Kinetic Modeling of Esterification of Ethylene Glycol

Kinetic Modeling of Esterification of Ethylene Glycol with Acetic Acid a

Vishnu P. Yadav , Rudra Palash Mukherjeeb, Kandi Bantrajc, and Sunil K. Maitya a

Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Ordnance Factory Estate, Yeddumailiram-502205, Andhra Pradesh, India. b Department of Chemical Engineering, National Institute of Technology Durgapur, Mahatma Gandhi Avenue, Durgapur-713209, West Bengal, India. c Department of Chemical Engineering, National Institute of Technology Rourkela-769008, Orissa, India. Abstract. The reaction kinetics of the esterification of ethylene glycol with acetic acid in the presence of cation exchange resin has been studied and kinetic models based on empirical and Langmuir approach has been developed. The Langmuir based model involving eight kinetic parameters fits experimental data much better compared to empirical model involving four kinetic parameters. The effect of temperature and catalyst loading on the reaction system has been analyzed. Further, the activation energy and frequency factor of the rate constants for Langmuir based model has been estimated. Keywords: Modeling, Esterification, Ethylene Glycol, Acetic Acid

INTRODUCTION The growing international energy crisis coupled with rising oil prices and increasing awareness on environment and pollution have made fuels derived from bio-mass an attractive alternative. The bio-oil produced CREDIT (BELOW)of TO pyrolysis BE INSERTED of ON THE FIRST PAGE EACH PAPER an duringLINE process bio-mass is OF now-a-days CP1298, International Conference on Modeling, Optimization, and Computing, (ICMOC 2010) edited by S. Paruya, S. Kar, and S, Roy © 2010 American Institute of Physics 978-0-7354-0854-8/10/$30.00

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emerging technology for the production renewable fuels and value added chemicals. The ethylene glycol obtained from bio-oil fraction can be utilized to produce ethylene glycol mono- and di-acetate that has suitable property for its application as a coolant. Development of kinetic model for industrially important reaction is quite useful for design and scale-up of the reactor. The esterification of ethylene glycol with acetic acid in the presence of cation exchange resin is a reversible reaction and proceeds in two steps as shown in Scheme 1 [1] . Though earlier it was widely believed that esterification reactions catalyzed by a solid resin is essentially secondorder reversible after an initial slow period [2], recent studies have shown that kinetic expressions based on the reactant and product adsorption on the catalyst represent the experimental results better [3][4]. Bart et al. stated that the adsorption of acid on the catalyst was also significant along with the fact that the reaction takes place between the adsorbed molecules of alcohol and that of acid in the bulk solution [5]. It was also reported that the use of activities instead of concentrations results only a slight improvement in the kinetic model [3]. In the present work, the kinetic models of esterification of ethylene glycol have been developed. The effect of temperature and catalyst loading on the reaction system has been studied and activation energy for the models developed has been calculated.

SCHEME 1. Esterification of ethylene glycol with acetic acid. 686


MODELING The kinetic modeling of esterification of ethylene glycol involves five components namely, ethylene glycol, acetic acid, ethylene glycol monoacetate, ethylene glycol diacetate, and water. Two kinetic models, empirical model and Langmuir-based model, were developed to correlate the experimental concentration versus time data [6].

Empirical Model In this model, the esterification and hydrolysis reactions was modeled considering 2nd order reaction [3]. An ideal homogeneous model was considered where all reactions took place in liquid phase with the catalyst used in granular form. Additionally, the mass-transfer resistances are considered to be negligible. The material balance of five components involved in the reaction system was done as shown by following five equations: d(CEG)/dt = -k1CEGCAA + k-1CEGMACWATER

(1)

d(CAA)/dt =-k1CEGCAA + k-1CEGMACWATER - k2CEGMACAA + k-2CEGDACWATER (2) d(CEGMA)/dt=-k2CEGMACAA+k-2CEGMACWATER+k1CEGCAA– k-1CEGMACWATER (3) d(CEGDA)/dt= k2CEGMACAA – k-2CEGMACWATER

(4)

d(CWATER)/dt=k1CEGCAA–k-1CEGMACWATER+k2CEGMACAA – k-2CEGDACWATER (5)

Langmuir Kinetic Model In the present work a kinetic model based on Langmuir approach was also developed. In this model, the reactions are considered as surface reaction controlled. It is also assumed that only EG, AA, EGMA, and EGDA were adsorbed on the surface of the catalyst. The rate of formation of the five components is given by the following differential equations. 687


dCEG/dt = -k1θEG θAA + k-1θEGMA θV

(6)

d(CAA)/dt= -k1θEGθAA+k-1θEGMAθV - k2θEGMAθAA +k-2θEGDAθV

(7)

d(CEGMA)/dt=-k2θEGMAθAA+k-2θEGMAθV+k1θEGθAA+k-1θEGMA θV

(8)

d(CEGDA)/dt = k2θEGMA θAA - k-2θEGMA θV

(9)

d(CWATER)/dt=-k1θEGθAA-k-1θEGMAθV+k2θEGMAθAA-k-2 θEGDA θV

(10)

Where, θAA=(KAACAA)/(1+KxCx) θAA=(KEGCEG)/( 1+KxCx) θAA=(KEGMACEGMA)/(1+KxCx) θAA=(KEGDACEGDA)/(1+KxCx) θV= 1- (θAA+ θEG+ θEGMA+ θEGDA) KxCx = KEGCEG+KAACAA+KEGMACEGMA+ KEGDACEGDA

PARAMETER ESTIMATION The fourth-order Runge-Kutta method was used to solve the differential equations involved in the models. The developed empirical model involves four rate constants and Langmuir-based model involves four rate constants and four equilibrium constants. The experimental data at various temperatures and catalyst loading available in literatures were used to estimate the kinetic parameters involved in the models using Levenberg and Marquardt algorithm. The optimization function, E, used for estimation of parameters is given below. E=

Σ[(EGCexp,i

-

EG

Cmodel,i)/

EG

Cmax]+Σ[(AACexp,i -

Cmodel,i)/AACmax]+Σ[(EGMACexp,i-EGMACmodel,i)/EGMACmax]+

AA

Σ [ (EGDACexp,i - EGDACmodel,i)/ EGDACmax]+ Σ [ (WATERCexp,i WATER Cmodel,i)/ WATERCmax]

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RESULTS AND DISCUSSION The estimated kinetic parameters for different catalyst loading using are shown in Tables 1-3 and Table 4-6 for Empirical and Langmuir based model respectively. For both of the developed models, the rate constants were found to increase with increasing temperature and catalyst loading. Table 4-6 depicts the decreasing trend of the adsorption equilibrium constants (KEG, KAA, KEGMA, KEGDA) with temperature as expected. TABLE 1. Estimated parameters for 0.5 wt% catalyst using Empirical model. T(K) k1 k-1 k2 k-2 (L mole-1 sec-1) (L mole-1 sec-1) (L mole-1 sec-1) (L mole-1 sec-1) 333 2.65×10-04 1.99×10-03 1.28×10-03 4.29×10-03 343 4.49×10-04 2.15×10-03 1.48×10-03 4.97×10-03 353 5.62×10-04 2.20×10-03 1.71×10-03 5.12×10-03 363 9.10×10-04 2.91×10-03 2.17×10-03 6.32×10-03 TABLE 2. Estimated parameters for 1.0 wt% catalyst using Empirical model. T(K) k1 k-1 k2 k-2 (L mole-1 sec-1) (L mole-1 sec-1) (L mole-1 sec-1) (L mole-1 sec-1) 333 4.23×10-04 4.97×10-04 1.69×10-03 4.64×10-03 343 8.70×10-04 6.25×10-04 2.32×10-03 6.17×10-03 353 9.50×10-04 6.04×10-04 1.10×10-03 3.25×10-02 -04 -04 -02 363 1.47×10 6.89×10 1.59×10 4.21×10-02 TABLE 3. Estimated parameters for 1.5 wt% catalyst using Empirical model. T(K) k1 k-1 k2 k-2 -1 -1 -1 -1 -1 -1 (L mole sec ) (L mole sec ) (L mole sec ) (L mole-1 sec-1) 333 9.70×10-04 7.91×10-04 3.17×10-03 6.82×10-03 -03 -04 -03 343 1.19×10 8.39×10 3.26×10 7.42×10-03 353 1.69×10-03 1.04×10-03 6.07×10-03 1.27×10-03 363 3.49×10-03 1.34×10-03 9.07×10-03 2.27×10-02

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TABLE 4: Estimated parameters for 1.0 wt% catalyst using Langmuir model. T Rate constants Equilibrium constants K KAA KEGMA KEG k (L k (L (L (L k k(K) EG 1 -1 2 2 333 343 353 363

mole-1 sec-1)

mole-1 sec-1)

mol-1 sec-1)

mole-1 sec-1)

0.21 0.28 0.29 0.51

0.18 0.23 0.39 0.42

0.15 0.22 0.23 0.44

0.90 0.10 0.25 0.51

DA

1.23 1.03 0.58 0.20

0.51 0.46 0.24 0.18

12.57 9.57 1.44 0.60

8.43 0.43 0.27 0.07

TABLE 5: Estimated parameters for 1.0 wt% catalyst using Langmuir model. T Rate constants Equilibrium constants k1(L k-1(L k2(L k-2(L (K) KEG KAA KEGMA KEGDA 333 343 353 363

mole-1 sec-1)

mole-1 sec-1)

mol-1 sec-1)

mole-1 sec-1)

0.59 0.70 0.72 0.88

0.24 0.28 0.42 0.55

0.83 1.18 1.20 1.40

1.15 1.25 1.31 1.53

1.09 0.87 0.80 0.74

0.38 0.36 0.33 0.32

6.21 3.53 1.43 0.53

12.77 1.45 5.61 21.01

TABLE 6: Estimated parameters for 1.5 wt% catalyst using Langmuir model. T Rate constants Equilibrium constants (K) KEG KAA KEGMA KEGDA k1(L k-1(L k-2(L k2(L 333 343 353 363

mole-1 sec-1)

mole-1 sec-1)

mol-1 sec-1)

mole-1 sec-1)

0.90 0.92 1.01 1.08

0.25 0.28 0.43 0.55

2.89 3.10 4.27 4.30

0.88 0.91 0.95 0.96

0.51 0.49 0.43 0.40

0.39 0.35 0.34 0.12

0.97 0.70 0.66 0.20

13.01 12.59 7.30 0.90

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(a) (b) FIGURE 2. (a)Comparison of concentration profile of components during esterification of Ethylene alcohol with acetic acid at 333K using 1wt% catalyst using Langmuir based model. (b) Arrhenius plot for reaction rates using 1wt% catalyst loading using Langmuir based model

The Langmuir based model involving eight parameters gave more accurate results than the four parameter based empirical model. The minimum average absolute deviation obtained using Langmuir based model was 11.45% compared to 12.4% obtained using empirical model at 333K with 0.5 (w/v) % catalysts loading. Average absolute deviation for all other conditions were also found to be lower in case of Langmuir based model than that of empirical model. Hence Langmuir based model is best suited for the reaction scheme under consideration. The Figure 2 (a) shows a comparison of experimental and calculated concentration profile Langmuir based model based on estimated parameters for a typical batch experiment at 333K using 1 wt% catalyst loading. The temperature dependence of the rate constants is k1, k-1, k2, k-2 is described by Arrhenius Law as given by k=k0 exp (-E/RT). The Arrhenius plot of ln(k) versus 1/T was made for different catalyst loading for Langmuir based model. Figure 2(b) shows a typical Arrhenius plot for 1 wt% catalyst. The frequency factors, k0, and activation energy, E, of each rate constants were estimated from the 691


slope and intercept of the linear fit lines of the Arrhenius plot as shown in Table 7. As shown in the table, the activation energy decreased on increasing the catalyst loading as expected. TABLE 7. Activation energy and frequency factor for different rate constants using Langmuir model. k1 k-1 k2 k-2 Cata -lyst (w/v )%

Frequ -ency Factor k0(L mole1 sec-1)

Activ ation energ y, E (KJ/ mol)

Frequen -cy Factor, k0 (Lmole1 sec-1)

Activ -ation energ y, E (KJ/ mol)

Frequen cy Factor, k0 (L mole1 sec-1)

Acti vatio energy,E (KJ/ mol)

Frequency Factor k0 (L mole1 sec1 )

Activati on energy, E (KJ/mol )

0.5

2692.7

26.11

13778.16

30.97

11368.94

30.91

60.74

1.0

45.67

11.95

7102.48

28.52

240.95

15.42

2.74×1 09 28.30

1.5

8.30

6.15

114.54

17.18

669.74

15.04

2.66

3.03

8.86

CONCLUSIONS The kinetic model for esterification of ethylene glycol with acetic acid in the presence of solid acid catalyst has been developed in the present work. Two kinetic model, (1) empirical model and (2) Langmuir, was developed and an algorithm based on Levenberg and Marckward was developed to estimate the kinetic parameters involved in the models. It was observed that the Langmuir model involving eight kinetic parameters fits experimental data much better compared to empirical model involving four kinetic parameters. The rate constants estimated at different temperature was used to develop the Arrhenius relationship of the different rate constants. The minimum activation energy 6.151 KJ/mol was obtained at 363K temperature and 1.5wt% of catalyst loading for the forward rate constant k1. 692


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Bastian Schmid, Michael Doker, and Jurgen Gmehling, “Esterification of Ethylene Glycol with Acetic Acid Catalyzed by Amberlyst 36” Ind. Eng. Chem. Res. 47, 2008, pp. 698- 703. 2. C.L. Levesque, A.M. Craig, “Kinetics of an Esterification with Cation-Exchange Resin Catalyst,” Ind. Eng. Chem. Res.40, 1948, pp. 96. 3. T. Popken, L. Gotze, J. Gmehling, “Reaction kinetics and chemical equilibrium of homogenously and heterogeneously catalyzed acetic acid esterification with methanol and methyl acetate hydrolysis,” Ind. Eng. Chem. Res. 39, 2000, pp. 2601–2611. 4. A. Chakrabarti, M.M. Sharma, “Cationic ion exchange resins as catalyst,” React. Polym. 20 1993, pp. 1-45. 5. Bart, H. J. Kaltenbrunner, W. and Landschutzer, H. “Kinetics of esterification of acetic acid with propyl alcohol by heterogeneous catalysis.” Int. J. Chem. Kinet. 28, 1996, pp. 649-656. 6. Vishnu Prasad Yadaw, “Study on Esterification of Ethylene Glycol With Acetic Acid in the Presence of Seralite SRC-120 and Molecular Sieve 13X Catalyst”, M.Tech thesis, National Institute of Technology Rourkella, 2010. 7. Thotla Suman, Seethamraju Srinivas, and Sanjay M. Mahajani, “Entertainer Based Reactive Distillation for Esterification of Ethylene Glycol and Acetic Acid”, Ind. Eng. Chem. Res., 48, 2009, pp. 9461–9470.

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