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Modeling of esterification of acetic acid with n-butanol in the presence of Zr(SO4)2·4H2O coupled pervaporation
Journal of Membrane Science 196 (2002) 171–178
Modeling of esterification of acetic acid with n-butanol in the presence of Zr(SO4 )2 ·4H2 O coupled pervaporation Qing Lin Liu a,∗ , Hong Fang Chen b a b
Department of Chemical Engineering, Xiamen University, Xiamen 361005, China Department of Chemical Engineering, Tianjin University, Tianjin 300072, China
Received 22 December 2000; received in revised form 6 June 2001; accepted 7 June 2001
Abstract Modeling of esterification of acetic acid with n-butanol in the presence of Zr(SO4 )2 ·4H2 O coupled pervaporation was studied in this paper. The influence of several process variables, such as process temperature, initial mole ratio of acetic acid over n-butanol, the ratio of the effective membrane area over the volume of reacting mixture and catalyst content, on the esterification was discussed. The calculated results for the conversion of n-butanol to water and permeation flux were consistence with the experimental data. The permselectivity and water content can be roughly estimated by the model equations. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Pervaporation; Esterification reaction; Poly(vinyl alcohol) membrane; Composite membranes
1. Introduction The use of pervaporation separation has received considerable attention during decade. Among the applications most of them concern separating one component from liquid feed mixture. For an example, this technique has been applied to acetobutylic fermentation so as to extract in situ the butanol produced thereby obtaining a greater glucose consumption and a greater higher production [1]. Combining a membrane with a chemical reaction, has been shown to offer advantages in a number of different instances. One way to classify the different situations in which membrane reactors are advantageous is by the type of reaction taking place, and using this scheme, most membrane reactor applications would be classified as either biological application ∗ Corresponding author. E-mail address: [email protected] (Q.L. Liu).
[2] or catalytic application [3]. It is clear that the separation of the products should be as fast and selective as possible in order to obtain a high yield for the reaction. One of potentials application is the use of pervaporation process to drive an equilibrated reaction. Reviews of the literature concerning catalytic membrane reactors reveal that a very large fraction of catalytic membrane reactor applications involve reversible reactions which reach a thermodynamically limited conversion level in a conventional reactor [4–9]. By conducting these reactions in a catalytic membrane wherein one product can selectively permeate through the membrane and out of the reaction zone, an overall conversion is attained which is much greater than that realized in the conventional reactor. A number of investigations have concerned on the application of hydrogen separation membranes to reversible gaseous reaction and will not be considered in the present study. Other recent investigations have been made
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Nomenclature A, B, E, and W Ci Ji Mi Ni Ni 0 Pi PW , PA R R0 S SA,B , SA,E
SW,B , SW,E
V X
acetic acid, n-butanol, butyl acetate and water, respectively concentration of component i in reacting mixture (mol l−1 ) permeation flux of component i (mol m−2 h−1 ) molar molecular weight of component i (g mol−1 ) molar number of component i (mol) molar number of component i at zero-time (mol) permeation parameter of component i (l m−2 h−1 ) parameters as a function of process temperature universal gas constant (J mol−1 K−1 ) initial molar ratio of acetic acid to n-butanol effective area of the membrane (m2 ) parameter concerning influence to acetic acid permeating by existing of n-butanol and butyl acetate parameter concerning influence to water permeating by existing of n-butanol and butyl acetate volume of reacting mixture (ml) conversion of n-butanol
Greek letter ρi density of component i in the liquid mixture on the application of water permeable membranes to liquid-phase reaction [10–21]. The objective of this study was an attempt to investigate the effect of operating parameters on the typical variable−water content in the reactor during the esterification of acetic acid with n-butanol in the presence of Zr(SO4 )2 ·4H2 O coupled, the extraction of water by pervaporation. Model equations for pervaporation-aided (PV-aided) esterification were
presented and their valid was verified by comparing the prediction to the experimental results.
2. Modeling of PV-aided esterification The esterification of acetic acid with n-butanol is in the form of the following equation: A+B↔E+W
(1)
In the case of n-butanol, non-permeating through the membrane (the amount of n-butanol or n-butyl acetate in the permeate is very small and can be negligible practically), the variation of n-butanol concentration can be expressed by dCB = k1 CA CB Ccat − k2 CW CE Ccat dt Here,
−
NA , V NW = , V
CA = CW So,
dCB 1 = 2 dt V
NB , V Ncat = V
CB = Ccat
dV dNB −NB +V dt dt
CE =
(2)
NE , V (3)
(4)
Substituting Eq. (4) into Eq. (2) gives dV Ncat dNB N W NE NB −V = k1 N A NB − (5) dt dt V keq The conversion of n-butanol to n-butyl acetate is written by X=
NB0 − NB NB0
(6)
The expression is valid for this study since acetic acid is in excess, and the permeating of n-butanol through the membrane is negligible. It is assumed that the permeation fluxes of component i (i = A, B, W and E) can be estimated in a binary liquid mixture of the water content less than of 10 wt.% by Ji = Pi Ci
(7)
Here, Pi is permeability coefficient and Ji is the permeation flux of i that can be modified in the quarter
Q.L. Liu, H.F. Chen / Journal of Membrane Science 196 (2002) 171–178
mixture on the basis of the binary mixture, so the amount of i in the permeate in moles of Qi can be obtained by t Qi = Ji S dt (8) 0
Differentiating Eq. (6) with respect to t gives dX dNB =− NB0 dt dt
(9)
For acetic acid we have NA = NA0 − NB0 X − QA
(10)
dQA = JA S dt
(11)
Differentiating Eq. (10) with respect to t gives dNA dX dQA = −NB0 − dt dt dt
(12)
Substituting Eq. (11) into Eq. (12) dNA dX + JA S + NB0 =0 dt dt
(13)
173
Isothermal operation is valid since the reaction heat is small. Ideal mixing is assumed in the reactor since the volume of reacting mixture is relatively large and is nearly constant. Following equations can be obtained by substituting Eq. (9) into Eqs. (13), (15) and (17) dNB dNA + JA S − =0 dt dt
(13A)
dNB dNW + JW S + =0 dt dt
(15A)
dNB dNE + =0 dt dt
(17A)
In the end, the variables; NA , NB , NE , NW , V can be solved simultaneously by the Eqs. (5), (13A), (15A), (17A) and (18) as an initial problem using the Runge–Kutta–Gill fourth-order method. The reaction rate constants for the esterification are shown in Eqs. (19) and (20), in which is demonstrated that forward reaction rate constant is larger than backward reaction in quantities:
Similarly, as for water and n-butyl acetate in the event of n-butyl acetate non-permeating through the membrane, we have
53.13 × 103 k1 = 4.531 × 106 exp − RT
(19)
NW = NW0 + NB0 X − QW
(14)
dNW dX + JW S − NB0 =0 dt dt
(20)
(15)
58.94 × 103 k2 = 4.376 × 106 exp − RT
NE = NB0 X
(16)
dNE dX − NB0 =0 dt dt
(17)
The volume of the liquid in the reactor, V, is given by Eq. (18) according to the additive of volume: V =
NA MA N B MB N E ME N W MW + + + ρA ρB ρE ρW
(18)
The model used following assumptions: 1. isothermal operation; 2. negligible permeating of n-butanol and butyl acetate through the membrane, which resulted from the PV separation of mixture of water/acetic acid/ n-butanol/butyl acetate; 3. ideal mixing for reactants in the reactor.
During PV separation of the quarter mixture of water/acetic acid/n-butanol/butyl acetate by the poly(vinyl alcohol) (PVA)/ceramic composite membranes, there was largely water and little acetic acid in the permeate while n-butanol or butyl acetate could be neglected. Fluxes of water and acetic acid permeation can be calculated when water concentration was less than 10 wt.%. The expressions of flux for water and acetic acid permeation are present in Eqs. (21) and (22), for which the parameters obtained from the PV separation of mixture of water/acetic acid/n-butanol/butyl acetate are displayed in [22]: JW = PW CW exp(SW,B CB + SW,E CE ) JA =
P A CW + M exp(SA,B CB + SA,E CE )
(21) (22)
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3. Experimental 3.1. Materials All reagents had purity better than 99% and were used without further purification. The poly(vinyl alcohol)/porous ceramic composite membranes prepared in our laboratory exhibited a good selectivity to water in the organic mixtures used [21]. 3.2. Esterification reaction with and without PV The esterifications with and without PV were carried out in a batch mode. The batch reactor for esterification studies was a thermostatic cell equipped with a mechanic stirrer. The experiments of PV-aided esterification were conducted in a stirred cell that served at the same time as a batch reactor and a PV cell. In the cell, the membrane of effective surface area of 34 cm2 was installed at the bottom of the cell and supported by a stainless steel plate. Each run was carried out simultaneously in the reactor without the membrane and in the PV cell using the same original mixture. The time at which the catalyst was added to the alcohol/acid mixture was referred to zero-time. Samples were withdrawn and analyzed by gas chromatography.
Fig. 1. Conversion of n-butanol to water both with and without pervaporation (T = 80◦ C; R0 = 1.60; C cat = 10.6 g l−1 ).
4. Results and discussion 4.1. Esterification compared to PV-aided esterification
Fig. 2. Water concentration in the reacting mixture for esterification both with and without pervaporation (T = 80◦ C; R0 = 1.60; C cat = 10.6 g l−1 ).
Fig. 1 shows the variation of conversion of n-butanol to water as a function of time for the esterification both with and without PV, respectively. It was indicated that PV enhanced the conversion and it was higher for the PV-aided esterification than for the reaction without PV. The variation of water concentration in the reacting mixture as a function of time for the reaction without PV and the PV-aided reaction is displayed in Fig. 2. It reflected that the water content for the reaction without PV was higher than for the PV-aided reaction due to water removal by PV. Figs. 3 and 4 show the permeation fluxes (both overall and partial) and permselectivity coefficient as a function time for the PV-aided process, the overall flux of permeation, partial fluxes of permeation and
Fig. 3. Permeation fluxes as a function of time (T = 80◦ C; R0 = 1.60; C cat = 10.6 g l−1 ).
Q.L. Liu, H.F. Chen / Journal of Membrane Science 196 (2002) 171–178
175
Fig. 4. Permselectivity coefficients as a function of time (T = 80◦ C; R0 = 1.60; C cat = 10.6 g l−1 ).
Fig. 6. Calculated curves compared to experimental points for permeation fluxes (T = 80◦ C; R0 = 2.34; C cat = 10.6 g l−1 ).
the permselectivity coefficient are obviously changed during the process, and it is known that the quantities of partial permeation flux of n-butanol is so small that its permeation through the membrane can practically be neglected during the process.
overall flux of permeation, partial fluxes of water and acetic acid permeation, respectively, and the agreement between them was roughly good. The calculated value for the overall permeation flux was less than the experimental one also because of the same reason described previous. Fig. 7 presents the permselectivity coefficient of water to acetic acid for the experimental points and the estimated results, which indicated that the agreement between them was acceptable. It is known from the model equations that the influencing operating parameters for the PV-coupled esterification was: process temperature (T); initial molar ratio of acetic acid to n-butanol (R0 ); ratio of the membrane area to the reacting mixture volume (S/V); the catalyst content (Ccat ).
4.2. Model equations verification The experimental points and the results of simulation for the conversion is given in Fig. 5, which reflected that both were in a good agreement. It was shown that the calculated value for the conversion was larger than the experimental one may probably due to the negligence of n-butanol permeating through the membrane by the model equations. Fig. 6 shows the calculated results and the experimental data for the
Fig. 5. Calculated curve compared to experimental points for n-butanol conversion (T = 80◦ C; R0 = 2.34; C cat = 10.6 g l−1 ).
Fig. 7. Calculated curves compared to experimental points for permselectivity coefficients (T = 80◦ C; R0 = 2.34; C cat = 10.6 g l−1 ).
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So, simulation was carried out for various process variables in the following section. The water contents in the reacting mixture were measured and compared with the calculated values in order to see if the model equations were valid for the coupling process. 4.3. The effects of process variables on PV-aided esterification Water concentration in the reactor is a typical variable to evaluate PV-aided esterification since its variation are result from water production rate and water removal rate. So process variables result in the variation in water concentration were chosen as a model to study the PV-esterification coupling. 4.3.1. The effect of temperature The reaction rate constants for the esterification are a function of process temperature, and were increased with the increase of the temperature. The accelerating of the reaction rate constant with the increase of the temperature for the forward reaction was faster than the backward process. So water production rate was higher in a higher temperature than in a lower temperature. Meanwhile, the permeation parameter for water is also varied with the temperature and was increased with the increase of the temperature. As a result, water permeation flux was increased with the increase of the process temperature. The model predictions and the experimental data for water content variation in the reacting mixture during the coupling process at 90, 80 and 70◦ C are plotted in Fig. 8, which indicated that simulation could predict the experimental points. The estimated values for mass fraction of water are larger than the experimental ones, which can be explained by the fact that the calculated values for the flux of water permeation are less than the experimental data (which reflected in Fig. 6). It is reflected in Fig. 8 that the difference in the values of water content between the experimental and the simulated become larger at a lower temperature. It may be attributed to that (dk1 /dT )/(dk2 /dT ) = 0.935 < 1 in the temperature range of 50–100◦ C, indicating the rate constant for the backward reaction reduced faster than for the forward reaction with the decrease of temperature, as well as k1 > k2 , so the difference between k1 and k2 is larger at a lower temperature. The water content in the reacting mixture during the process had
Fig. 8. Calculated curves compared to experimental points for water content in the reacting mixture over various temperature (R0 = 1.60; C cat = 13.33 g l−1 ; S/V = 23 m−1 ).
maximum amplitude and increased at the beginning. This may due to the fact that water production rate was higher than the rate of water removal by PV at the earlier stage during the process and was reverse when water content reached the maximum value. Water concentration had a higher maximum value for a higher process temperature. This may be explained by the fact that the acceleration for water production rate had a higher value at a higher temperature, so water content increased faster during the earlier reaction stage due to a slower backward reaction rate; while decreased faster later due to a higher backward reaction rate. 4.3.2. The effect of R0 It can be concluded from the model equations that R0 played a part in reaction rate but exerted no effect on kinetics of PV. Fig. 9 shows that water contents in the reactor between calculated results and experimental data are in good consistency. Water production rate is decreased with the increase of R0 and caused the maximum amplitude in water content lower at a higher R0 . The water contents in the reactor were lower for a higher R0 during the process, which was for the most part attributed to that R0 played no role in the kinetics of PV. 4.3.3. The effect of the catalyst content (Ccat ) The model fitting and experimental data for water content in the reactor at various Ccat are shown in Fig. 10, which again demonstrated that both are in good consistency. The variation of both forward and
Q.L. Liu, H.F. Chen / Journal of Membrane Science 196 (2002) 171–178
Fig. 9. Calculated curves compared to experimental points for water content in the reacting mixture over various R0 (T = 80◦ C; C cat = 13.33 g l−1 ; S/V = 23 m−1 ).
backward reaction rate occurred during the change of Ccat . The water production rate was higher for a higher Ccat since the forward reaction rate constant was higher than the backward one. Thus, the water contents in the reactor had higher maximum amplitude for a higher Ccat during the reaction. The water contents in the reactor were higher for a higher Ccat for a period at the beginning during the reaction and than were lower later. 4.3.4. The effect of S/V S/V exerted no influence on reactive kinetics but caused the variation of the water extraction rate. The effect of S/V on PV-aided esterification was similar to that of R0 , which resulted from the variation of water
177
Fig. 11. Calculated curves compared to experimental points for water content in the reacting mixture over various S/V (T = 80◦ C; R0 = 2.34; C cat = 13.33 g l−1 ).
contents in the reactor during the process. As a result of fitting between the experimental data and the calculated results for the water content in the reactor over various S/V during the process are shown in Fig. 11.
5. Conclusions The water contents in the reactor between numerical simulation and experimental results in quantities were roughly similar indicating that the model equations were valid for the PV-aided esterification. The process temperature and the catalyst concentration had a similar effect on the variation of water content during the process, so did the R0 and S/V.
Acknowledgements The support of Fujian Natural Science Foundation Grant no. F00022 in preparation of this article is gratefully acknowledged. References
Fig. 10. Calculated curves compared to experimental points for water content in the reacting mixture over various Ccat (T = 80◦ C; R0 = 1.60; S/V = 23 m−1 ).
[1] M.A. Larrayoz, L. Puigjaner, Study of n-butanol extraction through PV in acetobutylic fermentation, Biotechnol. Bioeng. 30 (1987) 692–696. [2] R.A. Kemp, A.R. Macrae, Esterification process, European Patent (EP) 506159 (1992). [3] G.K. Pearce, Esterification process, European Patent (EP) 210055 (1987).
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[4] K. Mohan, R. Govind, Analysis of equilibrium shift in isothermal reactors with a permselective wall, AIChE J. 34 (1988) 1493–1503. [5] K. Mohan, R. Govind, Analysis of a current membrane reactor, AIChE J. 32 (1986) 2083–2086. [6] K. Mohan, R. Govind, Effect of temperature on equilibrium shift in reactors with a permselective wall, Ind. Eng. Chem. Res. 27 (1988) 2064–2070. [7] N. Itoh, A membrane reactor using palladium, AIChE J. 33 (1987) 1576–1578. [8] Y.M. Sun, S.J. Khang, A catalytic membrane reactor: its performance in comparison with other types of reactors, Ind. Eng. Chem. Res. 29 (1990) 232–238. [9] S. Vemiya, N. Sato, H. Ando, E. Kikuchi, The water gas shift reaction assisted by a palladium membrane reactor, Ind. Eng. Chem. Res. 30 (1991) 585–589. [10] I.K. Song, W.Y. Lee, Methyl t-butyl ether decomposition in an inert membrane reactor composed of 12-tungstophosphoric acid catalyst and polyphenylene oxide membrane, Appl. Catal. A: Gen. 96 (1993) 53–63. [11] H. Kita, K. Tanaka, K. Okamoto, M. Yamamoto, The esterification of oleic acid with ethanol accompanied by membrane separation, Chem. Lett. (1987) 2053–2056. [12] M.O. David, Q.T. Nguyen, J. Neel, PV membranes endowed with catalytic properties based on polymer blends, J. Membr. Sci. 73 (1992) 129–141. [13] K. Okamoto, M. Yamamoto, Y. Otoshi, T. Semoto, PV-aided esterification of oleic acid, J. Chem. Eng. Jpn. 26 (5) (1993) 475–481.
[14] H. Kita, S. Sasaki, K. Tanaka, K.I. Okamoto, M. Yamoto, Esterification of carboxylic acid with ethanol accompanied by PV, Chem. Lett. (1988) 2025–2028. [15] J.F.F. Keurentjes, G.H.R. Janssen, J.J. Gorissen, The esterification of tartaric acid with ethanol; kinetics and shifting the equilibrium by means of PV, Chem. Eng. Sci. 49 (1994) 4681–4689. [16] X. Feng, R.Y.M. Huang, Studies of a membrane reactor: esterification facilitated by PV, Chem. Eng. Sci. 51 (1996) 4673–4679. [17] L. Bagnell, K. Cavell, A.M. Hodges, A.W.H. Mau, A.J. Seen, The use of catalytically active PV membranes in esterification reactions to simultaneously increase product yield, membrane permselectivity and flux, J. Membr. Sci. 85 (1993) 291–300. [18] Qinglin Liu, Peishi Jia, Hongfang Chen, Study on catalytic membranes of H3 PW12 O40 entrapped in PVA, J. Membr. Sci. 159 (1999) 233–241. [19] M.O. David, R. Gref, Q.T. Nguyen, J. Neel, PV-esterification coupling. I. Basic kinetic model, Trans. Inst. Chem. Eng. 69 (1991) 335–340. [20] M.O. David, R. Gref, Q.T. Nguyen, J. Neel, PV-esterification coupling. II. Modeling of the influence of different operation parameters, Trans. Inst. Chem. Eng. 69 (1991) 341–346. [21] Q.L. Liu, Y.S. Zhu, H.F. Chen, Esterification accompanied by PV using crosslinked PVA composite membrane, J. Chem. Eng. Chin. Univ. 11 (2) (1997) 172–176. [22] Q.L. Liu, Z.B. Zhang, H.F. Chen, Study on the coupling of esterification with pervaporation, J. Membr. Sci. 182 (2001) 173–181.
Modeling of esterification of acetic acid with n-butanol in the presence of Zr(SO4 )2 ·4H2 O coupled pervaporation Qing Lin Liu a,∗ , Hong Fang Chen b a b
Department of Chemical Engineering, Xiamen University, Xiamen 361005, China Department of Chemical Engineering, Tianjin University, Tianjin 300072, China
Received 22 December 2000; received in revised form 6 June 2001; accepted 7 June 2001
Abstract Modeling of esterification of acetic acid with n-butanol in the presence of Zr(SO4 )2 ·4H2 O coupled pervaporation was studied in this paper. The influence of several process variables, such as process temperature, initial mole ratio of acetic acid over n-butanol, the ratio of the effective membrane area over the volume of reacting mixture and catalyst content, on the esterification was discussed. The calculated results for the conversion of n-butanol to water and permeation flux were consistence with the experimental data. The permselectivity and water content can be roughly estimated by the model equations. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Pervaporation; Esterification reaction; Poly(vinyl alcohol) membrane; Composite membranes
1. Introduction The use of pervaporation separation has received considerable attention during decade. Among the applications most of them concern separating one component from liquid feed mixture. For an example, this technique has been applied to acetobutylic fermentation so as to extract in situ the butanol produced thereby obtaining a greater glucose consumption and a greater higher production [1]. Combining a membrane with a chemical reaction, has been shown to offer advantages in a number of different instances. One way to classify the different situations in which membrane reactors are advantageous is by the type of reaction taking place, and using this scheme, most membrane reactor applications would be classified as either biological application ∗ Corresponding author. E-mail address: [email protected] (Q.L. Liu).
[2] or catalytic application [3]. It is clear that the separation of the products should be as fast and selective as possible in order to obtain a high yield for the reaction. One of potentials application is the use of pervaporation process to drive an equilibrated reaction. Reviews of the literature concerning catalytic membrane reactors reveal that a very large fraction of catalytic membrane reactor applications involve reversible reactions which reach a thermodynamically limited conversion level in a conventional reactor [4–9]. By conducting these reactions in a catalytic membrane wherein one product can selectively permeate through the membrane and out of the reaction zone, an overall conversion is attained which is much greater than that realized in the conventional reactor. A number of investigations have concerned on the application of hydrogen separation membranes to reversible gaseous reaction and will not be considered in the present study. Other recent investigations have been made
0376-7388/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 6 - 7 3 8 8 ( 0 1 ) 0 0 5 4 3 - 9
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Nomenclature A, B, E, and W Ci Ji Mi Ni Ni 0 Pi PW , PA R R0 S SA,B , SA,E
SW,B , SW,E
V X
acetic acid, n-butanol, butyl acetate and water, respectively concentration of component i in reacting mixture (mol l−1 ) permeation flux of component i (mol m−2 h−1 ) molar molecular weight of component i (g mol−1 ) molar number of component i (mol) molar number of component i at zero-time (mol) permeation parameter of component i (l m−2 h−1 ) parameters as a function of process temperature universal gas constant (J mol−1 K−1 ) initial molar ratio of acetic acid to n-butanol effective area of the membrane (m2 ) parameter concerning influence to acetic acid permeating by existing of n-butanol and butyl acetate parameter concerning influence to water permeating by existing of n-butanol and butyl acetate volume of reacting mixture (ml) conversion of n-butanol
Greek letter ρi density of component i in the liquid mixture on the application of water permeable membranes to liquid-phase reaction [10–21]. The objective of this study was an attempt to investigate the effect of operating parameters on the typical variable−water content in the reactor during the esterification of acetic acid with n-butanol in the presence of Zr(SO4 )2 ·4H2 O coupled, the extraction of water by pervaporation. Model equations for pervaporation-aided (PV-aided) esterification were
presented and their valid was verified by comparing the prediction to the experimental results.
2. Modeling of PV-aided esterification The esterification of acetic acid with n-butanol is in the form of the following equation: A+B↔E+W
(1)
In the case of n-butanol, non-permeating through the membrane (the amount of n-butanol or n-butyl acetate in the permeate is very small and can be negligible practically), the variation of n-butanol concentration can be expressed by dCB = k1 CA CB Ccat − k2 CW CE Ccat dt Here,
−
NA , V NW = , V
CA = CW So,
dCB 1 = 2 dt V
NB , V Ncat = V
CB = Ccat
dV dNB −NB +V dt dt
CE =
(2)
NE , V (3)
(4)
Substituting Eq. (4) into Eq. (2) gives dV Ncat dNB N W NE NB −V = k1 N A NB − (5) dt dt V keq The conversion of n-butanol to n-butyl acetate is written by X=
NB0 − NB NB0
(6)
The expression is valid for this study since acetic acid is in excess, and the permeating of n-butanol through the membrane is negligible. It is assumed that the permeation fluxes of component i (i = A, B, W and E) can be estimated in a binary liquid mixture of the water content less than of 10 wt.% by Ji = Pi Ci
(7)
Here, Pi is permeability coefficient and Ji is the permeation flux of i that can be modified in the quarter
Q.L. Liu, H.F. Chen / Journal of Membrane Science 196 (2002) 171–178
mixture on the basis of the binary mixture, so the amount of i in the permeate in moles of Qi can be obtained by t Qi = Ji S dt (8) 0
Differentiating Eq. (6) with respect to t gives dX dNB =− NB0 dt dt
(9)
For acetic acid we have NA = NA0 − NB0 X − QA
(10)
dQA = JA S dt
(11)
Differentiating Eq. (10) with respect to t gives dNA dX dQA = −NB0 − dt dt dt
(12)
Substituting Eq. (11) into Eq. (12) dNA dX + JA S + NB0 =0 dt dt
(13)
173
Isothermal operation is valid since the reaction heat is small. Ideal mixing is assumed in the reactor since the volume of reacting mixture is relatively large and is nearly constant. Following equations can be obtained by substituting Eq. (9) into Eqs. (13), (15) and (17) dNB dNA + JA S − =0 dt dt
(13A)
dNB dNW + JW S + =0 dt dt
(15A)
dNB dNE + =0 dt dt
(17A)
In the end, the variables; NA , NB , NE , NW , V can be solved simultaneously by the Eqs. (5), (13A), (15A), (17A) and (18) as an initial problem using the Runge–Kutta–Gill fourth-order method. The reaction rate constants for the esterification are shown in Eqs. (19) and (20), in which is demonstrated that forward reaction rate constant is larger than backward reaction in quantities:
Similarly, as for water and n-butyl acetate in the event of n-butyl acetate non-permeating through the membrane, we have
53.13 × 103 k1 = 4.531 × 106 exp − RT
(19)
NW = NW0 + NB0 X − QW
(14)
dNW dX + JW S − NB0 =0 dt dt
(20)
(15)
58.94 × 103 k2 = 4.376 × 106 exp − RT
NE = NB0 X
(16)
dNE dX − NB0 =0 dt dt
(17)
The volume of the liquid in the reactor, V, is given by Eq. (18) according to the additive of volume: V =
NA MA N B MB N E ME N W MW + + + ρA ρB ρE ρW
(18)
The model used following assumptions: 1. isothermal operation; 2. negligible permeating of n-butanol and butyl acetate through the membrane, which resulted from the PV separation of mixture of water/acetic acid/ n-butanol/butyl acetate; 3. ideal mixing for reactants in the reactor.
During PV separation of the quarter mixture of water/acetic acid/n-butanol/butyl acetate by the poly(vinyl alcohol) (PVA)/ceramic composite membranes, there was largely water and little acetic acid in the permeate while n-butanol or butyl acetate could be neglected. Fluxes of water and acetic acid permeation can be calculated when water concentration was less than 10 wt.%. The expressions of flux for water and acetic acid permeation are present in Eqs. (21) and (22), for which the parameters obtained from the PV separation of mixture of water/acetic acid/n-butanol/butyl acetate are displayed in [22]: JW = PW CW exp(SW,B CB + SW,E CE ) JA =
P A CW + M exp(SA,B CB + SA,E CE )
(21) (22)
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3. Experimental 3.1. Materials All reagents had purity better than 99% and were used without further purification. The poly(vinyl alcohol)/porous ceramic composite membranes prepared in our laboratory exhibited a good selectivity to water in the organic mixtures used [21]. 3.2. Esterification reaction with and without PV The esterifications with and without PV were carried out in a batch mode. The batch reactor for esterification studies was a thermostatic cell equipped with a mechanic stirrer. The experiments of PV-aided esterification were conducted in a stirred cell that served at the same time as a batch reactor and a PV cell. In the cell, the membrane of effective surface area of 34 cm2 was installed at the bottom of the cell and supported by a stainless steel plate. Each run was carried out simultaneously in the reactor without the membrane and in the PV cell using the same original mixture. The time at which the catalyst was added to the alcohol/acid mixture was referred to zero-time. Samples were withdrawn and analyzed by gas chromatography.
Fig. 1. Conversion of n-butanol to water both with and without pervaporation (T = 80◦ C; R0 = 1.60; C cat = 10.6 g l−1 ).
4. Results and discussion 4.1. Esterification compared to PV-aided esterification
Fig. 2. Water concentration in the reacting mixture for esterification both with and without pervaporation (T = 80◦ C; R0 = 1.60; C cat = 10.6 g l−1 ).
Fig. 1 shows the variation of conversion of n-butanol to water as a function of time for the esterification both with and without PV, respectively. It was indicated that PV enhanced the conversion and it was higher for the PV-aided esterification than for the reaction without PV. The variation of water concentration in the reacting mixture as a function of time for the reaction without PV and the PV-aided reaction is displayed in Fig. 2. It reflected that the water content for the reaction without PV was higher than for the PV-aided reaction due to water removal by PV. Figs. 3 and 4 show the permeation fluxes (both overall and partial) and permselectivity coefficient as a function time for the PV-aided process, the overall flux of permeation, partial fluxes of permeation and
Fig. 3. Permeation fluxes as a function of time (T = 80◦ C; R0 = 1.60; C cat = 10.6 g l−1 ).
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Fig. 4. Permselectivity coefficients as a function of time (T = 80◦ C; R0 = 1.60; C cat = 10.6 g l−1 ).
Fig. 6. Calculated curves compared to experimental points for permeation fluxes (T = 80◦ C; R0 = 2.34; C cat = 10.6 g l−1 ).
the permselectivity coefficient are obviously changed during the process, and it is known that the quantities of partial permeation flux of n-butanol is so small that its permeation through the membrane can practically be neglected during the process.
overall flux of permeation, partial fluxes of water and acetic acid permeation, respectively, and the agreement between them was roughly good. The calculated value for the overall permeation flux was less than the experimental one also because of the same reason described previous. Fig. 7 presents the permselectivity coefficient of water to acetic acid for the experimental points and the estimated results, which indicated that the agreement between them was acceptable. It is known from the model equations that the influencing operating parameters for the PV-coupled esterification was: process temperature (T); initial molar ratio of acetic acid to n-butanol (R0 ); ratio of the membrane area to the reacting mixture volume (S/V); the catalyst content (Ccat ).
4.2. Model equations verification The experimental points and the results of simulation for the conversion is given in Fig. 5, which reflected that both were in a good agreement. It was shown that the calculated value for the conversion was larger than the experimental one may probably due to the negligence of n-butanol permeating through the membrane by the model equations. Fig. 6 shows the calculated results and the experimental data for the
Fig. 5. Calculated curve compared to experimental points for n-butanol conversion (T = 80◦ C; R0 = 2.34; C cat = 10.6 g l−1 ).
Fig. 7. Calculated curves compared to experimental points for permselectivity coefficients (T = 80◦ C; R0 = 2.34; C cat = 10.6 g l−1 ).
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So, simulation was carried out for various process variables in the following section. The water contents in the reacting mixture were measured and compared with the calculated values in order to see if the model equations were valid for the coupling process. 4.3. The effects of process variables on PV-aided esterification Water concentration in the reactor is a typical variable to evaluate PV-aided esterification since its variation are result from water production rate and water removal rate. So process variables result in the variation in water concentration were chosen as a model to study the PV-esterification coupling. 4.3.1. The effect of temperature The reaction rate constants for the esterification are a function of process temperature, and were increased with the increase of the temperature. The accelerating of the reaction rate constant with the increase of the temperature for the forward reaction was faster than the backward process. So water production rate was higher in a higher temperature than in a lower temperature. Meanwhile, the permeation parameter for water is also varied with the temperature and was increased with the increase of the temperature. As a result, water permeation flux was increased with the increase of the process temperature. The model predictions and the experimental data for water content variation in the reacting mixture during the coupling process at 90, 80 and 70◦ C are plotted in Fig. 8, which indicated that simulation could predict the experimental points. The estimated values for mass fraction of water are larger than the experimental ones, which can be explained by the fact that the calculated values for the flux of water permeation are less than the experimental data (which reflected in Fig. 6). It is reflected in Fig. 8 that the difference in the values of water content between the experimental and the simulated become larger at a lower temperature. It may be attributed to that (dk1 /dT )/(dk2 /dT ) = 0.935 < 1 in the temperature range of 50–100◦ C, indicating the rate constant for the backward reaction reduced faster than for the forward reaction with the decrease of temperature, as well as k1 > k2 , so the difference between k1 and k2 is larger at a lower temperature. The water content in the reacting mixture during the process had
Fig. 8. Calculated curves compared to experimental points for water content in the reacting mixture over various temperature (R0 = 1.60; C cat = 13.33 g l−1 ; S/V = 23 m−1 ).
maximum amplitude and increased at the beginning. This may due to the fact that water production rate was higher than the rate of water removal by PV at the earlier stage during the process and was reverse when water content reached the maximum value. Water concentration had a higher maximum value for a higher process temperature. This may be explained by the fact that the acceleration for water production rate had a higher value at a higher temperature, so water content increased faster during the earlier reaction stage due to a slower backward reaction rate; while decreased faster later due to a higher backward reaction rate. 4.3.2. The effect of R0 It can be concluded from the model equations that R0 played a part in reaction rate but exerted no effect on kinetics of PV. Fig. 9 shows that water contents in the reactor between calculated results and experimental data are in good consistency. Water production rate is decreased with the increase of R0 and caused the maximum amplitude in water content lower at a higher R0 . The water contents in the reactor were lower for a higher R0 during the process, which was for the most part attributed to that R0 played no role in the kinetics of PV. 4.3.3. The effect of the catalyst content (Ccat ) The model fitting and experimental data for water content in the reactor at various Ccat are shown in Fig. 10, which again demonstrated that both are in good consistency. The variation of both forward and
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Fig. 9. Calculated curves compared to experimental points for water content in the reacting mixture over various R0 (T = 80◦ C; C cat = 13.33 g l−1 ; S/V = 23 m−1 ).
backward reaction rate occurred during the change of Ccat . The water production rate was higher for a higher Ccat since the forward reaction rate constant was higher than the backward one. Thus, the water contents in the reactor had higher maximum amplitude for a higher Ccat during the reaction. The water contents in the reactor were higher for a higher Ccat for a period at the beginning during the reaction and than were lower later. 4.3.4. The effect of S/V S/V exerted no influence on reactive kinetics but caused the variation of the water extraction rate. The effect of S/V on PV-aided esterification was similar to that of R0 , which resulted from the variation of water
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Fig. 11. Calculated curves compared to experimental points for water content in the reacting mixture over various S/V (T = 80◦ C; R0 = 2.34; C cat = 13.33 g l−1 ).
contents in the reactor during the process. As a result of fitting between the experimental data and the calculated results for the water content in the reactor over various S/V during the process are shown in Fig. 11.
5. Conclusions The water contents in the reactor between numerical simulation and experimental results in quantities were roughly similar indicating that the model equations were valid for the PV-aided esterification. The process temperature and the catalyst concentration had a similar effect on the variation of water content during the process, so did the R0 and S/V.
Acknowledgements The support of Fujian Natural Science Foundation Grant no. F00022 in preparation of this article is gratefully acknowledged. References
Fig. 10. Calculated curves compared to experimental points for water content in the reacting mixture over various Ccat (T = 80◦ C; R0 = 1.60; S/V = 23 m−1 ).
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