without Pervaporation

Rate expressions for homogeneous and heterogeneous esterification are obtained from the experimental data using differential and integral methods. Exp...
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Ind. Eng. Chem. Res. 2003, 42, 2282-2291

Esterification of Lactic Acid and Ethanol with/without Pervaporation Daniel J. Benedict,†,‡ Satish J. Parulekar,*,† and Shih-Perng Tsai‡ Department of Chemical and Environmental Engineering, Illinois Institute of Technology, Chicago, Illinois 60616, and Energy Systems Division, Argonne National Laboratory, Argonne, Illinois 60439

Reactors coupled with membrane separation, such as pervaporation, can help enhance the conversion of reactants for thermodynamically or kinetically limited reactions via selective removal of one or more product species from the reaction mixture. An example of these reactions is esterification of carboxylic acids and alcohols. Esterification of lactic acid (C3H6O3) and ethanol (C2H5OH) is studied in well-mixed reactors with/without a solid catalyst (Amberlyst XN-1010) in this paper. Rate expressions for homogeneous and heterogeneous esterification are obtained from the experimental data using differential and integral methods. Experiments with a closedloop system of a “batch” catalytic reactor and a pervaporation unit reveal that fractional conversions of the two reactants and yield of ethyl lactate exceeding the corresponding maximum values in a reaction-only operation are obtained by stripping of the byproduct (water). The efficacy of pervaporation-aided esterification is illustrated by the substantial gains in fractional conversion of each reactant. A protocol for recovery of ethyl lactate from pervaporation retentate is proposed. Simulations based on empirical correlations for kinetics of esterification and pervaporation reveal the trends observed in experiments. 1. Introduction In recent years, there has been an increasing effort to combine downstream/upstream separation with reaction to improve the process performance. In this regard, membrane technology has emerged as one of the viable separation processes. Because membranes allow selective permeation of a component from a multicomponent mixture, membrane reactors can help to enhance the conversion of reactants for thermodynamically or kinetically limited reactions via selective removal of one or more product species from the reaction mixture. When multiple reactions are involved, the yield or selectivity of a desired product can be enhanced by controlled addition of one or more reactants and/or removal of one or more intermediates. Use of permselective membranes that are integrated into the reactor (the reactor walls composed of a membrane, the so-called membrane reactor) can permit this. Examples of processes where such an enhancement in yield/selectivity can be accomplished include a variety of consecutive-parallel reactions where an intermediate is the desired product. Several studies have been conducted on membrane reactors applied to gas-phase reactions such as catalytic dehydrogenation, hydrogenation, and decomposition reactions.1-8 However, much less work has been done on liquid-phase reactions because of a lack of suitable membranes with good permselectivity and solvent resistance. Pervaporation, a membrane process specially suited for organic-water and organic-organic separations,9-13 is an ideal candidate for enhancing conversion in reversible condensation reactions, generating water as * To whom correspondence should be addressed. Tel.: (312) 567-3044. Fax: (312) 567-8874. E-mail: [email protected]. † Illinois Institute of Technology. ‡ Argonne National Laboratory.

a product. Pervaporation is used to separate a liquid mixture by partly vaporizing it through a nonporous permselective membrane.10,11 The “feed” liquid mixture is allowed to flow along one side of the membrane, and a fraction of it, the “permeate”, is recovered in the vapor state on the other side of the membrane. The permeate is kept under vacuum by continuous pumping or is purged with a stream of carrier gas. Maintaining a low vapor pressure on the permeate side, eliminating thereby the effect of osmotic pressure, induces mass transport through the membrane in this process. The permeate is finally obtained in a liquid state after condensation. The permeate is enriched in the more rapidly permeating component of the feed mixture, whereas the remainder of the feed that does not permeate through the membrane, the “retentate”, is depleted in this component.11 Although the concept of using pervaporation to remove byproduct species dates back to the 1960s,14 only recently has this membrane process proven to be a viable separation technique. One example of condensation reactions is esterification of carboxylic acids and alcohols. Esterification reactions are characterized by thermodynamic limitations on conversion. To achieve a high ester yield, it is typical to use a large excess of one of the reactants, usually alcohol, or follow the reaction by distillation to remove in situ product(s) to drive the equilibrium to the ester side.15 While employing a large excess of one reactant leads to a higher cost of subsequent separations to recover the unused reactant, reactive distillation has several pitfalls, which have been outlined by Feng and Huang.13 Pervaporation-aided reactors are attractive in this regard because, being a rate-controlled separation process, the separation efficiency in pervaporation is not limited by relative volatility as in distillation, the energy consumption in pervaporation is low, and it can be carried out at a temperature that is optimal for the

10.1021/ie020850i CCC: $25.00 © 2003 American Chemical Society Published on Web 05/01/2003

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Figure 1. Schematic of the reaction-pervaporation system employed for homogeneous/heterogeneous esterification with/without pervaporation.

reaction. This last feature is particularly important for enzymatic esterification, where enzyme stability considerations impose severe restrictions on the operating temperature. Pervaporation-aided reactors have been used for esterification of carboxylic acids, such as acetic, erucic, oleic, propionic, tartaric, and valeric acids, and alcohols, such as benzyl alcohol, butanol, cetyl alcohol, ethanol, methanol, and propanol, with various acids or enzymes as catalysts.16-27 Substantial acceleration of these reactions can be achieved using appropriate commercially available solid catalysts. The increasing interest in pervaporation-aided esterification is also revealed by theoretical studies in the past few years.13,24-29 With this in mind, esterification of lactic acid (C3H6O3) and ethanol (C2H5OH) is studied in well-mixed batch reactors with/without a solid catalyst (Amberlyst XN1010) in this paper. Lactic acid is an important intermediate in glucose metabolism in most living systems. Rate expressions for homogeneous and heterogeneous esterification are obtained from the experimental data using differential and integral methods. The equilibrium conversion for this mildly exothermic reaction decreases with increasing temperature. Experiments with a closedloop system of a “batch” catalytic reactor and a pervaporation unit reveal that fractional conversions of the two reactants and a yield of ethyl lactate exceeding the corresponding maximum values in a reaction-only operation are obtained by stripping of the byproduct (water). The efficacy of pervaporation-aided esterification is illustrated by the substantial gains in fractional conversion of each reactant. A protocol for the recovery of ethyl lactate from pervaporation retentate is proposed. Simulations based on empirical correlations for kinetics of esterification and pervaporation reveal the trends observed in experiments. 2. Experimental Section 2.1. Reaction-Pervaporation System. The schematic of the reaction-pervaporation system is presented in Figure 1. Two reactors with volumes of the reaction mixture of 2 and 5 L were employed in all experiments. The 2 L reactor contained four spinning baskets [diameter ) 1.5 in., length ) 2.5 in., 400 mesh stainless steel

(SS) screen], each capable of holding up to 40 g of catalyst. The 5 L SS stirred contained solids reactor (SCSR) contained four spinning baskets (diameter ) 1.5 in., length ) 6.5 in., 400 mesh SS screen), each capable of holding up to 100 g of catalyst. Each reactor was heated with two resistance heaters clamped around the reactor. The process streams were well insulated with fiberglass insulation tape and foam pipe wrap. A magnetically coupled, explosion-proof centrifugal pump was employed to introduce the reactor feed. The reactor temperature was monitored by a T-type thermocouple and controlled by a proportional-integral-derivative controller. The reactor pressure was maintained with a silicon-braided Teflon-packed bearing mounted on the reactor head and was monitored by glycerin-filled pressure gauges. A bag filter (10 µm) was installed between the reactor and the pervaporation test cell, and a cold trap was placed between the test cell and the vacuum pump. The pervaporation membrane employed in the present study, a GFT-1005 membrane (Deutsche Carbone AG), is an organic acid-compatible, poly(vinyl alcohol)-based dehydration membrane. The pervaporation of water was accomplished by applying a vacuum on the permeate side of the pervaporation module by a 10-3 Torr vacuum pump. The permeate pressure was monitored by a 10-4 Torr vacuum transducer, which was connected to a digital vacuum indicator/controller. Permeate was condensed and collected in two 20 mL impingers at cryogenic temperatures with liquid nitrogen (-185 °C), with the permeate stream being well insulated between the pervaporation module and the impingers. During reaction-only (homogeneous or heterogeneous reaction) operation, the pervaporation module was bypassed. For conduct of the homogeneous reaction, the catalyst baskets were removed from the reactor. 2.2. Materials. Concentrated lactic acid (in water) is miscible in ethanol and hence suitable for esterification. The starting materials used in this study, therefore, were 88% (w/w; in water) lactic acid and anhydrous ethanol. Lactic acid and ethyl lactate (used as the product standard) were acquired from Aldrich Chemical, while ethanol was obtained from AAPER Chemical. Amberlyst XN-1010 (Rohm and Haas), a polymeric

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cation exchanger, was employed as the catalyst. Amberlyst XN-1010 is poly(styrenesulfonic acid) (PSSA) cross-linked with divinylbenzene. The key characteristics of the catalyst were density ) 5.29 g/mL, surface area ) 540 m2/g, particle size ) 0.2-1.2 mm, and maximum operating temperature ) 120 °C. 2.3. Analytical Procedures. Two 5 mL samples were withdrawn at each sampling instant. One sample was immediately cryofrozen (-185 °C) to stop the reaction in the sample and then transferred to a laboratory freezer (-80 °C). The frozen sample was later analyzed to estimate the concentrations of ethanol, ethyl lactate, and water using a gas chromatograph (GC). The second 5 mL sample was cooled to ambient temperature in a water bath and immediately analyzed to determine the density of the reaction mixture and lactic acid concentration. The former was determined by accurate and direct measurement of the mass and volume of each sample. The latter was determined by titration with 0.1 M NaOH after a 10-fold dilution of the sample with deionized water. All titrations were performed in triplicate. A Shimadzu GC-14A GC equipped with an AOC-1400 autosampler and an AOC-17 autoinjector was utilized to estimate concentrations of ethanol, ethyl lactate, and water in the reaction mixture. The GC had a thermal conductivity detector (TCD) in series with a flame ionization detector (FID) and was connected to a CR 501 Chromtopac integrator. The TCD and FID were connected to a Supelco 30 m capillary column. The autoinjector was fitted with a 0.5 µL SGE syringe, with the injection volume being 0.4 µL. Both FID and TCD utilized 99.999% pure helium as the carrier and reference gas, with 99.999% pure hydrogen and dry air being the flame sources for the FID. A carrier gas scrubber and carrier gas indicator were installed to eliminate the possibility of oxygen or water entering the chromatography column and causing oxidation of the gold-coated tungsten TCD filaments. The chromatography column (length ) 30 m, o.d. ) 0.32 mm, and film thickness ) 0.25 µm) was a water-tolerant Supelcowax 10, bondedphase medium-polarity poly(ethylene glycol) capillary column. A 1 m guard column was installed at the inlet to the capillary column to trap nonvolatile species such as lactic acid and protect the column from contamination. All reaction samples were analyzed by GC in quadruplicate by splitting each sample into two vials and setting the autoinjector for 2 injections per sample vial. Acetone was the internal standard (IS), and all calibration standards and all reaction samples were diluted 1:1 with IS. Acetone vials were placed between all sample vials to ensure that no residuals remained in the injector port or the column and that all samples were analyzed at the same conditions. 3. Results and Discussion 3.1. Homogeneous Esterification. The reaction under consideration is esterification of lactic acid (A) and ethanol (B) to generate ethyl lactate (C) and water (D).

A+BaC+D

(1)

The results from a batch homogeneous esterification experiment conducted at 95 °C in a pressurized closedloop system are presented in Figure 2. The phase portraits in Figure 2b reveal that the independent

Figure 2. Results from a batch homogeneous esterification experiment conducted at 95 °C. The concentrations of lactic acid (A), ethanol (B), ethyl lactate (C), and water (D) in the initial reaction mixture were 5.95, 6.37, 0.0, and 5.31 mol/L, respectively, and the initial reactor volume was 2 L. (a) Concentration profiles of lactic acid (A, [), ethanol (B, 9), ethyl lactate (C, 2), and water (D, b). (b) Phase portraits of CA and CB ([), CA and CC (9), and CA and CD (2). The straight lines denote the stoichiometric relations between CA and CJ (J ) B-D), viz., CJ ) CJ0 + νJ(CA0 CA), νJ ) -1 for J ) B and 1 for J ) C and D. Table 1. Additional Results from the Homogeneous Batch Esterification Experiment Conducted at 95 °C Large-Time Data ∆G ) -3.16 kJ/mol

K ) 2.810 789

XAe ) 0.522

Estimations of k1 and k2 (L/mol‚s) differential method k1 ) 8.361 × 10-6 k2 ) 2.975 × 10-6 integral method k1 ) 8.527 × 10-6 k2 ) 3.034 × 10-6

measurements of the concentrations of the four species participating in the esterification reaction essentially follow the appropriate stoichiometric relations. The various indicators for the chemical equilibrium for this reaction at this temperature, viz., equilibrium conversion of the stoichiometrically limiting reactant (lactic acid in the present case), equilibrium coefficient, and the Gibbs free energy change for the reaction, were obtained from the large-time data (Table 1). A candidate rate expression for this process is

(

r ) k1 CACB -

k1 1 C C , K) K C D k2

)

(2)

Both differential and integral methods of analysis of the

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experimental data were employed to estimate the kinetic coefficients k1 and k2 (Table 1). For the integral method, one needs to use the integrated version of the mass balances, which for the case of a single reaction carried out in a batch reactor under consideration here has the form

dXA CA ) r, XA ) 1 dt CA0

(3)

[ ]

and the following integral form30

2RXA qk1 β-q , , m) y ) mt, y ) ln 2RXA K 1+ β+q 1+

R ) CA0(K - 1),

β ) -[K(CA0 + CB0) + CC0 + CD0],

(

γ ) KCB0 -

)

CC0CD0 , q2 ) β2 - 4Rγ g 0 (4) CA0

In the differential method, the concentrations of the four species were expressed as polynomials in time and linear regression was employed to identify optimal k1 and k2.31 The consistency of the estimations is indicated by the less than 2% difference in the estimation of k1 and k2 by the two methods and the closeness of K values estimated from the differential method and the largetime behavior of the reaction process (Table 1). The validity of the rate expression in eq 2 was confirmed by the use of the integral method (eq 4). 3.2. Heterogeneous Esterification. The results from heterogeneous batch esterification experiments conducted at 75, 85, and 95 °C are presented in Figure 3. For the sake of brevity, profiles of only the desired product, ethyl lactate, are presented. The concentration profiles of the four species nearly followed the stoichiometric relations CJ ) CJ0 + νJ(CA0 - CA) with νB ) -1 and νC ) νD ) 1. The profiles of A and B thus were nearly parallel to each other, and the same was true for profiles of C and D (data not shown). A comparison of the profiles of CC in Figures 2 and 3 for T ) 95 °C reveals that the catalyst promotes esterification of ethanol and lactic acid as anticipated. This comparison also reveals a slower initial increase in CC in experiments with solid catalyst. The slower increase is attributable to the lags associated with heating of the reaction mixture and the catalyst to reaction temperature and wetting of the catalyst. An increase in the temperature leads to accelerated esterification as anticipated (Figure 3). The various indicators for the chemical equilibrium for the reaction process at these temperatures, obtained from the large-time data, are provided in Table 2. In a heterogeneous catalytic reaction process employing porous catalysts, the rate of an individual reaction is influenced by the following processes, which occur in series and parallel: external transport (from the bulk liquid to the external surface of the catalyst), intraparticle transport (porous diffusion), and the kinetics of reactions at the catalyst surface (adsorption/desorption and surface reaction steps). When either or both of the transport processes are the slower steps, the observed rate of reaction reflects the rate of a transport process

Figure 3. Concentration profiles of ethyl lactate in batch (heterogeneous) esterification experiments conducted at 75, 85, and 95 °C. The mass of the 5% (w/w) acid Amberlyst XN-1010 was 156.8 g, and the reaction volume and agitation speed for the catalyst assembly were 5 L and 98 rpm, respectively. The initial concentrations of lactic acid (A), ethanol (B), ethyl lactate (C), and water (D) were (mol/L): CA0 ) 4.5, CB0 ) 5.688, CC0 ) 0.0, and CD0 ) 5.14 at 75 °C, CA0 ) 5.95, CB0 ) 6.794, CC0 ) 0.0, and CD0 ) 5.947 at 85 °C, and CA0 ) 5.8, CB0 ) 6.668, CC0 ) 0.0, and CD0 ) 5.502 at 95 °C. The symbols 2, 9, and [ refer to data from experiments conducted at 75, 85, and 95 °C, respectively. Table 2. Results from the Heterogeneous Batch Esterification Experiments Conducted at 75, 85, and 95 °Ca T (°C) 75 85 95

XAe

K

0.557 3.023 366 0.534 2.884 329 0.535 2.781 769

k ∆G [L/(kg of KA (kJ/mol) catalyst)‚min] (L/mol) -3.201 -3.153 -3.130

0.3381 0.4137 0.6014

a (L/mol)

1.1515 0.380 861 0.8031 0.278 427 0.5603 0.201 429

a The initial reactor compositions for these experiments are listed in the legend for Figure 3. K ) exp(-∆G/RT).

and may be disguised as the reaction kinetics at the catalyst surface. Only experiments where the transport processes are not rate limiting must be considered for estimation of the true kinetics of catalytic reactions. Whether or not the transport processes are rate limiting can be determined using a variety of criteria already reported and widely used.30 The Weisz-Prater criterion32 is especially suitable at the stage of estimation of the kinetics of a catalytic reaction when the exact form of the rate expression is unknown. For example, the significance of external mass transport can be examined by comparing the concentration of a species in the bulk fluid (CJ, measured) to that at the external surface of the catalyst (CJs, estimated). For the reaction under consideration, mass balances around a catalyst particle lead to the following relations:

ψJ )

CJs Lrj ) 1 + νJ , J ) A-D, CJ kmJCJ 1 L rj ) r′Fc dz, νA ) νB ) -1, νC ) νD ) 1, L 0 R L) for a spherical catalyst (5) 3

∫

with rj being the experimentally observed reaction rate. The significance of the intraparticle mass transport can

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be estimated by evaluating the Weisz modulus (an observable)

ΦJ )

jrL2 , J ) A-D DeJCJ

(6)

The closeness of ψJ to unity implies that the external mass-transfer resistance is negligible, while ΦJ , 1 implies that the intraparticle mass-transfer resistance is negligible. For the results presented in Figure 3, throughout each experiment, ψJ’s (J ) A-D) were found to be near unity and ΦJ’s much less than unity. For example, for lactic acid (J ) A), at the three temperatures studied, the maximum value of ΦA was found to be 0.0201 (T ) 95 °C) and the minimum value of ψA was 0.9859 (T ) 85 °C).33 It is, therefore, evident that extraparticle and intraparticle transport resistances were minimal in these experiments and the observed kinetics represented the true kinetics of the catalytic reaction. Candidate rate expressions for the reaction in eq 1 based on single-site mechanisms34 were tested next to identify expression(s) that adequately represent the experimental data. Using differential method in conjunction with the linear regression method to analyze the data gathered in batch experiments, it was deduced that the rate expression that satisfactorily describes the experimental data has the following form (a, k, and K being functions of temperature):

r′ )

(

1 C C K C D CB + aCCCD

)

k CACB -

(7)

The values of the kinetic parameters in eq 7 at the three temperatures are reported in Table 2. From the denominator on the right-hand side of eq 7, it should be evident that adsorption of A (lactic acid) must be the rate-determining step in the single-site mechanism and the reaction products, ethyl lactate and water, are not adsorbed (or adsorbed insignificantly) onto the catalytically active sites. The reaction mechanism can thus be described as (r′ ) rA ) rsr)

(

A + S a AS, rA ) kA CACS AS + B a C + D + S,

(

rsr ) ksr CASCB -

)

CAS KA

(8a)

)

1 C C C (8b) Ksr C D S

For ksr . kA, the driving force for the surface reaction (8b) can be considered to be negligible, which upon using the active sites balance (Ct ) CS + CAS) leads to expression (7) with a ) KA/K and k ) kACt. The variations in the equilibrium coefficients for adsorption of lactic acid (KA) and the overall esterification reaction (K) and the kinetic coefficient k for the catalytic reaction with variation in temperature can be described by the van’t Hoff and Arrhenius relations, viz.,

∆HA ∆HR d d , , {ln K} ) {ln KA} ) 2 dT dT RT RT2 d E (9) {ln k} ) dT RT2

Figure 4. Determination of the activation energy and the heat of reaction for the catalytic reaction and the enthalpy of adsorption of lactic acid based on the data reported in Table 2. The symbols 9, [, and 2 denote the values of k, K, and KA, respectively, at the three temperatures.

From Figure 4, it can be deduced that, in the narrow temperature range under investigation, the heat of esterification reaction and the enthalpy of adsorption of lactic acid are invariant, with the values of these and other pertinent parameters for the catalytic reaction being reported in Table 3. The esterification of lactic acid and ethanol, therefore, is a mildly exothermic reaction, while adsorption of lactic acid is substantially more exothermic. 3.3. Heterogeneous Esterification with Pervaporation. The results from an experiment conducted at 95 °C, with the initial reaction mixture (5 L in volume) containing lactic acid, ethanol, and water in the molar ratios 1.00:2.348:1.1044 and being devoid of ethyl lactate, are presented in Figure 5. The agitation rate for this experiment was set at 48 rpm, the amount of catalyst used was 200 g, and the withdrawal rate from the reactor in the recirculation loop was kept at 2 gal/ min. With both reactants and both products remaining in the reaction phase, the fractional conversion of the stoichiometrically limiting reactant (lactic acid for the initial composition under consideration) at equilibrium can be deduced to be 0.714. The equilibrium conversion of lactic acid is obtained as per solution of the following:

NJ0 , NA0 J ) B-D (10)

K(1 - XA)(θB - XA) ) (θC + XA)(θD + XA), θJ )

with θB ) 2.348, θC ) 0, and θD ) 1.1044 in the present case. In the absence of stripping of one or both products from the reaction mixture, the equilibrium conversion represents the upper limit on the fractional conversion of the stoichiometrically limiting reactant. Throughout this experiment, variation in the density of the reaction mixture was insignificant. One can deduce that the reactor volume decreased with time because of the removal of water from the reaction mixture by pervaporation. Because the flux of water through the pervaporation membrane was not monitored in this experiment, estimation of the variation in the reactor volume with time is not possible. Nevertheless, a conservative estimate of the fractional conversion

Ind. Eng. Chem. Res., Vol. 42, No. 11, 2003 2287 Table 3. Thermokinetic Parametersa for Esterification of Lactic Acid and Ethanol Using Amberlyst XN-1010 Catalyst E ) 30.54 kJ/mol ∆HA ) -38.37 kJ/mol a

k0 ) 1.257 × 104 L/(kg of catalyst)‚min KA0 ) 2.02 × 10-6 L/mol

∆HR ) -4.441 kJ/mol

k ) k0 exp(-E/RT), and KA ) KA0 exp(-∆HA/RT).

Figure 5. Concentration profiles of lactic acid (A, ]), ethanol (B, 0), ethyl lactate (C, 4), and water (D, b) in a heterogeneous esterification with pervaporation experiment conducted at 95 °C. The mass of the 10% (w/w) acid Amberlyst XN-1010 was 200 g, and the reaction volume and agitation speed for the catalyst assembly were 5 L and 48 rpm, respectively. The concentrations of lactic acid, ethanol, ethyl lactate, and water in the initial reaction mixture were 4.31, 10.12, 0.0, and 4.76 mol/L, respectively.

of the stoichiometrically limiting reactant (XAL) can be obtained as

XA ) 1 -

(

)

NA CAV CA ) 1g XAL, XAL ) 1 NA0 CA0V0 CA0 (11)

On the basis of the last sample (at 81.65 h), XAL can be estimated to be 0.9855 (i.e., XA > 0.9855 at 81.65 h). It is evident that the fractional conversion in excess of the equilibrium conversion attainable in a reactor without product separation can be attained when one of the products (water) is selectively removed from the reaction mixture by pervaporation. As anticipated, the stripping of water pushes the equilibrium conversion very close to unity, demonstrating the efficacy of pervaporationaided esterification. The results from another experiment conducted at 95 °C, with ethanol being in excess in the initial reaction mixture, are presented in Figure 6. The composition of the initial reaction mixture was (concentrations in mol/ L) as follows: lactic acid, 5.76; ethanol, 6.93; water, 7.00; ethyl lactate, 0.0. A total of 5% (w/w) acid Amberlyst XN-1010 catalyst (amount ) 62.7 g) was added in the catalyst baskets, which were rotated at 98 rpm. The initial reaction mixture was 2 L in volume with a density of 1.036 kg/L, and the withdrawal rate from the reactor in the recirculation loop was 3.3 gal/min. Throughout this experiment, variation in the density of the reaction mixture was insignificant. At 95 °C and for the initial composition under consideration, with both reactants and products remaining in the reaction phase, the fractional conversion of lactic acid at equilibrium is 0.522 (eq 10). As discussed earlier, the reactor volume decreased with time owing to the selective removal of water by pervaporation. A

Figure 6. Concentration profiles of lactic acid (A, [), ethanol (B, 9), ethyl lactate (C, 2), and water (D, b) in a heterogeneous esterification with pervaporation experiment conducted at 95 °C. The mass of the 5% (w/w) acid Amberlyst XN-1010 was 62.7 g, and the reaction volume and agitation speed for the catalyst assembly were 2 L and 98 rpm, respectively. The concentrations of lactic acid, ethanol, ethyl lactate, and water in the initial reaction mixture were 5.76, 6.93, 0.0, and 7.0 mol/L, respectively.

conservative estimate of the fractional conversion of lactic acid is provided by XAL (defined in eq 11), which at the end of the experiment under consideration was 0.712. If the reaction is carried out sufficiently longer, near total utilization of lactic acid can be accomplished. The efficacy of pervaporation-aided esterification in increasing the equilibrium conversion of lactic acid is once again evident from these results. The phase portrait of the flux of water through the pervaporation membrane and the concentration of water on the feed side of the pervaporation unit (i.e., in the reactor) for this experiment is shown in Figure 7. The flux of water was correlated to the concentration of water on the feed side of the pervaporation membrane (i.e., in the reaction mixture) as

JD ) R1CDβ1, R1 ) 0.508, β1 ) 1.1242 (R1 and β1 at 95 °C) (12) with JD in kg/m2‚h and CD in mol/L. The high water flux in this experiment results from the high flow rate of the reaction mixture (increased turbulence) on the feed side of the pervaporation unit, higher operating temperature (95 °C) for the same (better adsorption of water by the membrane), and low permeate pressure (3.3 Torr; increased driving force for water transport across the membrane). For each time interval between consecutive samples, the flux of water was obtained as the ratio of the mass of water collected on the permeate side to the product of the membrane area and time interval. The value thus obtained is the average flux in that time interval. The flux of water through a pervaporation membrane is anticipated to depend on the operating temperature, with pervaporation being promoted with increasing

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Figure 7. Pervaporation flux profile in a semibatch heterogeneous esterification with pervaporation experiment conducted at 95 °C. The mass of the 5% (w/w) acid Amberlyst XN-1010 was 62.7 g, and the reaction volume and agitation speed for the catalyst assembly were 2 L and 98 rpm, respectively. The withdrawal rate from the reactor in the recirculation loop was 3.3 gal/min. The concentrations of lactic acid, ethanol, ethyl lactate, and water in the initial reaction mixture were 5.76, 6.93, 0.0, and 7.0 mol/L, respectively.

temperature. Pervaporation experiments with deionized water were conducted at different temperatures using the GFT-1005 membrane to estimate the apparent activation energy for pervaporation (Ep). From a plot of ln(JD) versus 1/T, Ep was estimated to be 53.652 kJ/ mol (data not shown).33 3.4. Recovery of Ethyl Lactate from the Pervaporation Retentate. Ethyl lactate can be removed from the pervaporation retentate by distillation. The transfer of ethanol accompanies the transport of ester from the liquid phase to the vapor phase. Mixtures of alcohols and esters are commonly known to form azeotropes. Some examples are methanol-methyl acetate, methanol-ethyl acetate, ethanol-ethyl acetate, and 1-butanol-butyl acetate. Azeotrope formation is not desirable because breaking an azeotrope increases considerably the downstream processing cost. The vaporliquid equilibrium (VLE) of mixtures of ethanol and ethyl lactate was, therefore, investigated at atmospheric pressure to examine if this binary system results in azeotrope formation. The results of the VLE study of ethanol-ethyl lactate are presented in Figure 8 and do not indicate azeotrope formation. Conventional distillation is, therefore, adequate to separate and recover ethyl lactate from the pervaporation retentate. On the basis of the results of the VLE study, a threestep vacuum distillation is utilized to separate ethanol and ethyl lactate from the pervaporation retentate. In the first step, the majority of ethanol (more volatile component) and some ethyl lactate (less volatile component) is recovered as distillate. In the second step, the remainder of ethanol and a large portion of ethyl lactate are obtained as distillate. The distillate from the third step is exclusively ethyl lactate. The information on the suggested operating parameters and the resulting distillate composition in the three steps is provided in Table 4. 3.5. Simulation for Pervaporation-Aided Esterification. The information on the kinetics of catalytic esterification (eq 7) and pervaporation of water (eq 12) is used next to simulate the performance of an esteri-

Figure 8. VLE diagram of ethanol (1) and ethyl lactate (2) at constant pressure (760 Torr) demonstrating no azeotrope formation. X1 and Y1 represent mole fractions of ethanol in the liquid and vapor, respectively. The temperatures at which VLE were established for ethanol mole fractions (X1) of 0.0, 0.022, 0.026, 0.082, 0.2, 0.331, and 1.0 were 154, 150, 148, 138, 121, 99, and 78 °C, respectively. Table 4. Distillation Parameters for Recovery of Ethyl Lactate (EtLac) from the Pervaporation Retentate (P, Pressure; Tb, Boiling Temperature; Tv, Vapor Temperature) first fraction second fraction third fraction

Tb ) 40-90 °C, P ) 25 Torr, Tv ) 65 °C (90% EtOH, 10% EtLac) Tb ) 96 °C, P ) 25 Torr, Tv ) 87 °C (75% EtLac, 25% EtOH) Tb ) 98-115 °C, P ) 25 Torr, Tv ) 89 °C (100% EtLac)

fication reactor coupled with a pervaporation system. The conservation equations for A-D and the total reaction mixture can be stated as

dNJ ) r′JW - FJ, NJ(0) ) NJ0, J ) A-D; FJ ) 0, dt d(FV) ) -FDMD, FD ) AmJD/MD; J ) A-C; dt -r′A ) -r′B ) r′C ) r′D ) r′ (13) In view of the stoichiometric relations in eq 13, the following relations can be obtained among the NJ’s (J ) A-D) and V.

NB ) NB0 - NA0 + NA, NC ) NA0 - NA, FV - F0V0 (14) ND ) ND0 + NC + MD Because the degrees of freedom for pervaporation-aided esterification is 2 (two independent rate processes), the number of linearly independent conservation equations in eq 13 is two. To simulate the performance of this system, it is, therefore, sufficient to solve an appropriate pair of conservation equations (one such pair being NA and the total mass of the reaction mixture, FV) in conjunction with relations (14). The results of simulation for pervaporation-aided esterification at conditions listed in Figure 6 (F ) F0 ) 1.036 kg/L and Am ) 0.0182 m2) are presented in Figure 9. The experimentally observed trends for concentrations of the four species (Figure 6) are revealed by the simulation. Any discrepancies between simulation re-

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the economic benefits of this process can be understood. Such an analysis, however, is beyond the scope of this paper. 4. Conclusions

Figure 9. Simulation results for heterogeneous esterification at 95 °C with pervaporation (solid curves) and without pervaporation (dashed curves) for conditions specified in the legend for Figure 6. (a) Profiles of XA and y ()V/V0). (b) Profiles of CA (lower solid and dashed curves) and CB (upper solid and dashed curves). (c and d) Profiles of CC and CD, respectively.

sults and experimental data are attributable in large part to an inability to precisely measure the flux of water through the pervaporation membrane. As mentioned earlier, the profile of flux of water was obtained as a piecewise constant function. This is an additional source for discrepancies between simulation results and experimental data. As was observed in the experiments (Figure 6), the simulation also predicts a maximum in the concentration of water. The results of simulation for esterification without pervaporation (FD ) JD ) 0) are also presented in Figure 9. In a reaction-only batch operation, the concentration of water (product) will increase with time (Figures 2a and 9d). When pervaporation is employed, the concentration of water in the reactor (operating in a semibatch mode) undergoes a maximum as a result of the effect of serial processes of production by reaction and removal by pervaporation. The rearranged form of the mass balance in eq 13 for water (D) shown in the following indeed reflects the two serial processes.

V

(

)

dCD CDMD ) r′W - FD 1 dt F

(15)

Water on the retentate side (reactor) in this case exhibits behavior typical of an intermediate in consecutive reactions. The simulations reveal that the esterification reaction can be driven to completion in a reactor coupled with a pervaporation unit. The maximum fractional reduction in the reactor volume, (V0 - V)/V0, corresponding to near complete conversion (XA ≈ 1) is 0.222. The technical feasibility of pervaporation-aided esterification for near total conversion of lactic acid to ethyl lactate has been demonstrated in this paper. It is anticipated that the benefits of increased production of the desired product (ester) in the separation-aided reaction process considered here will outweigh the costs associated with the additional equipment required, such as the pervaporation module and vacuum pump. A detailed cost-benefit analysis will be required before

Esterification of lactic acid and ethanol with/without solid catalyst and with/without pervaporation was studied in this paper. While the kinetics of homogeneous esterification resembles the kinetics for an elementary reversible reaction, for heterogeneous esterification, adsorption of lactic acid was deduced to be the ratedetermining step in the single-site mechanism, with ethyl lactate and water being adsorbed insignificantly onto the catalytically active sites. Fractional conversions in excess of the equilibrium conversion attainable in a reactor without product separation were attained by selective removal of water from the reaction mixture by pervaporation. Stripping of water pushes the equilibrium conversion very close to unity, demonstrating the efficacy of pervaporation-aided esterification. High water flux through the pervaporation membrane was obtained by maintaining a high recirculation rate for the reactor and a low permeate pressure. Pervaporation was promoted with increasing temperature. Conventional multistage distillation was adequate to separate and recover ethyl lactate from the pervaporation retentate because mixtures of ethanol and ethyl lactate are not prone to azeotrope formation. Simulations based on expressions for kinetics of esterification and pervaporation reproduced the trends observed in experiments. Acknowledgment This work was supported by the U.S. Department of Energy, Assistant Secretary for Energy Efficiency and Renewable Energy, under Contract W-31-109-Eng-38. D.J.B. was a recipient of a Laboratory Graduate Assistantship at Argonne National Laboratory. Nomenclature A ) lactic acid AS, S ) active sites occupied by A and vacant active sites, respectively Am ) membrane area (m2) a ) kinetic coefficient in eq 7 (L/mol) B ) ethanol C ) ethyl lactate CAS, CS ) concentrations of active sites occupied by A and vacant active sites, respectively CJ ) concentration of J (mol/L) CJs ) concentration of J at the external surface of a catalyst particle (mol/L) Ct ) total concentration of active sites D ) water DeJ ) effective diffusivity of J in the porous catalyst (cm2/ s) E ) activation energy for the kinetic group in a heterogeneous esterification reaction (kJ/mol) Ep ) activation energy for pervaporation (kJ/mol) FD ) molar flow rate of water through pervaporation membrane (mol/s) J ) species J JD ) flux of water through pervaporation membrane (kg/ m2‚h) K ) equilibrium coefficient for an esterification reaction KA ) equilibrium coefficient for adsorption of A (L/mol)

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k1, k2 ) kinetic coefficients for forward and reverse steps, respectively, in homogeneous esterification (L/mol‚s) k ) kinetic group in the rate expression for catalytic esterification [L/(kg of catalyst)‚min] kA, ksr ) kinetic coefficients for adsorption of lactic acid and surface reaction steps, respectively kmJ ) external mass-transfer coefficient for species J (cm/s) k0, KA0 ) provided in Table 3 [L/(kg of catalyst)‚min and L/mol, respectively] MD ) molecular weight of water (g/gmol) m, q, y ) defined in eq 4 NJ ) number of moles of J in the reactor (mol) R ) radius of the spherical catalyst particle (cm) R ) universal gas law constant (atm‚L/mol‚K) r ) rate of a homogeneous esterification reaction (mol/L‚s) rj ) volume-average reaction rate (experimentally observed) in the catalyst particle, defined in eq 5 (mol/L‚min) r′ ) rate of a heterogeneous catalytic reaction [mol/(kg of catalyst)‚min] r′J ) rate of formation of J by the catalytic reaction [mol/ (kg of catalyst)‚min] rA, rsr ) rates of adsorption of lactic acid and surface reaction, respectively [mol/(kg of catalyst)‚min] T ) absolute temperature (K) t ) time (h or s) V ) reactor volume (L) XA ) fractional conversion of A, defined in eq 3 XAL ) conservative estimate of XA, defined in eq 11 Greek Symbols R, β, γ ) defined in eq 4 R1, β1 ) parameters in eq 12 ∆G ) Gibbs free energy change for an esterification reaction (kJ/mol) ∆HA, ∆HR ) heats of adsorption of lactic acid and an esterification reaction, respectively (kJ/mol) ∆SR ) entropy change associated with an esterification reaction (J/mol‚K) νJ ) stoichiometric coefficient of J, -1 for A and B and 1 for C and D ψJ ) defined in eq 5 φJ ) Weisz modulus, defined in eq 6 F ) density of the reaction mixture (kg/L) Fc ) density of the catalyst particle (kg of catalyst/L) θJ ) defined in eq 10 for J ) B-D Subscripts e ) chemical equilibrium J ) species J 0 ) initial condition (t ) 0)

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Received for review October 28, 2002 Revised manuscript received March 20, 2003 Accepted March 20, 2003 IE020850I