- Email: [email protected]
Activity-based model of the hybrid process of an esterification reaction coupled with pervaporation
Separation and Purification Technology 16 (1999) 55–59
Activity-based model of the hybrid process of an esterification reaction coupled with pervaporation R. Krupiczka *, Z. Koszorz Polish Academy of Sciences, Institute of Chemical Engineering, ul.Baltycka 5, 44-100 Gliwice, Poland Received 25 March 1998; received in revised form 25 May 1998; accepted 3 September 1998
Abstract The hybrid process of the esterification of acetic acid with ethanol, coupled with pervaporation, was studied, and a simple, three-parameter model describing the concentration profiles in the process was built. This work suggests that the activity-based model is a better method for predicting concentration profiles than the concentration model, especially in the range of higher component concentrations in which the thermodynamic constants calculated on the basis of concentrations are not true constants. The experiments were performed using a wide range of initial molar ratios c /c (1:1; 2:1; 3:1; 5:1) with hydrophilic membrane PERVAP 1005 GFT and ethanol–acetic acid as the reaction et a mixture. Appropriate activities were calculated using the UNIFAC group contribution method. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Activity; Esterification; Hydrophilic; Membranes; Modelling
Nomenclature c a k f K(c) K(a) n A P M r M w t
concentration, mol/kg activities, mol/kg forward rate constant, kg2/mol2 h equilibrium constant (conc.) equilibrium constant (activity) permeate flux, mol/h membrane area, m2 permeability coefficient, kg/m2 h mass, kg reaction rate, mol/kg h water molar mass, kg/mol time, h
Subscripts i et
component ethanol
* Corresponding author. Tel.: +48 32 31 08 11; Fax: +48 32 31 03 18; e-mail: [email protected]
e w a cat
ethyl acetate water acetic acid catalyst ( p-toluenesulfonic acid)
1. Introduction Using membranes to separate products in a reversible reaction is an effective method for preparing some esters. By applying a hybrid process, such as esterification–pervaporation, it is possible to shift the equilibrium towards higher reaction yields [1,4,5]. Considerable savings can also be made in the amont of reactants required (as there is no need for a large amount of one of the starting components) and reduced reaction time. Finally, such a process eliminates the necessity to add toxic substances (such as benzene or toluene) to the
1383-5866/99/$ – see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S1 3 8 3- 5 8 66 ( 9 8 ) 0 01 1 1 -7
56
R. Krupiczka, Z. Koszorz / Separation and Purification Technology 16 (1999) 55–59
reaction medium, and may therefore lead to the development of more ecologically sound technologies. Any industrial application involved in this process demands a sound predictive model, and this work suggests that the activity-based model is preferable when predicting concentration profiles.
2. Hybrid process modelling 2.1. Kinetics of the reaction The reaction of acetic acid with ethanol displays first-order kinetics. The equilibrium constant and kinetic parameters required for the description of this reversible reaction could be based on concentrations occurring in the diluted reaction mixture. Unfortunately, parameters obtained in this way are not constant at higher concentrations (Table 1). This problem can be solved by estimating the required parameters using the component activities.
A
a a r=k c a a − w e f cat et a K(a)
B
(1)
where a , a , a and a are the appropriate activiet a w e ties and c ,k , K(a) are the catalyst concentration, cat f the forward reaction rate constant and the equilibrium constant, respectively, and can be evaluated by using the activities: a a K(a)= w e . a a et a Such an approach enabled us to consider the thermodynamic and kinetic constants as real constants (Table 1). The activity coefficients were estimated by using the UNIFAC group contribution method. Table 1 Thermodynamic pseudo and real constants and estimated values of the kinetic constant at different initial molar ratios Initial molar ratio c /c et a
K(c) K(a) k f
1:1
2:1
3:1
5:1
3.698 9.484 5.370
3.121 10.14 4.945
2.787 9.993 5.156
2.640 10.93 5.013
2.2. Kinetics of pervaporation In the pervaporation of organic solvents containing low volumes of water (below 20 wt.% – ca. 11 mol kg−1), an almost linear relationship was found between the permeation flux and water concentration [2,3,6 ]. The molar rate of the removal of water from the reaction mixture by pervaporation was assumed as the product of the permeability coefficient and concentration in the liquid: n =AP c w w w where A is the area of membrane.
(2)
2.3. Model of the process The change in water concentration during the process is associated with the volume of water formed in the reaction and removed by pervaporation. For the combination of pervaporation with the reaction system, we can define the profile of water concentration starting with the water mass balance: d(Mc ) w =−n +rM w dt
(3)
where M is total mass of reaction mixture in the reactor (feed side). Taking this into account, it can be said that only water passes through the membrane (see Table 2), and it is possible to assume that the total mass balance is: dM dt
=−n M w w
(4)
where M is the molar mass of water. w By introducing Eq. (4) into Eq. (3) and rearranging the equation produced, we have: dc n AP c w = w (c M −1)+r= w w (c M −1)+r. w w dt M w w M (5) By introducing Eq. (1) into Eq. (5), we finally obtain the water concentration profile in the
R. Krupiczka, Z. Koszorz / Separation and Purification Technology 16 (1999) 55–59
57
Table 2 Permeate fluxes and permeability coefficients at various feed concentrations Feed concentration (mol kg−1) Ester Quaternary system 4.837 5.854 4.935 Binary systems Ethanol 21.16 19.49 i-Propanol 15.08 13.68
Permeate flux (mol m−2h−1)
Permeability coefficient P w (kg m−2h−1)
Ethanol
Water
Acid
Ester
Ethanol
Water
Acid
7.640 7.875 10.91
7.800 3.844 2.188
1.373 0.9865 0.4108
1.48 ×10−2 0.91 ×10−2 2.50 ×10−2
10.2 ×10−2 3.91 ×10−2 7.17 ×10−2
20.81 10.68 5.762
1.87 ×10−3 3.33 ×10−3 8.30 ×10−3
2.668 2.779 2.633
Water 1.472 5.750
Ethanol 4.98 ×10−2 5.87 ×10−2
Water 4.123 15.04
2.801 2.616
Water 5.292 9.944
i-Propanol 9.09 ×10−2 10.9 ×10−2
Water 14.70 27.72
2.777 2.788
reactor:
A
B
dc a a AP c w= w w (c M −1)+k c a a − w e . et a w w f cat dt M K(a) (6) Similarly, it is possible to obtain the concentration profile of the acid:
A
B
dc AP c M a a k= w w w c −k c a a − w e . k f cat et a K(a) dt M
(7)
The set of differential equations (Eqs. (4), (6) and (7)) can be solved numerically by the Runge–Kutta procedure. During each iteration, all activity coefficients were calculated using UNIFAC. The concentration of the other components can be calculated by stoichiometry.
3. Experimental The pervaporation experiments were performed using hydrophilic membrane PERVAP 1005 delivered by GFT. Reactions were carried out in the apparatus consisting of the circulation setup and the membrane module with a total capacity of 650 ml and 0.01911 m2 of membrane area. A diagram of the experimental setup is presented in Fig. 1. Concentrations were analyzed chromatographically by VARIAN 3400 using the DB-WAX
Fig. 1. Experimental setup. 1 – circulation pump; 2 – pervaporation module; 3 – condenser; 4 – vacuum pump; 5 – thermostat.
capillary column. The kinetic and thermodynamic parameters k and K(a) were determined in the f independent experiments [6 ] performed at c /c et a 1:1, 2:1, 3:1 and 5:1 molar ratios and 70°C [ Table 1]. p-Toluenesulphonic acid was applied as a catalyst and its concentration remained constant (0.02100 [mol/kg]) throughout all experiments. All reagents used were at an analytical grade of 99.5% purity.
4. Results and conclusions The activity coefficients in the reaction mixture were calculated using the UNIFAC group contri-
58
R. Krupiczka, Z. Koszorz / Separation and Purification Technology 16 (1999) 55–59
Table 3 The example range of activity coefficients
Ester Ethanol Water Acid
Concentration (mol kg−1)
Activity coefficient c
Concentration (mol kg−1)
Activity coefficient c
0.001 9.390 0.278 9.390
1.750 0.9660 1.358 0.9116
10.14 0.671 0.391 1.080
1.053 1.753 2.269 1.568
bution method for four components. It was assumed that the low concentration of the catalyst does not influence the activities of the other components. An example of the activity coefficients’ variation range is given in Table 3. As K(a) behaves as a real constant, it is possible to establish the appropriate forward rate constant k . As was conf cluded, it was possible to estimate the kinetic parameter k by fitting the kinetic curve to the f experimental data. During this study, this was achieved by minimizing the mean squared error
Fig. 2. Concentration profiles based on experimental results and the activity model. Initial mole ratio ethanol:acid=2:1.
Fig. 3. Concentration profiles based on experimental results and the activity model. Initial mole ratio ethanol:acid=1.5:1.
method, the calculated results of which are shown in Table 1, and the mean value k =5.121 f [kg2/mol2 h] was obtained. The permeability coefficient used for the model was calculated on the basis of the pervaporation experiments using feed mixtures without a catalyst. This was carried out to prevent the reaction run. These experiments, using a quaternary mixture, show that the value P is the same as that obtained w in the binary system (see Table 2) [2,3]. The mean value of P used in this work was determined to w be 2.771 [kg/m2 h]. A comparison of the measured concentrations with those calculated according to the model shows sound agreement (Figs. 2 and 3) when the activities are used. The model is independent of the initial molar ratios due to the stability of thermodynamic and kinetic constants. The efficiency of the process is strongly related to the ratio of membrane area to the mass of mixture: A/M. Several simulations were performed with the use of presented model to indicate the influence of parameter A/M on the concentrations in reaction mixture. It can be seen from Fig. 4 that by changing the value of A/M, it
Fig. 4. Concentration changes in ester and water during the reaction coupled with PV at different A/M ratios. Initial molar ratio ethanol:acid=1:1.
R. Krupiczka, Z. Koszorz / Separation and Purification Technology 16 (1999) 55–59
is possible to efficiently shift the reaction equilibrium and obtain a reasonably pure ester directly after the reaction. Selection of the A and M values to be used is determined from an economic point of view.
Acknowledgment The work was performed with additional support from State Committee for Scientific Research by research project no. 3T09C 01910.
59
References [1] J.F.T. Keurentjes, G.H.R. Janssen, J.J. Gorissen, Chem. Engng Sci. 49 (1994) 4681–4689. [2] K. Okamoto, M. Yamamoto, Y. Otoshi, T. Semoto, M. Yano, K. Tanaka, H. Kita, J. Chem. Engng Japan 26 (5) (1993) 475–481. [3] M.-O. David, R. Gref, T.Q. Nguyen, J. Neel, Trans. Inst. Chem. Engng 69 (A) (1991) 335–340. [4] M.-O. David, R. Gref, T.Q. Nguyen, J. Neel, Trans. Inst. Chem. Engng 69 (A) (1991) 341–346. [5] P. Schaetzel, M.-O. David, R. Gref, T.Q. Nguyen, J. Neel, Proceedings of the 5th International Conference on Pervaporation Procedures, in: Chem. Ind., Bakish Materials Corp., Engelwood. [6 ] Z. Koszorz, Ph.D. Thesis, Institute of Chemical Engineering, Polish Academy of Sciences, Gliwice, 1998.
Activity-based model of the hybrid process of an esterification reaction coupled with pervaporation R. Krupiczka *, Z. Koszorz Polish Academy of Sciences, Institute of Chemical Engineering, ul.Baltycka 5, 44-100 Gliwice, Poland Received 25 March 1998; received in revised form 25 May 1998; accepted 3 September 1998
Abstract The hybrid process of the esterification of acetic acid with ethanol, coupled with pervaporation, was studied, and a simple, three-parameter model describing the concentration profiles in the process was built. This work suggests that the activity-based model is a better method for predicting concentration profiles than the concentration model, especially in the range of higher component concentrations in which the thermodynamic constants calculated on the basis of concentrations are not true constants. The experiments were performed using a wide range of initial molar ratios c /c (1:1; 2:1; 3:1; 5:1) with hydrophilic membrane PERVAP 1005 GFT and ethanol–acetic acid as the reaction et a mixture. Appropriate activities were calculated using the UNIFAC group contribution method. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Activity; Esterification; Hydrophilic; Membranes; Modelling
Nomenclature c a k f K(c) K(a) n A P M r M w t
concentration, mol/kg activities, mol/kg forward rate constant, kg2/mol2 h equilibrium constant (conc.) equilibrium constant (activity) permeate flux, mol/h membrane area, m2 permeability coefficient, kg/m2 h mass, kg reaction rate, mol/kg h water molar mass, kg/mol time, h
Subscripts i et
component ethanol
* Corresponding author. Tel.: +48 32 31 08 11; Fax: +48 32 31 03 18; e-mail: [email protected]
e w a cat
ethyl acetate water acetic acid catalyst ( p-toluenesulfonic acid)
1. Introduction Using membranes to separate products in a reversible reaction is an effective method for preparing some esters. By applying a hybrid process, such as esterification–pervaporation, it is possible to shift the equilibrium towards higher reaction yields [1,4,5]. Considerable savings can also be made in the amont of reactants required (as there is no need for a large amount of one of the starting components) and reduced reaction time. Finally, such a process eliminates the necessity to add toxic substances (such as benzene or toluene) to the
1383-5866/99/$ – see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S1 3 8 3- 5 8 66 ( 9 8 ) 0 01 1 1 -7
56
R. Krupiczka, Z. Koszorz / Separation and Purification Technology 16 (1999) 55–59
reaction medium, and may therefore lead to the development of more ecologically sound technologies. Any industrial application involved in this process demands a sound predictive model, and this work suggests that the activity-based model is preferable when predicting concentration profiles.
2. Hybrid process modelling 2.1. Kinetics of the reaction The reaction of acetic acid with ethanol displays first-order kinetics. The equilibrium constant and kinetic parameters required for the description of this reversible reaction could be based on concentrations occurring in the diluted reaction mixture. Unfortunately, parameters obtained in this way are not constant at higher concentrations (Table 1). This problem can be solved by estimating the required parameters using the component activities.
A
a a r=k c a a − w e f cat et a K(a)
B
(1)
where a , a , a and a are the appropriate activiet a w e ties and c ,k , K(a) are the catalyst concentration, cat f the forward reaction rate constant and the equilibrium constant, respectively, and can be evaluated by using the activities: a a K(a)= w e . a a et a Such an approach enabled us to consider the thermodynamic and kinetic constants as real constants (Table 1). The activity coefficients were estimated by using the UNIFAC group contribution method. Table 1 Thermodynamic pseudo and real constants and estimated values of the kinetic constant at different initial molar ratios Initial molar ratio c /c et a
K(c) K(a) k f
1:1
2:1
3:1
5:1
3.698 9.484 5.370
3.121 10.14 4.945
2.787 9.993 5.156
2.640 10.93 5.013
2.2. Kinetics of pervaporation In the pervaporation of organic solvents containing low volumes of water (below 20 wt.% – ca. 11 mol kg−1), an almost linear relationship was found between the permeation flux and water concentration [2,3,6 ]. The molar rate of the removal of water from the reaction mixture by pervaporation was assumed as the product of the permeability coefficient and concentration in the liquid: n =AP c w w w where A is the area of membrane.
(2)
2.3. Model of the process The change in water concentration during the process is associated with the volume of water formed in the reaction and removed by pervaporation. For the combination of pervaporation with the reaction system, we can define the profile of water concentration starting with the water mass balance: d(Mc ) w =−n +rM w dt
(3)
where M is total mass of reaction mixture in the reactor (feed side). Taking this into account, it can be said that only water passes through the membrane (see Table 2), and it is possible to assume that the total mass balance is: dM dt
=−n M w w
(4)
where M is the molar mass of water. w By introducing Eq. (4) into Eq. (3) and rearranging the equation produced, we have: dc n AP c w = w (c M −1)+r= w w (c M −1)+r. w w dt M w w M (5) By introducing Eq. (1) into Eq. (5), we finally obtain the water concentration profile in the
R. Krupiczka, Z. Koszorz / Separation and Purification Technology 16 (1999) 55–59
57
Table 2 Permeate fluxes and permeability coefficients at various feed concentrations Feed concentration (mol kg−1) Ester Quaternary system 4.837 5.854 4.935 Binary systems Ethanol 21.16 19.49 i-Propanol 15.08 13.68
Permeate flux (mol m−2h−1)
Permeability coefficient P w (kg m−2h−1)
Ethanol
Water
Acid
Ester
Ethanol
Water
Acid
7.640 7.875 10.91
7.800 3.844 2.188
1.373 0.9865 0.4108
1.48 ×10−2 0.91 ×10−2 2.50 ×10−2
10.2 ×10−2 3.91 ×10−2 7.17 ×10−2
20.81 10.68 5.762
1.87 ×10−3 3.33 ×10−3 8.30 ×10−3
2.668 2.779 2.633
Water 1.472 5.750
Ethanol 4.98 ×10−2 5.87 ×10−2
Water 4.123 15.04
2.801 2.616
Water 5.292 9.944
i-Propanol 9.09 ×10−2 10.9 ×10−2
Water 14.70 27.72
2.777 2.788
reactor:
A
B
dc a a AP c w= w w (c M −1)+k c a a − w e . et a w w f cat dt M K(a) (6) Similarly, it is possible to obtain the concentration profile of the acid:
A
B
dc AP c M a a k= w w w c −k c a a − w e . k f cat et a K(a) dt M
(7)
The set of differential equations (Eqs. (4), (6) and (7)) can be solved numerically by the Runge–Kutta procedure. During each iteration, all activity coefficients were calculated using UNIFAC. The concentration of the other components can be calculated by stoichiometry.
3. Experimental The pervaporation experiments were performed using hydrophilic membrane PERVAP 1005 delivered by GFT. Reactions were carried out in the apparatus consisting of the circulation setup and the membrane module with a total capacity of 650 ml and 0.01911 m2 of membrane area. A diagram of the experimental setup is presented in Fig. 1. Concentrations were analyzed chromatographically by VARIAN 3400 using the DB-WAX
Fig. 1. Experimental setup. 1 – circulation pump; 2 – pervaporation module; 3 – condenser; 4 – vacuum pump; 5 – thermostat.
capillary column. The kinetic and thermodynamic parameters k and K(a) were determined in the f independent experiments [6 ] performed at c /c et a 1:1, 2:1, 3:1 and 5:1 molar ratios and 70°C [ Table 1]. p-Toluenesulphonic acid was applied as a catalyst and its concentration remained constant (0.02100 [mol/kg]) throughout all experiments. All reagents used were at an analytical grade of 99.5% purity.
4. Results and conclusions The activity coefficients in the reaction mixture were calculated using the UNIFAC group contri-
58
R. Krupiczka, Z. Koszorz / Separation and Purification Technology 16 (1999) 55–59
Table 3 The example range of activity coefficients
Ester Ethanol Water Acid
Concentration (mol kg−1)
Activity coefficient c
Concentration (mol kg−1)
Activity coefficient c
0.001 9.390 0.278 9.390
1.750 0.9660 1.358 0.9116
10.14 0.671 0.391 1.080
1.053 1.753 2.269 1.568
bution method for four components. It was assumed that the low concentration of the catalyst does not influence the activities of the other components. An example of the activity coefficients’ variation range is given in Table 3. As K(a) behaves as a real constant, it is possible to establish the appropriate forward rate constant k . As was conf cluded, it was possible to estimate the kinetic parameter k by fitting the kinetic curve to the f experimental data. During this study, this was achieved by minimizing the mean squared error
Fig. 2. Concentration profiles based on experimental results and the activity model. Initial mole ratio ethanol:acid=2:1.
Fig. 3. Concentration profiles based on experimental results and the activity model. Initial mole ratio ethanol:acid=1.5:1.
method, the calculated results of which are shown in Table 1, and the mean value k =5.121 f [kg2/mol2 h] was obtained. The permeability coefficient used for the model was calculated on the basis of the pervaporation experiments using feed mixtures without a catalyst. This was carried out to prevent the reaction run. These experiments, using a quaternary mixture, show that the value P is the same as that obtained w in the binary system (see Table 2) [2,3]. The mean value of P used in this work was determined to w be 2.771 [kg/m2 h]. A comparison of the measured concentrations with those calculated according to the model shows sound agreement (Figs. 2 and 3) when the activities are used. The model is independent of the initial molar ratios due to the stability of thermodynamic and kinetic constants. The efficiency of the process is strongly related to the ratio of membrane area to the mass of mixture: A/M. Several simulations were performed with the use of presented model to indicate the influence of parameter A/M on the concentrations in reaction mixture. It can be seen from Fig. 4 that by changing the value of A/M, it
Fig. 4. Concentration changes in ester and water during the reaction coupled with PV at different A/M ratios. Initial molar ratio ethanol:acid=1:1.
R. Krupiczka, Z. Koszorz / Separation and Purification Technology 16 (1999) 55–59
is possible to efficiently shift the reaction equilibrium and obtain a reasonably pure ester directly after the reaction. Selection of the A and M values to be used is determined from an economic point of view.
Acknowledgment The work was performed with additional support from State Committee for Scientific Research by research project no. 3T09C 01910.
59
References [1] J.F.T. Keurentjes, G.H.R. Janssen, J.J. Gorissen, Chem. Engng Sci. 49 (1994) 4681–4689. [2] K. Okamoto, M. Yamamoto, Y. Otoshi, T. Semoto, M. Yano, K. Tanaka, H. Kita, J. Chem. Engng Japan 26 (5) (1993) 475–481. [3] M.-O. David, R. Gref, T.Q. Nguyen, J. Neel, Trans. Inst. Chem. Engng 69 (A) (1991) 335–340. [4] M.-O. David, R. Gref, T.Q. Nguyen, J. Neel, Trans. Inst. Chem. Engng 69 (A) (1991) 341–346. [5] P. Schaetzel, M.-O. David, R. Gref, T.Q. Nguyen, J. Neel, Proceedings of the 5th International Conference on Pervaporation Procedures, in: Chem. Ind., Bakish Materials Corp., Engelwood. [6 ] Z. Koszorz, Ph.D. Thesis, Institute of Chemical Engineering, Polish Academy of Sciences, Gliwice, 1998.