Reaction Kinetics for the Heterogeneously Catalyzed Esterification of

Ind. Eng. Chem. Res. 2008, 47, 5313–5317

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Reaction Kinetics for the Heterogeneously Catalyzed Esterification of Succinic Acid with Ethanol Aspi K. Kolah, Navinchandra S. Asthana, Dung T. Vu, Carl T. Lira, and Dennis J. Miller* Department of Chemical Engineering & Materials Science, Michigan State UniVersity, East Lansing, Michigan 48824

The reaction kinetics of the reversible esterification reaction of succinic acid with ethanol to form monoethyl and diethyl succinate are presented. The reaction was studied in batch isothermal experiments catalyzed by macroporous Amberlyst-15 ion-exchange resin. Experimental data were obtained between 78 and 120 °C at different mole ratios of ethanol to succinic acid and at ion-exchange resin catalyst concentrations from 1 to 5 wt % of solution. Kinetic modeling was performed using a pseudohomogeneous mole fraction model which acceptably fits the experimental data. The kinetic model is useful for the design and simulation of processes such as reactive distillation for diethyl succinate formation. 1. Introduction Organic acid esters, produced by the reaction of organic acids and alcohols, can be entirely biorenewable or “green” chemicals that replace petroleum-based solvents. Succinic acid (1,4butanedioic acid, herein SA) can be esterified with alcohols such as ethanol and n-butanol through a series reaction to yield diethyl succinate (DES) and di-n-butyl succinate. A schematic reaction scheme for esterification of succinic acid with an alcohol is shown in Figure 1. In addition to having low toxicity and low vapor pressure, succinate esters have exceptional solvent properties and thus find commercial application as solvents and in consumer products such as paint strippers. In addition, succinate esters are intermediates in the production of poly butylene succinate (PBS) polymers, a polyester composed of SA and 1,4-butanediol having attractive properties for broad application in automobiles and consumer goods. The 1,4-butanediol is produced by hydrogenation of succinate ester,1,2 hence the entire PBS polymer is a succinate based, biorenewable material. Esters of SA (primarily dimethyl esters) are also being investigated for their insulinotropic potential in rats.3–7 A conventional process for DES production involves a stirred batch or continuous reactor with sulfuric acid as a homogeneous catalyst. Because the extent of reaction is thermodynamically limited, intermediate product removal and multiple reaction stages are required to achieve complete SA conversion. Many of the difficulties in using homogeneous catalysts can be eliminated through the use of heterogeneous catalysts such as ion exchange resins or supported clays. The heterogeneous catalyst allows easy mechanical separation of the catalyst from reaction media by decantation or filtration, reduces or eliminates corrosion problems, and facilitates continuous process operation. For reviews on the use of heterogeneous ion exchange resins as catalysts prior to 1995, the reader is referred to the works of Olah et al.,8 Chakrabarti and Sharma,9 and Sharma et al.10 For a more recent review, the reader is referred to the work of Harmer and Sun.11 Prior information in the literature on the kinetics of SA esterification with ethanol or n-butanol is scarce. Saigo et al.12 have synthesized succinic acid esters using phosphinechalcogenide as a catalyst. Recently, Benedict et al.13 have described * To whom correspondence should be addressed. Tel.: 1-517-3533928. Fax: 1-517-432-1105. E-mail: [email protected].

a process for the pervaporation-assisted esterification of lactic acid and SA with downstream ester recovery using Amberlyst XN-1010 and Nafion NR50 as catalyst. At present no information is available in the open literature describing the kinetics of SA esterification with ethanol in the presence of ion-exchange resin catalysts. Thus, we have conducted isothermal experimental batch studies on the esterification of SA with ethanol in the presence of Amberlyst-15 ion-exchange resin as catalyst. A pseudohomogeneous mole fraction based kinetic model is presented for correlation of the experimental data. This kinetic model is useful for designing processes such as continuous SA esterification using reactive distillation. 2. Experimental Details 2.1. Materials. For the kinetic experiments, anhydrous succinic acid crystals (>99%), herein SA, were obtained from Sigma-Aldrich. Absolute ethanol (>99%) and HPLC grade water were obtained from J. T. Baker, Inc. The strong cation exchange resin catalyst Amberlyst-15 (Rohm and Haas, Philadelphia, PA) was obtained in H+ form (dry, 0.6 mm beads) and was used without modification; the resin acidity as specified by the manufacturer is 4.6 equiv H+/kg dry resin. Purity of all chemicals was checked by gas chromatography or HPLC. 2.2. Analysis. The presence of succinic acid (SA), monoethyl succinate (MES), and diethyl succinate (DES) was first confirmed by GC-MS analysis of their trimethyl silyl (TMS) derivatives. For reaction samples, SA and its ethyl esters (MES and DES) were quantitatively analyzed on a Hewlett-Packard 1090 HPLC using a reversed phase C18 column (Novapak, 3.9 mm × 150 mm) held at 40 °C. Water/acetonitrile (ACN) mixtures, buffered at pH of 1.3, were used as the mobile phase (0.8 mL/min) in a gradient mode (0% ACN at t ) 0 min to 60% ACN at t ) 20 min to 90% ACN at t ) 25 min to 0% ACN at t ) 28 min). The species were quantified by UV detection (Hitachi L400H) at a wavelength of 210 nm. Succinic acid and DES were identified and quantified by comparing HPLC retention time and peak area with their respective calibration standards. Pure standard for MES could not be commercially obtained. On a mass basis, the response factor for DES was found to be 1.11 times higher than that for SA; therefore, the response factor for MES was calculated as an average of response factors for SA and DES. Using this response

10.1021/ie0706616 CCC: $40.75  2008 American Chemical Society Published on Web 07/09/2008

5314 Ind. Eng. Chem. Res., Vol. 47, No. 15, 2008

Figure 1. Esterification of succinic acid with an alcohol. Table 1. Summary of Kinetic Studies and Average Prediction Errors

run no.

figure no.

1 2 3 4 5 6 7 8 9 10 11 12

S1 2 S2 S3 S4 S5 S6 S9 S7 S8 S10 S11

initial mole ratio EtOH:SA

catalyst loading (wt %)

temp (°C)

average error (%) in succinate species mole fraction (Frel, eq 14)

10:1 10:1 10:1 10:1 10:1 10:1 10:1 10:1 10:1 10:1 15:1 20:1

2 2 2 2 2 1 3 5 1 5 2 2

78 90 100 110 120 90 90 90 78 78 90 90

25 29 23 17 18 28 22 25 26 19 27 28

average error (absolute) in succinate species mole fraction (Fabs, eq 13) 0.0048 0.0052 0.0035 0.0025 0.0025 0.0052 0.0029 0.0035 0.0057 0.0045 0.0028 0.0022

factor for MES, the carbon balance for each reaction sample, based on carbon in the starting SA, was in the range of 100 ( 10%. Reaction samples were analyzed for water content using a Varian 3700 gas chromatograph equipped with thermal conductivity detector (TCD) and a stainless steel column (4 m × 3.25 mm) packed with a stationary phase of Porapak Q. The column oven temperature was held at 413 K for two minutes, then ramped at 20 K/min to 493 K, where it was held for 6 min. n-Butanol was used as an internal standard. High purity helium (99.999%) was used as carrier gas at a flow rate of 20 mL/min. The injector and detectors were maintained at 493 K. Samples were analyzed for ethanol and byproduct diethyl ether (DEE) using a Perkin-Elmer Sigma-2000 gas chromatograph equipped with flame ionization detector (FID) and a bonded-phase fused silica capillary column (SPB-5, 30 m × 0.53 mm). The column oven was held at 313 K for 7 min, ramped at 2 K/min to 473 K where it was held for 5 min. Anhydrous toluene was used as an internal standard. High purity helium (99.999%) was used as carrier gas at a flow rate of 10 mL/min. The injector and detectors were maintained at 493 K. 2.3. Batch Kinetic Experiments. Esterification reactions at 78 °C were performed in a 2 × 10-4 m3 jacketed glass reactor equipped with a recirculating constant temperature oil bath. The reaction volume was ∼1.1 × 10-4 m3. A spiral coil condenser, open to the atmosphere, was placed on top of the reactor. The glass reactor was equipped with temperature and stirrer speed monitoring devices and a sampling port. In operation, measured quantities of ethanol and succinic acid were added to the reactor, and heating and stirring were started simultaneously. Once the desired temperature was achieved, usually in about 15 min, catalyst (Amberlyst-15 ion-exchange resin) was added for the case of resin catalyzed reactions and the stirring speed was increased to 800 rpm. This point in time was considered as the zero reaction time. Samples were withdrawn at specific time intervals and immediately transferred to an ice bath (prior to analysis) in order to ensure that no further reaction took place. Esterification reactions above 78 °C were performed in a 1 × 10-4 m3 stainless steel autoclave (5000 Multireactor System, Parr Instrument Co.) equipped with temperature and stirrer speed

Figure 2. Catalytic esterification of succinic acid with ethanol. Reaction conditions: mole ratio of ethanol to succinic acid, 10:1; Amberlyst 15 cation exchange resin catalyst loading, 2 wt %; reaction temperature, 90 °C. (9) SA; (b) MES; (2) DES.

Figure 3. Initial rate of succinic acid esterification vs catalyst loading. Reaction conditions: mole ratio of ethanol to succinic acid, 10:1. (() -90; (9) -78 °C.

monitors and a sampling port. In operation, measured quantities of ethanol, SA, and catalyst for resin-catalyzed reactions were added to the reactor and heating was started with slow stirring. The total reaction volume was maintained between 5.5 × 10-5 to 6.0 × 10-5 m3. The desired temperature was achieved in about 15 min, at which time the stirring rate was increased to 740 rpm. This time was considered as the zero reaction time. Samples were withdrawn at specific time intervals through a cooled metal tube and immediately transferred to an ice bath in order to ensure no further reaction took place before analysis. All samples were analyzed using the method described in section 2.2. 3. Results and Discussion Batch kinetic experiments were carried out to study the effects of reaction temperature, catalyst loading, and initial reactant molar ratio on the cation-exchange resin catalyzed esterification of SA with ethanol. It was observed from varying stirrer speed in initial experiments that conversion rates were unaffected at stirring speeds above 500 rpm, so all kinetic experiments were performed at 800 rpm to avoid external mass transfer limitations. Table 1 shows the reaction conditions for all of the experiments performed in this work. In Table 1, catalyst loading (wt %) is based on mass of the liquid phase. Ethanol:SA molar ratios >10:1 were required because of limited succinic acid solubility (∼12 wt %) in ethanol at low temperature. A set of time trajectories of SA, MES, and DES at typical batch esterification conditions is shown in Figure 2. The species time trajectories for all other experiments are presented as Figures S1-S12 in the Supporting Information.

Ind. Eng. Chem. Res., Vol. 47, No. 15, 2008 5315

The dependence of the succinic acid conversion rate on temperature over the range from 78 to 120 °C is given in Figures S1-S4 of the Supporting Information. The effect of catalyst loading on initial SA esterification rate at an ethanol:SA molar feed ratio of 10:1 is shown in Figure 3. The initial SA esterification rate was determined by fitting the experimental succinic acid mole fraction vs time with a polynomial equation and then evaluating the derivative at t ) 0. The initial SA esterification rate is proportional to catalyst loading, an indication that the observed reaction kinetics are independent of external mass transport resistances. Additional experiments at different catalyst loadings are given in Figures S5-S9. The effect of the ethanol:SA initial reactant mole ratio was studied at 90 °C and 2% catalyst loading; results are given in Figures S10 and S11.

rate constants ki are included in the effectiveness factor in the model equations. The complete equations are solved to determine the values of kinetic constants that best describe the reaction data. 4.3. Mole Fraction based Kinetic Model. On the basis of the reactions in eqs 1 and 2, a pseudohomogeneous, mole fraction based kinetic model for ion-exchange resin-catalyzed SA esterification has been developed, and kinetic data from a wide range of reaction conditions, including runs 1-12 in Table 1, have been used to determine kinetic constants for the reactions. The rate of formation of each species in the reaction mixture is described by eqs 5–9 below: -

4.1. Kinetic Pathways. Reactions 1 and 2 below describe the pathways involved in the esterification of SA with ethanol. k1

SA + EtOH {\} MES + W

wcatk1η1

(1)

-

k1/Keqx,1 k2

MES + EtOH {\} DES + W

(2) -

k2/Keqx,2

Reactions 1 and 2 are the series reactions to form DES from SA via intermediate formation of MES (eq 1). 4.2. Mass Transfer Considerations. The influence of intraparticle mass transfer resistances on Amberlyst-catalyzed esterification was evaluated by first calculating of the observable modulus (ηφ2) and implementation of the Weisz-Prater criterion (ηφ2 , 1) for each experiment. Taking the initial rate as the maximum rate for each experiment, calculating the liquid phase effective diffusivity of succinic acid in ethanol as 5.8 × 10-10 m2/s via the Wilke-Chang equation, and applying the experimental observation (via volumetric measurement) that the ion-exchange resin particle swells by 50% upon exposure to ethanol to a particle diameter of 0.69 mm, the values of observable modulus ranged from 0.3 at 78 °C to 1.5 at 120 °C. The reaction is thus moderately mass transfer limited at the temperature range investigated. Succinic acid esterification is therefore somewhat more rapid than for other acids in similar esterification studies.14–16 Mass transfer limitations were accounted for by including the intraparticle effectiveness factor in the kinetic model developed herein. Although the esterification reactions are bimolecular and reversible, the effectiveness factors are calculated assuming that reactions 1 and 2 (eqs 1 and 2) are irreversible, first order, isothermal reactions. This is justified because ethanol is always in considerable excess (>10:1 molar ratio with succinic acid) and the equilibrium conversion in all experiments exceeds 98% for reaction 1 (eq 1) and 82% for reaction 2 (eq 2). The resulting equations for Thiele modulus (φ) and effectiveness factor (η) are given as φi ) (dp/6)(kiFcatxEtOH/Fsoln)0.5 i ) 1, 2

(3)

ηi ) tanh(φi)/φi i ) 1, 2

(4)

where the catalyst and solution densities in eq 3 are required to place the rate constant on a per unit volume catalyst basis and the ethanol mole fraction, taken as the average over the experiment, reflects the pseudofirst order assumption in the effectiveness factor calculation. In the kinetic model presented in the next section, the preexponential factors and activation energies for the forward

) )

(5)

dxMES xDESxW ) wcatk2η2 xMESxEtOH + dt Keqx,2

-

4. Kinetic Modeling

( (

dxSA xMESxW ) wcatk1η1 xSAxEtOH dt Keqx,1

( (

(

xMESxW - xSAxEtOH Keqx,1

) )

)

dxDES xDESxW ) wcatk2η2 - xMESxEtOH dt Keqx,2

dxEtOH xMESxW ) wcatk1η1 xSAxEtOH + dt Keqx,1

(

wcatk2η2 xMESxEtOH -

(

xDESxW Keqx,2

)

(7)

)

(8)

)

(9)

dxW xMESxW ) wcatk1η1 - xSAxEtOH + dt Keqx,1

(

wcatk2η2 where

(6)

xDESxW - xMESxEtOH Keqx,2

( )

-EA,i (10) RT 4.4. Chemical Equilibrium Constants. The chemical equilibrium constants are given by ki ) k0i exp

Keqx,i )

∏x

νi i,eq

(11)

The value of mole fraction equilibrium constants Keqx,i for reactions under consideration were determined by analysis of the experimental data at long reaction times (e.g., approaching equilibrium) and were found to be 5.3 and 1.2 for the formation of MES and DES, respectively. These constants were taken to be independent of temperature. 4.5. Determination of Rate Constants. The kinetic eqs 5–9 were numerically integrated via a fourth order Runge-Kutta method using ordinary differential equation solver ode23 in Matlab 7.0 to determine optimum values of the four adjustable kinetic parameters for the resin-catalyzed reactions, the preexponential factors k01 and k02, and the energies of activation EA,1 and EA,2. Starting with an initial set of rate constants, the liquid phase mole fractions for all species over the course of reaction were calculated and compared with the experimental values. The four kinetic parameters were then incremented sequentially in order to minimize the sum of the mean square differences given by

Fmin2 )

∑

(xj,cal - xj,expt)2

samples

nsamples

(12)

5316 Ind. Eng. Chem. Res., Vol. 47, No. 15, 2008

this value with TOF values for other organic acid esterification reactions that we have investigated in our laboratory. At the same conditions, the TOF for lactic acid esterification17 with ethanol is 13 1/h; for citric acid,16 the TOF for the first esterification step is 2.1 1/h. The similarity in TOF between lactic acid and succinic acid is not surprising; however, the significantly lower TOF for citric acid suggests steric hindrance associated with multiple carboxylic acid functionalities on citric acid or more generally a reduced access of the bulkier citric acid molecule to the resin acid sites.

Table 2. Parameters for Resin-Catalyzed Succinic Acid Esterification with Ethanol parameter 0

k1 k20 EA,1 EA,2 Keqx,1 Keqx,2

units

value

kgsoln/kgcats kgsoln/kgcats kJ/kmol kJ/kmol

5.3×107 8.0×107 66000 70000 5.3 1.2

Table 3. Effectiveness Factors for Succinic Acid Esterification temperature (K) 351 363 373 383 393

η1 eq 1

η2 eq 2

0.94 0.88 0.80 0.70 0.60

0.97 0.95 0.90 0.84 0.76

5. Conclusions

After this optimization, the calculated mole fractions of the succinate components (SA, MES, DES) were compared to the corresponding experimental values to calculate an average absolute error in mole fraction (Fabs) and a relative average error in percent (Frel), giving the mean relative deviation, represented both absolutely and on a percentage basis, shown below.

Fabs )

Frel )

∑

∑

|xj,cal - xj,expt|

samples

samples

|

nsamples xj,cal - xj,expt xj,expt

nsamples

(13)

|

Succinic acid esterification kinetics were studied at reaction temperature from 78 to 120 °C, ethanol:SA initial mole ratios from 10:1 to 20:1, and Amberlyst 15 cation exchange resin loadings from 1% to 5% of solution. Esterification kinetics are described using a mole fraction based pseudohomogeneous model that includes intraparticle mass transfer limitations expressed as effectiveness factor for a first order irreversible reaction. The rate expressions describe the kinetics of MES and DES formation over a wide range of catalyst concentration, reactant molar ratios, and temperature. The model presented can be conveniently used for design and scale-up of integrated processes like reactive distillation for synthesis of DES. Acknowledgment Financial support from the National Corn Growers Association and the U.S. Department of Energy are greatly appreciated.

× 100 %

(14)

The values of the kinetic parameters are shown in Table 2. Predicted mole fractions are given as continuous lines in Figure 2 and Figures S1-S11 in the Supporting Information. It can be observed from the Figures and from Table 2 that the model predicts succinic acid esterification experimental data reasonably well. The values of the absolute mole fraction error Fabs and relative mole fraction error Frel are reported in Table 1. For SA, the average percent error in mole fraction is highest in the region when the SA concentration is low. Large errors are also observed in the case of DES in the initial reaction period up to about 300 min, where its concentration is low. Values of the effectiveness factors for each reaction at each temperature are given in Table 3. The reaction exhibits significant mass transport resistances at temperatures above 100 °C. It should be noted that we attempted to fit the kinetic data without including intraparaticle mass transport limitationssthe average errors were one to two percentage points higher than when effectiveness factor was included. For the reaction system under consideration, the formation of diethyl ether from the etherification reaction of two molecules of ethanol has not been included, since the esterification reaction is very fast in comparison to the kinetics of diethyl ether formation. The kinetics of diethyl ether formation over Amberlyst 15 resin have been reported in an earlier publication from the authors’ laboratory.16 The turnover frequency (TOF, (mol SA/mol H+ sites/h)) for SA to MES on Amberlyst 15 resin acid sites can be easily determined from the acid site density (4.6 mol H+/kg resin), catalyst loading (wcat), initial SA concentration (mol/kgsol), and rate constant k1. At 90 °C and an initial SA concentration of 1.0 mol/kgsol in ethanol, corresponding to a 19:1 EtOH:SA feed ratio, the turnover frequency is 12/h. It is interesting to compare

Nomenclature and Units DES ) diethyl succinate dp ) Amberlyst 15 ion-exchange resin catalyst particle diameter; 1.1 × 10-4 m EA,i ) energy of activation for reaction i (kJ/kmol), i ) 1, 2 EtOH ) ethanol ki ) rate constant for catalyzed reaction i, i ) 1, 2 (kgsoln/kgcat s) k0i ) pre-exponential factor for catalyzed reaction i, i ) 1, 2 (kgsoln/ kgcat s) Keq,i ) mole fraction based reaction i equilibrium constant, i ) 1, 2 MES ) monoethyl succinate R ) gas constant; 8.31 (kJ/kmol K) SA ) succinic acid T ) temperature (K) W ) water wcat ) catalyst concentration (kgcat/kgsoln) xj ) mole fraction of jth component in liquid phase solution ηi ) intraparticle effectiveness factor for reaction i (i ) 1, 2) φi ) Thiele modulus for reaction i (i ) 1, 2) Fcat ) catalyst particle density; 1200 (kg/m3) Fsoln ) reaction solution density; 880 (kg/m3) Subscripts i ) reaction index j ) component in solution

Supporting Information Available: Graphs of species concentration vs time for a wide range of reaction conditions. This material is available free of charge via the Internet at http://pubs.acs.org. Literature Cited (1) Turek, T.; Trimm, D. L. The Catalytic Hydrogenolysis of Esters to Alcohols. Catal. ReV. Sci. Eng. 1994, 36 (4), 645.

Ind. Eng. Chem. Res., Vol. 47, No. 15, 2008 5317 (2) Attig, T. G.; Graham, A. M. Process and Catalysts for the Manufacture of Gamma-Butyrolactone and 1,4-Butanediol by Hydrogenation of Maleic Acid. U.S. Patent 4,827,001, 1989. (3) Mukala-Nsengu, A.; Ferna´ndez-Pascual, S.; Martı´n, F.; Martı´n-delRı´o, R.; Tamarit-Rodriguez, J. Similar Effects of Succinic Acid Dimethyl Ester and Glucose on Islet Calcium Oscillations and Insulin Release. Biochem. Pharmacol. 2004, 67, 981. (4) Laghmich, A.; Ladrie`re, L.; Dannacher, H.; Bjo¨rjling, F.; Malaisse, W. J. New Esters of Succinic Acid and Mixed Molecules Formed by Such Esters and a Meglitinide Analog. Study of Their Insulinotropic Potential. Pharmacol. Res. 2000, 41, 543. (5) Kadiata, M. N.; Malaisse, W. J. Opposite Effects of D-Glucose Pentaacetate and D-Galactose Pentaacetate Anomers on Insulin Release Evoked by Succinic Acid Dimethyl Ester in Rat Pancreatic Islets. Life Sci. 1999, 64, 751. (6) Ladrie`re, L.; Malaisse-Lagae, F.; Verbruggen, I.; Willem, R.; Malaisse, W. J. Effects of Starvation and Diabetes on the Metabolism of [2,3-13C] Succinic Acid Dimethyl Ester in Rat Hepatocytes. Metabolism 1999, 48, 102. (7) Leclercq-Meyer, V.; Malaisse, W. J. Potentiation of Glucagon-Like Peptide 1- Insulinotropic Action by Succinic Acid Dimethyl Ester. Life Sci. 1996, 58, 1195. (8) Olah, G. A.; Iyer, P. S.; Prakash, G. K. S. Synthesis 1986, 513. (9) Chakrabarti, A.; Sharma, M. M. Cationic Ion-Exchange Resin as Catalyst. React. Funct. Polym. 1993, 20, 1. (10) Sharma, M. M. Some Novel Aspects of Cationic Ion Exchange Resins as Catalysts. React. Funct. Polym. 1995, 26, 1.

(11) Harmer, M. A.; Sun, Q. Solid Acid Catalysis Using Ion Exchange Resins. Appl. Catal., A 2001, 221, 45. (12) Saigo, K.; Hashimoto, Y.; Hayashi, M. Catalysts for Bisalkoxycarbonylation of Olefins and Manufacture of Succinic Acid Esters. Jpn. Kokai Tokkyo Koho 2000, 200271485. (13) Benedict, D. J.; Parulekar, S. J.; Tsai, S. P. Pervaporation-Assisted Esterification of Lactic and Succinic Acids with Downstream Recovery. J. Membr. Sci. 2006, 281, 435. (14) Gangadwala, J.; Mankar, S.; Mahajani, S. Esterification of Acetic Acid with Butanol in the Presence of Ion-Exchange Resins as Catalysts. Ind. Eng. Chem. Res. 2003, 42, 2146. (15) Asthana, N.; Kolah, A.; Vu, D.; Lira, C. T.; Miller, D. J. A Continuous Reactive Separation Process for Ethyl Lactate Formation. Org. Process Res. DeV. 2005, 9, 599. (16) Kolah, A.; Asthana, N. S.; Vu, D. T.; Lira, C. T.; Miller, D. J. Reaction Kinetics of the Catalytic Esterification of Citric Acid with Ethanol. Ind. Eng. Chem. Res. 2007, 46, 3180. (17) Asthana, N. S.; Kolah, A. K.; Vu, D. T.; Lira, C. T.; Miller, D. J. A Kinetic Model for the Esterification of Lactic Acid and Its Oligomers. Ind. Eng. Chem. Res. 2006, 45, 5251.

ReceiVed for reView May 9, 2007 ReVised manuscript receiVed March 31, 2008 Accepted May 6, 2008 IE0706616