beyond the equilibrium conversion, which is the maximum conversion that would be obtained if membrane permeation were not applied. The two lines in the figure labelled with og(S/Vo) equal to ~ and 0 represent the upper and the lower limits of the reactor performance. It is clear that the gap between the two limits becomes larger as the reaction time increases, indicating that the reaction is increasingly facilitated by membrane pervaporation. At a given reaction time, the higher the value of og(S/Vo), the higher the conversion. This is obvious because the concentration of water in the reactor will be reduced more rapidly when the membrane is more permeable and/or when the membrane area per unit reaction volume is larger. Since it is the joint effect of S, V0 and co that influences the reactor performance, it is natural to anticipate that numerous combinations of the three independent variables may achieve essentially the same results. Therefore, in membrane reactor design low permeability of a membrane can be compensated by using larger membrane area for a given reactor

volume to be treated. For the given case of illustration, the reactor performance approaches the upper limit when e,'(S/Vo)= 1 h - t ; further increase in o9(S/Vo) value leads to little improvement. Considering that for many currently available membranes o~ is usually in the order of 10 -2 m/h (Kita et al., 1988; David et al., 1991a; Okamoto et al., 1993) and that the membrane area accommodated per unit volume of membrane module can be considerably high (particularly for spiral wound and hollow fiber modules), it is feasible to achieve sufficiently high values of m(S/Vo) in practical pervaporation-aided reactors by coupling a pervaporation unit with the reactor, as shown schematically in Fig. l(b). Figure 3 illustrates how water concentration changes with reaction time; for convenience relative concentration Cw/Co vs time is plotted. Note that Co is equal to the water concentration that would be obtained at complete conversion in a simple batch reactor. The figure shows that when membrane is used to enhance the reaction, water concentration undergoes a maximum as reaction proceeds in time. This is caused by two competing effects: one is the water formation due to reaction, which tends to cause water build-up in the reactor, and the other water removal by pervaporation, which tends to lower water concentration in the reactor. During the early period of reaction, the rate of chemical reaction is high, whereas water concentration is low and so is the rate of water removal from the reactor. Consequently, water concentration gradually increases until it reaches maximum when its formation rate and removal rate become equal. Thereafter the water removal is faster than formation, resulting in depletion of water in the reactor. Naturally, for a given reaction system, the larger the value of og(S/Vo), the shorter the time required for water to reach maximum concentration and the smaller the magnitude of the maximum water concentration, as shown in Fig. 3. It should be mentioned that for some enzymatic esterifications, a certain amount of water in the reactor is essential to maintain the catalytic activity of the enzymes


Studies of a membrane reactor


1.0 0.9








~ 0.5



MO.5 0.4

w(S/V,), h-'


0.3 0.2

0,0Ol 0



0,1 0.0

I 10


I 20

0,0 :30




70 8 0 90 Time, hr


100 110 120 1:30 140 150

Fig. 4. Variation of reaction rate during the course of reaction.

1.of/ -



Fig. 6. Conversion vs reaction time for different Ow values. kl = 10-4 m3/molh; co(S/Vo) = 0.5 h- 1. 2.0



/ ~ 8FI





O.S x 0.5 0.4




1.6 1.4 1,2


Jl.o 0w=2



0.5 0.4

02 0.2 0.1 0.C






SO 80

70 SO 90 100 110 120 130 140 150 Time, hr


"1 20




Time, hr

Fig. 5. Effect of excess of one reactant on conversion of the limiting reactant, kl = 10-4 m3/mol h; co(S/Vo) = 0.5 h-1.

Fig. 7. Variation of water concentration with reaction time when water is initially present in the reactor, kl = 10 -4 m3/molh; o~(S/Vo) = 0.5 h- 1.

(Kwon et al., 1995; Nijhuis et al., 1992), and thus there exists an optimal water concentration. In such cases, an appropriate expression showing water concentration dependence of reaction rate constant is needed to determine the optimal water concentration. The variation of reaction rate with time is shown in Fig. 4. As reaction proceeds, reaction rate decreases. Such a decrease in reaction rate is, however, slowed down by the use of a membrane because selective removal of water further concentrates the reactants. When the reactant species are in stoichiometric proportion, as is the case discussed here, the reaction rate will eventually be reduced to zero. Thus, despite that pervaporation can shift the equilibrium toward the ester side and go beyond equilibrium conversion, it cannot drive the reaction to completion, i.e. X = 1, in a finite time scale, no matter how large is the value of co(S/Vo). However, when one of the reactant species is used in excess, a complete conversion of the other is achievable, as shown in Fig. 5. This is confirmed by the results of an early experiment that the final reaction mixtures did not contain water after 60 h of reaction of acetic acid and butanol (in excess) at 155°C (Jennings and Binning, 1960). Apparently, the larger

the extent of the excess, the faster the reaction to reach completion. This is superior to simple batch reactor where no matter what the excess of one reactant, the limiting reactant is never completely reacted. Water (one of the products) and alcohol (one of the reactant) or a mixture thereof are the c o m m o n reaction media for esterification (National Bureau of Standards, 1951). When water is present in the reactor, the thermodynamic equilibrium conversion will be decreased. Surprisingly, coupling the reaction with pervaporation can significantly tolerate the presence of water. Figure 6 shows that for the case for which the calculation is performed, the conversion is hardly affected when Ow changes from 0 to 2, whereas the equilibrium conversion in a batch reactor is estimated to decline by approximately 50%. The tolerance for water is attributed to the fact that the higher the water concentration, the larger the permeation rate through the membrane, making water content reach low level rapidly, as shown in Fig. 7. When water is used as the reaction medium, the water content in the early period of reaction may be considerably high, but fortunately the reaction rate at this stage is not sensitive to product concentration. When the influence of product



_ ~ ~- - •

03 P/ OZJ /


Ke=2) IK~--So3. . . . . . . .

...."~i=~0-'~/mo~.h ......." K'~=Z "


0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 Time. hr

Fig. 8. Effects of reaction rate constant kl and equilibrium constant Ke on reactor performance.

concentration on reaction rate becomes significant as reaction proceeds, water content has already been reduced to a low level by pervaporation. This is one of the favorable characteristics of the membrane reactor. Figure 8 illustrates the effects of reaction rate constant kl and equilibrium constant Ke on the reactor performance. It is shown that at a given time, the facilitation of the reaction by a membrane tends to be more significant as kl increases and/or Ke decreases. This is understandable based on the magnitude of reaction rate and the position of reaction equilibrium. Fast reactions with severe equilibrium limitations benefit the most from continuous removal of by-product by a membrane. In practice, a large ka value is always preferred and can be obtained by elevating reaction temperature and using a suitable catalyst, while little control over Ke value can be achieved. Only slight variation in Ke with temperature is expected for esterification reactions in which the difference in enthalpy of products and reactants is small, as is the case ethanol acetic acid esterification (Butler and Berlin, 1972). However, increasing temperature often enhances membrane permeability significantly. It is obvious that the reaction temperature, another important operating parameter, influences the performance of a membrane reactor primarily through its effects on permeation rate and reaction rate. CONCLUSIONS A parametric study of pervaporation-facilitated esterification was carried out. It was illustrated that both conversion and reaction rate can be enhanced by using pervaporation to remove water from the reactor simultaneously. Conversions exceeding equilibrium limits can be achieved, and a complete conversion of one reactant is obtainable when the other reactant is in excess, no matter how small the excess is. In a membrane reactor, the presence of water, which can be either reaction medium or impurity of the reacting reagent, can be tolerated. There exist upper and lower

limits in reactor performance. Important operating parameters that influence reactor performance include membrane permeability, membrane area and volume of the reaction mixtures to be treated. When such variables are fixed, the facilitation of the reaction is most significant for fast reactions with severe equilibrium limitations. Operating temperature influences reactor performance through its influence on reaction rate and membrane permeability.

Acknowledgements--Financial support by the Environmental Science and Technology Alliance Canada (ESTAC) and by the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. NOTATION C Co J k~ k2 Ke M r ro S t v V V0 X Xe Y

concentration, mol/m 3 initial concentration of limiting reactant, mol/m 3 permeation flux through membrane, mol/m 2 s forward reaction rate constant, m3/mol s backward reaction rate constant, m3/mols equilibrium constant, dimensionless molar mass, kg/mol reaction rate, mol/m3 s initial reaction rate, mol/m3 s membrane area, m 2 reaction time, s function defined by eq. (5), dimensionless volume of reaction mixture, m 3 initial volume of reaction mixture, m 3 conversion, dimensionless equilibrium conversion, dimensionless function defined by eq. (6), dimensionless

Greek letters quantity defined by eq. (18), s -1 fl quantity defined by eq. (15), s -1 ? quantity defined by eq. (16), s-1 quantity defined by eq. (13), dimensionless 0i ratio of initial concentration of component i to initial concentration of the limiting reactant ( = C i/ Co), dimensionless p density, kg/m 3 quantity defined by eq. (17), s -1 o~ parameter characterizing membrane permeability, m/s Subscripts A limiting reactant B more a b u n d a n t reactant W water E ester i species i in reactor REFERENCES

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