Kinetic Analysis of Oleic Acid Esterification Using Lipase as Catalyst in

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Ind. Eng. Chem. Res. 2010, 49, 1071–1078

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Kinetic Analysis of Oleic Acid Esterification Using Lipase as Catalyst in a Microaqueous Environment Mohd Sabri Mahmud,† Tomasz Safinski,† Mark I. Nelson,‡ Harvinder S. Sidhu,§ and Adesoji A. Adesina*,† Reactor Engineering & Technology Group, School of Chemical Sciences & Engineering, UniVersity of New South Wales, Sydney 2052, Australia; School of Mathematics & Applied Statistics, UniVersity of Wollongong, Wollongong 2522, Australia; and School of Physical, EnVironmental and Mathematical Sciences, ADFA, Canberra, ACT 2600, Australia

This paper reports the lipase-catalyzed esterification of oleic acid (with ethanol) in a batch reactor at temperatures between 298 and 338 K using a wide range of the reactant ratio, β (0 < β < 2). All kinetic runs were performed under conditions of negligible transport limitations. The sigmoidal behavior evidenced from the initial rate-substrate concentration curve suggests the allosteric nature of the acrylic-supported Aspergillus lipase, and hence, the data were described by a non-Michaelis Menten kinetic model. The associated oleic acid binding coefficient and ethanol inhibition constant were obtained as 2.382 and 1.643 mmol L-1, respectively. The allosteric effect was attributed to conformational change in the enzyme site occasioned by the presence of trace amounts of water formed within the first few minutes of the reaction. Indeed, the transient water concentration profile at different β values revealed an initial overshoot in water concentration before the relaxation to final equilibrium value after about 6 h. The appearance of the initial overshoot increased with decreasing β. The water concentration history is symptomatic of two first-order interacting processes fed by a self-propagating input consistent with the two-enzyme state concerted symmetry proposition for nonlinear feedback autoregulatory behavior. The rate-temperature envelope showed a maximum at about 318 K, suggesting protein denaturation above this temperature. Even so, a fit of the rate data obtained between 298 to 318 K gave an activation energy of 22.4 kJ mol-1, typical of many enzymatic reactions. FTIR spectra of the catalysts displayed peaks at 1723.23 and 1666.12 cm-1 assigned to COO- and NH2+ groups, respectively, for both fresh and used specimens. BET measurements, however, revealed a significant drop in surface area between fresh (165 m2 g-1) and used (5-20 m2 g-1) catalysts. This was attributed to pore blockage of the immobilized enzyme by the relatively large oleic-acyl-lipase complex left after the reaction. 1. Introduction Current interest in the diversification of clean and sustainable energy resources to mitigate the negative impacts of fossil fuels on climate change has drawn attention to the beneficial properties of biofuel as a net zero CO2 emitter. For instance, biodiesel, which is essentially the mono alkyl ester of free fatty acids (FFAs) can be synthesized from vegetable oils and bioethanol. Conventional commercial biodiesel production employs the acid-catalyzed esterification of the FFAs at fairly high temperatures (423-498 K) in specialized corrosionresistant vessels. In particular, the inorganic acid (or alkali)catalyzed reaction suffers from poor product selectivity. Recent studies dealing with lipolytic enzyme esterification of different FFAs with both low and high molecular weight alcohols have demonstrated that improved alkyl ester selectivity may be obtained with typically high conversions (70-95%) over a 6-10 h period at temperatures between 293 and 333 K.1-4 There are, however, conflicting views on the mechanistic inferences and related kinetic models for lipase-catalyzed esterification of these fatty acids in part due to the limited range of reactant ratio used by different investigators (for instance, compositions around the stoichiometric ratio, 0.9-1.2) and the complex nature of the enzyme activation depending on the solvent medium.3,5 * Corresponding author. Tel.: +61 2 9385 5268. Fax: +61 2 9385 5966. E-mail: [email protected]. † University of New South Wales. ‡ University of Wollongong. § School of Physical, Environmental and Mathematical Sciences.

Specifically, water is a coproduct of the esterification reaction, and the use of lipolytic enzyme as a probe for the lipid-water interface has been reported by Wieloch et al.6 because of its unusual kinetics. The lag time observed during the action of pancreatic lipase on racemic 1,2-didodecanoylglycerol transesterification was attributed to product accumulation at the substrate-water interface. Foresti et al.2 also showed that water has multiple effects on solvent-free enzymatic esterification. The reaction rate-water content curve has two peaks. The first was located between 0.2 and 3 wt % (water-oleic acid mixture), suggesting that the trace amount of water in the reacting medium was necessary to activate the enzyme, while a second peak detected at ∼20 wt % implies that a distinct aqueous phase had provided room for extraction of the products from the reactive (organic) phase, hence shifting equilibrium to the right-hand side of the reaction Oleic Acid (OA) + Ethanol (EtOH) T Ethyl Oleate (EO) + Water (W) (1) Paiva et al.5 hypothesized that the active site in the lipolytic enzyme is hydrophobic and covered by a “lid” (which has a top hydrophilic side and an interior hydrophobic face) so that, when flip-flopped, it permits the binding of the acyl group of the acid (or ester) to form a lipase-OA intermediate that undergoes surface reconfiguration as depicted in steps B and C in Figure 1 to release water, creating microheterogeneity around the hydrophilic lid face, which rolls back to ensure access of the adjacent hydroxyl compound (EtOH in this case) and, hence, formation of fatty acid alkyl ester (FAAE), or ethyl oleate. The

10.1021/ie900704n  2010 American Chemical Society Published on Web 07/29/2009

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Figure 1. Schematic diagram of steps in monophasic reaction during enzymatic esterification involving oleic acid and ethanol.

Figure 2. Reactor setup.

latter is subsequently released while the reactive hydrophobic site becomes vacant for the binding of a new substrate molecule. The water released further activates the adjacent lipase site via a lid roll-back, as indicated in step E. The completion of this catalytic cycle suggests that an equilibrium will exist between the two states of the enzyme site. When an enzyme exhibits such a regulatory property due to exceptional sensitivity to changes in substrate (or product)

concentration, the rate behavior will deviate from classical Michaelis-Menten kinetics. This phenomenon may be attributed to cooperativity and allosteric properties of the enzyme.7 As a result, an investigation of the reaction in a medium initially free of water will contribute toward an understanding of the role of allosterism and co-operativism in enzymatic reactions, particularly in biofuel synthesis, since inorganic catalysts do not necessarily exhibit this behavior. Hence, this is the rationale for using a microaqueous environment (water only being produced in the course of the experimental run) in the present work. Furthermore, in this study, we provide an interpretative framework for the apparently divergent views hitherto reported through detailed kinetic analysis of rate data collected using reactant concentration ratio ranging from substoichiometric to suprastoichiometric values for the esterification of oleic acid with ethanol in a solvent-free medium. Moreover, we supplement our discussion with an examination of the transient water concentration profiles to gain insight into the water-induced conformational changes in the enzyme site state. This unique dimension of lipase-catalyzed esterification has neither been reported nor addressed in previous kinetic contributions. In this study, all stable participating species in the reaction were monitored with time in order to gain a reliable knowledge of the product selectivity, without any assumptions on the reaction stoichiometry. Additionally, kinetic experiments were conducted under conditions with negligible internal or external transport

Figure 3. Regression models and profiles of (a) conversion and (b) concentration of ethyl oleate for three representative reactant ratios.

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Table 1. Summary of Model Parameters in Eq 2 oleic acid/ ethanol ratio, β

CA0 (mmol L-1)

XSS (OA or EtOH)

exponential constant, ΨA (min-1)

0.01 0.05 0.1 0.25 0.5 0.625 0.75 1 1.2 1.4 1.6 2

0.1620 0.6662 1.0906 1.7655 2.2243 2.3463 2.4353 2.5565 2.185 1.907 1.6926 1.381

0.3039 0.7339 0.7841 0.8227 0.8494 0.894 0.8721 0.8266 0.7341 0.8127 0.8143 0.8142

0.0069 0.0048 0.0043 0.0047 0.011 0.0105 0.0156 0.0266 0.0244 0.0254 0.0242 0.0174

intrusions due to reported effects of support pore structural evolution in the course of the reaction.5,7,8 Both BrunauerEmmett-Teller (BET) measurement and Fourier transform infrared (FTIR) spectroscopic data on the fresh and used catalysts were collected to complement rate data analysis.

Figure 5. Effect of catalyst loading on reaction rate.

2. Experimental Section 2.1. Materials. Commercial Novozym 435 (Aspergillus niger derived lipase) was supplied as an immobilized enzyme on macroporous acrylic resin (90-800 µm particles) by Novozyme Pty. Ltd. Oleic acid (95% purity) used for reaction and highperformance liquid chromatography (HPLC)-grade methanol (99.5%) were obtained from Ajax Fine Chemicals (Sydney, Australia), while absolute ethanol (99%) was provided by APS Chemicals (Sydney, Australia). Chemicals required for Karl Fischer titration for the water content determination, namely, Hydranal Composite 5 titrant, Hydranal CompoSolvent, and Hydranal Standard 5, were purchased from Sigma Aldrich. The same vendor supplied the analytical oleic acid (98%) and ethyl oleate (98%) for the GC calibration. 2.2. Equipment and Methods. All reaction runs were carried out in a 500 mL cylindrical Pyrex glass vessel (i.d. ) 7 cm, height ) 15 cm) equipped with a 5-port flange lid, four equally spaced baffles, and a 6-bladed flat impeller driven by a Heidolph electrical motor (model RZR-2021). The reactor configuration, baffles, and impeller dimensions as well as its clearance from the vessel bottom were chosen to ensure optimum mixing for the viscous oleic acid-ethanol mixture, in accordance with the design specification detailed by Walas.9 The entire reactor assembly was placed in an isothermal silicone oil bath, as illustrated in Figure 2. Experiments were conducted using oleic acid/ethanol ratio, β, at 12 values (0 < β < 2) spanning both sides of the

Figure 6. Logarithmic plot of reaction rate as a function catalyst particle size.

Figure 7. Plot of ln(-r)/ln dp slope versus time at which initial rate was determined.

Figure 4. Oleic acid reaction rate dependency on stirring speed.

stoichiometric ratio ) 1.0. Preliminary runs with β > 2.5 gave negligible ethyl oleate formation rate. Thus, experimental β values starting from 0.01 to 2.0 were examined using a working reactant volume of 300 mL for each run. The reactant mixture was typically charged with 1 wt % immobilized enzyme particles (mean size, dp ) 383 µm), except for runs designed to investigate the influence of catalyst loading and particle size required for the delineation of conditions for the avoidance of internal transport limitations. A stirring speed of 1200 rpm was also used to ensure minimal external transport effects, as later justified. The pH’s of all runs were measured by hightemperature Eutech electrode. The activity of the immobilized

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Figure 8. Initial reaction rate versus oleic acid as the limiting reactant (β < 2.0).

Figure 10. Comparison between model 4 and experimental data.

spectrophotometer equipped with a Smart Collector) via IR spectra analysis obtained between 650 and 4000 cm-1. Results and Discussion 3.1. Transport Analysis. The conversion-time curves for typical runs are shown in Figure 3a along with associated ethyl oleate transient concentration profiles in Figure 3b. The exponential rise character of these curves suggest that the conversion, XA, progression may be captured by XA ) XSS[1 - exp(-ψAt)]

(2)

where A is the limiting reactant (OA or EtOH) and the ethyl oleate production also follows Figure 9. Water transient profiles for representative runs with three different substrate ratios. Symbols denotes experimental points. Continuous and dashed lines are model predictions.

CEO ) CEO,SS[1 - exp(-λt)]

Thus, the instantaneous substrate disappearance rate inside the batch reactor was estimated from

Table 2. Estimates of Parameters for the Transient Water Model (Eq 7) β

k (mmol L-1)

γ (min-1)

ξ

τ (min)

0.5 1.0 1.4

1.5045 1.5445 0.7101

6.8627 × 10-12 0.0021 0.0091

0.0153 0.9950 0.0041

1.4538 37.6900 0.1442

lipase is reportedly stable10 within the range 3 e pH e 6.5. Incidentally, the pH’s observed for all runs performed in this investigation were between 3.7 and 4.3. Filtered aliquots (200 µL) taken at regular intervals (5-30 min) were homogenized and diluted with methanol and analyzed on a Shimadzu flame ionization detector (FID) capillary GC (model 17A) fitted with a liquid autosampler-autoinjector and fused silica column (0.25 mm × 30 m StabilWax-DA) to obtain transient concentration measurements of the oleic acid, ethanol, and ethyl oleate based on external standard calibrations. Portions of the diluted aliquots were also subjected to a Karl Fischer titration method on a Mettler Toledo autotitrator (model DL38) to secure the water concentration history in the course of the reaction. Used catalyst was filtered from the substrate as the concentration of OA remained unchanged and washed with ethanol 95% and ultrapure Milli-Q water prior to overnight drying at 318 K in a Labec oven. Fresh and used catalyst samples were then characterized for areal assessment (using the BET flow method on a Micrometrics Autochem 2910) and surface structure determination (on a Nexus Nicholet FTIR

(3)

-rA ) CA0

dX ) CA0XSSψAexp(-ψAt) dt t

(4)

while the related ethyl oleate production, rEO, is given by rEO )

dCEO ) CEO,SSλ exp(-λt) dt

(5)

The parameters XSS, ψ, CEO,SS, and λ were obtained from nonlinear fit of the data for each run using SigmaPlot 10 software as shown in Table 1. Figure 4 shows the influence of stirring speed on the oleic acid consumption rate, -rOA, (using t ) 50 min in eq 4). It is seen from this plot that the reaction rate became insensitive to stirring speed higher than 800 rpm, suggesting that external mass transfer resistance may be neglected at rotational velocities above this limit. Thus, a stirring speed of 1200 rpm was used in subsequent runs. The relative importance of the combined internal mass transport and reaction resistances to the external transport resistance was determined from a plot of the reciprocal rate (CA0/(-rA)) against the inverse of the catalyst loading, 1/m, as shown in Figure 5, from11 CA0 -rA

)

(

)

1 1 1 1 1 1 1 ) + + + · kbab m kcap krxnη kbab m kr

(6)

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Table 3. Model Determination model 1

Foresti-Pedernera-Ferreira-Bucala model3 -r )

2

[

Vmax(COACEtOH) Km,OA ′ V 2 Km,EtOH COA + Km,OA CEtOH + ′ ′ CEtOH + K i,EtOH Km,OA Km,W ′ ′ r C + Vmax COACEtOH + C C Keq EO Ki,EO EO EtOH

VmaxCEO CEO COA 1+ + Km,EO Ki,OA

[ ( Km,EO

Vmax ) 0.066 mmol L-1 min-1 Km,EtOH′ ) 8.009 mmol L-1

0.993

]

(Km,OA′)/(Ki,EO) ) 4.105 (Km,W′)/(Keq) ) -7.075 r Vmax ) 3.318 mmol L-1 min-1

(Km,OA′)/(Ki,EO) ) 20.353

)]

Chulalaksananukul-Condoret-Delorme-Willemot model13

-r )

VmaxCOACEtOH CEtOH + Km,EtOHCOA + COACEtOH 1+ ki

(

[

Km,OACEtOH

4

R2

Km,OA′ ) -27.526 mmol L-1

Paiva-Balcao-Malcata model5 -r )

3

variables

equation

)

0.892

Vmax ) 0.019 mmol L-1 min-1 Km,OA ) -1.181 mmol L-1

0.964

Ki,EtOH ) -2.358 mmol L-1 Km,EtOH ) 0.948 mmol L-1 Vmax ) 0.916 mmol L-1 min-1

this study -r )

]

Vmax ) 0.032 mmol L-1 min-1 Km,EO) 0.635 mmol L-1 Ki,OA ) 0.983 mmol L-1

[

Km,OACEtOH COACEtOH

(

x y CEtOH VmaxCOA

)

CEtOH 1+ + Km,EtOHCOA+ ki

where η denotes effectiveness factor, krxn is the pseudoreaction rate constant, kb is the interfacial mass transfer coefficient between the organic and aqueous phases, ab is the corresponding interfacial area, and kc denotes mass transfer coefficient from organic to enzyme particle surface. It is manifest from the slope and intercept of the linear plot that the combined resistances are more than 16 times bigger than the external (liquid-solid interfacial) transport resistance. Given that the latter was already deemed negligible, the ratecontrolling step would be due to either the intraparticle transport effect or the reaction resistance. Further discrimination between these two phenomena based on the variation of reaction rate on enzyme particle size is depicted in Figure 6. This plot also serves to justify the estimation of initial rate at time t ) 50 min in eq 4. The family of lines shown in Figure 6 were based on the rate determined from eq 4 at various values below 100 min. This was then plotted in terms of ln r versus ln dp.

0.984

]

Km,OA) 2.382 mmol L-1 (x+y)

Ki,EtOH ) 1.643 mmol L-1 Km,EtOH ) 13.159 mmol L-1 x ) 0.632 y ) 0.785

The data demonstrate that internal transport resistance is practically nil for initial rate determined at t ) 40 min since the exponent, n, with respect to the particle size, dp, in (-rexp)

Figure 12. Selectivity (-rEO/-rA) against OA/EtOH ratio.

Figure 11. Residual plot for the models.

Figure 13. Correlation between initial reaction rate and reaction temperature.

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water content overshoot and the time of its appearance is dependent on the initial substrate ratio, β. Since the transient water concentration profile appears to be a damped sinusoidal, the water-stimulated conformational change during lipase-catalyzed esterification of oleic acid may be conceptually represented as the dynamics of two first-order interacting processes containing a first-order generative term for water. Thus,

[

Cw ) k exp(-γt) 1 -

1

√1 - ξ2

( -ξtτ ) sin( t√1 τ- ξ

exp

tan-1 Figure 14. Variation in BET surface area of used catalysts from runs with different reactant ratios, β.

) -rintrinsicdpn, estimated from regression analysis as 0.0465, is significantly close to zero. In fact, the exponent n appears to be a function of time and may be regarded as a measure of the conditioning of catalyst particles to the solvent environment due to internal pore structural changes and species transport before reaction dominance. Specifically, the functionality is adequately described by n ) n0 - Rt (cf. Figure 7) where the slope, R ) 0.0179, is the rate of internal pore structure change in the solvent and the intercept, n0 ) 0.7611, is a pore-structure constant. In order to exclude the interference of transport and pore-structure evolution, the initial rate data from all runs were collected by evaluating eq 4 (or eq 5) at t ) 50 min where n ≈ 0 (t g tcr ) n0/R). This anomalous behavior due to catalyst pore-structure acclimatization in the solvent has been reported for enzyme systems supported on similar material.6,12 As a result of this finding, the mean catalyst particle diameter used in our runs was 383 µm (determined from Retsch sieve analysis) to facilitate easy filtration from the liquid phase without jeopardizing kinetic validity. 3.2. Reaction Mechanism and Diagnosis. The activity response of an enzyme that obeys classical Michaelis-Menten kinetics to increasing substrate concentration exhibits a hyperbolic character. However, as may be seen from Figure 8, the plot of the initial reaction rate (a measure of the lipase activity) against oleic acid concentration displays a sigmoidal curve, suggesting the non-Michaelian mechanism involved in the oleic acid-ethanol esterification reaction. As indicated in the Introduction section, the lipase site is activated by water due to conformational change in the structure of the enzyme. Consistent with the proposition of Paiva et al.,5 the binding of oleic acid to the site in the “closed” lid state led to local microheterogeneity as the initial water molecule is formed. The latter then induces a roll-back of the lid due to its hydrophilic nature and subsequent propagation through the protein molecule to another binding site with more molecules of water formed. Intuitively, one would expect the water content to rise initially in the organic liquid phase medium; nevertheless, as the microaqueous phase builds up, the reverse reaction involving the hydrolysis of the ethyl oleate product sets in, causing a downturn in water production and, hence, a perturbation in the dynamic equilibrium between the two allosteric states of the enzyme site. Since ethanol also has finite solubility in both the organic and microaqueous phases, this feedback mechanism will be evinced by an initial overshoot in the transient water concentration profile before an exponential relaxation to the final equilibrium water content. Interestingly, Figure 9, which shows the experimental water concentration history, confirms this proposition, albeit the magnitude of the

2

+

(√ ))] 1 - ξ2 ξ

(7)

where the parameters are as defined in the Nomenclature. Nonlinear regression analysis of the data in Figure 9 to eq 7 produced the estimates in Table 2. In this case, the magnitude and time of appearance of the initial overshoot increased with decreasing β, suggesting that the amount of water initially formed increased at higher initial ethanol concentration. As expected, the rise time (time taken for the water concentration to reach the ultimate value for the first time) also increased with increasing initial ethanol content (decreasing β), probably due to ethanol inhibition on the water production rate. These attributes are consistent with the existence of at least two conformational and reversible states of the site structure proposed for allosteric enzymes by Monod, Wyman, and Changeux (MWC) in their concerted-symmetry model7 and represented by R0 T T0, where R0 and T0 are the substrate accessible sites with different affinities for water (closed-lid and open-lid positions, respectively). This is in accordance with the Paiva et al.5 proposal in Figure 1. Since lipase-catalyzed esterification is a bisubstrate reaction with water as the first product released, the Ping Pong Bi Bi mechanism may be written as L + OA S L - OA

(M1)

L - OA S L - FW

(M2)

L - FW S L - F + W

(M3)

L - F + EtOH S L - FEtOH

(M4)

L - FEtOH S L - EO

(M5)

L - EO S L + EO

(M6)

where eq M1 represents the formation of the acyl-lipase intermediate from whence water is released as a result of the conformational change represented by eq M3. The attraction of the alkyl donor to the resulting enzyme complex, L - F, yields an alkyl-acyl-lipase entity that undergoes a second reconfiguration (cf. eq M5) to produce the ester with concomitant release of the original enzyme site, as seen in eq M6. Formal kinetic models3,5,13 derived from this mechanism may then be evaluated based on the steady-state rate data obtained as a function of the substrate concentration. Figure 10 shows the rate depending on the oleic acid/ethanol concentration ratio for the present investigation. The results of the nonlinear regression analysis of the kinetic models are summarized in Table 3. Although models 1-3 provided a reasonably good fit of the data, the procurement of negative estimates for some parameters constitutes a physical oddity. However, model 4, which allows for the allosteric regulation of the enzyme activity via the introduction of the exponents x and y for the two

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Figure 15. FTIR spectra for fresh (red) and used catalysts from runs with β ) 1.4, 0.4, and 1.0 in descending order.

substrates gave a comparable fit (R2 ) 0.984) to the Foresti et al.3 model (R2 ) 0.993) with all kinetic constants being positive. The residual plot (cf. Figure 11) for all models also lends credence to the choice of model 4 as the most appropriate representation of the lipase-catalyzed esterification across the entire β range. Figure 12 plots the ethyl oleate selectivity as a function of β. It is evident that only mild and relatively diffused variation in selectivity occurred with respect to the substrate concentration ratio, suggesting that the proposed kinetic mechanism for EO production is applicable over the wide composition spectrum examined. Significantly, the composition-average ethyl oleate selectivity of 0.95 is within the range (0.70-0.95) reported in the literature,1,14 although many of these investigations were performed within a narrow window (0.9 e β e 1.2). The discrepancy between the theoretical selectivity (100%) and the observed value (95%) may be due to the loss of oleic acid as residual acyl-lipase complex on the catalyst particle, since GC analysis did not reveal the presence of possible side-products such as diethyl ether in the reaction broth. Figure 13 represents the Arrhenius plot for the rate data obtained between 298 to 338 K using a substrate concentration ratio of 0.9. It is clear from these data that rate went through a maximum at about 318 K, beyond which protein denaturation probably caused lipase deactivation. On the basis of data obtained between 293 and 318 K, the activation energy for the lipase-catalyzed esterification was estimated as 22.4 kJ mol-1, similar to values for many enzymatic reactions.7 However, the protein denaturation is characterized by an even lower (de)activation energy of 4.82 kJ mol-1, indicating that esterification rate would experience a precipitous decrease if carried out at higher temperatures (beyond 318 K.). Examination of the immobilized catalyst structure by BET measurements (physical characterization) and FTIR analysis (surface structure chemical finger-printing) revealed that the acrylic-supported lipase suffered a significant decrease in surface area after usage, as may be seen in Figure 14 probably due to blockage of the macroporous by the relatively large residual

oleic acyl-lipase complex left after reaction. The plot, in fact, shows that the variation in the reduced BET surface of the used catalyst with respect to β (>0.05) is small and lacks a discernible pattern, similar to the behavior seen in the ethyl oleate selectivity with the same variable. This would suggest that the residual oleic acyl-lipase is the common causal factor for these two phenomena (surface area and selectivity reduction). Interestingly, FTIR spectra obtained for various catalyst samples shown in Figure 15 also confirm the existence of characteristic peaks of belonging to the acyl group (COO-) at 1723.23 cm-1 and the NH2+ group at 1662.81 cm-1. The decrease in the peak intensity between the fresh and used catalysts at each wavenumber is evident and appears to be uncorrelated with variation in β, consistent with the previous observations for ethyl oleate selectivity and BET area. 4. Conclusions Oleic acid esterification with ethanol has been carried out in a stirred batch reactor containing suspended particles of immobilized lipase. Kinetic data were collected under conditions with minimal transport intrusions (stirring speed of 1200 rpm using mean particle size of 383 µm) over a wide range of the substrate concentration ratio, β (0 < β < 2), covering situations with excess oleic acid and ethanol inhibition. The sigmoidal response curve for the enzyme activity implicated the presence of allosteric effects during esterification. As a result, a modified Ping Pong Bi Bi kinetic model containing parameters capturing these nonlinear phenomena was proposed and adequately described the steady-state rate data when compared with extant literature models. Arrhenius treatment of the rate data for temperature between 298 and 338 K revealed the existence of a critical temperature (318 K) beyond which protein denaturation caused a precipitous loss in enzyme activity. Even so, the estimated activation energy of 22.4 kJ mol-1 was found for the reaction in the range 298-318 K. The reaction is also characterized by a high ethyl oleate selectivity of ∼95%. However, the diffused variation in

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product selectivity with substrate concentration ratio, β, seems to parallel the trend seen in the BET area of the used catalysts, and both appear to be due to a common causal factor, namely, the presence of residual acyl-lipase complex during the reaction. FTIR spectra of the fresh and used catalyst samples also confirmed this relationship. Acknowledgment This work was supported by a grant from the UNSW Engineering-ADFA research collaboration scheme. M.S.M. is a recipient of an academic training scholarship from the Ministry of Higher Education, Malaysia. Nomenclature ab ) interfacial area between organic and aqueous phases C ) concentration (mmol · L-1) dp ) particle size (µm) Keq ) equilibrium constant Ki ) inhibition constant K′m ) a modified Michaelis-Menten coefficient k ) nascent equilibrium water constant kb ) interfacial mass transfer coefficient between organic and aqueous phases kc ) mass transfer coefficient from organic to enzyme particle surface krxn ) pseudo reaction rate constant m ) catalyst loading (g) n ) power for particle size, dp r ) reaction rate (mmol · L-1 · min-1) t ) time (min) Vmax ) maximum velocity or reaction rate r Vmax ) maximum rate of reactant consumption X ) conversion x ) degree of allosteric effect with the presence of oleic acid y ) degree of allosteric effect with the presence of ethanol Greek Letters R ) proportional coefficient of slope progression of ln(-r) - ln dp curves β ) molar ratio of oleic acid/ethanol γ ) relaxation coefficient for the equilibrium value λ ) exponential rise coefficient of ethyl oleate η ) effectiveness factor τ ) frequency factor ξ ) damping factor ψ ) exponential rise coefficient of conversion Acronyms (may be used as subscripts or superscripts) 0 ) initial or inlet condition A ) limiting reactant FFA ) free fatty acid

EtOH ) ethanol EO ) ethyl oleate F ) oleic acid intermediate on lipasic active site as water released FW ) lipase surface oleic acid-water complex exp ) experimental L ) lipase OA ) oleic acid SS ) steady state T ) absolute temperature (Kelvin) W ) water

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ReceiVed for reView May 1, 2009 ReVised manuscript receiVed June 27, 2009 Accepted June 30, 2009 IE900704N