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Ind. Eng. Chem. Res. 2000, 39, 4094-4099
Kinetics of Catalytic Esterification of Acetic Acid and Amyl Alcohol over Dowex Ming-Jer Lee,* Hsien-Tsung Wu, and Ho-mu Lin
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Department of Chemical Engineering, National Taiwan University of Science and Technology, 43, Keelung Road, Section 4, Taipei 106-07, Taiwan
The kinetic behavior of the heterogeneous esterification of acetic acid with amyl alcohol over an acidic cation-exchange resin, Dowex 50Wx8-100, was investigated. The experiments were conducted in a fixed-bed reactor at temperatures from 323 to 393 K and at molar ratios of feed (amyl alcohol to acetic acid) from 1 to 10. The equilibrium conversion of acetic acid was found to increase with increasing reaction temperature. A water-rich phase (the second liquid phase) appeared in the reacting mixture when the feed composition was close to stoichiometric. Gas bubble formation was observed when the reaction temperature was as high as 393 K. The kinetic data were correlated with the quasi-homogeneous, Langmuir-Hinshelwood, Eley-Rideal, and modified Langmuir-Hinshelwood models. The modified Langmuir-Hinshelwood model yielded the best representation for the kinetic behavior of the reaction over wide ranges of temperature and feed composition. Introduction Reactive distillation is an attractive method for improving process efficiency. This technique has been used in chemical plants for the syntheses of methyl tertbutyl ether (MTBE), ethyl acetate, cumene, ethyl benzene, etc. For process development, a reliable model is needed to represent accurately the kinetic behavior of such reacting systems. In the past decade, related kinetic studies have emphasized either etherification or esterification, such as the syntheses of MTBE, tert-amyl methyl ether (TAME), tert-amyl ethyl ether (TAEE), ethyl tert-butyl ether (ETBE), methyl acetate, ethyl acetate, and amyl acetate (Lee et al.1). Acidic cationexchange resins were widely used to accelerate the reactions, leading to heterogeneous reaction systems. In general, the rate of a heterogeneous reaction is affected by external/internal diffusion, adsorption/desorption, surface reaction, and the nonideality of the reacting mixtures. Several kinetic models have been adopted to describe the kinetic behavior of heterogeneous etherification and esterification. The quasihomogeneous (Q-H) model, which is in the same form as the power-law model for homogeneous reactions, has commonly been applied to generate residue-curve maps for reactive-distillation systems (Venimadhavan et al.2). The Q-H model can be derived on the basis of the Langmuir-Hinshelwood formalism by assuming that surface reaction is the controlling step and adsorption is weak for all components (Xu and Chuang3). Provided that the adsorption of reactants is important, the rate expression depends on the adsorption mechanism. Whenever the rate-determining step is the surface reaction between adsorbed molecules, the Langmuir-Hinshelwood (L-H) model is applicable to correlations of the kinetic data. On the other hand, the Eley-Rideal (ER) model has been applied if the rate-limiting step is the surface reaction taking place between one adsorbed * Author to whom correspondence should be addressed. Tel: 886-2-2737-6626. Fax: 886-2-2737-6644. E-mail:
[email protected].
species and one nonadsorbed reactant from the liquid phase. Because of the strong affinity of resins for water, the activity of water in the catalyst gel phase, where the reaction occurs, is remarkably different from that in the liquid phase. To consider the nonlinear distribution of the water concentration in the catalyst, Gonzalez and Fair4 modified the L-H formalism by introducing an empirical exponent to the activity of water in the rate expression. This modification improved the accuracy of kinetic data correlation for hydration of isoamylenes. The nonideality of each species in liquid mixtures was represented by the activity coefficient, which is usually calculated from a solution model with the binary parameters determined from phase-equilibrium data. If the phase-equilibrium data are unavailable in the literature, a group-contribution method, for example, the UNIFAC model (Fredenslund et al.5), is a common choice for these purposes. Amyl acetate has been used in industries as a solvent, an extractant, a polishing agent, etc. It can be synthesized from acetic acid and amyl alcohol via an esterification. However, ternary azeotropes were found in the mixtures of amyl alcohol/amyl acetate/water (Berg and Yeh6), leading to difficulty in the subsequent purification processes. Reactive distillation could be an effective method for overcoming the difficulty and further simplifying the manufacturing processes. In the present study, the kinetic behavior of the heterogeneous esterification of acetic acid with amyl alcohol is studied in a fixed-bed reactor using Dowex 50Wx8-100 (an acidic cation-exchange resin) as a catalyst. The emphasis is placed on investigating both temperature and feedcomposition effects. The kinetic data are correlated with the Q-H, L-H, E-R, and modified L-H models. Experimental Section Amyl alcohol (99%), acetic acid (99.8%), and Dowex 50Wx8-100 were supplied by Aldrich Chemical Co. The purity of amyl alcohol and acetic acid was verified by gas chromatographic analysis, and the compounds were
10.1021/ie0000764 CCC: $19.00 © 2000 American Chemical Society Published on Web 10/05/2000
Ind. Eng. Chem. Res., Vol. 39, No. 11, 2000 4095 Table 1. Results of the Esterification Measurements series of runs
T (Κ)
θBo
W (g)
size (mesh)
103 × CAo (mol cm-3)
range of τ (g min cm-3)
range of XA
XAe
Kx
1 2 3 4 5 6 7 8 9 10 11
323 353 363 373 383 393 353 353 353 353 353
6 6 6 6 6 6 10 3 1 6 6
4.047 4.047 4.047 4.047 4.047 4.047 4.047 4.047 4.047 2.015 4.016
60 60 60 60 60 60 60 60 60 60 70
1.4096 1.4096 1.4096 1.4096 1.4096 1.4096 0.8740 2.6086 6.0269 1.4096 1.4095
0.93-34.13 0.93-6.39 0.90-3.44 0.93-4.21 0.94-2.47 0.88-2.13 0.93-6.87 0.89-9.95 1.30-10.93 0.6-5.13 0.91-5.96
0.100-0.895 0.405-0.898 0.544-0.893 0.645-0.921 0.797-0.923 0.818-0.950 0.409-0.933 0.356-0.938 0.326-0.595 0.295-0.882 0.422-0.904
0.913 0.924 0.927 0.931 0.934 0.964 0.946 0.871 0.646 0.924 0.924
1.90 2.22 2.33 2.47 2.62 5.10 1.84 2.75 3.33 2.22 2.22
used without further purification. The apparatus and its operating procedure have been detailed elsewhere (Lee et al.1). A peristaltic pump (Masterflex Products; maximum flow rate ) 6 cm3 min-1) constantly charged the prepared reactant mixture into the reaction section. The volumetric flow rate of feed was periodically calibrated with pure water. Dowex 50W beads with an average particle size of 0.25 mm (60 mesh) and glass wool were packed in the fixed-bed reactor. The catalyst loading (W) was 4.05 g for the base case. The reaction temperature was regulated to within (0.1 K by circulating thermostatic silicon oil through the reactor’s jacket. A precision digital thermometer with an RTD platinum sensor (model 1506, Hart Scientific Co.) measured the reaction temperature to an accuracy of (0.02 K. Once a steady state was attained, the product was collected in a sampling flask. About 10 cm3 of acetone was then added to the sample to avoid the formation of two liquid phases during the titration. The amount of unreacted acetic acid in the sample was analyzed with a 0.1 N standard solution of NaOH (Acros) through a digital buret (Bibby, U.K.; accuracy ) (0.01 cm3). The results of sample analysis have been verified by gas chromatography. At least four replicated samples were taken under each of experimental conditions, and the reproducibility was to within (2%. The conversion of acetic acid was calculated from the difference between its inlet and outlet concentrations at the reactor. A complete conversion curve was obtained by performing the experiments with various flow rates. In the measurement of equilibrium conversion, the outlet of the product stream was totally recycled until the conversion approached a constant. Experimental Results The kinetics of amyl acetate synthesis was studied at temperatures from 323 to 393 K with four different molar feed ratios (θΒο ) 1, 3, 6, and 10, where θΒο is the molar ratio of amyl alcohol to acetic acid). In total, 11 series of runs were performed in this study. In each series, the experiments were conducted with various volumetric flow rates of feed (F) at a fixed condition of reaction temperature and feed composition. The contact time (τ) of reactants with catalyst is defined as
τ ) W/F
(1)
A wide range of volumetric flow rates of feed was covered in the experiments for which the conversion of acetic acid (XA) varied from moderate to near equilibrium. The equilibrium conversion of acetic acid (XAe) was also determined for each series. Table 1 summarizes the experimental results, and the experimental kinetic data for each run are tabulated as Supporting Information.
Figure 1. Conversion of acetic acid at θBo ) 6 over different temperatures.
Figure 1 presents the variation of XA with contact time for different reaction temperatures. It shows that the higher temperature yields the greater conversion of acetic acid at a fixed contact time. Increasing temperature is apparently favorable for acceleration of the forward reaction. The equilibrium conversion, XAe, also increases with an increase in temperature, but the variation is so small that the heat effect on the chemical equilibrium could be insignificant. Figure 2 illustrates the conversion variation with contact time at 353.15 K under different feed compositions. At a given contact time, greater conversions are achieved as the reaction takes place with higher θΒο. The equilibrium conversion is rather sensitive to feed composition. As can be seen from Table 1, XAe decreases from 0.946 to 0.646 when θΒο decreases from 10 to 1 at 353.15 K. Figure 3 compares the performance of Dowex 50Wx8-100 with that of Amberlyst 15 (Wu7) for the esterification, revealing that Dowex 50Wx8-100 is better than Amberlyst 15 for promoting the reaction. From visual inspection, the product mixtures were found to form a homogeneous liquid phase when values of θΒο were greater than or equal to 3. However, a second liquid phase (water-rich droplets) appeared in the reacting system, especially in the upper section of the reactor, when the experiments were performed with a stoichiometric feed composition. Gas-bubble formation was also observed when the reactor was operated at 393 K, higher than the bubble points of the reacting
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Figure 2. Conversion of acetic acid at 353 K over different feed compositions.
Figure 4. Variation of Kx with temperature.
Figure 5. Variation of Kx with feed composition (θBo). Figure 3. Comparison of performance of Dowex 50Wx8-100 with that of Amberlyst 15 at 353 K.
mixtures at atmospheric pressure (Lee and Liang8). Even though the presence of a second phase (liquid or vapor) in the reaction system increased the uncertainty in the composition analysis, the experimental XA values could also be reproduced to within (2%. The tabulated values of Kx in Table 1 were calculated from the equation
Kx )
X2Ae (1 - XAe)(θBo - XAe)
(2)
with experimental values of XAe and θBo. The above equation was derived on the basis of the following elementary reaction:
A+BTC+D where A, B, C, and D refer to acetic acid, amyl alcohol,
amyl acetate, and water, respectively. There is a linear relationship between ln Kx and 1/T at temperatures below 383 K, as shown in Figure 4. The value of Kx, however, becomes dramatically large at 393 K, probably because gas-bubble (water vapor, mainly) formation reduces the opportunity for the reverse reaction hydrolysis to proceed. Figure 5 illustrates the effects of feed composition on Kx. Although formation of the second liquid phase occurs at θBo )1, Kx increases smoothly with decreasing θBo over the entire range of feed composition. To investigate the influence of the transport resistance resulting from either film diffusion or pore diffusion, we also implemented the experiments with about one-half catalyst loading (2.015 vs 4.047 g) and/or with smaller catalyst particle size (0.21 vs 0.25 mm or 70 vs 60 mesh). Figure 6 compares the conversions measured from three series of experiments at 353 K and θΒο ) 6, indicating that all experimental points are close to a smooth curve. The effects of film diffusion and pore
Ind. Eng. Chem. Res., Vol. 39, No. 11, 2000 4097
(c) The L-H model Af exp -rA )
( )(
)
(6)
)
(7)
Ar -Eo aAaB - aCaD RT Af
(1 + KBaB + KDaD)2
(d) The E-R model Af exp -rA )
( )(
Ar -Eo aAaB - aCaD RT Af
(1 + KBaB + KDaD)
(e) The Modified L-H model Af exp -rA )
Figure 6. Conversion of acetic acid under different amounts and particle sizes of catalyst at 353 K and θBo ) 6.
diffusion appear to be negligible under the experimental conditions of interest. Correlation of Kinetic Data The kinetic data were correlated with a mass-balance equation for acetic acid around the entire packed-bed reactor through
W/(103 FA) )
dX
∫0X -rAA A
-rA ) Af exp
( )(
)
Ar -Eo xAxB - xCxD RT Af
-rA ) Af exp
( )(
)
Ar -Eo aAaB - aCaD RT Af
(8)
[(1/RHS)i - (103FA/W)i]2 ∑ i)1
(9)
where N is the number of data points and the dimension of 1/RHS is the same as that of reaction rate in mol min-1 (kg dry catalyst)-1. The total number of data points used in parameter estimation is 73. Table 3 presents the correlated results, indicating that the modified L-H model yields the best representation. As Table 2. Binary Parameters of the NRTL Model for Acetic Acid (1)/Amyl Alcohol (2)/Amyl Acetate (3)/Water (4)a,b (i, j)
Aij (K)
Aji (K)
Rij
(1, 2) (1,3) (1,4) (2,3) (2,4) (3,4)
-51.55 -8.82 80.90 -112.18 13.62 24.51
117.13 58.55 3.01 238.68 627.91 377.02
0.47 0.47 0.47 0.3 0.3 0.2
a Parameters are taken from Lee and Liang.8 b Activity coefficient expression of the NRTL model (Renon and Prausnitz10) is given by
c
∑τ G x ji
ln γi )
(5)
)
N
(4)
(b) The Q-H Model with nonideal-solution assumption (Q-HNIDS)
R 2
where Af and Ar are the Arrhenius preexponential factors for the forward and the reverse reactions, respectively. Parameters KB and KD are the adsorption constants for amyl alcohol and water, respectively. The derivation of the L-H and the E-R formalisms has been given by Carberry.9 The right-hand-side (RHS) integral in eq 3 was calculated with Simpson’s numerical integration method. The NRTL model (Renon and Prausnitz10), with binary parameters reported by Lee and Liang,8 was applied to calculate the activity coefficients for the reacting species, if the solution is considered nonideal. Table 2 gives the binary parameters of the NRTL model. The objective function (π) for parameter estimation was defined as
π)
(a) The Q-H Model with ideal-solution assumption (Q-HIDS)
Ar -Eo aAaB - aC(aD)R RT Af
[1 + KBaB + KD(aD) ]
(3)
where FA () F × CAo) is the molar flow rate of acetic acid in the feed stream. The rate expression -rA depends on the assumed reaction mechanism. Four types of rate expressions, including the quasi-homogeneous (Q-H) model, Langmuir-Hinshelwood (L-H) model, Eley-Rideal (E-R) model, and the modified L-H model of Gonzalez and Fair,4 were adopted to correlate the kinetic data for all experimental conditions. The heat effect on the chemical equilibrium of this reaction is so minor that the activation energy of the reverse reaction can be reasonably assumed to be the same as that of the forward reaction. Because the affinities of the resin for water and alcohol are stronger than those for acid and ester, the adsorption terms for acetic acid and amyl acetate are thus neglected in the L-H, E-R, and modified L-H models. The rate expression for each model is given as follows:
( )(
ji j
j)1 c
∑G
kixk
k)1
xjGij
c
+
∑ ∑G j)1
c
c
[τij - (
∑ x τ G /∑ G r rj
r)1
rj
kixk)]
k)1
kixk
k)1
where Gij ) exp(-Rijτij) and Gji ) exp(-Rijτji) with
τij ) Aij/T, τji ) Aji/T, and τii ) τjj ) 0.
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Table 3. Results of Data Correlation model
10-8 × Af (mol min-1 kg-1)
Eo (kJ mol-1)
10-8 × Ar (mol min-1 kg-1)
KB
KD
πa (mol2 min-2 kg-2)
AADb (mol min-1 kg-1)
biasc (mol min-1 kg-1)
Q-HIDS Q-HNIDS L-H E-R modified L-Hd
0.2247 0.2221 2.9114 5.4242 1.2914
43.787 44.016 47.920 48.031 46.411
0.0564 0.0262 0.2825 0.6214 1.6143
0.987 6.092 0.820
1.507 8.643 9.107
4.073 3.892 1.756 1.690 0.988
0.1554 0.1364 0.1047 0.1016 0.0844
0.0770 0.0447 -0.0064 -0.0039 -0.0102
a
Defined in eq 9.
b
N N AAD ) 1/N∑i)1 |(1/RHS)i - (103 FA/W)i|. c Bias ) 1/N∑i)1 |(1/RHS)i - (103 FA/W)i|.
d
R ) 3.
Conclusions
Figure 7. Comparison of correlated results with experimental FA/W.
also shown in the table, the Q-H model with the idealsolution assumption (Q-HIDS) qualitatively describes the kinetic behavior of the esterification. Some degree of improvement is made over the Q-H model when the nonideality of the liquid phase is taken into account in the Q-HNIDS model. Whereas the results from the L-H model are comparable to those from the E-R model, these two models are obviously better than the Q-HNIDS model. Consideration of the adsorption effect appears to improve the accuracy of the data correlation. The modified L-H model with the empirical parameter R ) 3, which accounts for the distribution of water adsorbed in the resin, can further reduce the sum of square deviations (π) by about one-half. Figure 7 illustrates a comparison of the calculated values of 1/RHS (i.e., calculated FA/W) from the Q-H and the modified L-H models with the experimental FA/W. The results from the modified L-H model are in a good agreement with the experimental values and are much better than those from the Q-H model, especially in the regions near chemical equilibrium. The dashed curves in Figures 1 and 2 are the calculated results from the modified L-H model, which show that the model is capable of representing the kinetic behavior over wide ranges of reaction temperature and feed composition. The best rate expression for this esterification system over Dowex 50Wx8-100 is given by
-rA )
[a a (-5582 T )
(1.2914 × 108) exp
A B
- 1.250aC(aD)3]
[1 + 0.820aB + 9.107(aD)3]2 (10)
The kinetic behavior for the esterification of acetic acid with amyl alcohol at temperatures from 323 to 393 K and at molar feed ratios (θBo) from 1 to 10 has been investigated experimentally by using a fixed-bed reactor with Dowex 50Wx8-100 as a catalyst. Whereas the equilibrium conversion of acetic acid was found to increase slightly with an increase in temperature, it increases appreciably with an excess of amyl alcohol in the feed. An extraneous phase was formed when the reaction took place at higher temperatures or at stoichiometric feed. The formation of a gaseous phase, when the reactor operated at 393 K, is of great advantage for the forward reaction esterification. Under the investigated conditions, the absence of mass-transfer resistance was verified experimentally. The quasihomogeneous, Langmuir-Hinshelwood, Eley-Rideal, and modified Langmuir-Hinshelwood models have been applied to correlate the kinetic data. The modified L-H model with R ) 3 appears to represent the kinetic behavior of this catalytic esterification over wide ranges of reaction temperature and feed composition. Acknowledgment The financial support of the Chinese Petroleum Co., ROC, through Grant NSC 88-CPC-E011-04 is gratefully acknowledged. Supporting Information Available: Tablulation of the experimental kinetic data for each run. This material is available free of charge via the Internet at http://pubs.acs.org. Nomenclature a ) activity A, B, C, D ) acetic acid, amyl alcohol, amyl acetate, and water, respectively Af ) Arrhenius preexponential factor for the forward reaction (mol min-1 kg-1) Aij, Aji ) binary parameters in the NRTL model, K Ar ) Arrhenius preexponential factor for the reverse reaction (mol min-1 kg-1) c ) number of components CAo ) inlet concentration of acetic acid (mol cm-3) Eo ) activation energy (kJ mol-1) F ) volumetric flow rate of feed (cm3 min-1) FA ) molar flow rate of acetic acid in feed (mol min-1) KB, KD ) adsorption constant for amyl alcohol and water Kx ) (composition) equilibrium constant N ) number of data points -rA ) reaction rate of acetic acid (mol min-1 kg-1) R ) gas constant (kJ mol-1 K-1) T ) temperature (K) W ) catalyst loading (g) xi ) mole fraction for component i XA ) conversion of acetic acid R ) power constant in kinetic expression
Ind. Eng. Chem. Res., Vol. 39, No. 11, 2000 4099 Rij ) nonrandomness factor in the NRTL model γ ) activity coefficient θBo ) molar ratio of feed (amyl alcohol to acetic acid) π ) objective function (mol2 min-2 kg-2) τ ) contact time () W/F) (g min cm-3) Subscripts A, B, C, D ) acetic acid, amyl alcohol, amyl acetate, and water, respectively e ) at equilibrium state i ) component i ij ) i-j pair interaction
Literature Cited (1) Lee, M. J.; Wu, H. T.; Kang, C. H.; Lin, H. M., Kinetic Behavior of Amyl Acetate Synthesis Catalyzed by Acid Cation Exchange Resin. J. Chin. Inst. Chem. Eng. 1999, 30, 117. (2) Venimadhavan, G.; Buzad, G.; Doherty, M. F.; Malone, M. F. Effect of Kinetics on Residue Curve Maps for Reactive Distillation. AIChE J. 1994, 40, 1814. (3) Xu, Z. P.; Chuang, K. T. Kinetics of Acetic Acid Esterification over Ion Exchange Catalyst. Can. J. Chem. Eng. 1996, 74, 493.
(4) Gonzalez, J. C.; Fair, J. R. Preparation of Tertiary Amyl Alcohol in a Reactive Distillation Column. 1. Reaction Kinetics, Chemical Equilibrium, and Mass-Transfer Issues. Ind. Eng. Chem. Res. 1997, 36, 3833. (5) Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. GroupContribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures. AIChE J. 1975, 21, 1086. (6) Berg, L.; Yeh, A. The Breaking of Ternary Acetate-AlcoholWater Azeotropic by Extractive Distillation. Chem. Eng. Commun. 1986, 48, 93. (7) Wu, H. T. Kinetics of Heterogeneous Esterification for Production of Amyl Acetate. MS Thesis, National Taiwan University of Science and Technology, Taipei, Taiwan, R.O.C., 1998. (8) Lee, L. S.; Liang, S. J. Phase and Reaction Equilibria of Acetic Acid-1-Pentanol-Water-n-Amyl Acetate System at 760 mmHg. Fluid Phase Equilib. 1998, 149, 57. (9) Carberry, J. J. Chemical and Catalytic Reaction Engineering, 2nd ed.; McGraw-Hill: New York, 1976. (10) Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135.
Received for review January 18, 2000 Revised manuscript received August 9, 2000 Accepted August 16, 2000 IE0000764
