Kinetics of Synthesis and Hydrolysis of Ethyl Benzoate over Amberlyst

In the determination of kinetic parameters, the right-hand-side integrals of eq 4 (denoted as RHSf) and eq 5 (denoted as RHSr) were calculated with Si...
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Ind. Eng. Chem. Res. 2005, 44, 725-732

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Kinetics of Synthesis and Hydrolysis of Ethyl Benzoate over Amberlyst 39 Ming-Jer Lee, Pei-Lin Chou, and Ho-mu Lin* 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 synthesis and hydrolysis of ethyl benzoate over an acidic cationexchange resin, Amberlyst 39, was investigated with a fixed-bed reactor at atmospheric pressure. The esterification of benzoic acid with ethanol was implemented at temperatures between 323.15 and 353.15 K under various molar ratios of feed, θB0 (ethanol to benzoic acid). The hydrolysis of ethyl benzoate was also conducted in the same temperature range with a variety of molar ratios of feed, θC0′ (ethyl benzoate to water) and θB0′ (ethanol to water). The equilibrium conversion of benzoic acid in the esterification was found to increase with an increase in both temperature and θB0. Additionally, the relative adsorption constants between two reacting species were determined from adsorption experiments. The magnitudes of the adsorption constants follow the order water > ethanol > ethyl benzoate > benzoic acid. The kinetic data of both the synthesis and hydrolysis of ethyl benzoate were simultaneously correlated with the quasi-homogeneous, Eley-Rideal, and Langmuir-Hinshelwood-Hougen-Watson (LHHW) models. The LHHW model yielded the best representation for the kinetic behavior of the liquid-solid catalytic synthesis and hydrolysis of ethyl benzoate. Introduction There are many alternative methods, such as solvent extraction,1 homogeneous extractive distillation,2 heterogeneous extractive distillation,3 adsorption,4 and supercritical fluid extraction,5 for separating azeotropic mixtures of water and alcohols. Recently, Hong et al.6 addressed a reactive distillation method for the recovery of ethanol from the azeotropic aqueous solution by using an acidic ion-exchange resin as a catalyst and ethyl benzoate as an auxiliary agent. The main idea for crossing the azeotropic barrier was based on the combination effects of selective sorption and reaction in the acidic ion-exchange resin, together with consideration of its phase equilibrium behavior. The amount of water in the liquid phase could be reduced due to highly selective sorption of water from water/ethanol solution by ion-exchange resins.7,8 The amount of water could further decrease and that of ethanol increase simultaneously by contacting water with ethyl benzoate over the acidic ion-exchange resins. Benzoic acid, a low volatile and high added value compound, is also produced via the hydrolysis of ethyl benzoate. Due to the low volatilities of ethyl benzoate and benzoic acid, ethanol with a minor amount of water is expected to be recovered from the top of a reactive distillation column and the heavier components, benzoic acid and ethyl benzoate, are expected to be recovered from the bottom. The performance of this reactive distillation unit is governed not only by the phase equilibrium behavior of the mixtures but also by the sorption behavior in the resins and the kinetic behavior of the hydrolysis of ethyl benzoate. The related experimental studies are essentially needed for the development of the separation process. To understand the phase behavior in the * To whom correspondence should be addressed. Phone: 886-2-2737-6643. Fax: 886-2-2737-6644. E-mail: [email protected].

reactive distillation process unit, Hong et al.6 measured the multiphase equilibrium (both vapor-liquid equilibrium and vapor-liquid-liquid equilibrium) data for the mixtures containing water, ethanol, and ethyl benzoate. Most recently, Hone9 and Wu10 have measured the solid-liquid equilibrium and vapor-liquid equilibrium data, respectively, for the related benzoic acid-containing binary systems. Plazl11 studied the esterification of benzoic acid with ethanol by conventional and microwave heating in a stirred tank reactor. Pipus et al.12 further investigated this esterification in a tubular reactor, catalyzing with sulfuric acid and Amberlyst 15, respectively, at temperatures from 323.15 to 353.15 K. The rate of disappearance of benzoic acid was simply expressed by an irreversible quasi-homogeneous model with ideal-solution assumption. The reaction rate was found to be second order with respect to benzoic acid, while ethanol was in large excess. In their proposed kinetic model, the adsorption effect was neglected. As far as we know, the adsorption behavior in this solidliquid catalytic reaction system has not been investigated yet. In the present study, adsorption experiments were conducted for three binary mixtures composed of the reacting species over Amberlyst 39. The mutually relative adsorption constants between two compounds were determined by fitting the experimental results to the adsorption model developed by Song et al.13 The kinetic behavior of the synthesis and hydrolysis of ethyl benzoate was also systematically investigated with a fixed-bed reactor, in which acidic ion-exchange resin beads, Amberlyst 39, were packed with glass wool layer by layer. The experiments were conducted over a variety of feed compositions and temperatures under atmospheric pressure. Several representative models have been developed to represent the kinetic behavior of heterogeneous etherification and esterification. The quasi-homogeneous (QH) model, similar to the power-law model for

10.1021/ie049437w CCC: $30.25 © 2005 American Chemical Society Published on Web 01/21/2005

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Ind. Eng. Chem. Res., Vol. 44, No. 4, 2005

homogeneous reactions, has commonly been used in data correlations (e.g., Pupis et al.12) and in the generation of residue-curve maps for reactive distillation systems (e.g., Venimadhavan et al.14). If adsorption effects are significant, either the Eley-Rideal (ER) model or the Langmuir-Hinshelwood-Hougen-Watson (LHHW) model was often adopted to correlate the kinetic data. The LHHW model was derived under the assumption that the rate-limiting step is the surface reaction between adsorbed molecules, while the ER model was derived by assuming that the rate-determining step is the surface reaction between one adsorbed species and one nonadsorbed reactant from the liquid phase. In this work, the kinetic data of both the synthesis and hydrolysis of ethyl benzoate were simultaneously correlated with the QH, ER, and LHHW models over the entire experimental conditions. While the nonideality of the reacting solutions was taken into account in the kinetic models, the activity coefficients of the constituents were calculated from the nonrandom two-liquid (NRTL) model (Renon and Prausnitz15). Experimental Section Chemicals. Amberlyst 39, an acidic cation-exchange resin, was manufactured by Rohm and Hass (U.S.A.). According to the report from the supplier, the particle sizes are within 200-1180 µm, the concentration of acid sites is >5.0 equiv kg-1, and the upper operable temperature is ∼393 K. The resin beads were washed with ethanol, dried, and sieved before use. Benzoic acid (99 mass %) and ethyl benzoate (99 mass %) were supplied by Acros (U.S.A.), ethanol (99.5 mass %) was purchased from Shimakyu (Japan), and deionized distillated water was prepared in our laboratory. The purity of the above chemicals was checked by gas chromatographic analysis, and these substances were used without further purification. Adsorption Experiment. The adsorption chamber was made of glass with a jacket and well insulated. Its internal volume is ∼16 cm3. Thermostatic water is circulated through the jacket to maintain the temperature of the chamber within (0.2 K. The temperature of the adsorption chamber was measured with a mercury thermometer. Its readings were calibrated with a precision digital thermometer (model 1560, Hart Scientific Co., U.S.A.) accurate to ∼ (0.1 K. In each adsorption run, ∼1.6 g of dried Amberlyst 39 beads and a proper amount of binary solution were charged in the chamber. To minimize the vaporization during the adsorption run, the vapor space in the adsorption chamber was left as small as possible. The loaded solution was prepared gravimetrically with an electronic balance, which can be as accurate as (0.1 mg. The uncertainty of the composition for the prepared solution was thus estimated to be ∼ (0.0002 in mole fraction. To minimize the effect of evaporation during the solution preparation, the heavier component was loaded first. The contents of the chamber were agitated vigorously with a magnetic stirrer for at least 5 h in each run. The liquid sample was then taken, and its composition was determined by using a gas chromatograph (model 8700, China Chromatography Co., Taiwan) with a thermal conductivity detector. High-purity helium (99.99%) was used as a carrier gas. A stainless steel column (length, 2 m; o.d., 0.3175 cm) packed with Porapak Qs 80/100 was utilized for the separation of

the constituent compounds. Calibrations were made with gravimetrically prepared samples in the experimental composition range. At least four samples were taken in an individual run. The equilibrium composition of the liquid phase was obtained by the average of the replicated samples. The uncertainty of the sample analysis for the minor components is ∼ (0.001 in mole fraction. Kinetics Experiment. The apparatus for kinetic data measurements and its operation procedure have been detailed elsewhere (Lee et al.16). An HPLC pump (model PU-1580, Jasco, Japan; flow rate range, 1 × 10-3 to 10 cm3 min-1; accuracy of flow rate, (2%) constantly charged the prepared reactant mixture into the reaction section of the column. The volumetric flow rate of feed has been calibrated with pure water. Dried Amberlyst 39 beads with an average particle size of 0.42 mm (40 mesh) and glass wool were packed in the fixed-bed reactor. The dried catalyst loading, W, was 7.1103 g for the case of the base. The reaction temperature was controlled to within (0.2 K by circulating thermostatic silicon oil through the reactor jacket. The outer part of the jacket was well insulated. A precision digital thermometer with a platinum RTD sensor (model 1560, 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 into the sample to avoid forming two liquid phases during the titration. The amount of benzoic acid in the sample was analyzed with a 0.1 N standard solution of NaOH (Acros) through a buret (accuracy, (0.05 cm3; Glasfirn, Germany). The samples were also frequently analyzed with gas chromatography to check if there were any byproducts in the samples. At least four replicated samples were taken under each of the experimental conditions, and the reproducibility was within (2%. The conversion of benzoic acid (in the synthesis of ethyl benzoate) or water (in the hydrolysis of ethyl benzoate) was determined from the inlet and outlet concentrations of benzoic acid. A complete conversion curve was obtained by performing the experiments with various flow rates. In the measurement of equilibrium conversion, the outlet of product stream was totally recycled until the conversion approached a constant. Experimental Results Adsorption. The data treatment of adsorption experiments was done by following the method given by Song et al.13 For an isothermal nonreactive binary adsorption system, Kipling17 expressed an overall material balance as

n0∆x ) n1sx2 - n2sx1 m

(1)

where n0 is the total initial number of moles in the liquid phase, ∆x is the change in the mole fraction in the liquid phase, m is the mass of the absorbent, and nis is the number of moles of component i adsorbed on the surface per unit mass of absorbent. Making several assumptions on the nature of the adsorbed layer and the assumption of an ideal solid phase, Song et al.13 further derived a material-balance equation in terms of the mole fraction and the activity of component i, xi and ai ()xiγi), a ratio of the adsorption equilibrium constants for any two

Ind. Eng. Chem. Res., Vol. 44, No. 4, 2005 727 Table 1. Parameters of the NRTL Modela for the Mixtures Containing Benzoic Acid (1), Ethanol (2), Ethyl Benzoate (3), and Water (4) (i-j)

Aij/R (K)

Aji/R (K)

Rij

data type

source

(1-2) (1-3) (1-4) (2-3) (2-4) (3-4)

833.0 646.74 4984.4 11.83 -189.22 829.67

-426.0 -32.57 419.14 238.93 802.18 2685.37

0.3 0.3 0.3 0.2 0.2 0.2

SLE VLE VLE VLE VLE and VLLE VLE and VLLE

Hone9 Wu10 Wu10 Hong et al.6 Hong et al.6 Hong et al.6

a

water, three binary systems including water/ethanol, ethanol/ethyl benzoate, and ethanol/benzoic acid were investigated. While the water/ethanol and ethanol/ethyl benzoate systems were measured at 333.15 K, the ethanol/benzoic acid system was measured at 303.15 K to minimize the possibility of esterification during the adsorption experiments. Due to the solid solubility limitation of benzoic acid dissolving in ethanol at 303.15 K, the adsorption experiments of the ethanol/benzoic acid system were implemented with x1 values greater than 0.8. Figure 1 shows the experimental results for these three binary systems, in which the smooth curves represent the calculated values from eq 2. Table 2 gives the correlated results, indicating that the adsorption strengths follow the order water > ethanol > ethyl benzoate > benzoic acid. The ratio of the adsorption constants of benzoic acid/ethyl benzoate/ethanol/water is 1:4.65:20.0:112.5. These relative adsorption constants will be introduced in the LHHW and ER models to reduce the number of undetermined parameters during the kinetic data correlation. Kinetics. Synthesis of Ethyl Benzoate. The kinetics of ethyl benzoate synthesis was studied at temperatures from 323.15 to 353.15 K with three different molar feed ratios (θΒ0 ) 5, 7, and 9, where θΒ0 is the molar ratio of ethanol to benzoic acid). Six series of runs were conducted in this study. All the experiments were operated at atmospheric pressure. 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

( )

The expression of the NRTL model is the following: c

∑ ln γi )

c

τjiGjixj

j)1

+

c

∑G x

∑ ∑G x j)1

li l

∑x τ G r rj

xjGij

c

c

lj l

l)1

l)1

rj

r)1

τij -

c

∑G x

lj l

l)1

where Gij ) exp(-RijAij/RT) and Gji ) exp(-RijAji/RT). Table 2. Correlated Results mixture (1) + (2)

ns (mol g-1)

K1,2

AAD (%)a

water + ethanol ethanol + ethyl benzoate ethanol + benzoic acid

0.007 67 0.018 43 0.018 00

5.63 4.30 20.0

1.9 6.4 3.2

a

AAD (%) )

( ) ( ) ∑ ( )

100 N

N

|

n0∆x m

-

m

i

n0∆x

i)1

n0∆x

calcd

m

exptl

|

i

exptl i

where N is the number of data points.

τ ) W/F

substances, K1,2, and the total number of moles of the adsorbed compounds per unit mass of adsorbent, ns:

A wide range of volumetric flow rates of feed was covered in the experiments for which the conversion of benzoic acid, XA, varied from very small to near equilibrium. The equilibrium conversion of benzoic acid, XAe, was also determined for each series. Table 3 summarizes the experimental conditions and the results of measurements for each run. The experimental kinetic data are tabulated as Supporting Information. Figure 2 presents the variation of XA with contact time for the reaction taking place at θΒ0 ) 5 over a temperature range of 323.15-353.15 K. It shows that the higher temperature yields the greater conversion of benzoic acid at a fixed contact time. Increasing temperature is favorable for acceleration of the esteri-

s

n0∆x n (K1,2a1x2 - a2x1) ) m K1,2a1 + a2

(3)

(2)

The values of the parameters K1,2 and ns can be determined by fitting the results of isothermal adsorption experiments to eq 2. In the present study, the NRTL model (Renon and Prausnitz15) was used to calculate the activity coefficient, γi. Table 1 lists the related binary parameters of the NRTL model, which were determined from experimental phase equilibrium data.6,9,10 To determine the adsorption constants of benzoic acid, ethanol, and ethyl benzoate relative to

Table 3. Experimental Results of the Synthesis of Ethyl Benzoate run

T (K)

θB0

W (g)

size (mesh)

103CA0 (mol cm-3)

range of τ (g min cm-3)

range of XA

XAe

Kca

Kγb

Kac

1 2 3 4 5 6

323.15 333.15 343.15 353.15 333.15 333.15

5 5 5 5 7 9

7.1103 7.1103 7.1103 7.1103 7.1103 7.1103

40 40 40 40 40 40

2.5409 2.5409 2.5409 2.5409 1.9595 1.5937

7.1-711 7.1-711 7.1-711 4.7-711 14.2-711 14.2-711

0.025-0.567 0.049-0.765 0.111-0.862 0.136-0.902 0.104-0.810 0.104-0.842

0.851 0.892 0.919 0.936 0.915 0.935

1.17 1.79 2.55 3.37 1.62 1.67

6.28 6.05 5.84 5.65 5.84 5.74

7.35 10.85 14.9 19.0 9.46 9.56

a

Kc was calculated from

Kc ) b

xCexDe XAe2 ) xAexBe (1 - XAe)(θB0 - XAe)

Kγ was calculated from

Kγ ) c

Ka was calculated from Ka ) KcKγ.

γCeγDe γAeγBe

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Figure 1. Results of adsorption experiments for the binary systems (a) water (1) + ethanol (2) at 333.15 K, (b) ethanol (1) + ethyl benzoate (2) at 333.15 K, and (c) ethanol (1) + benzoic acid at 303.15 K over Amberlyst 39. Table 4. Experimental Results of the Hydrolysis of Ethyl Benzoate run

T (K)

θB0′

θC0′

W (g)

size (mesh)

103CD0 (mol cm-3)

range of τ (g min cm-3)

range of XD

7 8 9 10 11 12 13 14 15

323.15 333.15 343.15 353.15 333.15 333.15 333.15 333.15 333.15

7.42 7.42 7.42 7.42 1.0 1.2 1.6 2.0 2.16

8 8 8 8 0.5 1.0 2.0 4.0 8.0

7.1103 7.1103 7.1103 7.1103 7.1103 7.1103 7.1103 7.1103 7.1103

40 40 40 40 40 40 40 40 40

0.6263 0.6263 0.6263 0.6263 6.7723 4.3275 2.5131 1.4115 0.7737

35.6-711 35.6-711 14.2-711 7.1-474 142.2-711 71.1-711 142.2-711 47.4-711 35.6-711

0.020-0.240 0.047-0.324 0.040-0.358 0.048-0.350 0.0065-0.0283 0.0068-0.0482 0.0212-0.1068 0.0250-0.2431 0.0439-0.531

fication of benzoic acid with ethanol. The equilibrium conversion, XAe, also increases with increasing temperature. Figure 3 illustrates the conversion varying with contact time at 333.15 K under different feed compositions. At a given contact time, greater conversions are obtained as the reaction operates at higher θΒ0.

Hydrolysis of Ethyl Benzoate. The kinetics of the hydrolysis of ethyl benzoate was also investigated experimentally at 323.15-353.15 K with a variety of feed compositions. Table 4 lists the experimental conditions and the results of the hydrolysis. Figure 4 presents the conversion curves of water with a fixed feed com-

Ind. Eng. Chem. Res., Vol. 44, No. 4, 2005 729

Figure 2. Kinetic behavior of the synthesis of ethyl benzoate with θB0 ) 5 over different temperatures.

Figure 3. Kinetic behavior of the synthesis of ethyl benzoate at 333.15 K over different feed compositions.

Figure 5. Kinetic behavior of the hydrolysis of ethyl benzoate at 333.15 K over different feed compositions.

conversion of water also increases with increasing temperature. Figure 5 illustrates the effect of feed composition on the conversion of water at 333.15 K. It shows that the conversion of water is relatively low ( ethanol > ethyl benzoate > benzoic acid. The kinetic data of both the synthesis and hydrolysis of ethyl benzoate were simultaneously correlated with the quasi-homogeneous, EleyRideal, and Langmuir-Hinshelwood-Hougen-Watson models. The Langmuir-Hinshelwood-Hougen-Watson model was capable of representing the kinetic behavior of the liquid-solid catalytic synthesis and hydrolysis of ethyl benzoate over the entire experimental conditions. Acknowledgment The financial support from the National Science Council, Taiwan, through Grant No. NSC 92-2214-E011002 is gratefully acknowledged. Supporting Information Available: Table of the experimental kinetic data for runs 1-15. This material is available free of charge via the Internet at http://pubs.acs.org. Nomenclature a ) activity A, B, C, and D ) benzoic acid, ethanol, ethyl benzoate, and water, respectively Af ) Arrhenius preexponential factor of the forward reaction (mol min-1 kg-1) Aij/R and Aji/R ) interaction energy parameters in the NRTL model (K) Ar ) Arrhenius preexponential factor of the reverse reaction (mol min-1 kg-1)

c ) number of components CA0 ) inlet concentration of benzoic acid (mol cm-3) CD0 ) inlet concentration of water (mol cm-3) E0,f ) activation energy of the forward reaction (kJ mol-1) E0,r ) activation energy of the reverse reaction (kJ mol-1) F ) volumetric flow rate of feed (cm3 min-1) FA ) molar flow rate of benzoic acid in feed (mol min-1) FD ) molar flow rate of water in feed (mol min-1) ∆hf ) molar heat of ethyl benzoate synthesis (kJ mol-1) kf ) rate constant of forward reaction (mol min-1 kg-1) kr ) rate constant of reverse reaction (mol min-1 kg-1) KD ) adsorption equilibrium constant of water Ka ) equilibrium constant in terms of activity Kc ) equilibrium concentration ratio Kγ ) equilibrium constant in terms of activity coefficient K1,2 ) ratio of adsorption constants between components 1 and 2 m ) mass of absorbent (g) n0 ) total initial number of moles in the liquid phase (mol) nis ) number of moles of component i adsorbed on the surface per unit mass of absorbent (mol g-1) ns ) the constant total number of moles which can be accommodated in the adsorbed phase by unit mass of solid (mol g-1) N ) number of data points Nf ) number of data points of synthesis of ethyl benzoate Nr ) number of data points of hydrolysis of ethyl benzoate p ) number of parameters in the kinetic models -rA ) reaction rate of benzoic acid (mol min-1 kg-1) -rD ) reaction rate of water (mol min-1 kg-1) R ) gas constant (kJ mol-1 K-1) T ) temperature (K) W ) catalyst loading (g) x ) mole fraction ∆x ) change in the mole fraction in the liquid phase X ) conversion R ) nonrandomness in the NRTL model γ ) activity coefficient θB0 ) molar ratio of feed (ethanol to benzoic acid) θB0′ ) molar ratio of ethanol to water θC0′ ) molar ratio of ethyl benzoate to water π ) objective function (mol2 min-2 kg-2) τ ) contact time ()W/F) (g min cm-3) Subscripts A, B, C, and D ) benzoic acid, ethanol, ethyl benzoate, and water, respectively e ) at equilibrium state f ) forward reaction i ) component i r ) backward reaction Superscripts exptl ) experimental value calcd ) calculated value

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Received for review June 26, 2004 Revised manuscript received November 16, 2004 Accepted November 23, 2004 IE049437W