1612
I n d . Eng. C h e m . Res. 1990,29, 1612-1621
Enzymatic Resolution with a Multiphase Membrane Bioreactor: A Theoretical Analysis Dauh-rurng Wu, Georges Belfort, and Steven M. Cramer* Bioseparations Research Center, Department of Chemical Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180-3590
A mathematical formulation was developed for the simulation of multiphase enzyme membrane reactors which have been shown to have great utility for the enzymatic resolution of stereoisomers. In this analysis, two cases are considered substractive resolution, in which the unreacted stereoisomer of the substrate is recovered in the organic stream, and product resolution, where the optically pure product of the enzymatic reaction is recovered in the aqueous stream. A parametric investigation of the effects of the specific rate constant, membrane thickness, and partition coefficient was carried out. A dimensionless analysis was used to examine the effects of Thiele modulus, Biot number, and enantiomeric ratio on the performance of this reactor/separator system. In addition, the relationship between throughput and membrane thickness was studied for a variety of operating conditions. A membrane thickness limit was observed with respect to product optical purity, indicating that there may be significant advantages to employing relatively thin membranes with high enzyme loading for enzymatic resolution systems. The analysis presented here is a useful tool for the optimization of multiphase membrane reactor systems for enzymatic resolution. 1. Introduction The production of optically pure compounds is a major challenge facing the pharmaceutical and specialty chemical industries. Enzymes have recently been successfully employed for a variety of asymmetric organic syntheses (Whitesides and Wong, 1985; Jones, 1986; Margolin and Klibanov, 1987; Sonnet, 1988; Cramer and Horvath, 1989a,b). These enzymatic reactions are characterized by products of high optical purity due to the stereospecificity of the biocatalysts employed. Enzymes have also shown great utility for the kinetic resolution of racemic mixtures. Lipase, a relatively inexpensive enzyme, has been widely employed as a biocatalyst for such reactions. Esters of chiral epoxy alcohols have been produced by lipase-catalyzed hydrolysis (Lander and Whitesides, 1984). The resolution of racemic organic acids and alcohols has been carried out by using both enzymatic esterification and transesterification reactions (Cambou and Klibanov, 1984a,b; Kirchner et al., 1985). Lipase has also been used for stereoselective oligomerization (Margolin et al., 1987) as well as the preparation of optically pure @-blockers(Kloosterman et al., 1988). Chen et al. (1982) reported on the biochemical resolution of enantiomers in homogeneous solution and developed mathematical relationships between conversion and optical purity of the recovered substrate or product. Heterogeneous emulsion systems have also been used for the kinetic resolution of esters. These systems employed both free and immobilized enzyme along with an organic phase dispersed within the aqueous environment (Lavayre et al., 1982; Lander and Whitesides, 1984). The organic phase was introduced to increase the solubility of the hydrophobic substrates in these systems. However, these emulsion reactors suffer from low productivity due to severe mass-transfer limitations as well as the requirement for downstream phase separation. Multiphase enzyme hollow fiber reactors have been successfully employed for the efficient kinetic resolution of racemic mixtures (Matson and Quinn, 1986; Matson and Lopez, 1989). Matson and Lopez (1989) have investigated the diffusional effects on the stereoselectivity in spherical
* To whom correspondence should
be addressed.
0888-5885/90/2629-1612$02.50/0
catalyst particles. Their work demonstrated that diffusional limitations in immobilized enzyme systems can result in reduced stereospecificity. Thus, while these immobilized enzyme systems have been shown to have significant advantages in enzymatic resolution, they also suffer from reductions in effective enantioselectivity of the enzyme. In this paper, we present a mathematical treatment of multiphase enzyme membrane reactors and examine the performance of these systems under a variety of operating conditions. 2. Theory
A number of theoretical analyses have been reported in the literature for predicting the performance of hollow fiber bioreactors, some of which are described in Table I. While these studies investigated the performance of batch and continuous systems with a variety of kinetic expressions, they were limited to a single liquid phase. Furthermore, these analyses did not address the performance of membrane bioreactors in chiral resolution. Figure 1 shows a schematic diagram of a flat sheet membrane reactor operated in the countercurrent recycle mode with differential conversion per pass. I t has been established that recycle differential reactors can be readily treated as a batch stirred reactor of constant volume (Levenspiel, 1962). In this paper we will represent these recycle systems as batch reactors. These simulations are expected to yield results representative of the countercurrent recycle systems employed for industrial-scale kinetic resolutions. In Figure 1, the origin of the lateral coordinate, z , is located at the organic-membrane interface. Enzyme is entrapped in the hydrophilic membrane. The hydrophobic substrate is introduced into the system in the organic solvent stream. The substrate partitions from the organic phase into the hydrophilic membrane, where it is converted to a polar product. In kinetic resolution, one stereoisomer of the substrate is converted to product faster than the other due to the stereoselectivity of the enzyme. Due to partitioning effects, the polar products remain in the aqueous phase and are removed from the system by the aqueous sweeper stream. The unreacted nonpolar substrates are in turn removed by the organic stream. 0 1990 American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 8, 1990 1613 Table I. Analyses of Enzyme Hollow Fiber Bioreactors mass transport in the enzyme location operation mode membrane reaction' sponge matrix backflush convection and m-m - diffusion 1, m-m diffusion lumen batch/recycle 1, m-m diffusion sponge matrix steady-state continuous m-m diffusion sponge matrix batch/recycle m-m diffusion sponge matrix unsteady-state continuous diffusion steady-state shell any continuous convection and 1, m-m sponge matrix steady-state continuous diffusion 0, 1, m-m diffusion steady-state shell continuous diffusion 0, 1, m-m steady-state shell continuous
comments well-mixed both sides
ref Prenosil and Hediger, 1988
well-mixed shell axial and radial concn gradients in lumen well-mixed lumen axial and radial concn gradients in lumen axial and radial concn gradients in lumen axial and radial concn gradients in lumen well-mixed lumen
Trujillo, 1987 Kim and Cooney, 1976; Prenosil and Hediger, 1985 Prenosil and Hediger, 1988 Kleinstreuer and Agarwal, 1986
axial concn gradient in lumen
Heath and Belfort, 1987
Davis and Watson, 1985 Schonberg and Belfort, 1987; Catapano et al., 1988 Webster and Shuler, 1978
0, 1, m-m, and any designate zero, first-order, Michaelis-Menten, and any reaction rate laws, respectively.
Organic Membrane
E
E
A2
i ' Aqueous
with initial conditions
Aqueous
L
In order to describe this system quantitatively, material balances for the substrates and products in the organic, membrane, and aqueous phases must be solved simultaneously. Diffusion of components through the membrane is assumed to be the only mechanism of transport. The assumptions employed in these analyses were isothermal conditions, homogeneous distribution of enzyme in the membrane, no convective flow in the membrane, fint-order substrate kinetics, well-mixed organic and aqueous phases, pseudo-steady-state conditions in the membrane. The material balance for species i in the organic phase is given by
k
i
Figure 1. Schematic of a recycle multiphase membrane bioreactor.
The first-order enzymatic reactions for kinetic resolution can be represented as
Ci, = Co, for i = A, B at t = 0
(6)
and
Ci, = 0, for i = P, Q at t = 0
(7) The material balance for species i in the aqueous phase is given by
kb
B-Q where the ratio of the specific rate constants, k , / k b (enantiomeric ratio, E ) , is significantly greater than one. Conversion, y, is based on the disappearance of substrate A. The enantiomeric excess (ee) is a measure of the optical purity of a given mixture and can be defined for substractioe resolution as (3) cP - cQ -
cP
+
cQ
(9)
The material balances for species i in the membrane with first-order reaction kinetics are given by
D
d2Cb
-= k , C b dz2
d2CBm dz2
D--
and for product resolution as ee(P) =
with initial conditions Ci, = 0, for i = A, B,P , Q at t = 0
- Ek aC B m
(4)
In this paper, two modes of operation are considered: substractive resolution, in which the unreacted stereoisomer of the substrate is recovered in the organic stream, and product resolution, where the optically pure product of the enzymatic reaction is recovered in the aqueous stream. Each case has unique characteristics and will therefore be examined separately.
The boundary conditions at the membrane surfaces assuming a linear driving force approximation to film mass transport are given by
1614 Ind. Eng. Chem. Res., Vol. 29, No. 8, 1990
kgo(Cio- Ci,K,) = -D dCi,/dz, for i = A, B at z = 0 (14)
50.0
I
kgo(Cio- CimKp) -D dCi,/dz, for i = P, Q at z = 0 (15) k,(Ci,
- Ciw)= -D dCi,/dt, for i = A, B, P, Q at z = 6 (16)
The film mass-transport coefficient can be readily obtained by using the Graetz correlation (Brauer, 1985) for laminar flow:
Sh = 1.615(ReS~(d/L))’/~
(17)
In order to simplify the multiparameter system and its analysis, eqs 5-16 were nondimensionalized and are given below. The dimensionless material balance for species i in the organic phase is given by dCi0/d7 = (dCi,/dZ)i=oAo
(18)
with initial conditions Cio= 1, for i = A, B a t
T
=0
(19)
and
Ci0 = 0, for i = P, Q a t
7
(20)
=0
The dimensionless material balance for species i in the aqueous phase is given by dCiw/d7 = -(dCi,/dZ),=,A,
-.”
0.0 10.0 10.0 ao.0 40.0 60.0 80.0 70.0 80.0 90.0 100.0
TnlELE MODULUS ($)
Figure 2. Relationship between EefIand the Thiele modulus in the batch/recycle system.
An analytical solution for the relationship between the and the Thiele modulus effective enantiomeric ratio (Eeff) (4) is obtained for the simple case of negligible film mass-transport limitations on both sides of the membrane:
(21)
with initial conditions
cosh 4
KfJ6
K,
DI$
1+---
Ciw= 0, for i = A, B, P, Q a t
T
=0
(22)
sinh I$
The dimensionless material balances for species i in the membrane are given by (23) (30)
The boundary conditions at the membrane surfaces are given by Bi&Cio- K,Ci,) = -d(?im/dZ, for i = A, B at z = 0 (27) B&(Ci0- K,Ci,)
= -dCi,/dZ,
for i = P, Q at 5 = 0 (28) Biw(Cim- Ciw) = -dCim/dZ, for i = A, B, P, Q at
= 1 (29)
A relationship between the enantiomeric ratio, conversion, and optical purity has been established for homogeneous kinetic resolution systems by Chen et al. (1982). Matson and Lopez (1989) have modeled the kinetic resolution using enzymes immobilized in spherical particles. In their formulation, an effective enantiomeric ratio was defined which includes the effects of transport limitations on the apparent kinetics of the reaction. An analogous expression can also be obtained for the flat sheet system.
where K ” = Kg (1 - l/K8). Numerical Procedure. A Runge-Kutta numerical procedure (Carnahan et al., 1969) combined with a Newton-Raphson shooting method (Burden and Faires, 1985) was employed to solve the system of linear ordinary differential equations. The initial species concentrations in the bulk phases were first used to generate species concentration profiles in the membrane at the column inlet. The first derivative of each component’s concentration profiie at the membrane surface was then used to calculate the bulk concentration of the species in the two phases at the next temporal coordinate, and this procedure was repeated for successive time increments for the batch/recycle system. The grid sizes were adjusted to assure no numerical dispersion. Simulations. The performance of the membrane reactor for both substractive and product resolution was investigated under a variety of simulation conditions. The parameters employed in these simulations were obtained from Stanley and Quinn (1987) and Lopez (1989). 3. Results and Discussion The effects of diffusion limitations on the effective stereoselectivity of spherical enzymatic particles has been studied by Matson and Lopez (1989). In this paper, we present a model for multiphase enzyme membrane reactors and examine the performance of these systems under a variety of operating conditions.
Ind. Eng. Chem. Res., Vol. 29, No. 8, 1990 1615 Equation 30 describes the analytical relationship between the effective enantiomeric ratio and Thiele modulus and was derived for the batch system. This mathematical relationship, depicted in Figure 2, demonstrates that E,fl approaches the square root of the intrinsic enantiomeric ratio with increasing Thiele modulus, in agreement with the results reported for the spherical enzyme system (Matson and Lopez, 1989). Thus, while these immobilized enzyme systems have significant advantages for enzymatic resolution, they also suffer from reductions in the effective enantioselectivity of the enzyme. These effects will be studied in detail in the parametric investigations reported below. A representative set of concentration profiles of the model substrates (A, B) and products (P, Q ) in the membrane, organic and aqueous phases is presented in parts a-c of Figure 3, respectively. A rapid decrease in concentration of the more reactive substrate, A, is observed in both the membrane and organic phases as compared to the less reactive substrate, B. In the aqueous phase, the concentration of product P is seen to rise rapidly, while the concentration of product Q increases at a lower rate. In kinetic resolution, the goal is to recover the unreacted substrate B in the organic phase or the product P in the aqueous phase, at specified levels of optical purity. Clearly, as seen in parts b and c of Figure 3, there are optimal times at which to terminate the reaction for either substractive or product resolution. Substraetive Resolution. The first-order rate constant, k,, is a function of both the intrinsic specific activity of the enzyme as well as the enzyme loading. In fact, both the selection of the specific enzyme for a given reaction and the degree of enzyme loading are critical design parameters for a multiphase reactor/separator system. Accordingly, the effect of k, was examined as shown in Figure 4. It is seen that the an increase in k, resulted in both a higher conversion of A and optical purity of B for a specified reaction time. Indeed, for substractive resolution, the conversion and ee follow the same qualitative trends. Accordingly, figures given below for substractive resolution will present either conversion or ee plots in the interest of brevity. In order for the recycle differential reactor system to be accurately represented by a batch system, the conversion per pass must be limited to less than 5 % . Accordingly, relatively fast linear velocities must be employed, resulting in minimal effects of linear velocity on both the conversion and ee of the resolved substrate. The effect of substrate partition coefficient between the organic and aqueous phases, K,, was seen to have a significant effect on the optical purity as shown in Figure 5. Higher partition coefficients resulted in decreased optical purity at a specified time of reaction. Clearly, a lower partition coefficient results in more substrate transported into the aqueous membrane environment,resulting in more rapid depletion of the substrate from the organic phase. The conversion was seen to follow the same qualitative trend. These simulations indicate that organic phases with relatively low substrate partition coefficients should be employed for substractive resolution. However, these reactors are often operated with substrate-saturated aqueous streams. Under these conditions, substrate concentration in the aqueous phase is independent of the partition coefficient. Thus, in practice, organic solvents with high partition coefficients are generally employed to minimize the volume of the recirculating organic phase. In order to conduct an investigation of this multiparameter system, a dimensionless analysis was employed to
0.0
10.0
80.0
PO.0
40.0
60.0
MEMBRANE THICKNESS (pm)
0.01
1
\
P
. \ .
0.00 0.0
10.0
10.0
10.0
40.0
10.0
TIME (mln)
’
0.00 0.0
’ 10.0
10.0
ao.0
40.0
-
00.0
TIME (mln)
Figure 3. Concentration profiles in the multiphase membrane bioreactor. 6 = 50 pm, k, = 10.0 s-l, K = 60,L = 20 cm, W = 10 cm, = 0.1 M, Kp = 0.01, H = 0.05 cm, Di = 2 X cm2/s, CA,o d = E = 50. Profiles in the membrane, organic, and aqueous phases are shown in a, b, and c, respectively. Membrane profiles at 1,2,3, and 4 min are indicated by plots a, b, c, and d, respectively, in a.
1616 Ind. Eng. Chem. Res., Vol. 29, No. 8, 1990 1.0
,
/-
/
I
1.0
m W
2
1 0
0.8
Fr
0.4y
v)
m
3 v)
v) v)
'
2
0 a
0.4
Y
0 c 2
0.2
I
0.2
W
0.0
0.0
10.0
20.0
50.0
40.0
1
0.0
0.0
50.0
10.0
20.0
50.0
40.0
80.0
TIME (mln)
TIME (mln)
Figure 5. Effect of the substrate partition coefficient on ee(B) in substractive resolution. Simulation conditions as stated in Figure
1.0
3. m
g
0.8
m
3 v)
TIME (mln)
Figure 4. Effect of the enzymatic rate constant on the conversion of substrate A and enantiomeric excess of substrate B in substractive resolution. Simulation conditions as stated in Figure 3.
examine the effects of Thiele modulus, Biot number, and enantiomeric ratio on the performance of this reactor/ separator. While the ratio of the membrane volume to phase volume, A, had an effect on the time required to attain a specified conversion, A had no effect on the relationship between optical purity and conversion in substractive resolution. The effect of Thiele modulus on the relationship between conversion and optical purity was investigated as shown in Figure 6a. High Thiele modulus resulted in a decreased optical purity of B for a specified level of conversion. A higher value of Thiele modulus reflects a lower iternal diffusion relative to the enzymatic reaction rate, resulting in a decreased effective enantiomeric selectivity with a concomitant decrease in optical purity of the resolved substrate B. In fact, this effect is more pronounced in product resolution, as described below. The Biot number is a measure of the relative importance of film mass transport to internal diffusion. In this study, the water side Biot number had a negligible effect on reactor performance due to the relatively low concentrations at the membrane-aqueous stream interface. On the other hand, high Biot numbers for the membrane-organic
stream interface resulted in increased optical purity at a fixed conversion, as shown in Figure 6b. Clearly, these external mass-transport limitations had less of an effect on the effective enantiomeric selectivity than the internal mass-transport limitations described in Figure 6a. Figure 6c demonstrates the effect of intrinsic enantiomeric selectivity on the performance of substractive resolution systems. As expected, more stereospecific enzyme systems yielded higher optically pure compounds. In fact, this effect is much more pronounced in product resolution as described below. Product Recovery. The performance of multiphase bioreactors in product resolution is significantly more sensitive to the operating conditions than in substractive resolution. The effect of the specific rate constant on the optical purity of product P was examined as shown in Figure 7. While an increase in k , resulted in the rapid conversion of A as described above in Figure 4, increased enzymatic activity had an adverse effect on the optical purity of the product in product resolution. A high specific activity of the enzyme membrane caused more rapid depletion of substrate A and increased conversion of the less reactive substrate, resulting in decreased optical purity of the product. Thus, a t lower enzyme loadings, one can achieve higher optical purity of the product a t a given conversion. Practically speaking, this requires a greater surface area reactor with lower enzyme loadings or a relatively thin membrane with high enzyme loading as described below. While for substractive resolution the membrane thickness has a minimal effect on the reactor performance for the range evaluated (50-250 pm), the membrane thickness had a significant effect on the optical purity in product resolution as demonstrated in Figure 8. Increased membrane thickness caused more complete conversion of substrate A in the membrane, resulting in increased conversion of the less reactive substrate. This decreased effective enantiomeric selectivity of the membrane resulted in lower optical purity of the product as shown in the figure. Clearly, when high optical purity of the product is required, relatively thin membranes are desirable. The effect of substrate partition coefficient, K,, between the organic and aqueous phases was examined for product resolution as shown in Figure 9. The partition coefficient was seen to have an opposite effect in product resolution
Ind. Eng. Chem. Res., Vol. 29, No. 8,1990 1617 1.0
m
n
58
3
0
0.0
0.8
83
v)
$
0
c
0.4
5
P
lO\
01
::
f
\
U
v)
Y
I
E
m
8
O.O
0.4
0
5ia
0.2
Z W
5
0.2
0.0
0.0 ..
0.0
0.2
0.0
0.4
0.0
0.0
1.0
6.0
3 cn 8
1' Y
20.0
20.0
ao.0
O'O 0.0
0.0
0.0 0.4
c
8
5
16.0
Figure 7. Effect of the enzymatic rate constant on enantiomeric excess of product P in product recovery. Simulation conditions as stated in Figure 3 with the exception of E = 100.
blr
1.0 r
B
10.0
TIME (mln)
CONVERSION OF SUBSTRATE A
0.4 0.2
5 0.2
0.0 0.0
0.2
0.0
0.4
0.0
1.0
CONVERSION OF SUBSTRATE A 0.0 6c
TIME (mln)
1.0
Figure 8. Effect of the membrane thickness on ee(P) in product recovery. Simulation conditions as stated in Figure 7.
m
3
v)
1.0 O'(
m
a
03
8
5
0.0
8
v)
t:
g
s:
p 8 5
0.0
0.0
8
0.4
v) v)
# Y
O.'
0
0.2
0.0
zi
E
Z
a
0.0
0.0
0.2
0.4
0.0
0.8
1.0
0.6
CONVERSION OF SUBSTRATE A
Figure 6. Dimensionlessanalysis of the relationship between ee(B) and conversion of substrate A in substractive resolution. 6 = 2.0, Bi, = 0.058, Bi, = 0.058, E = 50, K , = 60,K p = 0.01,A = 0.1. (a) Effect of the Thiele modulus. (b) Effect of the Biot number. Plots for Bi, = 0.58,0.058, and 0.0058 are indicated by a, b, and c, respectively. (c) Effect of the enantiomeric selectivity.
0.4
0.0
10.0
20.0
30.0
40.0
50.0
TIME (mln)
Figure 9. Effect of the substrate partition coefficient on ee(P) in product recovery. Simulation conditions as stated in Figure 7.
1618 Ind. Eng. Chem. Res., Vol. 29, No. 8, 1990
as compared to the substractive resolution mode. While lower partition coefficients resulted in more rapid conversion, they also caused decreased optical purity of the product. The Thiele modulus was shown to have a profound impact on the relationship between optical purity and conversion in product resolution as shown in Figure loa. Again, this is due to a slower internal diffusion relative to the enzymatic reaction rate for high Thiele modulus values. Thus, it is critical to operate product resolution systems under conditions reflected by a low Thiele modulus. This figure clearly demonstrates that product resolution is significantly more sensitive to the effects of internal diffusion limitations than the substractive resolution mode depicted in Figure 6a. The effect of Biot number was also examined for product resolution, as shown in Figure lob. The Biot number was shown to have a significant effect on the relationship between optical purity of the product and conversion. Again, this effect was more pronounced for product resolution than for the substractive resolution simulations depicted in Figure 6b. Figure 1Oc demonstrates the effect of intrinsic enantiomeric selectivity on the performance of product resolution systems. As expected, more stereospecific enzyme systems yielded higher optically pure compounds. Optimization, While the above parametrization yielded important information on the effects of various lumped parameters on the relationship between optical purity and conversion, what is really required is an optimization of the throughput of these systems. Accordingly, we examined the effect of various parameters on product throughput in both substractive and product resolution. Here, throughput is defined as the rate of substrate or product production a t a specified level of optical purity (ee = 96%) per unit membrane surface area. Since the optical purity is a strong function of conversion in these systems, each simulation was terminated once the optical purity was achieved for a specified membrane thickness. Parts a-c of Figure 11 examine the effect of intrinsic enantiomeric selectivity, substrate partition coefficient, and specific rate constant, respectively, on the relationship of throughput to membrane thickness in substractive resolution. Parts a and b of Figure 11 exhibited optimal throughputs at a membrane thickness of roughly 30 pm. These figures employed a constant enzymatic rate constant of 10 s-l. Under these conditions, while the optimum membrane thickness remained constant, the throughputs were dramatically increased with increasing intrinsic enantiomeric selectivity and decreasing substrate partition coefficient. Figure l l c examined the effect of enzymatic rate constant on the throughput in substractive resolution. An increase in the rate constant resulted in both an increased throughput and a shift of the optimum membrane thickness to lower values. Clearly, these results indicate that relatively thin membranes with high enzyme loading are desirable for substractive resolution. Parts a-c of Figure 1 2 examine the effect of intrinsic enantiomeric selectivity, substrate partition coefficient, and specific rate constant, respectively, on the relationship of throughput to membrane thickness in product recovery. Since the optical purity decreases with conversion as shown in Figure 10, each simulation was terminated once the optical purity was achieved for a specified membrane thickness. In fact, the simulations shown in Figure 12 illustrate that the desired optical purity of the product could not be attained once the membrane thickness exceeded a certain value for a given set of operating condi-
1.0
n
&
0.8
3
8 EU 0
0.6
v)
v)
4w 0
0.4
K
f
E z a z
0.2
Lu
0.0
CONVERSION OF SUBSTRATE A 1011
1.0 r
t
n
Q
0.8
0
8n Y
0
0.8
v)
20
3 0
0.4
85
0.2
a
u
z w
I 00
0.2
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0.0
0.0
10
CONVERSION OF SUBSTRATE A 10
0
0 Y
0
0.8 -
v)
2
sw
0
0.4 -
a
f0
2u 5
0.2 -
on
I 0.0
0.2
0.4
0.8
0.8
io
CONVERSION OF SUBSTRATE A
Figure 10. Dimensionless analysis of the relationship between ee(P) and the conversion of substrate A in product recovery. 4 = 2.0, Bi, = 0.058, Si, = 0.058,E = 100,K , = 60,Kp = 0.01,A = 0.1. (a) Effect of Thiele modulus. (b) Effect of Biot number. (c) Effect of enantiomeric selectivity.
Ind. Eng. Chem. Res., Vol. 29, No. 8,1990 1619
c
-
PE
a.0
-
sn
2.6
-
g8
a.6
'
a
10.0 14.0
'*'O
10.0
8
8.0
5n
8.0
'P I
-
1.6
18.0
E
-
2.0
20.0
4.0
2.0
0.0
ao.0
00.0
~ " ~ ' " " " " " ' ' " " '
0.0
l.o~"'""'""'"'""''" 80.0
1~0.0
160.0
3.6
-
3;
3.0
-
c
NE E a
-E
d
g
F cn m
3 8
2.6
-
2.0
-
1.6
-
"
MEMBRANE THICKNESS (pm)
MEMBRANE THICKNESS (pm)
-f
l ' " ' A " ' ' l
18.0 -
10.0
-
14.0
-
12.0 10.0 8.0
I-
z
6.0
EP! :
4.0
-
E
2.0
o . o ~ " " " " " " " " " " ' " ' l 0.0
30.0
60.0
0.0
80.0
120.0
0.0 10.0 20.0 30.0 40.0 60.0 00.0 70.0 80.0 90.0
wo.0
MEMBRANE THICKNESS (pm)
MEMBRANE THICKNESS (pm)
I , I2c
8.0
40.0
-
36.0
C
mE E a
s
32.0
T
28.0
n.
g8
20.0
8
16.0
24'0
E
2
I
P E 0 . 0 ~ ' " " ' 0.0 10.0
110.0
m.0
6.0 4.0
i///
I
0.0
" ' " ' " " . " " . ~
lw.o
12.0
2w.o
MEMBRANE THICKNESS (pm)
Figure 11. Optimization of throughput in subtractive resolution. Simulation conditions as stated in Figure 3. (a) Effects of enantiomeric selectivity. (b) Effect of the substrate partition coefficient. (c) Effect of the enzymatic rate constant.
0.0
60.0
180.0
240.0
a2o.o
400.0
MEMBRANE THICKNESS (pm)
Figure 12. Optimization of throughput in product resolution. Simulation conditions a8 stated in Figure 3 with the exception of E = 200. (a) Effect of enantiomeric selectivity. (b) Effect of the substrate partition coefficient. (c) Effect of enzymatic rate constant.
1620 Ind. Eng. Chem. Res., Vol. 29, No. 8, 1990
tions. A membrane thickness limit was observed for each parametric plot and is represented by an open circle in these figures. In practice, however, these limits are never approached due to the exceedingly short reaction times required and the dilute product concentrations obtained under these limiting conditions. Figure 12a indicates that an increase in the inherent enantiomeric selectivity enables the use of a thicker membrane for a specified optical purity. Although lower E values resulted in higher apparent throughputs for thin membrane systems, these results are due to the extremely short reaction time required in nonselective enzymatic systems. In fact, a high E value is always desirable in product recovery systems. While Figure 9 indicated that the enantiomeric excess of the product decreased more rapidly for lower K,, Figure 12b indicates that the throughput dramatically increases with decreasing substrate partition coefficient. This apparent contradiction can be readily explained by considering the basis of the two simulations. Although the enantiomeric excess decreases with decreasing K,, the rate of conversion is significantly increased. Thus, the run time required to achieve a specified level of optical purity is greatly reduced resulting in increased product throughput. Figure 12c examined the effect of enzymatic rate constant on the throughput in product recovery. An increase in the rate constant resulted in a dramatic increase in product throughput and a smaller range of membrane thickness which could be employed for a given resolution. A product concentration of 0.09 M at the desired optical purity could be achieved with membrane thicknesses of 3.9, 17, or 62 ym containing specific activities of 100, 10, and 1 sv1, respectively. However, the production rate for the 3.9-~m-membranesystem is 9.17 mmol/(m2 min) as compared to 1.45 for the 62-ctm-membrane system. Thus, these simulations indicate that there may be a significant advantage to employing relatively thin membranes with high enzyme loading for product resolution. We are presently developing thin membrane composite enzyme systems for this purpose, which will be the subject of a future report. 4. Conclusion
A mathematical formulation was developed for the simulation of multiphase enzyme membrane reactors which have been shown to have great utility for the enzymatic resolution of stereoisomers. The performance of multiphase bioreactors in product recovery was significantly more sensitive to the operating conditions than in substractive resolution. While an increase in the enzyme loading resulted in rapid conversion and high optical purity in substractive resolution, higher enzyme loadings produced decreased optical purity in product recovery. Thicker membranes produced decreased optical purity in product recovery and had a minimal effect in substractive resolution. Higher partition coefficients gave rise to elevated optical purity in product recovery and decreased optical purity in substractive resolution. Optical purity was increased in both product and substractive resolution by increasing the Biot number, increasing the enantiomeric ratio, or decreasing the Thiele modulus. Elevated throughputs were obtained in both product and substractive resolution by increasing the specific rate constant, increasing the enantiomeric selectivity, or decreasing the partition coefficient. A membrane thickness limit was observed in product recovery, and the results indicate that there may be significant advantage to employing relatively thin membranes with high enzyme
loading for enzymatic resolution systems. The analysis presented here is a useful tool for the optimization of multiphase membrane reactor systems for enzymatic resolution, which will be the subject of a future report. Acknowledgment We thank Dr. Jorge L. Lopez of Sepracor Inc. for bringing this problem to our attention and encouraging us to do this analysis. Nomenclature A = effective membrane area, cm2
Bi
= Biot number, k,6/D
C = concentration, M
C = dimensionless concentration C/C O D = intramembrane diffusion coefficient, cmz/s E = enantiomeric ratio of specific rate constant, k , / k b Eeff= effective enantiomeric ratio ee(B) = enantiomeric excess of component B, (C, - C,)/(CB + C), ee(P) = enantiomeric excess of product P, (C, - C,)/(C, +
CQ)
H = height of the chamber, cm k , = specific rate constant of substrate A, s-l kb
= specific rate constant of substrate B,
k = mass-transfer coefficient, cm/s
hB, = partition coefficient of substrate between organic and
aqueous phases K , = partition coefficient of product between organic and aqueous phases L = reactor length, cm Re = Reynold number, U d / u Sh = Sherwood number, k d / D Sc = Schmidt number, u/d t = time, s L‘ = velocity of streams, cm/s V = volume, cm3 z = lateral distance from the membrane surface, cm i = dimensionless lateral distance from the membrane surface, ZJT,
Greek Symbols 6 = membrane thickness, cm = Thiele modulus, 6 ( k , / D ) 1 / z T = dimensionless time, Dt/62 . I = ratio of the membrane volume to the system volume,
SA/ V 1 =
conversion, 1 - C,
Subscripts i = species of compounds o = organic phase 6’= aqueous phase m = membrane
Superscript o = initial condition
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Ind. Eng. Chem. Res. 1990,29, 1621-1626 Cambou, B.; Klibanov, A. M. Preparative Production of Optically Active Esters and Alcohols Using Esterase-Catalyzed Stereospecific Transesterification in Organic Media. J. Am. Chem. SOC. 1984,106, 2687-2692. Carnahan, B.; Luther, H. A.; Wilkes, J. 0. Applied Numerical Methods; Wiley: New York, 1969. Catapano, G.; Iorio, G.; Drioli, E.; Filosa, M. Experimental Analysis of a Cross-flow Membrane Bioreactor with Entrapped Whole Cells: Influence of Transmembrane Pressure and Substrate Feed Concentration on Reactor Performance. J. Membr. Sci. 1988,35, 325-338. Chen, C.-S.; Fujimoto, Y.; Girdaukas, G.; Sih, C. J. Quantitative Analyses of Biochemical Kinetic Resolutions of Enantiomers. J. Am. Chem. SOC. 1982, 104, 7294-7299. Cramer, S. M.; Horvath, C. Peptide Synthesis with Immobilized Carboxypeptidase Y. Biotechnol. Bioeng. 1989a, 33, 344-353. Cramer, S. M.; Horvath, C. Peptide Synthesis and Deamidation with Chemically Modified Immobilized Carboxypeptidase Y. Enzyme Microb. Technol. 198913, 11, 74-79. Davis, M. E.; Watson, L. T. Analysis of a Diffusion-Limited Hollow Fiber Reactor for the Measurement of Effective Substrate Diffusivities. Biotechnol. Bioeng. 1985, 27, 182-186. Heath, C.; Belfort, G. Immobilization of Suspended Mammalian Cells: Analysis of Hollow Fiber and Microcapsule Bioreactors. Ado. Biochem. Eng./Biotechnob 1987, 34, 1-31. Jones, J. B. Enzymes in Organic Synthesis. Tetrahedron 1986,42, 3351-3403. Kim, S.4.; Cooney, D. 0. An Improved Theoretical Model for Hollow-Fiber Enzyme Reactors. Chem. Eng. Sci. 1976, 31, 289-294. Kirchner, G.; Scollar, M. P.; Klibanov, A. M. Resolution of Racemic Mixtures via Lipase Catalysis in Organic Solvents. J.Am. Chem. SOC.1985, 107, 7072-7076. Kleinstreuer, C.; Agarwal, S. S. Analysis and Simulation of HollowFiber Bioreactor Dynamics. Biotechnol. Bioeng. 1986, 28, 1233-1240. Kloosterman, M.; Elferink, V. H. M.; Iersel, J. V.; Roskam, J.-H.; Meijer, E. M.; Hulshof, L. A.; Sheldon, R. A. Lipases in the Preparation of 0-Blockers. TIBTECH 1988,6, 251-256. Ladner, W. E.; Whitesides, G. M. Lipase-Catalyzed Hydrolysis as a Route to Esters of Chiral Epoxy Alcohols. J. Am. Chem. SOC. 1984, 106, 7250-7251.
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Lavayre, J.; Verrier, J.; Baratti, J. Stereospecific Hydrolysis by Soluble and Immobilized Lipases. Biotechnol. Bioeng. 1982,24, 2175-2187. Levenspiel, 0. Chemical Reaction Engineering; an Introduction t o the Design of Chemical Reactors; Wiley: New York, 1962. Lopez, J. L. Personal communication, 1989. Margolin, A. L.; Klibanov, A. M. Peptide Synthesis Catalyzed by Lipases in Anhydrous Organic Solvents. J. Am. Chem. SOC.1987, 109, 3802-3804. Margolin, A. L.; Crenne, J.-Y.; Klibanov, A. M. Stereoselective Oligomerizations Catalyzed by Lipases in Organic Solvents. Tetrahedron Lett. 1987,28, 1607-1610. Matson, S. L.; Lopez, J. L. Multiphase Membrane Reactors for Enzymatic Resolution: Diffusional Effects on Stereoselectivity. In Frontiers in Bioprocessing; CRC Press: Boca Raton, FL, 1989; pp 391-403. Matson, S. L.; Quinn, J. A. Membrane Reactors in Bioprocessing. Ann. N.Y. Acad. Sci. 1986,469, 152-165. Prenosil, J. E.; Hediger, T. Scale-up of Membrane Fixed Enzyme Reactors: Modelling and Experiments. Desalination 1985, 53, 265-278. Prenosil, J. E.; Hediger, T. Performance of Membrane Fixed Biocatalyst Reactors. 1: Membrane Reactor Systems and Modelling. Biotechnol. Bioeng. 1988,31, 913-921. Schonberg, J. A,; Belfort, G. Enhanced Nutrient Transport in Hollow Fiber Perfusion Bioreactors: a Theoretical Analysis. Biotechnol. Prog. 1987, 3, 80-89. Sonnet, P. E. Enzymes for Chiral Synthesis. CHEMTECH 1988,18, 94-98. Stanley, T. J.; Quinn, J. A. Phase-Transfer Catalysis in a Membrane Reactor. Chem. Eng. Sci. 1987, 42, 2313-2324. Trujillo, E. M. Transient Response of Encapsulated Enzymes in Hollow-Fiber Reactor. Biotechnol. Bioeng. 1987, 29, 529-543. Webster, I. A,; Shuler, M. L. Mathematical Models for Hollow-Fiber Enzyme Reactors. Biotechnol. Bioeng. 1978,20, 1541-1556. Whitesides, G. M.; Wong, C.-H. Enzyme as Catalysts in Synthetic Organic Chemistry. Angew. Chem., Znt. Ed. Engl. 1985, 24, 617-638.
Received for review August 8, 1989 Revised manuscript received February 21, 1990 Accepted March 14, 1990
Study of Temperature-Programmed Desorption of tert -Butylamine To Measure the Surface Acidity of Solid Catalysts And& T. Aguayo, Jos6 M. Arandes, Martin Olazar, and Javier Bilbao* Departamento de Ingenieria Quimica, Universidad del Pais, Vasco. Apartado 644, 48080 Bilbao, Spain
The technique of temperature-programmed desorption of tert-butylamine is described to measure the surface acidity of solid catalysts. The use of this base has advantages over the use of ammonia, pyridine, and n-butylamine. The desorption measurement is carried out by two methods, gas chromatography and thermogravimetry, and the advised conditions are described for both methods. Catalysts of SiOz/A1,03, bifunctionals of Ni-Si02/A1,03, and a commercial cracking zeolite have been studied. A comparison of the desorption results with those of the other acidity measurement techniques (such as titration with n-butylamine in the liquid phase and kinetic measurement of isomerization of n-butenes as the test reaction) allows the acidity measured with tert-butylamine desorption to be classified as strong, corresponding to the active sites in most of the reactions among the hydrocarbon compounds catalyzed by acids. Introduction The greatest difficulty found in the characterization of acidic catalysts is the measurement of surface acidity-the origin of the activity of these catalysts in the reactions among hydrocarbon compounds. In the relevant literature, revisions of the methods described to measure the acidity are compiled (Benesi and Winquist, 1978) and can be classified into four groups: (A) titration, (B) spectroscopic measurement by IR, ( C ) test reactions, (D) adsorption-desorption of bases. 0888-5885/90/2629-1621$02.50/0
All the methods have disadvantages, and in general, the more rigorous methods have the disadvantage of being more complex and/or more costly. The first two methods give information about the acidity of the catalysts at room temperature, while the latter two methods have the advantage that they give information about the acidity for a temperature near the one to be used in the reaction. The most traditional method (Benesi, 1956, 1957) is titration of the finely ground catalysts with n-butylamine, in liquid medium (benzene), using colored indicators of 0 1990 American Chemical Society
