Enzymatic Production of Decyl Acetate: Kinetic Study in - American

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Ind. Eng. Chem. Res. 2010, 49, 7168–7175

Enzymatic Production of Decyl Acetate: Kinetic Study in n-Hexane and Comparison with Supercritical CO2 Adriano S. Ribeiro,† Manuela V. Oliveira,*,† Sı´lvia F. Rebocho,† Olga Ferreira,‡ Pedro Vidinha,§ Susana Barreiros,§ Eugeńia A. Macedo,† and Jose´ M. Loureiro† LSRE/LCM - Laboratory of Separation and Reaction Engineering, Faculdade de Engenharia da UniVersidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal, LSRE/LCM - Laboratory of Separation and Reaction Engineering, Departamento de Tecnologia Quı´mica e Biolo´gica, Instituto Politećnico de Bragança, Campus de Santa Apolońia, 5301-857 Bragança, Portugal, and REQUIMTE/CQFB, Departamento de Quı´mica, FCT, UniVersidade NoVa de Lisboa, 2829-516 Caparica, Portugal

The kinetics of the lipase-catalyzed synthesis of decyl acetate, by the transesterification reaction of vinyl acetate with decanol, was investigated at 30 °C using n-hexane as the solvent. Novozym 435 was found to be the most active catalyst among the immobilized lipases tested. Given the nonideality of the reaction mixture, only a thermodynamic activity-based kinetics was found to be suitable to represent the experimental data in the entire range of compositions tested (0.1-1.4 M). The reaction follows a ping-pong bi-bi mechanism, in which inhibition only by excess of alcohol was identified. Although intraparticle diffusional limitations were detected, intrinsic kinetic parameters were obtained by crushing the catalyst particles. The results were compared to those obtained with supercritical CO2 as the solvent. For the conditions tested, Candida antarctica lipase B showed higher activity in the organic medium. 1. Introduction Decyl acetate is a long-chain ester that finds applications in two major areas: the food and fragrance/cosmetic industries. Because this high-value-added product occurs naturally only in expensive oils that are not readily available in large amounts, it is economically important to develop production methods from cheaper and more broadly available raw materials, responding, at the same time, to market demands. The current preference for natural products has resulted in a significant increase in the market for flavors of biotechnological origin. In this field, enzymatic synthesis can play a major role because enzymes, as Nature’s catalysts, might provide a path to “natural” products. In fact, U.S. and EU legislation consider as natural the products resulting from enzymatic synthesis.1 Also, compared with the traditional chemical routes, the use of enzymes, such as lipases, as biocatalysts to produce this kind of high-value-added ester constitutes a more sustainable and environmentally friendly alternative: enzymatic synthesis requires lower reaction temperatures, presents higher selectivity, and offers easier downstream processing.2-4 Since the late 1980s, it has been well established that enzymes are active in organic media.3,4 Over the past decade, with the growing attention paid to these processes, ester synthesis by enzyme catalysis (particularly by lipases) in organic media has become a major area of research.2,5-14 Also, the use of supercritical fluids (SCFs), especially supercritical CO2 (sc-CO2), as nonaqueous solvents for enzyme-catalyzed reactions has been a fertile area of research.15-18 Several articles have suggested that an enzyme-catalyzed reaction in sc-CO2 provides superior results to those obtained in conventional organic solvents.19-21 Conversely, several reports also indicate that some enzymecatalyzed reactions perform better in organic solvents than in * To whom correspondence should be addressed. Tel.: + 351 225081672. Fax: +351 225081449. E-mail: [email protected]. † Universidade do Porto. ‡ Instituto Politećnico de Bragança. § Universidade Nova de Lisboa.

sc-CO2.22-24 High diffusion and mass-transfer rates, easy product recovery without a trace of solvent, and reduction of organic waste are some advantages of SCFs with respect to organic solvents. Attractive features of sc-CO2 also include nontoxicity, nonflammability, availability in large amounts at low cost, low environmental impact, and low critical temperature. Although sc-CO2-based systems present several benefits over organic-based ones, industry is always looking for practical applications, and factors such as low reaction rates, low volumetric productivities, and high plant costs can represent important obstacles to the industrial implementation of a process. In fact, many reactants have low solubilities in CO2, even under supercritical conditions,25 which directly limits the volumetric productivity and, at the same time, increases the plant “footprint”. This, combined with the fact that high-pressure equipment can be quite expensive, can lead to economic limits for enzymatic sc-CO2-based systems. In a previous work, we studied decyl acetate (DA) enzymatic synthesis under supercritical conditions, using sc-CO2 as the solvent. Novozym 435 (immobilized Candida antarctica lipase B) was used to catalyze the transesterification between decanol (DOH) and vinyl acetate (VA). Decanol concentrations above 0.18 M could not be used because of solubility limitations at 100 bar and 35 °C.18 This limitation, along with the relatively low observed reaction rates, might represent an important drawback for the industrial development of an sc-CO2-based process for the enzymatic production of decyl acetate. In this work, we investigated the same reaction but using n-hexane as the solvent. The major objective was to compare its efficiency, from kinetic and productivity points of view, with the sc-CO2-based system, to determine whether it could be more attractive for industrial application. Several commercial immobilized lipases were tested, and the influence of intraparticle diffusion was studied to access the presence of mass-transfer limitations. Intrinsic kinetic parameters were determined, assuming a ping-pong bi-bi mechanism with inhibition by the alcohol. It is shown that only a thermodynamic activity-based

10.1021/ie902026d  2010 American Chemical Society Published on Web 07/02/2010

Ind. Eng. Chem. Res., Vol. 49, No. 16, 2010

kinetic equation is able to describe the reaction process in n-hexane, because of the nonideality of the reaction mixture. The results are discussed with reference to the experiments performed in a previous work with sc-CO2 as the solvent.18 2. Experimental Section 2.1. Experiments in n-Hexane. All reactions were performed isothermally at 30 °C and atmospheric pressure, in magnetically stirred jacketed reactors with 100 mL capacity, using a reaction mixture volume of 40 mL and n-hexane as the solvent. The catalysts used were not subjected to any adjustment of the water content of the support. Because the reaction studied is irreversible, as long as the required time is provided, full conversions of the limiting substrate can always be attained. The presence of side reactions was ruled out because no additional peaks were detected in the chromatographic analysis, and the amount of decyl acetate formed was always consistent with the decrease in concentration of the limiting reactant. To assess whether the reaction could proceed in the absence of the catalyst, blank runs were also performed for 24 h, maintaining all conditions but without any catalyst, and no conversion was detected. 2.1.1. Catalyst. Novozym 435, Lipozym TL-IM, and Lipozym RM-IM were kindly provided by Novozymes. Amano PSC-I, Amano PSC-II, Amano PSD, Amano F-AP 15, Amano AYS, and Amano AK-20 were kindly provided by Amano Enzyme Inc. For each catalyst, the enzyme content was determined using the Lowry method26 with a preliminary desorption step as described elsewhere.18 In the case of Novozym 435, particles were sieved into three size groups, namely, 460, 360, and 240 µm, and the enzyme content was determined for each group. 2.1.2. Chemicals. Vinyl acetate, decanol, and decyl acetate were obtained from Sigma-Aldrich (>99 wt %). n-Hexane was purchased from Merck (pro-analysis). For the Lowry method, the following chemicals were used: sodium carbonate anhydrous (>99.5 wt %, Fluka), potassium sodium tartrate (>99 wt %, Riedel-de Hae¨n), copper(II) sulfate pentahydrate (>99 wt %, Riedel-de Hae¨n), sodium hydroxide (Pronolab), Folin-Ciocalteau reagent (Merck), and bovine serum albumin (SigmaDiagnostics). 2.1.3. Apparatus and Experimental Technique. In a typical experiment, the reaction mixture (VA, DOH, and n-hexane), previously prepared, was introduced in the reactor and heated to the desired temperature. Once the reaction temperature (30 °C) had been reached, the catalyst particles (previously weighted) were added, initiating the reaction (time zero). At given time intervals, 200 µL samples were withdrawn for analysis. The system volume (40 mL) was assumed to be constant during the reaction because the sampling volume could be considered negligible. The system was stirred using a magnetic bar that was padded with soft paper to prevent the otherwise observed crushing of the particles (especially the smallest size) as a result of the repeated shear from the bar. Although several other methods were tested to prevent the crushing of the particles, this was the one that gave the best results. In fact, by padding the bar, the collisions between the particles and the bar were softened, and the particles did not crush during the reaction. To ensure that the paper did not affect the reaction, a blank run was performed without the enzyme, and no conversion was detected. When particle crushing was necessary, it was performed either with a pestle (for small quantities) or with a magnetic stirrer bar. All experiments were performed in duplicate.

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Table 1. Enzymatic Content of the Catalysts Tested catalyst

enzymatic content (g of protein/g of particles)

Amano AK-20 Amano AYS Amano F-AP 15 Amano PSC-I Amano PSC-II Amano PSD Lipozym RM-IM Lipozym TL-IM Novozym 435

0.139 0.184 0.239 0.237 0.058 0.078 0.090

2.1.4. Sample Analysis. The samples were analyzed on a gas chromatograph (Varian CP 3800, Palo Alto, CA) equipped with a thermal conductivity detector (TCD) and an autosampler (Varian CP 8400). The compounds were separated in a column with a 25-m length, 0.53-mm inner diameter, and 0.25-µm film thickness (Varian CP-Wax 57 CB). Helium N60 (10 mL/min) was used as the carrier gas. The injector, detector, and oven temperatures were set at 270, 340, and 165 °C, respectively. Response factors were determined with synthetic mixtures of the pure components. All samples were analyzed in triplicate. 2.2. Experiments in sc-CO2. Experiments were performed in a variable-volume stainless steel batch reactor equipped with a sapphire window and with loading and sampling valves. Reactions were carried out isothermally at 35 °C and 100 bar and using a reaction mixture volume of ca. 15 mL. Novozym 435 was used as the catalyst with no adjustment of the water content of the support. More experimental details are given elsewhere.18 3. Results and Discussion The influence of several parameters, such as catalyst type, stirring speed, catalyst particle size, and initial concentration of substrates, was studied for the lipase-catalyzed synthesis of decyl acetate by the transesterification reaction of DOH with VA in n-hexane. 3.1. Enzyme Screening. Nine different immobilized enzymes were tested. Table 1 presents the enzyme content (mass of protein per unit mass of particle) obtained for each catalyst. The enzyme content of Amano PSC II and Amano PSD could not be determined by the method adopted, because the enzyme is covalently attached to the support. Figure 1 shows the initial reaction rates, r0, expressed both per mass of catalyst particles and per mass of enzyme, obtained with each catalyst for the reaction of VA and DOH in n-hexane at 30 °C at an equimolar initial concentration of 0.1 M of each substrate. Clearly, Novozym 435 is the most active catalyst toward the reaction: the initial reaction rate obtained with Novozym 435 is almost 3 times that obtained with Amano PSCII, the second most active catalyst. Candida antarctica lipase B (CALB), immobilized in the Novozym particles, is also the most active enzyme from among those for which the enzyme content could be determined. Novozym 435 was therefore selected for all subsequent work. 3.2. Evaluation of External Diffusion Limitations. To ensure the absence of external diffusion limitations in all experiments, the stirring speed was gradually increased until it had no influence on the evolution of the observed concentrations of the substrates (data not shown), which occurred for a stirring speed of around 350 rpm. This test was performed at 30 °C with a 0.1 M concentration of each substrate and 240-µm particles (the smallest particle size available). The smallest particle size was used to determine the adequate stirring speed, because it is the case that requires the strongest agitation.27,28

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Figure 1. Initial reaction rates obtained with the commercial immobilized enzymes tested: open bars, per unit mass of catalyst particle; black bars, per unit mass of enzyme. Equimolar initial concentrations of 0.1 M and 30 °C for all assays. Table 2. Enzymatic Content for Each Particle Size Group of Novozym 435 average particle enzymatic content fraction of support diameter (µm) (mg of protein/g of particles) with enzymea (% v/v) 460 360 240 a

92 108 125

70.9 81.6 95.6

Calculated based on a 77.6-µm enzyme shell.

If external diffusion limitations are negligible for the smallest particle size, then they will also be negligible for larger particles, when the same stirring speed is used. Similar values have been reported previously by other authors.29,30 To ensure a margin of safety, all subsequent experiments were performed at 500 rpm. 3.3. Evaluation of Internal Diffusion Limitations. As described in our previous work, Novozyme 435 catalyst particles present an egg-shell-type distribution; that is, the enzyme is located in an external shell of the particle, with the shell thickness being independent of the particle size and most likely depending only on the time for diffusion and the concentration of CALB in the immobilization solution, which can vary for each production batch. With this kind of enzyme distribution, the enzymatic content increases as the particle size decreases.18 As the production batch used in this work was different from that of our previous work, the enzymatic content was determined for each size group (Table 2). Based on these results, and because the production batch now used presents a higher specific enzymatic content, the enzyme shell thickness should then be higher. Applying the calculation procedure described in our previous work, we estimated, for the production batch used, an enzyme outer shell thickness of 77.6 µm, independent of the particle size, with an average error of ca. 2%. This value is indeed higher than the 60 µm reported before.18 Because the enzyme thickness is independent of the particle size, the diffusion path for substrates to access the enzyme active sites is the same regardless of the particle size, and internal mass-transfer resistances (if present) should also be the same. Figure 2 (open symbols) shows the results of three experiments performed under the same conditions, where only the particle size group was varied. The same amount of enzyme (but not of

Figure 2. Effect of particle size on the conversion as a function of time: (O) 460 µm, (0) 360 µm, (∆) 240 µm, (2) 240 µm crushed. Dotted curves are trend lines. Equimolar initial concentrations of 0.1 M, 2.76 mg of enzyme, and 30 °C for all assays.

catalyst particles) was used. For the 460- and 360-µm particles, the conversion curves overlapped, as expected, but an increase in the reaction rate was observed for the smaller 240-µm particles, although only after some time of reaction. Even with the magnetic bar padded with soft paper, after some time, it was difficult to avoid the crushing of some of the smallest particles (240 µm), and the results obtained might be due to that crushing, which might, by itself, indicate the presence of internal diffusion limitations. To further study this behavior and continue testing for the presence of internal diffusion limitations, 240-µm particles were crushed into a fine powder, and new reactions were performed with the same experimental conditions. The results obtained are shown in Figure 2 (solid symbols) and indicate a large enhancement of the reaction rate due to the consequent reduction of the particle size. Thus, internal diffusion limitations are indeed present when the reactions are performed with uncrushed particles. No such a behavior was found in experiments with sc-CO2 as the solvent,18 although it is worth mentioning that no experiments with crushed catalyst particles were performed because of experimental limitations: reproducible sampling turned out to be impossible with crushed particles. Figure 3 shows a comparison between the initial reaction rates obtained in n-hexane and in sc-CO2, with uncrushed particles, for equimolar initial concentrations of VA and DOH. With respect to mass-transfer limitations, two main conclusions can be drawn: (i) When using uncrushed particles, within each medium, internal mass-transfer resistances can be considered the same for the different particle sizes, which is in accordance to the egg-shell-type distribution reported for the Novozyme 435 particles.18 (ii) Internal mass-transfer resistances do exist in the case of n-hexane medium: the initial reaction rate almost triples when crushed particles are used. In the case of the sc-CO2, internal mass-transfer resistances, if present, should be lower than in n-hexane, because mass-transfer rates are expected to be enhanced by the SCF’s gaslike diffusivities and low viscosities. Another important conclusion from Figure 3 concerns the observed (uncrushed) initial reaction rate in each medium. Although being (more) limited by internal mass transfer, the reaction proceeds almost twice as fast in n-hexane as in sc-


Figure 3. Comparison between initial reaction rates obtained in n-hexane and in sc-CO2 for different particle sizes and equimolar initial concentrations of VA and DOH: 0.05 M in sc-CO2 and 0.10 M in n-hexane. n-hexane, 30 °C for all assays; sc-CO2, 35 °C and 100 bar for all assays.

Figure 4. Comparison between initial reaction rates obtained in sc-CO2 and in n-hexane for different equimolar initial concentrations of VA and DOH. n-hexane, 30 °C for all assays; sc-CO2, 35 °C and 100 bar for all assays.

CO2; however, the initial concentrations used (0.10 M in n-hexane/0.05 M in sc-CO2) are also twice their counterparts. Therefore, upon comparing the case of nearly identical initial concentrations (Figure 4, 0.10 M in n-hexane/0.092 M in scCO2), it can be seen that the reaction still proceeds faster (ca. 38%) in n-hexane than in sc-CO2. It is also important to notice that, for equimolar initial concentrations of 0.18 M (DOH solubility limit verified in sc-CO2 at 100 bar and 35 °C18), the initial reaction rate in sc-CO2 is only ca. 26% higher when compared to 80% lower equimolar initial concentrations (0.10 M) in n-hexane. Because the reaction is most likely less limited by rates of diffusion in sc-CO2 than in n-hexane, these results seem to indicate that the reaction is limited by intrinsic kinetics in sc-CO2; that is, the enzyme is less active in sc-CO2 than in n-hexane. One of the reasons for this might be the role that the water content of the support plays in each medium.31-35 It is known that enzymes need only a small amount of water to maintain their active conformation; on the other hand, an excessive water content have been reported to have negative effects on enzyme’s activity;31,32 that is, there is an optimum

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Figure 5. Volumetric productivity of decyl acetate that can be obtained in a batch reactor using sc-CO2 or n-hexane as the solvent.

value for the water content of the support, that might differ, for example, with the reaction medium and reaction conditions.31 As mentioned in the Experimental Section, the catalyst particles used in this work, both in n-hexane and in sc-CO2, were not subjected to any adjustment of the water content of the support (i.e., the supports were used as supplied). A comparison of water adsorption isotherms in sc-CO2 and n-hexane31 showed that scCO2 appears to be much more hydrophilic than n-hexane. Thus, even with similar initial water levels in the support, the water content in the vicinity of the enzyme will be lower in the scCO2 than in the n-hexane medium, which can lead to a more pronounced decrease in the enzyme’s activity in the supercritical medium. It is worth mentioning that the activities in both media could be improved with optimization of the solid water content. It is also obvious from Figure 4 that, for the tested conditions, operating in n-hexane enables a much faster reaction because much higher initial concentrations can be used than in sc-CO2. For example, with a 0.50 M equimolar initial concentration of substrates in n-hexane (and higher concentrations can be achieved), the initial reaction rate is 3 times higher than when using sc-CO2 as the solvent at the DOH solubility limit mentioned above (0.18 M).18 One advantage of using n-hexane as the solvent compared to sc-CO2 is the increase in the volumetric production, defined as kilograms of product per unit of reactor volume. Because the byproduct (vinyl alcohol) of the reaction between DOH and VA immediately tautomerizes to acethaldeyde, making the overall reaction irreversible, full conversions of the limiting substrate can always be attained. Therefore, with respect to volumetric productivity, the highest value in each medium is attained for equimolar initial concentrations, corresponding also to the highest purity because the substrates are completely consumed, and as no regeneration steps are needed to recover the unreacted reagents, costs are also reduced. Figure 5 shows the values of the volumetric productivity that are possible to obtain in each medium. The values presented are intended to represent two scenarios: (i) “typical” initial equimolar concentrations (0.10 M in n-hexane/0.05 M in sc-CO2) and (ii) limiting cases, that is, the solubility limit of DOH in sc-CO2 and 1.0 M when n-hexane is used as the solvent (i.e., the solvent represents ca. 70% v/v). Therefore, it is possible to obtain between 2 (typical) and 5.5 (limiting) times more ester production in n-hexane than in sc-CO2 with the same reactor volume.

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Figure 6. Comparison between initial reaction rates obtained in n-hexane and in sc-CO2 for different initial concentrations of one of the substrates: (a) n-hexane, DOH ) 0.1 M and 30 °C; sc-CO2, DOH ) 50 mM, 35 °C, and 100 bar. (b) n-hexane, VA ) 0.1 M and 30 °C; sc-CO2, VA ) 50 mM, 35 °C, and 100 bar.

Figure 7. Experimental (points) and simulated (lines) results for different reaction conditions. (O, - · · -) AV ) DOH ) 0.1 M, 1.0 mg of enzyme; (0, - · -) AV ) DOH ) 0.1 M, 2.0 mg of enzyme; (∆, - - -) AV ) DOH ) 0.1 M, 2.5 mg of enzyme; (], - - -) AV ) DOH ) 0.5 M, 2.5 mg of enzyme; (9, s) VA ) 1.0 M, DOH ) 0.1 M, 2.0 mg of enzyme; (b, s) AV ) 1.4 M, DOH ) 0.1 M, 2.0 mg of enzyme. Crushed particles and 30 °C for all assays. Simulated results calculated with concentration-based kinetic parameters.

3.4. Effect of Initial Concentration of Substrates and Products. With the aim of developing a kinetic model with n-hexane as the solvent, experiments with different initial concentrations of the substrates were performed. When necessary, to avoid the influence of internal mass transfer, 240-µm crushed particles were used. Experiments with an initial concentration of decyl acetate (0.02 and 0.05 M; data not shown) were also carried out, revealing no enzyme inhibition by the product and, consequently, a significantly larger affinity of the enzyme for the substrates. As verified for sc-CO2,18 the reaction was enhanced by higher concentrations of VA and inhibited when DOH was in excess (Figure 6), as a result of the competitive inhibition by the alcohol. Moreover, as shown in Figure 7 (solid symbols), when the initial concentration of DOH was fixed at 0.1 M and the initial concentration of VA was increased, the conversion curves

for VA concentrations of 1.0 and 1.4 M practically overlapped, indicating that, for VA concentrations above 1.0 M, the concentration of VA no longer influenced the reaction rate. Once again, the effect of mass-transfer resistance when operating with n-hexane can be observed in Figure 6. In the case of excess VA, the initial reaction rate with crushed particles was ca. 3 times higher than that with uncrushed particles, for all of the VA concentrations tested. For excess DOH, the behavior was different: the inhibition by higher concentrations of DOH was lower for uncrushed particles. For example, whereas an increase of 5 times in the concentration of DOH (from 0.1 to 0.5 M) resulted in a 43% reduction in the initial reaction rate for crushed particles, the inhibition was only 18% when uncrushed particles were used. This behavior is a consequence of intraparticle mass-transfer resistance because the concentrations reaching the enzyme active centers with uncrushed particles were lower than in the liquid bulk phase. Although experiments with sc-CO2 were run with uncrushed particles, the inhibition by excess DOH in this medium was quite similar to that observed in n-hexane with crushed particles, which might be an indication that the reaction is less limited by rates of diffusion in sc-CO2 than in n-hexane. For example, an increase of 3 times in the concentration of DOH in sc-CO2 (from 0.05 to 0.15 M) resulted in a 44% reduction in the initial reaction rate. 3.5. Intrinsic Kinetic Model. It was shown that the kinetics of the transesterification reaction of vinyl acetate with decanol can be satisfactorily described by a simplified form of the pingpong bi-bi mechanism with inhibition by the alcohol, with the reaction rate (r) being described in terms of concentrations by the equation18 r)

(

rmax

)

KDOH KVA [DOH] +1 1+ + [VA] KI_DOH [DOH]

(1)

where rmax is the maximum reaction rate; [VA] and [DOH] are the VA and DOH concentrations, respectively; KVA and KDOH are the Michaelis-Menten constants for VA and DOH, respectively; and KI_DOH is the competitive inhibition constant for DOH.


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37,39,40

Table 3. Concentration- and Activity-Based Intrinsic Kinetic Parameters for the Novozym 435 Catalyzed Transesterification Reaction of Vinyl Acetate with Decanol in n-Hexane at 30 °C parameter

concentration-baseda

activity-based

rmax KVA KDOH KI_DOH SSQ/Npointsb

0.909 mol genz-1 min-1 0.604 M 0.195 M 0.912 M 3.6 × 10-2 M2

0.542 mol genz-1 min-1 0.0862 0.0788 0.125 3.9 × 10-2 M2

a Data from experiments with equimolar initial concentrations of substrates were not included in the optimization; in this case, no set of parameters was found that could describe all of the experiments performed. b SSQ, sum of the squared residues; Npoints, number of data points.

The strategy described in our previous work18 was used to obtain the kinetic parameters of the reaction in n-hexane: (i) First, obtain initial estimates of the parameters; this was achieved by fitting the limiting cases when the concentration of one of the reactants was much larger than the concentration of the other, thus simplifying eq 1 by allowing some parameters to be eliminated. (ii) Then, fit all of the data at once (more than 100 data points were used in the optimization, covering a range from 0.1 to 1.25 M initial concentrations of each substrate), using as initial guesses the values obtained in the first step. The kinetic parameters were determined by fitting the model to the experimental data, through minimization of the sum of the squared residues, using a multivariable optimization technique with adaptive random search.36 To obtain intrinsic kinetic constants, only experiments with crushed particles were used in the optimization. The parameters values are presented in Table 3. Equation 1, a concentration-based kinetic equation, gave good results when the initial concentrations of both substrates were not the same, but failed to describe the reaction process when equimolar initial concentrations were used (Figure 7). In fact, the sum of the squared residues (SSQ) shown in Table 3 for the concentration-based model includes data only from experiments with nonequimolar initial concentrations of substrates because no set of parameters was found when data from experiments with equimolar initial concentrations were also included in the optimization. That is, the reported SSQ value accounts only for nonequimolar conditions, which are the only conditions for which the concentration-based model correctly describes the experiments. Although activity-based kinetic equations are rarely addressed for enzyme catalysis, they have received some attention,37-41 with the purpose of calculating kinetic parameters that are independent of the solvent used to perform the reactions. This would considerably reduce the experimental work required for both solvent selection and kinetic modeling and should be possible as long as the solvent does not interact with the active site of the enzyme and the several binding and unbinding steps

do not depend on the solvent. It has been shown that, although the dependence of kinetic parameters on the solvent is significantly reduced by this approach, some deviations still occur.40 One solvent-adapted parameter to account for the residual solvent effects was introduced by Sandoval et al.40 with satisfactory results. For a given solvent, the application of a thermodynamic activity-based kinetic equation is also relevant when the reaction mixture is highly nonideal and the activity coefficients of the substrates change significantly within the range of concentrations used. Because of the difference in polarity between DOH and the other components, the reaction mixture becomes nonideal. This nonideality is shown by the values of the liquid-phase activity coefficients, γ, that differ largely from unity for DOH and, to some extent, for VA (Table 4). The γ values were calculated by the modified UNIFAC model of Dortmund42 because, relatively to the original UNIFAC method, this model significantly improves the description of phase equilibria at lower concentrations, which is precisely the region where the concentration-based kinetic model fails to predict the experimental results. From Table 4, for all components, it is important to notice that (i) the variation of the γ values through the reaction is higher in the case of equimolar initial concentrations of substrates and (ii) the maximum γ values occur for equimolar initial concentrations of 0.1 M (i.e., the more dilute solution). This is consistent with some of the differences that were found between the experimental and predicted reaction rates for equimolar initial concentrations of 0.1 M. For equimolar initial concentrations of 0.1 M, the final γVA value is more than 1.5 times larger than that for the nonequimolar experiments, and for DOH, the difference is even higher (7.7 times larger than when its initial concentration is 1.3 M). This behavior is expected for polar components, such as alcohols or acids, when diluted in nonpolar solvents such as n-hexane. It is important to highlight also that, for equimolar initial concentrations, γDOH increases more than γVA. This difference is more pronounced for the equimolar initial concentrations of 0.5 M: Whereas γDOH increases by 157%, γVA increases by only 37%. Because the magnitude of the inhibitory effect depends on the DOH/VA activity ratio, the inhibition will become larger as the reaction proceeds. Equation 2 is the activity-based version of the ping-pong bibi kinetic equation with competitive inhibition by DOH r)

ramax

(

)

a a aDOH KDOH KVA 1+ a + +1 aVA aDOH KI_DOH

(2)

Table 4. Initial and Final Liquid-Phase Activity Coefficients at 30 °C for Different Initial Substrate Concentrations γDOH

γVA

γdecyl acetate

γacetaldehyde

γn-hexane

initial VA/DOH (M)

initial

finala

initial

finala

initial

finala

initial

finala

initial

finala

0.10:0.10 0.14:0.14 0.50:0.50 0.10:0.50 0.10:1.00 0.10:1.30 1.00:0.10 1.20:0.10

10.80 9.09 3.73 4.36 2.53 2.05 5.32 4.80

12.91 11.26 5.07 4.69 2.62 2.11 5.76 5.14

4.49 4.26 3.17 3.49 3.07 2.93 3.28 3.06

4.70 4.48 3.26 3.50 3.06 2.91 3.35 3.13

1.57 1.50 1.18 1.26 1.17 1.16 1.23 1.17

1.65 1.58 1.21 1.28 1.16 1.15 1.26 1.20

3.36 3.06 1.64 2.11 1.58 1.39 2.12 1.98

4.02 3.82 2.69 2.32 1.67 1.46 2.30 2.12

1.00 1.01 1.06 1.04 1.11 1.16 1.04 1.05

1.00 1.00 1.03 1.04 1.10 1.15 1.04 1.05

a

Calculated for full conversion of the limiting substrate; for the limiting substrate, the activity coefficients are infinite-dilution values.

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rate. As shown in Figure 7 (solid symbols), the concentrationbased model is not able to predict this effect. 4. Conclusions

Figure 8. Experimental (points) and simulated (lines) results for different reaction conditions. (O) AV ) DOH ) 0.1 M, 1.0 mg of enzyme; (0) AV ) DOH ) 0.1 M, 2.0 mg of enzyme; (∆) AV ) DOH ) 0.1 M, 2.5 mg of enzyme; (]) AV ) DOH ) 0.5 M, 2.5 mg of enzyme; (9) VA ) 1.0 M, DOH ) 0.1 M, 2.0 mg of enzyme; (b) AV ) 1.4 M, DOH ) 0.1 M, 2.0 mg of enzyme; (2) AV ) 0.1 M, DOH ) 0.5 M, 2.5 mg of enzyme; ([) AV ) 0.1 M, DOH ) 1.0 M, 2.5 mg of enzyme. Crushed particles and 30 °C for all assays. Simulated results calculated with activity-based kinetic parameters.

where ai represents the activity of component i and the superscript a indicates an activity-based parameter. This kinetic equation is valid if the liquid-phase activity coefficients for the enzyme, its complexes, and transition states are either constant over the entire range of concentrations or have similar values.37 In the first case, as the liquid-phase activity coefficients might not necessarily be equal, the kinetic constants would become lumped parameters that include a ratio of the liquid-phase activity coefficients of either the enzyme or one of its complexes and the respective transition state. The intrinsic kinetic parameters obtained using eq 2 are presented in Table 3. In this case, the SSQ value presented was calculated with all the data, that is, both equimolar and nonequimolar initial concentrations of substrates. Figure 8 compares the experimental points and the simulated curves obtained with eq 2, using the activity-based kinetic parameters presented in Table 3. As can be seen, the activitybased equation is able to satisfactorily describe the reaction process throughout the entire range of tested concentrations, indicating that the differences between the experimental data and the predictions obtained with the concentration-based rate equation can be related to the thermodynamic nonideality of the reaction mixture. Regarding the reactions performed with excess vinyl acetate, the activity-based model predicts that, for high concentrations of this substrate (1.4 M), the reaction rate will begin to decrease slightly, as verified experimentally (see Figures 6a and 7). When a aVA. aDOH (and also aVA. KVA ), eq 2 reduces to r)

rmax a KDOH aDOH

(3)

+1

Thus, increasing VA concentration above a certain level would not have a direct impact in the reaction rate. However, in this case, a higher concentration of this substrate will decrease the activity coefficient of DOH, ultimately decreasing the reaction

The enzymatic transesterification of vinyl acetate and decanol in n-hexane was studied, with particular emphasis on the influence of internal diffusion, enzyme distribution, and the initial concentration of substrates, as well as the determination of the intrinsic kinetic parameters. A preliminary enzyme screening showed that Novozym 435 was the most active catalyst for the reaction studied. Internal diffusion limitations were shown to exist but could be eliminated by reducing the particle size through crushing, which enabled the development of an intrinsic kinetic model. The intrinsic kinetic parameters were calculated, showing that a ping-pong bi-bi kinetic model with competitive inhibition by the alcohol was in good agreement with the experimental data in the range of compositions tested as long as an activity-based kinetic equation was used. Only this equation correctly accounts for the thermodynamic nonideality of the reaction mixture, which makes it more suitable to describe this reaction process. In comparison with the results previously obtained with scCO2 as the solvent, this work showed that, under the conditions tested, operating with n-hexane enables a much faster reaction, even when mass-transfer resistances are present. Because the reaction is much less limited by rates of diffusion in sc-CO2, under the conditions tested, the enzyme is more active in n-hexane than in sc-CO2. Although there are several advantages of using SCFs (and, in particular, sc-CO2) with respect to organic solvents, the higher reaction rates and volumetric productivities in n-hexane make the latter more attractive for industrial applications, and consequently, use of n-hexane as a solvent is worth continued investigation. Acknowledgment The authors thank Fundaçaõ para a Cieˆncia e Tecnologia (Portugal) for A.S.R.’s Ph.D. grant (SFRH/BD/13084/2003) and for the financial support of the project POCI/EQU/56732/2004, FEDER for financing LSRE (FEDER/POCI/2010), Professor Romualdo Salcedo from FEUP for the optimization code, and Novozymes and Amano Enzyme Inc. for kindly providing the catalysts. Literature Cited (1) Serra, S.; Fuganti, C.; Brenna, E. Biocatalytic Preparation of Natural Flavours and Fragrances. Trends Biotechnol. 2005, 23, 193. (2) Gandhi, N. N.; Patil, N. S.; Sawant, S. B.; Joshi, J. B. LipaseCatalysed Esterification. Catal. ReV.-Sci. Eng. 2000, 42, 439. (3) Zaks, A.; Klibanov, A. M. Enzymatic Catalysis in Organic Media at 100°C. Science 1984, 224, 1249. (4) Klibanov, A. M. Enzymes That Work in Organic Solvents. CHEMTECH 1986, 16, 354. (5) Yadav, G. D.; Dhoot, S. B. Immobilized Lipase-Catalysed Synthesis of Cinnamyl Laurate in Non-Aqueous Media. J. Mol. Catal. B: Enzym. 2009, 57, 34. (6) Daneshfar, A.; Ghaziaskar, H. S.; Shiri, L.; Manafi, M. H.; Nikorazm, M.; Abassi, S. Synthesis of 2-Ethylhexyl-2-ethylhexanoate Catalyzed by Immobilized Lipase in n-Hexane: A Kinetic Study. Biochem. Eng. J. 2007, 37, 279. (7) Zhang, T.; Yang, L.; Zhu, Z. Determination of Internal Diffusion Limitation and Its Macroscopic Kinetics of the Transesterification of Cpb Alcohol Catalyzed by Immobilized Lipase in Organic Media. Enzyme Microb. Technol. 2005, 36, 203. (8) Rassy, H. E.; Perrard, A.; Pierre, A. C. Application of Lipase Encapsulated in Silica Aerogels to a Transesterification Reaction in Hydrophobic and Hydrophilic Solvents: Bi-Bi Ping-Pong Kinetics. J. Mol. Catal. B: Enzym. 2004, 30, 137.

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ReceiVed for reView December 21, 2009 ReVised manuscript receiVed May 24, 2010 Accepted June 21, 2010 IE902026D

Enzymatic Production of Decyl Acetate: Kinetic Study in - American

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