Experimental Studies and Mass-Transfer Analysis of the Hydrolysis of

Ind. Eng. Chem. Res. 2004, 43, 2017-2029

2017

Experimental Studies and Mass-Transfer Analysis of the Hydrolysis of Olive Oil in a Biphasic Zeolite-Membrane Reactor Using Chemically Immobilized Lipase Anupam Shukla and Anil Kumar* Department of Chemical Engineering, Indian Institute of Technology, Kanpur, India 208016

Chemically modified zeolite-clay composite membranes have been used for the immobilization of porcine lipase using glutaraldehyde to provide a chemical linkage between the enzyme and the membrane. The lipase-immobilized membrane has been used in a biphasic enzyme membrane reactor (EMR) for the hydrolysis of olive oil, and the performance of the EMR has been evaluated in terms of the apparent volumetric reaction rate based on the volume of the aqueous phase used for the extraction of the fatty acids. The reactor system behaves as though it involved an irreversible reaction with negligible product inhibition. The effects of various operating parameters (pH, solvent, olive oil concentration, and temperature) on the performance of the EMR were evaluated. A model that divides the system into two regions, charged pores and an unstirred film adjacent to the pores, describes the mass transfer on the aqueous side of the reaction sites located at the pore mouth. The process involves the transport of Na+, OH-, and RCOO- ions where the film is considered as an electroneutral region while the space-charge model is used to describe transport inside the charged pores. The solution scheme requires the ion concentration and its gradient only at the pore end, and using the experimental data, the pore-wall potential was determined to be about -0.5 mV. 1. Introduction A membrane reactor (MR) provides important process integration in which membrane-based separation occurs simultaneously with reaction in a single module. This type of reactor found increasing applications in the pharmaceutical and fine-chemical industries where expensive catalysts/enzymes are used.1 In most cases, the function of the membrane is to keep the catalyst within the module and prevent it from exiting with the process streams. In many cases, the catalyst is immobilized on the membrane to provide better/more selective contact with the reactant(s). Some of the important applications of MRs reported in recent literature include the degussa acylase process, the reductive amination of trimethylpyruvate, and the synthesis of L-carnitine.1-3 The conventionally used technique for fat hydrolysis is the Colgate Emery process, which gives a high conversion (97-98%) but is highly energy intensive and consumes about 790 MJ/kg of fat split.4 This process operates at high temperature (150-260 °C) and pressure (∼5 MPa), where some degradation of product quality, which might be undesirable, especially from the point of view of use in the cosmetic and pharmaceutical industries.5 This has generated interest in the development of better alternatives for fat hydrolysis. Enzymecatalyzed hydrolysis occurs at room temperature and under mild conditions, thereby offering a better alternative to the classical technology. Enzymatic splitting of fats for industrial purposes was attempted as early as 1890 and 1938, but it did not make much headway because of the low reaction rate, low conversion, and difficulty in design and operation. Traditional types of * To whom correspondence should be addressed. E-mail: [email protected]. Tel.: +91 512 2597195. Fax: +91 512 2590104.

reactors used for this purpose include fluidized beds, stirred batches, continuous stirred tank reactors (CSTRs), and packed-bed columns.6,7 A new development in this field is the use of enzyme membrane reactors (EMRs),8-10 in which the membrane is used both for catalyst support and for the selective removal of product(s). As lipase substrates (oils and fats) have limited solubilities in water, the reaction can be performed in multiphase enzyme reactors. Lipase is known to act on the oilwater interface,11 and EMRs are ideal for such a situation, given that the membrane (containing the enzyme) forms the boundary between the two phases. Immobilization of lipases has been achieved either by physical processes or by means of chemical linkages. The former method of immobilization can be performed through microencapsulation in lipid vesicles, containment in reverse micelles, entrapment in polymeric materials, and entrapment in ultrafiltration hollow fibers. Various carriers used have included PVC, agarose, Celite, silica gel, chitin, chitosan, kieselguhr, and poly(styrene-divinylbenzene) copolymer.12 The technique of chemical attachment can be done by covalent bonding, ion exchange, or cross-linking. The most common agent used for the chemical binding of enzymes is glutaraldehyde, and the other agents used for this purpose are cyanogen bromide and carbodiimide. Immobilization causes a change in the microenvironment of the enzyme and can therefore lead to the inhibition or enhancement of its activity.12 Immobilization, on the other hand, is known to increase the stability of the enzyme, especially against thermal deactivation. In addition, an investigation of the role of metal ions on lipase activity has shown that the hydrolytic activity of pancreatic lipase is increased in the presence of calcium and sodium ions.13,14 A review of the literature suggests that zeolites, which have exchangeable metal ions, have not previously been used for lipase immobilization.

10.1021/ie030682+ CCC: $27.50 © 2004 American Chemical Society Published on Web 03/17/2004

2018 Ind. Eng. Chem. Res., Vol. 43, No. 9, 2004

In this work, we report the immobilization of pancreatic lipase through covalent linking to the surface of a zeolite-clay composite membrane (Z1 membrane) having imine/amine groups on its surface.15 The membrane is reacted with glutaraldehyde to obtain free aldehyde groups on the membrane surface, and the lipase is then reacted with these free aldehyde groups and bound to the membrane surface. The enzyme-immobilized membrane is used in a biphasic EMR for the hydrolysis of olive oil, and its performance is evaluated in terms of the volumetric rate of fatty acid production based on the volume of the aqueous phase. The effects of different organic solvents (pentane, hexane, and heptane) for the olive oil, the concentration of olive oil, the temperature, and the pH of the aqueous phase on the performance of the EMR are determined. Fatty acid formed during the reaction is extracted into the aqueous phase at alkaline pH in the form of RCOO- ions, and the aqueous phase also contains OH- and Na+ ions. A model is proposed to describe the mass transfer phenomenon of the ions on the aqueous side of the reaction sites (enzyme located at the pore mouth) wherein the entire system is divided into two regions. The first region (I) consists of an electroneutral unstirred film adjacent to the pore end, and the second region (II) comprises the charged pores themselves. In light of the experimental data, the flux and concentration profile of OH- ions in region I is considered to be at steady state, whereas those of the Na+ and RCOO- ions are allowed to change with time. The space-charge model is used to describe the transport of ions inside the pores, and the equations of the spacecharge model are solved using a scheme that requires ion concentrations and their gradients only at the pore end. In this process, the wall potential of the pores is simultaneously determined.

Figure 1. Schematic diagram showing the mass transfer taking place inside the membrane and on the aqueous side of the membrane.

near the enzyme20 at a concentration that can be approximated as constant, as was done by Molinari et al.7 Thus, from the kinetics point of view, eq 1 can be written as

T h G + 3F

The reaction mechanism and the rate expressions for the hydrolysis are quite complex;21 however, the reaction has been modeled in the literature22 using the Michaelis-Menten model. According to this model, the reaction mechanism can be written as k1

-1

2.1. Reaction Kinetics. The hydrolysis of olive oil is a multistep reversible reaction, but in the literature,4 the rate constants of all of the steps have been assumed to be equal because of olive oil’s high oleic acid content (∼75%)16 and the independence of the degree of hydrolysis on the type of the fatty acid.17 The overall reaction can be represented as

T + 3W h G + 3F

(1)

where T stands for triglyceride, W for water, G for glycerin, and F for fatty (oleic) acid. The degree of conversion of the main reactant (T) can be related to the fatty acid concentration by

XT )

k2

8 TE 98 E + F T+E9 k

2. Theoretical Aspects

[F] - [F]0 3[T]0

(2)

where the square brackets indicate the concentration of the species and the subscript 0 stands for the initial value of the concentration. A biphasic EMR represents a continuous microenvironment for the reaction, and the fatty acid formed is continuously extracted into the aqueous phase maintained at a basic pH by adding adequate amounts of NaOH solution. Extraction is enhanced by the formation of resonance-stabilized RCOO- ions.19 Because the applied pressure is very low, only diffusion resistance to mass transfer exists. In a continuous microenvironment (such as in an EMR), the water forms a monolayer

(3)

(4)

where E stands for enzyme and TE for the enzymesubstrate complex. 2.2. Mass-Transfer Model. The hydrolysis of olive oil occurs at the enzyme located at the mouth of the pores in the membrane. The extraction of the fatty acid is facilitated by the reaction of the acid molecule with the OH- ions, which is assumed to be instantaneous.

RCOOH + OH- f RCOO- + H2O

(5)

Figure 1 presents a schematic diagram showing the mass-transfer phenomenon. In this figure, AA′ represents the reaction front, and the oleic acid molecule formed at the enzyme sites (at the pore mouth) migrates toward this reaction front. The OH- ions in the aqueous phase at the right-hand side of AA′ move toward the reaction front, where they are consumed and RCOOions are generated. The RCOO- ions diffuse toward the bulk of the aqueous phase because of the concentration gradient. To maintain a constant aqueous-phase pH, NaOH is continuously added. The region to the right of reaction front thus contains Na+ (hereafter referred to as ion 1), OH- (hereafter referred to as ion 2), and RCOO- (hereafter referred to as ion 3) ions. Because the diffusivity of OH- ions (5.29 × 10-9 m2/s) is much larger (about 1000 times) than that of RCOOH (1.2 × 10-12 m2/s, evaluated using the modified Wilke-Chang equation23), the reaction front is assumed to lie at the pore mouth for the short reaction time considered in this

Ind. Eng. Chem. Res., Vol. 43, No. 9, 2004 2019

work. The mass transport occurring inside the support of the membrane is assumed to be similar to that occurring outside, and so, the entire system can be divided into two regions. The first region (region I) consists of an unstirred film from the pore end to the bulk of the aqueous phase. The second region (region II) comprises the pore of the membrane, and the ion transport is described using the space-charge model with no fluid flow. Mass Transfer in Region I. Figure 1b shows a schematic diagram of region I, which consists of an unstirred film of thickness δ. For very low rates of mass transfer, the film thickness is related to the masstransfer coefficient by

k)

D δ

(6)

ion concentration, and so the region can be assumed to be electroneutral. The flux equations for the ions can thus be written as

kd ) 0.023Re7/8Sc1/4 D

(7)

where

Re )

Fud µ

Sc )

and

µ FD

In the above equations, d is the diameter of the cylindrical compartment, F is the fluid density, µ is the fluid viscosity, and u is the velocity of water in the aqueous compartment. The thickness is evaluated using the diffusivity data for OH- ion, as it has the highest diffusion-coefficient value. The flux of ions is given by

dCi DiziFCi dΦ Ji ) -Di dx RT dx

(8)

where Ci is concentration of ion i, Di is its diffusivity, zi is its valency, Φ is the electrical potential, R is the universal gas constant, and T is the absolute temperature. The electrical potential is related to the charge density by the Poisson equation as 3

d2 Φ

F )-

dx2

ziCi ∑ i)1

dC1 D1z1FC1 E dx RT

(12a)

J2 ) -D2

dC2 D2z2FC2 E dx RT

(12b)

J3 ) -D3

dC3 D3z3FC3 E dx RT

(12c)

In the absence of reaction and assuming a constant diffusion coefficient, the continuity equations for the ions can be written as

and the mass-transfer coefficient can be evaluated using the relation given in the literature24 for transport through a membrane

Sh )

J1 ) -D1

∂Ci ∂2Ci DiFziE ∂Ci ) -Di 2 ∂t RT ∂x ∂x

where t represents the time. As described below, it was found experimentally that, for the short reaction times (60-120 min) considered in this work, a constant rate of addition of NaOH is required to maintain the pH in the aqueous compartment at a constant value. As the flux and bulk concentration of ion 2 are constant, it can be assumed that the flux and concentration profile of ion 2 in region I do not change with time. Thus, for ion 2, eq 13 can be solved to give the concentration profile

C2 ) p21 exp(-R2x) + p22

J2 )

(9)

(15)

3

ziJi ) 0 ∑ i)1

3

(10)

(16)

Taking the partial derivative of eq 10 with respect to time and using the fact that ∂C2/∂t ) 0, we obtain

∂C1 ∂C3 ) ∂t ∂t

and substituting eq 10 into eq 9, we obtain

(say)

βVaq Ac

where Vaq is the volume of the aqueous phase and Ac is the cross-sectional area of the aqueous compartment (20 cm2). Also, the condition of net zero current flow gives the following relationship among the ion fluxes

Region I is assume to be electroneutral, i.e.

dΦ ) constant ) E dx

(14)

where p21 and p22 are constants and R2 ) z2FE/RT. The flux of ion 2 can be calculated from the rate of addition of NaOH (β) as

ziCi ) 0 ∑ i)1

(11)

where E is the electric field. In the absence of any externally applied field, this electric field has to be selfgenerated, which implies existence of unbalanced charge (i.e., a nonelectroneutral region). It will be shown later (section 4.3) that the charge required for the generation of this field is only a minute fraction of the prevailing

(13)

(17)

Using eqs 10, 13, and 17, we obtain

(D1 - D3)

∂2C1 ∂x2

+

FE(D1z1 - D3z3) ∂C1 ) RT ∂x -D1

∂2C2 ∂x

2

-

FED1z1 (18a) RT


(D1 - D3)

∂2C3 ∂x

2

+

FE(D1z1 - D3z3) ∂C3 ) RT ∂x -D3

∂2C2 ∂x2

-

FED3z3 ∂C2 (18b) RT ∂x

The above equation can be solved to give the concentration profiles of ions 1 and 3 as

C1 ) p11 exp(-R1x) + p12 + A1 exp(-R2x)

(19a)

C3 ) p31 exp(-R3x) + p32 + A3 exp(-R2x)

(19b)

where the pij are constants and

A1 ) A3 )

p21(D3z3FE/RT - D3R2) R2(D1 - D3) - FE/RT(D1z1 - D3z3) p21(D1z1FE/RT - D1R2) R2(D1 - D3) - FE/RT(D1z1 - D3z3)

This completes the establishment of the governing equations for the region I, which can be solved by the scheme described below. Solution Scheme. The various physical and experimental data required for model calculations are the diffusion coefficients of the ions (Di), rate of addition of NaOH (β), cross-sectional area of the aqueous compartment (Ac), volume of the aqueous compartment (Vaq), R, and the temperature. The diffusion coefficients of ions 1 and 2 are evaluated from infinite-dilution equivalent conductance values given in the literature,25 and that of ion 3 is assumed to be equal to the diffusion coefficient of oleic acid. It was found that the penetration of ion 3 into the aqueous phase is less than the film thickness values determined from eqs 6 and 7. The film thickness () depth of penetration of ion 3) is therefore determined simultaneously using the algorithm depicted in Figure 2 for the solution of the concentration profiles of the ions at a particular instant of time characterized by a given value of C30. In step 1, a value for the flux of ion 3 at the pore end (x ) 0) is assumed. In step 2, a value for the film thickness is assumed. In step 3, a value for the electric field is assumed. In step 4, eqs 12b and 14 are used to evaluate k21 and k12, i.e., the concentration profile of ion 2. In step 5, J10 (the flux of ion 1 at x ) 0) is determined from the condition of zero net current. Using these values and eqs 12 and 19, the concentration profiles for ions 1 and 3 are evaluated, and so, the concentrations of the ions (Cib) at x ) δ are evaluated using eq 13. If C1b - C2b - C3b (electroneutrality condition) is more than 0.1% of the minimum of Cib, a new value of the electric field is assumed, and steps 4 and 5 are repeated until the desired tolerance is achieved. If C3b is either negative or greater than 10-10, a new value of the film thickness δ is assumed, and steps 3-5 are repeated until the desired tolerance is achieved. In step 6, the net accumulation of ion 3 inside the film is calculated in two different ways using the following relations

∆C3 ) (J30 - J3)Ac ∆t ) Ac

δ ∫x)0

∂C3 dt ∂t

(20)

Figure 2. Flowchart showing the algorithm used to solve the equations describing the ion transport in region I.

If the difference between these two different evaluations of ∆C3/∆t is more than the tolerance limit (0.1%), then we go back to step 1, assume a different value of J30, and repeat the entire procedure until the tolerance limit is satisfied. Because a one-to-one correspondence exists between the time and the ion 3 concentration at x ) 0 (C30), the variation of C30 with time is evaluated in the following way: For a given value of C30, the rate of change of C30 (∂C30/∂t) is evaluated using the above algorithm. This value of ∂C30/∂t is assumed to remain constant for a variation of 0.1% in C30, and thus, the time required for C30 to increment by 0.1% of its value is obtained. By successively repeating this procedure, the variation of C30 with time can be determined. Mass Transfer in Region II (inside a Pore). The ion transport inside the pores is described by the spacecharge model, and the fluid velocity inside the pores is zero in accordance with experimental findings that no flow of the aqueous phase into the oil compartment or of the oil into the aqueous compartment occurs. In the space-charge model, the ion transport is described by


the Nernst-Planck equation as (in cylindrical coordinates)

∂Ci DiFziCi dΦ ji ) -Di ∂x RT dx

(21)

where ji is the local flux of ion i along the pore length, R is the universal gas constant, F is the Faraday constant, and T is the temperature in Kelvin. The flux along the r direction is taken as zero. The electrical potential Φ can be considered to be composed of two parts, i.e.

Φ(x,r) ) φ(x) + ψ(x,r)

(22)

The concentration distribution inside the pores is given by the Boltzmann equation

(

)

ziFψ RT

h i(x) exp Ci(x,r) ) C

(23)

where C h i is the (real or fictitious) concentration of ion i in the electroneutral region, so that the following relation holds among these concentrations

h2 - C h3 ) 0 C h1 - C

(24)

The radial potential distribution inside the pores is given by the Poisson-Boltzmann equation as

FC h1 Fψ 1 ∂ ∂ψ sinh r )r ∂r ∂r RT

( )

( )

(25)

The above equation is solved analytically in the form of an infinite power series, and the solution is given in Appendix 1. Using eqs 21-23, the flux of ion i can be written as

(

)

ziFψ dC h i FDiziCi dφ RT dx RT dx

ji ) -Di exp -

(26)

The total flux of ion i through a pore is given by

∫0a jir dr ) ki,1

Ji ) 2π

dC hi dφ + ki,2 dx dx

(27)

where the values of ki,j are given in Table 1. The net current flow at any cross section of a pore is zero and is given by

I ) J1 - J2 - J3 ) 0

(28)

Using eqs 24, 27, and 28 and eliminating dφ/dx and dC h 3/dx, the ion fluxes can be written as

J1 ) f11

dC h1 dC h2 + f12 dx dx

(29)

J2 ) f21


(30)

J3 ) f31


(31)

where the fi,j values are given in Table 2. Assuming a pseudo-steady-state condition, the total flux of each of the ions as calculated by eqs 29-31 is the same as that calculated from film theory. Using eqs 29-31, the three

Table 1. Expressions for ki,j

∫ exp(-zRTFψ)r dr -z Fψ r dr ) 2πD ∫ exp( RT ) -z Fψ r dr ) 2πD ∫ exp( RT )

k11 ) 2πD1 k21 k31

a

a

2

2

0

a

3

1

0

3

0

∫ exp(zRTFψ)r dr h -2πFD z C ) ∫ exp(zRTFψ)r dr RT h -2πFD z C ) ∫ exp(zRTFψ)r dr RT

k12 ) k22 k32

h1 -2πFD1z1C RT 2 2

2

a

1

0

a

2

0

3 3

3

a

3

0

Table 2. Expressions for fi,j k11 - k31 f11 ) k11 + k12 k12 - k22 - k32 k11 - k31 f21 ) k22 k12 - k22 - k32 k11 - k31 f31 ) k31 + k32 k12 - k22 - k32

k21 - k31 f12 ) -k12 k12 - k22 - k32 k21 - k31 f22 ) k21 - k22 k12 - k22 - k32 k21 - k31 f32 ) -k31 - k32 k12 - k22 - k32

unknown parameters, namely, the wall potential, dC h 1/ dx|x)0, and dC h 2/dx|x)0 can be evaluated. Additional Information. The model was solved using MATLAB software, and the program code can be obtained from the corresponding author. 3. Experimental Section 3.1. Immobilization of Lipase on the Membrane. 3.1.1. Reaction of the Z1 Membrane with Glutaraldehyde. The Z1 membrane was prepared according to the procedure described in ref 15. The reaction mixture was prepared in a 50 mM sodium phosphate buffer solution by adding glutaraldehyde to a final concentration of 5% by weight. The Z1 membrane was kept at the bottom of a beaker, and 100 mL of the reaction mixture was poured over it and then stirred gently. The beaker was maintained at 18 °C for 6 h, after which the membrane was removed and washed thoroughly with a 50 mM solution of sodium phosphate buffer to remove excess glutaraldehyde. This membrane is hereafter referred to as the Z2 membrane. 3.1.2. Enzyme Loading. Porcine pancreatic lipase, supplied by SD Fine Chemical Company (Mumbai, India), was used without further purification. The lipase solution was prepared by adding 5 g of enzyme powder to 100 mL of 50 mM sodium phosphate buffer solution. The Z2 zeolite membrane was kept at the bottom of a beaker, and 100 mL of the reaction mixture was poured over it and then stirred gently for 12 h at 25 °C. After the reaction, the membrane was removed and washed with a sodium phosphate buffer solution. The leftover reaction mixture and the buffer solution used to wash the membrane were collected and used to determine the enzyme loading. 3.1.3. Determination of Enzyme Activity. The activity of the enzyme was determined by a standard test described in the literature26 that is based on the action of the enzyme on olive oil. The substrate used in this test is an emulsion of olive oil in water stabilized using gum arabic and also containing calcium ions and sodium tauroglucate salt to enhance the enzyme activity. This test is reported to be less variable and, thus, more accurate. The pH of the emulsion is maintained at 8.0 by adding the requisite amount of sodium hydroxide solution (20 mM), and a blank run rate is determined. Then, the enzyme is added, and the reaction rate is determined from the amount of sodium hydroxide solution used to maintain the pH of the


reaction mixture at 8.0. In the calculation of the rate, the blank rate is taken into account, and the enzyme activity is reported in terms of units per milligram of powder. One unit is defined as the rate of production of 1 µmol of fatty acid per minute. 3.2. Biphasic Enzyme Membrane Reactor. The biphasic membrane reactor consists of two cylindrical compartments, each 75 mL in volume, with an arrangement for holding the membrane (membrane area ) 20 cm2) between the compartments. A water bath is used to maintain the temperature of the reactor at a constant value. In the compartment facing the active membrane surface, 300 mL of substrate (olive oil in organic solvents) is circulated at a rate of 400 mL/min, and the circulation rate is maintained constant throughout the experiments. In the other compartment, 300 mL of water at basic pH is circulated using a peristaltic pump. The pH of the water is maintained at a constant value by adding 10 mM NaOH solution and following the procedure given in the literature;9 the amount thus added is used to determine the amount of fatty acid extracted by the water and the apparent volumetric reaction rate. The EMR performance is reported in terms of the apparent volumetric reaction rate (millimoles per liter per hour) based on the volume of the aqueous phase. 3.2.1. Effect of pH on the Performance of the EMR. To determine the effect of pH on the performance of the EMR, the pH of the aqueous phase was varied from 7.5 to 9.5. The temperature of the reactor was maintained at 30 °C, and a solution of 26.66 vol % olive oil in heptane was used in the organic phase. The water circulation rate was maintained at 400 mL/min, and the reaction was carried out for 60 min. The pH was kept in a narrow range because lipase is known to be unstable at high pH and the partition of fatty acid into aqueous and organic phases is affected unfavorably at lower pH. 3.2.2. Effect of Temperature on the Performance of the EMR. To analyze the effect of temperature on the performance of the EMR, three different temperatures (20, 30, and 40 °C) were used, and the reaction was carried out for about 120 min. The pH of the aqueous phase was maintained at 9.5, the water circulation rate was 400 mL/min, and the organic phase was 26.66 vol % olive oil in heptane. We did not use temperatures beyond this range, because the enzyme activity is reported to change at higher temperature as a result of thermal deactivation and also to change at a lower temperature. 3.2.3. Effects of Various Organic Solvents on Catalyst Activity. The catalytic activity of lipase and its regioselectivity/stereoselectivity are known to be affected by the medium in which the reaction is carried out. In view of this fact, the effect on the performance of the EMR of using alkanes as solvents for olive oil was determined. For this purpose, solutions of olive oil (concentration of 26.66 vol %) in pentane, hexane, and heptane were used. The pH of the water used for extracting reaction products was kept at 9.5; the reaction was carried out for 275 min, and the amount of fatty acid extracted as a function of time was recorded. 3.2.4. Effect of Olive Oil Concentration on the Performance of the EMR. The EMR was operated at three different concentration of olive oil. The concentrations used were 13.33, 26.66, and 40% (by volume), and heptane was used as the solvent. Water at a pH of 9.5

Figure 3. FTIR spectra of the Z1 and Z2 zeolites.

was used for the extraction of the fatty acids, and the circulation rate was kept at 400 mL/min. In addition, pure olive oil was taken in the organic compartment, and the performance of the EMR was determined. 4. Result and Discussion 4.1. Enzyme Immobilization. Figure 3 shows the FTIR spectra of the Z1 and Z2 zeolites, from which it can be seen that the peaks corresponding to the imine/ amine groups (1548 and 3374 cm-1) decrease considerably and a new peak at 1645 cm-1 corresponding to the carbonyl groups appears. This confirms the occurrence of the reaction with glutaraldehyde and the presence of the free aldehyde groups on the surface. The lipase solution (105 mL) used for immobilization was prepared in excess, and a small amount of it (5 mL) was used to determine the activity of the enzyme by the procedure described in section 3.1.3. The activity was found to be 14.84 units/mg of enzyme powder, which means that a total of 74 200 units of enzyme were used for immobilization. After the reaction, the total activity of the residual solution and the water used to wash the membrane to remove the loosely held enzyme from the membrane was determined by the same procedure and found to be 52 700 units. This implies that the activity of the immobilized enzyme should be about 21 500 units. The activity of the enzyme immobilized on the membrane was also determined by the same procedure and found to be 32 500 units. The increase in the activity of the enzyme upon immobilization was thus found to be 51%. This increase in activity might be due to the presence of sodium ions in the zeolite and/or to the interaction of the charge sites of the zeolite with the polar residues of the amino acids of the active site of the enzyme. In the course of the experiments, the enzyme-loaded membrane was used for more that 60 h of reaction over a period of 25 days, and the enzyme activity was found to remain unchanged, indicating that the immobilized enzyme is highly stable. 4.2. Effects of Operating Variables on the Performance of the Biphasic EMR. The performance of

Ind. Eng. Chem. Res., Vol. 43, No. 9, 2004 2023 Table 3. Volumetric Reaction Rates of the EMR under Various Operating Conditions temp (°C) pHa 20 30 30 30 30 30c 30 30 30 30 30 40

9.5 7.5 8.0 8.5 9.0 9.5 9.5 9.5 9.5 9.5 9.5 9.5

solvent

conc (vol %)

heptane 26.66 heptane 26.66 heptane 26.66 heptane 26.66 heptane 26.66 heptane 26.66 heptane 13.33 heptane 40.00 100.00 pentane 26.66 hexane 26.66 heptane 26.66

circulation rate Vr × 103 (mL/min) (mmol L-1 h-1) Vr/Vr,litb 400 400 400 400 400 400 400 400 400 400 400 400

52.9 24.9 25.7 35.2 55.2 81.9 45.3 101 267 61.6 78.9 161

0.78 0.37 0.38 0.52 0.81 1.20 0.67 1.48 3.93 0.90 1.16 2.37

a Aqueous-phase pH. b V -3 mmol L-1 h-1) is taken r,lit (68 × 10 from Figure 8 of Giorno et al.9 c Base case.

the biphasic EMR was evaluated in terms of the apparent volumetric reaction rate (millimoles per liter per hour) based on the volume of the water used for the extraction of the fatty acid. To check for errors in the determination of the reaction rate, a blank run was performed in which a membrane without enzyme was used; in this case, it was found that the pH of the aqueous phase did not change. The experimental data on fatty acid production exhibited a linear trend and was regressed using a linear function (R2 > 0.99 for most cases) to determine the rate. The linear trend can be explained as follows: For short times, the so-called initial rate period, the concentration of products is low, so the reversible nature of the reaction can be neglected. Assuming the diffusion resistance to mass transfer for both the organic and aqueous phases to be constant with time, the concentrations in these phases can be assumed to be constant with time because of the large concentrations in the bulk. This implies that all of the enzyme molecules are saturated during the reaction and, thus, that only the second part of eq 4 determines the overall reaction rate. The overall rate can therefore now be written as

V)

d[F] ) k2[E]0 ) Vm dt

(23)

Integrating this equation and using eq 2, we obtain

[F] - [F]0 ) 3[T]0XT ) Vmt

(24)

The volumetric reaction rates were also found to be extremely high, and Table 3 lists all of the volumetric rates obtained for the various operating conditions studied in this work. It can be noticed from the table that the reaction rates are extremely high, and the best case gives a reaction rate (∼270 × 10-3 mmol L-1 h-1) that is 4 times higher than the value reported in the literature9 for a similar EMR using the same immobilization technique on an aromatic polyamide membrane (68 × 10-3 mmol L-1 h-1). The base case rate (sixth row of Table 3) is about 1.2 times higher. The operating variables selected in this study are the pH, solvent used for the olive oil, concentration of the olive oil, and temperature. All of the variables were varied in ranges that would avoid any damage to the enzyme and, thus, to its activity. 4.2.1. Effect of pH. The pH was varied from 7.5 to 9.5 in this study as pH’s lower than 7.5 would unfavorably affect the partition of olive oil into the aqueous and

Figure 4. Effect of pH on Vr of the EMR.

organic phases and the lipase is known to be unstable at high pH. Figure 4a shows data on the production of the fatty acid with time for various pH’s, with the solid lines representing the results of the regression of the data. For each case, the correlation coefficient was found to be more than 0.99. The slopes of the lines were used for the calculation of the apparent volumetric reaction rates and are shown in Figure 4b. As can be seen from this plot, the apparent volumetric reaction rate (Vr) increases with increasing pH. 4.2.2. Effect of Temperature. Three different temperatures of 20, 30, and 40 °C were used in this study. Figure 5 shows the data on fatty acid production as a function of time, with the solid line representing the linear regression of the data (R2 > 0.99 for all cases). It can be seen from this figure that, as the temperature increases, the rate of fatty acid production also increases. This is expected from the Arrhenius law, which indicates that the reaction rate increases with temperature. Also, there is no thermal deactivation of lipase in the temperature range employed in this work. 4.2.3. Effect of Solvent. In this study, three homologous nonpolar solvents (pentane, n-hexane, and nheptane) were used. Figure 6 presents the corresponding data on fatty acid production as a function of time, which were linearly regressed (R2 > 0.99) to determine Vr. It can be noticed that the Vr values for heptane and pentane are almost the same (the difference is less than the experimental error involved) whereas the Vr value


Figure 5. Effect of temperature on the performance of the EMR.

Figure 7. Effect of the concentration of olive oil in the organic phase on the performance of the EMR.

Figure 6. Effect of solvent on the performance of the EMR.

for hexane is much lower. Thus, the variation of Vr exhibits no trend with the number carbons in the solvent. 4.2.4. Effect of Concentration. Four different concentrations of olive oil (13.33, 26.66, 40, and 100 vol %) in the organic phase with heptane as the solvent were used for this study. The pH and circulation of the aqueous phase were kept at 9.5 and 400 mL/min, respectively, and the temperature was maintained at 30 °C. Figure 7 shows the data for the production of fatty acid as a function of time, which were regressed linearly (R2 > 0.99) to evaluate Vr. It can be noticed that Vr increases with increasing concentration. 4.3. Determination of Mass-Transfer Rate and Wall Potential. Because the pH of the aqueous phase is constant, the flux of ion 2 (OH-) can be calculated from the rate of addition of NaOH. The experimental data show that, for all cases, the rate of addition of NaOH was constant and, hence, the flux of ion 2 was constant; for the base case, it was calculated to be 6.8 × 10-12 kmol m-2 s-1. It was found (as indicated by the negative value of the concentration of ion 3) that the penetration of ion 3 into the aqueous phase was less than the value of film thickness determined from the mass-transfer coefficient given in the literature,24 which

Figure 8. Growth of the film in region I and variation of the concentration of ion 3 at the boundary of region I of the aqueous phase.

is valid for cross-flow membrane systems. The film thickness is, therefore, determined by the penetration of ion 3, and Figure 8 shows the growth of film thickness with time for the base case. Time zero was taken as the instant when the ion 3 concentration at x ) 0 was 0.01 mmol/m3, so that the film thickness was more than 10 times the approximate ion size (∼0.6 nm). As can be seen from this figure, the film thickness initially grew slowly (up to 80 min) and then increased rapidly. The film thickness after 2 h was about 565 nm, which is considerably smaller than the value obtained from the mass-transfer correlation (∼950 µm). Figure 8 shows the variation of the ion 3 concentration at x ) 0 with time, which exhibits a trend similar to that of the film thickness. This concentration increased slowly at the beginning and then increased rapidly. The ion 3 concentration at x ) 0 after 2 h was 3 mmol/m3, which is small. Figure 9 shows the concentration profiles of the three ions at three different times. It can be seen that the ion concentration varies in such a way that the sum of the ion 2 and 3 concentrations is equal to the concentration of ion 1. It can also be noticed that, although the ion 1


the average ion concentration prevailing inside the film. Thus, the film (region I) can be assumed to be electroneutral. It can also be noticed that the fluxes of these ions are extremely small compared to their concentrations in the film (∼10-6 kmol m-2 s-1), and so the pseudo-steadystate assumption at the boundary of regions II and I can be made. For the determination of the wall potential and mass-transfer rate in region II, the radius of the pores of the membrane was taken to be equal to the average of the pore size range (7 nm) in the Z1 membrane, which was determined in a previous work using the bubble-point method.15 The pore length was determined from the cross-sectional view of the membrane and was found to be 96 µm, and the porosity of the membrane was determined to be 0.39. The solution scheme outlined in section 2.2 requires the ion concentrations and their gradients only at the pore end (i.e., at the boundary of regions I and II). The ion concentrations were already determined in the solution of region I. The pseudo-steady-state assumption at the boundary of regions I and II implies that the fluxes of ions on both sides of the boundary are the same. The system of eqs 29-31 is solved simultaneously by first assuming a value for the wall potential and evaluating the factors fi,j. Then, using the gradients, the ion concentrations are determined by applying successive substitution to eqs 30 and 31. Using the values so obtained, the flux of ion 3 is evaluated and compared to the value determined from the film region (region I). The wall potential is varied, and the entire procedure is repeated until the flux of ion 3 is within the tolerance limit (taken as relative tolerance ) 10-3) of the value obtained from the film region (region I). The wall potentials thus determined were found to lie in the range between -0.4 are -0.7 mV for the various sets of experimental data of this work. The space-charge model uses the potential of the double layer in the aqueous phase, and the low value of the wall potential is therefore due to the extremely low concentrations of the ions in the aqueous phase. The wall potential value was found not to change with a change in pore radius ((20%), which might due to the fact that the Debye length is quite large (λ/a ≈ 7-10, where λ is the Debye length and a is the pore radius) and, therefore, the potential profile inside the pores remains the same for such variations in the pore radius. 5. Conclusion

Figure 9. Concentration profiles of the ions in region I at the three different times t ) 0, t ) 80 min, and t ) 120 min. The profiles were determined using the base case experimental data.

and 2 concentrations are initially almost the same, as time increases, the difference between them increases because of an increase in the concentration of ion 3. The value of the electric field calculated from the simulation was ∼2 × 103 V/m, and using the formula for the electric field near a planar charged conductor (i.e., E ) σ/), the charge density required to generate this field was calculated to be 1.42 × 10-6 C. This corresponds to a value of C1 - C2 - C3 (deviation from electroneutrality) of ∼1.6 × 10-14 kmol/m3, which is less than 0.001% of

A novel modified zeolite-clay composite membrane was used for the chemical immobilization of lipase using a bifunctional compound (glutaraldehyde) to provide a chemical linkage between the enzyme and the membrane. This modified membrane was used in a biphasic EMR configuration for the hydrolysis of olive oil, and the performance of the EMR was evaluated in terms of the apparent volumetric reaction rate based on the volume of the aqueous phase used for the extraction of the fatty acids. The system behaved as though it involved an irreversible reaction with no signs of product inhibition. The effects of various operating parameters (pH, solvent, olive oil concentration, and temperature) on the performance of the EMR were evaluated. The maximum apparent reaction rate (∼270 × 10-3 mmol L-1 h-1) was found to be about 4 times higher, and the base case rate (∼82 × 10-3 mmol L-1 h-1) was about 1.2 times higher, than the value re-


ported9 for a similar EMR using the same technique for immobilization of the enzyme but a different membrane (68 × 10-3 mmol L-1 h-1). The immobilized form of the enzyme was found to be highly stable and was used for more than 60 h of reaction over a period of 25 days without any noticeable change in activity. A model is proposed to describe the mass transfer of the ions on the aqueous side of the reaction sites (enzyme molecule located at the pore mouth). The model divides the entire system into two regions, an unstirred film adjacent to the pores and the charged pores themselves. Film theory was used to describe the transport of the ions in the first region, and the space-charge model was used for the second region. The extremely low rate of ion flux in the system justifies the use of the pseudo-steady-state assumption and enables the use of a solution scheme for the space-charge model that requires the ion concentrations and their gradients only at the pore end. The wall potential determined from the model was found to lie in the range between -0.4 and -0.7 mV. Appendix 1: Series Solution of the Poisson-Boltzmann Equation The Poisson-Boltzmann equation can be written in nondimensional form as

h 1 1 ∂ ∂ψ η ) 2 sinh(ψ h) η ∂η ∂η λ

( )

Fψ r , η) RT a

(

)

The boundary conditions for this equation are

|

∂ψ h )0 ∂η η)0

∑ i)0

∞

∑R CRajraksalt‚‚‚

ain )

r + s + t + ‚‚‚ ) n and

j + k + l + ‚‚‚ ) i The first condition states that each term on the righthand side of eq A6 is a product of n factors, and the second condition states that the sum of the powers of η for each factor is equal to i. The coefficients CR can be calculated by realizing that they represent the number of ways of selecting n objects (coefficients ai) from n boxes (one from each box) such that r of them are of type aj, s are of type ak, etc.; their values are given by

CR )

∞

1

λ

)

1 λ

)

or

1 2

λ (A2c)

We assume that the solution of eq A1 can be written in the form of an infinite power series ∞

ψ h )

aiηi ∑ i)0

(A3)

Substituting this series into eq A2a, one sees that a1 must equal 0 for the boundary conditions to be satisfied, or

a1 ) 0

∞

ai2R+1ηi ∑ i)0

(i + 2)2ai+2ηi ) ∑ ∑ 2 i)0 R)0 (2R + 1)!

(A2b)

|

n! r!s!t!‚‚‚

∞

2

∂ψ h Fqa )q j) ∂η η)1 RT

(A6)

such that

(A2a)

ψ h |η)1 ) ψ hw

ajηj)n ∑ j)0

ainηi ) (

Substituting the expressions for ψ h n/n! into eq A5, we obtain

RT κ λ) , κ) a 2F2c(x)

and

∞

ψ hn )

(A1)

where

ψ h )

To simplify the right-hand side of the above equation, each term inside the summation is expanded (i.e., ψ h n/ n!) in terms of the increasing powers of η as follows

( ∑ ∑ (∑ ∞

∑∑ ∑

R)0i)0 ∞

) )

ajraksalt‚‚‚

∞

r!s!t!‚‚‚

ajraksalt‚‚‚

∞

i)0R)0

r!s!t!‚‚‚

ηi

ηi

(A7)

where r + s + t + ‚‚‚ ) 2R + 1 and j + k + l + ‚‚‚ ) i. The coefficients of each ηi on left- and right-hand sides of the above equation should be equal, and by comparing them, the relationships among the parameters ai can be obtained. Evaluation of Odd-Numbered Coefficients. We first show that the coefficients aβ where β is an odd integer are zero as follows. Comparing the coefficients of ηβ-2 in eq A7, we obtain 2

β aβ )

(A4)

1

∞

(

∑∑

λ2 R)0

)

ajraksalt‚‚‚ r!s!t!‚‚‚

(A8)

where We show below (in eq A9) that, in fact, all of the oddnumbered coefficients in this series are zero. Substituting eq A3 into the Poisson-Boltzmann equation, we obtain ∞

(i + 2) ai+2η ∑ i)0 2

i

)

1

∞

∑

ψ h 2i+1

λ2i)0(2i + 1)!

r + s + t + ‚‚‚ ) R and

j + k + l + ‚‚‚ ) β - 2 (A5)

The fact that β is odd means that (β - 2) is also odd, and hence, the second condition of the above equation

Ind. Eng. Chem. Res., Vol. 43, No. 9, 2004 2027 Table A1. First Eleven Nonzero Coefficients of the Series Solution of the Poisson-Boltzmann equation

requires at least one of the indexes j, k, l, ..., to be odd. This means that all terms on the right-hand side of eq A8 contain at least one term with an odd-numbered (which is lower that β) subscript. The coefficient aβ will, therefore, be zero if all of the coefficients with odd subscripts lower than β are zero. It has been shown (eq A4) that a1 ) 0, and therefore, a3 ) 0 (because all coefficients with odd subscripts lower than 3 are zero), which implies that a5 ) 0, and so on. In general, then, we can write

aβ ) 0 for β ) 1, 3, 5, ...

(A9)

Evaluation of Even-Numbered Coefficients. To evaluate the coefficients ai with even-numbered subscripts, we again consider eq A8, which gives the general relationship among coefficients. It can easily be seen that, on collecting terms having the same combination of all other coefficients except a0, we obtain one of the

following two series

ajraksalt‚‚‚

(

a03

a05

)

1+ + + ‚‚‚ ) j!k!l!‚‚‚ 3! 5! ajraksalt‚‚‚ ajraksalt‚‚‚ ∞ a02i+1 ) sinh(a0) (A10a) j!k!l!‚‚‚ i)0(2i + 1)! j!k!l!‚‚‚

∑

(

ajraksalt‚‚‚ a02 j!k!l!‚‚‚

2!

+

a04 4!

+

a06 6!

)

+ ‚‚‚ )

ajraksalt‚‚‚ j!k!l!‚‚‚

ajraksalt‚‚‚ j!k!l!‚‚‚

∞

a02i

) ∑ i)0(2i)!

cosh(a0) (A10b)

As the sum of indices of all factors including a0 is an odd number (because R is an odd number and r + s + t ‚‚‚ ) R), we arrive at a simple rule for generating the expression for the coefficients having even-numbered


Figure A1. Improvement in the accuracy of the series solution with increasing number of terms of the series. The nondimensional wall potential is -5.0, λ is kept at 0.4, and the maximum number of nonzero terms considered is 11. The star symbols (*) represent the values obtained from the numerical computation, whereas the solid lines show the values obtained from the series solution.

Figure A2. Comparison of the solution of the Poisson-Boltzmann equation obtained by using numerical integration and series solution. The λ value is fixed at 0.4 and the wall potential value is varied. The star symbols (*) represent the values obtained from the numerical computation, whereas the solid lines show the values obtained from the series solution.

subscripts. For any coefficient (say, a2i), find all possible combination of a2jrj (j < i) such that the sum of the 2j’s is equal to 2(i - 1). If the sum of the rj’s is an even number, then multiply the combination a2jrj (j < i) by sinh(a0); otherwise, multiply it by cosh(a0). The righthand side of eq A8 can be obtained by taking all such possible combinations, and by equating this with the left-hand side, the coefficient a2i can be evaluated. Table A1 gives the first 11 nonzero coefficients of the series for the case of a uni-univalent electrolyte. It can be noticed that a0 is the only independent term in the series finally obtained and that all of the other coefficients are expressed as functions of a0. Determination of a0 will complete the solution of the equation and can be achieved by using the second boundary condition of the Poisson-Boltzmann equation (eq A2b) as given below

∑a2i ) ψw

at η ) 1

(A11)

The left-hand side of the above equation is a function of a0, and the evaluation of function is very simple and extremely fast if one realizes that the electrical potential at the axis of the cylinder is a0. Its value, therefore, is lower than or equal to the wall potential in magnitude and is of the same sign as the wall potential [i.e., a0 ∈ (0,ψw)]. Using this fact, it can be further shown that the left-hand side of equation A11 is a monotonic function, and the determination of a0 is, therefore, extremely fast. The accuracy of the series solution of the PoissonBoltzmann equation depends on the number of terms in the series (N0) used to evaluate solution. In addition, for a fixed number of terms in the series, the accuracy of the solution also depends on the wall potential and the ratio of the Debye-Huckel parameter to the pore radius. In most practical cases, the value of the nondimensional wall potential varies in the range of 0 to (7, and the same range was considered in evaluation of the accuracy of the series solution of Poisson-Boltzmann equation. Variation of Accuracy with Number of Terms. To evaluate the effect of the number of terms in the

Figure A3. Comparison of the solution of the Poisson-Boltzmann equation obtained using numerical integration and series solution. The nondimensional wall potential is fixed at -3.0, and λ is varied.

series on the accuracy of the solution, we compared the solution of the Poisson-Boltzmann equation obtained by a numerical technique with the solutions obtained by considering different numbers of terms in the series. Figure A1 shows a comparison of the solution of the equation for a nondimensional wall potential value of -5.0 and a λ value of 0.4. A horizontal line is obtained if N0 ) 1, and as N0 is increased the solution moves continuously closer to the value obtained from the numerical integration. It can be noticed from this figure that the accuracy of the series solution increases rapidly with increasing number of terms. For the parameters used in this figure, an accurate solution is obtained by using the first 11 nonzero terms. Variation of Accuracy with Wall Potential and λ. For a fixed number of terms, the accuracy of the series solution is found to increase with an increase in the value of λ and to decrease with an increase in the value of the wall potential. Figures A2 and A3 show a comparison of the series solution (considering 15 terms)


with numerical solution for different values of the wall potential and λ. It can be noticed that 15 terms gives results within 0.5% of the value obtained from the numerical computation. It can also be noticed that the number of terms required to obtain accurate solution is not very large and the computation load remains small. Literature Cited (1) Woltinger, J.; Drauz, K.; Bommarius, A. S. The membrane reactor in fine chemicals industry. Appl. Catal. A: Gen. 2001, 221, 171-185. (2) Bommarius, A. S.; Drauz, K.; Groeger, U.; Wandrey, C. Membrane bioreactors for the production of enantiomerically pure R-amino acids. In Chirality in Industry; Collins, A. N., Sheldrake, G. N., Crosby, J., Eds.; Wiley: London, 1992; pp 371-397. (3) Hoeks, F. W. J. M. M.; Muhle, J.; Bohlen, L.; Psenicka, I. Process integration aspects for the production of fine chemical illustrated with the biotransformation of γ-butyrobetaine into L-carnitine. Chem. Eng. J. 1996, 61, 53-61. (4) Sonntag, N. O. V. Fat splitting and glycerol recovery. In Fatty Acids in Industry; Johnson, R. W., Fritz, E., Eds.; Marcel Dekker: New York, 1989; pp 22-72. (5) Potts, R. H.; Makerhide, V. J. Fatty Acids and Their Industrial Application; Marcel Dekker: New York, 1968; pp 2830. (6) Liebermann, R. B.; Ollis, D. F. Hydrolysis of particulate tributyrin in a fluidized lipase reactor. Biotechnol. Bioeng. 1975, 17, 1401-1419. (7) Molinari, R.; Santoro, M. E.; Drioli, E. Study and comparison of two enzyme membrane reactors for fatty acid and glycerol production. Ind. Eng. Chem. Res. 1994, 33, 2591-2599. (8) Giorno, L.; Molinari, R.; Drioli, E.; Bianchi, D.; Cesti, P. Performance of biphasic organic/aqueous hollow fiber reactor using immobilized lipase. J. Chem. Technol. Biotechnol. 1995, 64, 345352. (9) Giorno, L.; Molinari, R.; Natoli, M.; Drioli, E. Hydrolysis and regioselective transesterification catalyzed by immobilized lipases in membrane bioreactor. J. Membr. Sci. 1997, 125, 177187. (10) Hoq, M. M.; Yamane, T.; Shimizu, S.; Funada, T.; Ishida, S. Continuous hydrolysis of olive oil by lipase in microporous hydrophobic membrane reactor. J. Am. Oil Chem. Soc. 1985, 62 (6), 1016-1021. (11) Carriere, F.; Thirstup, K.; Boel, E.; Verger, R.; Thim, L. Structure-function relationships in naturally occurring mutants of pancreatic lipase. Protein Eng. 1994, 7, 563-569.

(12) Villeneuve, P.; Muderhwa, J. M.; Graille, J.; Haas, M. J. Customizing lipase for biocatalysis: a survey of chemical, physical and molecular biological approaches. J. Mol. Catal. B: Enzym. 2000, 9, 113-148. (13) Malcatta, F. X.; Reyes, H. R.; Garcia, H. S.; Hill, C. G.; Amundson, C. H. Kinetics and mechanisms of reactions catalyzed by immobilized lipases. Enzymol. Microb. Technol. 1992, 14, 426446. (14) Garcia, H. R.; Amundson, C. H.; Hill, C. H. Partial characterization of the action of an Aspergillus niger lipase on butteroil emulsion. J. Food Sci. 1991, 56, 1233-1237. (15) Potdar, A.; Shukla, A.; Kumar, A. Effect of gas-phase modification of analcime zeolite membrane on the separation of surfactant by ultrafiltration. J. Membr. Sci. 2002, 210, 209-225. (16) Fomuso, L. B.; Akoh, C. C. Lipase-catalyzed acidolysis of olive oil and caprylic acid in a bench-scale packed bed bioreactor. Food Res. Int. 2002, 35, 15-21. (17) Jensen, B. H.; Galluzzo, D. R.; Jensen, R. G. Studies on free and immobilized lipase from Mucor miehei. J. Am. Oil Chem. Soc. 1988, 65, 905-910. (18) Yamane, T.; Hoq, M. M.; Shimizu, S. Kinetics of continuous hydrolysis of olive oil by lipase in microporous hydrophobic membrane bioreactor. Yukagaku 1986, 35 (1), 10-17. (19) Morrison, R. T.; Boyd, R. N. Chimica Organica, 5th ed.; Editrice Ambrosiana: Milano, Spain 1991; p 877. (20) Klibanov, E. M. Enzyme catalysis in anhydrous organic solvents. Trends Biochem. Sci. 1989, 14, 141-147. (21) Tsai, S. W.; Chang, C. S. Kinetics of lipase-catalyzed hydrolysis of lipids in biphasic organic-aqueous systems. J. Chem. Technol. Biotechnol. 1993, 57, 147-154. (22) Hsu, T.; Tsao, G. T. Convenient method for studying enzyme kinetics. Biotechnol. Bioeng. 1979, 21, 2235-2246. (23) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. (24) Porter, M. C. Membrane filtration. In Handbook of Separation Techniques for Chemical Engineers, 2nd ed.; Schweitzer, P. A., Ed.; McGraw-Hill: New York, 1988; pp 2-41. (25) Coury, L. Conductance measurements part I: Theory. Curr. Sep. 1999, 18, 91-96. (26) Worthington, V., Ed. Worthington Enzyme Manual: Enzymes and Related Biochemicals. Available at http://www. worthington-biochem.com/manual/L/PL.html.

Received for review August 20, 2003 Revised manuscript received January 21, 2004 Accepted February 3, 2004 IE030682+

Experimental Studies and Mass-Transfer Analysis of the Hydrolysis of

Recommend Documents