J. Chem. Tech. Biotechnol. 1992, 54, 249-255
Mathematical Modelling and Simulation of a Recycle Dialysis MembFane Reactor in a Reversed Micellar System Chen-Li Chiang* & Shau-Wei Tsai Department of Chemical Engineering, National Cheng Kung University, Tainan, Taiwan (Received 22 August 1991; revised version received 9 January 1992; accepted 28 January 1992)
Abstract: A mathematical framework was developed for the evaluation of a recycle dialysis membrane reactor (RDMR). The lipase-catalyzed hydrolysis of olive oil in an AOT-iso-octane reversed micellar system was employed as a model. Three specific operational strategies have been considered, namely batch, fedbatch, and fed-batch-bleed. Simulation shows the conversion of substrate to be strongly dependent on efficient use of the substrate, since the permeability coefficients of both substrate and product are quite similar. Sensitivity analyses were performed to assess the influences of various parameters (membrane area, substrate feed rate, solvent bleed rate and permeability) on the performance of the reactor in different modes of operation. The analyses presented are useful to assist the optimization of the operational strategy used for the RDMR system.
Key words : reversed micelles, lipase, inhibition operational strategy, effective membrane area.
NOTATION
Subscript i Initial state 1 Source phase 2 Receiver phase
Effective area of membrane (cm2) Total mass of enzyme in the reactor (mg) Rate constant in the Michaelis-Menten equation (U mg-' enzyme) Dissociation constant for the complex EP* (mol dm-3) Michaelis constant (mol dm-3) Substrate feed rate (cm3 min-') Product concentration (mol dm-3) Product permeability coefficient (m s-') Substrate permeability coefficient (m s-l) Receiver solvent bleeding rate (cm3min-l) Substrate concentration based on ester bond (mol dm-3) Reaction time (min) Volume of solution (cm3) Degree of substrate conversion
1 INTRODUCTION
* Present address : Institut fur Enzymtechnologie, KFA Jiilich, PO Box 2050, 5170 Julich, Germany. 249
In 1977 Martinek eb a1.l demonstrated cl-chymotrypsin activity in reversed micelles of Bis(2-ethylhexyl) sodium sulfosuccinate (AOT) in octane. Since then, a variety of enzymes, surfactants, solvents and substrates have been used for studying enzymatic reactions in reversed micelles ;to date about 30 enzymes have been involved in the catalytic activity studies as reported in recent review^.^-^ The reversed micellar system has received considerable attention during the past decade since it is one of the most powerful tools for conversion of apolar compounds by However, several factors have contributed to the under-utilization of reversed micellar systems in commercial biotechnology. Foremost amongst these is the limited theoretical understanding and hence predictability of the time course analysis for the reaction with a high - substrate concentration. In addition,
J. Chem. Tech. Biotechnol. 0268-2575/92/$05.00. 0 1992 SCI. Printed in Great Britain
Chen-Li Chiang, Shau- Wei Tsai
250 the problems of retention of reversed micelles and product recovery from the surfactants employed are also significant. Recently, Tsai and Chiang'l used Cundidu rugosa lipase to investigate the hydrolysis of a high concentration olive oil in an AOT-iso-octane reversed micellar system. The hydrolytic reaction obeyed Michaelis-Menten kinetics. The rate equation was analyzed in the time course reaction and found to be in agreement with the experimental results. A recycle dialysis membrane reactor (RDMR), integrating both reaction and separation, was successfully employed for continuous hydrolysis of olive oil in the AOT-iso-octane system in the authors' laboratory. Continuous runs were performed up to 48 h and 93.4% rejection of reversed micelles was obtained. The mathematical formulations, involving coupled enzymatic reaction and mass transfer, were also developed to describe the operation of the RDMR system." In order to estimate quantitatively and improve performance of the RDMR system, the process must be designed and simulated for different operational strategies. Given the above background, the aims of the present work have been to develop a useful mathematical framework whereby performance evaluation of the RDMR system might be simulated to yield ultimately an optimized operational strategy.
2 MATERIALS AND METHODS 2.1 System description The system used was constructed to describe the operation of the RDMR system and previously employed for a study of the enzymatic reaction in reversed micelles." A schematic of the system is illustrated in Fig. 1. As described previously,12 a stirred tank reactor is coupled to a dialysis membrane cell in a semi-closed-loop configuration via a suitable peristaltic pump. The cell contains the appropriate semi-permeable membrane which retains the reversed micelles yet passes the product molecules. During operation, the source reservoir is initially filled with both substrate and reversed micelles containing enzyme, whilst the receiver reservoir contains only organic solvent. The entire contents of both source and receiver reservoirs are continuously pumped through the membrane cell and recycled back to these reservoirs, respectively. The extension of feed stream of substrate and bleed stream of receiver solvent, as shown in Fig. 1, makes the RDMR system more suitable for various operational schemes.
Substrate feeding
Solvent refill R
Dialysis cell I I I I
+R
Source phase
Receiver phase
Solvent bleeding
Fig. 1. Process scheme of an RDMR used for an AOT-isooctane reversed micelle model system.
stream. Thus, both the substrate feed rate and receiver solvent bleed rate are zero in batch operation. Another mode of operation is known as semi-batch or fed-batch operation. This mode differs from batch operation only in that the reactor has a feed stream and allows the substrate to be fed continuously as the reaction proceeds. In this case, only the receiver solvent bleed rate is zero. The strategy of fed-batch-bleed operation is the same as for fed-batch operation, except that input and removal of the receiver solvent is continuous.
3 MATHEMATICAL SIMULATION 3.1 Mathematical formulation
In the authors' previous study," it was demonstrated that the hydrolytic reaction exmained obeys classic Michaelis-Menten kinetics. Competitive inhibition by the main product, oleic acid, was observed. The assumptions employed in the authors' analyses were those of well mixed source and receiver reservoirs: no enzyme deactivation, and no fouling in the membrane. In order to describe this system quantitatively, the material balance must be solved simultaneously by coupling the enzymatic reaction with mass transfer for both substrate and product. The comparative changes of mathematical formulation for various operational schemes may be expressed as follows :
(4)
2.2 Operational strategies A batch operation mode has neither feed nor effluent
with initial conditions : at t = 0 , P~ = 4, Pz = 0,S ,
=
S,, S ,
=0
(5)
25 1
Evaluation of a recycle dialysis membrane reactor
where S and P are the product and substrate concentration ;PM, s and PM, are the permeability coefficients of substrate and product, respectively; k,,, is the turnover number; K M is the Michaelis constant; K , is the dissociation constant; Mi is the feed rate of substrate; and R is the bleed rate of solvent in the receiver. The concentration of substrate, based on the ester bond in olive oil, was defined as follows: S (mol dm-3) =
191.5 S (g ~ m - ~ ) 56.1
Moreover, the degree of substrate conversion was calculated from eqn (7) as:
X=
total product yield total substrate input
(7)
where the total product yield is the sum of the products in the source, receiver and bleed phases. The total substrate input includes the initial input and the sum of continuous input as the reaction proceeds.
3.2 Numerical procedure A Runge-Kutta method was employed to solve the system of coupled first-order ordinary differential equations. The Runge-Kutta method is a fourth-order integration procedure which is both stable and selfstarting.13The parameters used in these simulations were obtained from the authors' previous results11~12 and are listed in Table 1. To assess the quantitative influence of the various parameters on the performance of the reactor under different modes of operation, sensitivity analyses were performed using computer simulation. The first series of mathematical simulations were conducted to examine the influence of the effective membrane area on the
TABLE 1 Parameters Used in the Mathematical Simulation of a Recycle Dialysis Membrane Reactor with an AOT-iso-octane Reversed Micellar System
Parameter
performance of reactor. In these simulations, the effective membrane area was varied between 0 and 500 cm'. The second series of simulations was developed to investigate the influence of the substrate feed rate on the performance of the reactor. The substrate feed rates used in these simulations were 0-0.022 cm3 min-l. The third series of simulations, only for the case of the fedbatch-bleed operation, was conducted to study the influence of the receiver solvent bleed rate on the performance of the reactor. The bleed rates used in these simulations were 0-0.5 cm3 min-' and the substrate feed rate was maintained constant a t 0.01 1 cm3 min-'.
RESULTS AND DISCUSSION
4
In order to demonstrate the importance of product inhibition phenomena during enzymatic hydrolysis of olive oil in AOT-iso-octane reversed micelles, two types of reaction mechanisms were considered. One is that no inhibition mechanism operated; the second is with a competitive inhibition mechanism. If the product was removed as formed, there would be no inhibition. The simulated time course of the reaction for batch operation without separation ( A = 0) is shown in Fig. 2. This graph shows that the reaction would proceed much faster if the product were removed as it was formed (indicated by dotted line). After approximately five hours, the substrate conversion is 60 % where inhibition is assumed and 95 YO for the situation where no inhibition is simulated. Thus, the strong inhibitory effect of oleic acid on lipase would appear to be an important factor to consider in the design of a large scale process. With this in mind, it is quite reasonable to assess the influence of the various
96
c
I
/
/
Value 67.1 pmol min-' mg-' e:nzyme 0.505 mg 0.7 17 mol dm-3 0.089 rnol dm-3 3.87 x lo-' m s-' 3.57 x m s0-500 cm2 0-0.022 cm3 min-l 0 0 5 cm3 min-' 0.683 mol dm-3 0 rnol dm-3 16.7 h
/
I
_ _ _ _ NO
INHIBITION
__ INHIBITION
0' 0
"
200
"
400
'
I
800
"
800
i "
1000
t (min) Fig. 2. Comparison of time course of substrate conversion between product inhibition and no product inhibition mechanism, using AOT-iso-octane reversed micelle model system under batch operation without separation ( A = 0). (----) No product inhibition; (-) product inhibition.
252
Chen-Li Chiang, Shau- Wei Tsai
parameters on the performance of a reactor for different operational strategies. Figure 3 illustrates the effects of effective membrane area on substrate conversion at different substrate feed rates. The common belief is that a large membrane area is more productive since inhibitory products would then be removed faster when formed. Such is not the case, as shown in Fig. 3, which indicates the decrease in conversion as membrane area increases. The effects of membrane area on the product yield trend similarly, as shown in Fig. 4. In order to investigate these unexpected results, the effects of the membrane area on substrate leakage and on product removal were examined as shown in Figs 5 and 6 , respectively. These graphs clearly
'""L
'
'
'
indicate that an increase of membrane area resulted in both increased substrate leakage and increased removal of inhibitory products. While increased substrate leakage has an adverse effect on the conversion of substrate, an increased removal of inhibitory product has a positive effect on the conversion of the substrate. In this case, the increase of effective membrane area would only marginally alleviate product inhibition and would actually intensify substrate leakage. Overall, an increase of effective membrane area does not improve the process. Figure 3 also demonstrates the effects of substrate feed rate on substrate conversion. With the smaller membrane areas (less than 150cm2), conversion decreases as the substrate feed rate increases. Conversely, when larger membrane areas are used (greater than 300 cm2),
7
0.040
~
J
1 MI= 0.0 ___...
mL/min MI= 0.0055 mL/min M,= 0.0110 mL/min MI= 0.0220 mL/min
F 2 0.018 PI F4
a
MI= 0.0 mL/min MI= 0.0055 mL/min --__ MI= 0.0110 mL/min --- MI= 0.0220 mL/min
0.008
0
100
200
,300
400
500
A (cm)
0.000
Fig. 3. The effects of membrane area of an RDMR on substrate conversion at different substrate fecd rates using an AOT-iso-octane reversed micelle model system. (-) M , = 0 cms min-'; (----) M , = 0.0055 cm3 min I ; (----) M , = 0.01 1 cm3 min (---) M I = 0022 cm3 min-I.
'
0
'
'
100
'
I
200
'
I
d 500
400
300
A (crn2)
Fig. 5. The effects of membrane area of an RDMA on substrate leakage at different substrate feed rates using an AOT-isooctane reversed micelle model system. Key as Fig. 3.
0.096
- M____ MI1 &
0.0
ml/min
._____ 0.0055 mL/min
M,= 0.0 mL/min ___._. M,= 0.0055 mL/min
0.024
----
Mi= 0.0110 ml/&
_ _ _ &= 0.000
k
0
-
100
d
-
200
0.0220 mL/min -
,300
d
400
i
500
A (cm) Fig. 4. The effects of membrane area of an RDMR on product yield at diffcrent substrate feed rates using an AOT-iso-octane rcvcrscd micelle model system. Key as Fig. 3.
--0.00' 0
'
I
100
'
0.0110 mL/mjn
MI= 0.0220 mL/mm
I
200
I
,300
'
'
400
'
J
500
A (cm)
Fig. 6. The effects of membrane are of an RDMR product concentration in the receiver phase at different substrate feed rates using an AOT-iso-octane reversed micelle model systcm. Key as Fig. 3.
Evaluation of a recycle dialysis membrane reactor
conversion increases as the substrate feed rate increases. However, the effects are less significant for the larger membrane areas. Figure 4 shows the potential advantage of higher product yield which might be gained by increasing the substrate feed rate. A higher substrate feed rate corresponds to a higher substrate leakage. The extra cost of substrate leakage should be amply compensated for by higher product yield-a compromise between high product yield and high substrate leakage should be found. Theoretically, inhibitory products may be continuously removed by the bleed stream during the conversion process and this may accelerate the dialysis rate. Thus, the fed-batch-bleed operation seems to permit development of an inherently more efficient continuous process. Figure 7 demonstrates the effects of the receiver solvent bleed rate on substrate conversion. With smaller membrane area (less than 100 cm2),conversion increases as the bleed rate increases. However, the effects are not significant. With a larger membrane area (greater than 100 cm2), conversion decreases as the bleed rate increases (except R = 0 1 cm3min-'). The case of R = 0.1 cm3min-l is particularly interesting since the curve is intermediate between the curves for R = 0 and R = 0.3 cm3 min-'. These unexpected results may also be explained by substrate leakage, including leakage in receiver and bleed phase, as shown in Fig. 8. Substrate leakage increases as the bleed rate increases, except for R = 0.1 cm3min-', with larger membrane area. The product concentration in source phase, Pl,is plotted against membrane surface area for a variety of R values in Fig. 9. From the figure, PI is observed to decrease as R increases. As described above, the removal of inhibitory products
253 could be responsible for higher substrate conversion, but not in the RMDR system. Losses are more likely due to substrate leakage since, inevitably, both the molecules of substrate and product are of low molecular weight and therefore easily permeate. Of particular significance to the present study is that the permeability coefficient of the substrate is almost the same as the permeability coefficient of the product. Which of the three mode is preferable may only be decided by careful consideration of the particular situation. In order to reduce substrate leakage, an alternative method of operation was investigated. First, reaction medium was initially operated in batch mode for 16.7 h, then recirculated through the dialysis cell, using an effective membrane area of 500 cm2.The receiver solvent
t
--
w / ,
0.03
3 F
2
,,/
0.02
rn
B
R= 0.0 mL/min R= 0.1 mL/min R= 0.3 mL/min R = 0.5 mL/min
(0
--0
.
Y 0
0
0
U 100
'
I
200
'
'
I
300
I
400
'
'
500
A (cm')
Fig. 8. The effects of membrane area of an RDMR on product yield at different receiver solvent bleed rates using an AOT-isooctane reversed micelle model system. Key as Fig. 7.
R= 0.0 mL/min R= 0.1 mL/min R= 0.3 mL/min R= 0.5 mL/min
0.64
L?i
0.48
- R= 0.0 mL/min -.-.__ R = 0.1 mL/min ___-
20
--_
R= 0.3 mL/min R= 0.5 mL/min
0.161
,
,
Mathematical Modelling and Simulation of a Recycle Dialysis MembFane Reactor in a Reversed Micellar System Chen-Li Chiang* & Shau-Wei Tsai Department of Chemical Engineering, National Cheng Kung University, Tainan, Taiwan (Received 22 August 1991; revised version received 9 January 1992; accepted 28 January 1992)
Abstract: A mathematical framework was developed for the evaluation of a recycle dialysis membrane reactor (RDMR). The lipase-catalyzed hydrolysis of olive oil in an AOT-iso-octane reversed micellar system was employed as a model. Three specific operational strategies have been considered, namely batch, fedbatch, and fed-batch-bleed. Simulation shows the conversion of substrate to be strongly dependent on efficient use of the substrate, since the permeability coefficients of both substrate and product are quite similar. Sensitivity analyses were performed to assess the influences of various parameters (membrane area, substrate feed rate, solvent bleed rate and permeability) on the performance of the reactor in different modes of operation. The analyses presented are useful to assist the optimization of the operational strategy used for the RDMR system.
Key words : reversed micelles, lipase, inhibition operational strategy, effective membrane area.
NOTATION
Subscript i Initial state 1 Source phase 2 Receiver phase
Effective area of membrane (cm2) Total mass of enzyme in the reactor (mg) Rate constant in the Michaelis-Menten equation (U mg-' enzyme) Dissociation constant for the complex EP* (mol dm-3) Michaelis constant (mol dm-3) Substrate feed rate (cm3 min-') Product concentration (mol dm-3) Product permeability coefficient (m s-') Substrate permeability coefficient (m s-l) Receiver solvent bleeding rate (cm3min-l) Substrate concentration based on ester bond (mol dm-3) Reaction time (min) Volume of solution (cm3) Degree of substrate conversion
1 INTRODUCTION
* Present address : Institut fur Enzymtechnologie, KFA Jiilich, PO Box 2050, 5170 Julich, Germany. 249
In 1977 Martinek eb a1.l demonstrated cl-chymotrypsin activity in reversed micelles of Bis(2-ethylhexyl) sodium sulfosuccinate (AOT) in octane. Since then, a variety of enzymes, surfactants, solvents and substrates have been used for studying enzymatic reactions in reversed micelles ;to date about 30 enzymes have been involved in the catalytic activity studies as reported in recent review^.^-^ The reversed micellar system has received considerable attention during the past decade since it is one of the most powerful tools for conversion of apolar compounds by However, several factors have contributed to the under-utilization of reversed micellar systems in commercial biotechnology. Foremost amongst these is the limited theoretical understanding and hence predictability of the time course analysis for the reaction with a high - substrate concentration. In addition,
J. Chem. Tech. Biotechnol. 0268-2575/92/$05.00. 0 1992 SCI. Printed in Great Britain
Chen-Li Chiang, Shau- Wei Tsai
250 the problems of retention of reversed micelles and product recovery from the surfactants employed are also significant. Recently, Tsai and Chiang'l used Cundidu rugosa lipase to investigate the hydrolysis of a high concentration olive oil in an AOT-iso-octane reversed micellar system. The hydrolytic reaction obeyed Michaelis-Menten kinetics. The rate equation was analyzed in the time course reaction and found to be in agreement with the experimental results. A recycle dialysis membrane reactor (RDMR), integrating both reaction and separation, was successfully employed for continuous hydrolysis of olive oil in the AOT-iso-octane system in the authors' laboratory. Continuous runs were performed up to 48 h and 93.4% rejection of reversed micelles was obtained. The mathematical formulations, involving coupled enzymatic reaction and mass transfer, were also developed to describe the operation of the RDMR system." In order to estimate quantitatively and improve performance of the RDMR system, the process must be designed and simulated for different operational strategies. Given the above background, the aims of the present work have been to develop a useful mathematical framework whereby performance evaluation of the RDMR system might be simulated to yield ultimately an optimized operational strategy.
2 MATERIALS AND METHODS 2.1 System description The system used was constructed to describe the operation of the RDMR system and previously employed for a study of the enzymatic reaction in reversed micelles." A schematic of the system is illustrated in Fig. 1. As described previously,12 a stirred tank reactor is coupled to a dialysis membrane cell in a semi-closed-loop configuration via a suitable peristaltic pump. The cell contains the appropriate semi-permeable membrane which retains the reversed micelles yet passes the product molecules. During operation, the source reservoir is initially filled with both substrate and reversed micelles containing enzyme, whilst the receiver reservoir contains only organic solvent. The entire contents of both source and receiver reservoirs are continuously pumped through the membrane cell and recycled back to these reservoirs, respectively. The extension of feed stream of substrate and bleed stream of receiver solvent, as shown in Fig. 1, makes the RDMR system more suitable for various operational schemes.
Substrate feeding
Solvent refill R
Dialysis cell I I I I
+R
Source phase
Receiver phase
Solvent bleeding
Fig. 1. Process scheme of an RDMR used for an AOT-isooctane reversed micelle model system.
stream. Thus, both the substrate feed rate and receiver solvent bleed rate are zero in batch operation. Another mode of operation is known as semi-batch or fed-batch operation. This mode differs from batch operation only in that the reactor has a feed stream and allows the substrate to be fed continuously as the reaction proceeds. In this case, only the receiver solvent bleed rate is zero. The strategy of fed-batch-bleed operation is the same as for fed-batch operation, except that input and removal of the receiver solvent is continuous.
3 MATHEMATICAL SIMULATION 3.1 Mathematical formulation
In the authors' previous study," it was demonstrated that the hydrolytic reaction exmained obeys classic Michaelis-Menten kinetics. Competitive inhibition by the main product, oleic acid, was observed. The assumptions employed in the authors' analyses were those of well mixed source and receiver reservoirs: no enzyme deactivation, and no fouling in the membrane. In order to describe this system quantitatively, the material balance must be solved simultaneously by coupling the enzymatic reaction with mass transfer for both substrate and product. The comparative changes of mathematical formulation for various operational schemes may be expressed as follows :
(4)
2.2 Operational strategies A batch operation mode has neither feed nor effluent
with initial conditions : at t = 0 , P~ = 4, Pz = 0,S ,
=
S,, S ,
=0
(5)
25 1
Evaluation of a recycle dialysis membrane reactor
where S and P are the product and substrate concentration ;PM, s and PM, are the permeability coefficients of substrate and product, respectively; k,,, is the turnover number; K M is the Michaelis constant; K , is the dissociation constant; Mi is the feed rate of substrate; and R is the bleed rate of solvent in the receiver. The concentration of substrate, based on the ester bond in olive oil, was defined as follows: S (mol dm-3) =
191.5 S (g ~ m - ~ ) 56.1
Moreover, the degree of substrate conversion was calculated from eqn (7) as:
X=
total product yield total substrate input
(7)
where the total product yield is the sum of the products in the source, receiver and bleed phases. The total substrate input includes the initial input and the sum of continuous input as the reaction proceeds.
3.2 Numerical procedure A Runge-Kutta method was employed to solve the system of coupled first-order ordinary differential equations. The Runge-Kutta method is a fourth-order integration procedure which is both stable and selfstarting.13The parameters used in these simulations were obtained from the authors' previous results11~12 and are listed in Table 1. To assess the quantitative influence of the various parameters on the performance of the reactor under different modes of operation, sensitivity analyses were performed using computer simulation. The first series of mathematical simulations were conducted to examine the influence of the effective membrane area on the
TABLE 1 Parameters Used in the Mathematical Simulation of a Recycle Dialysis Membrane Reactor with an AOT-iso-octane Reversed Micellar System
Parameter
performance of reactor. In these simulations, the effective membrane area was varied between 0 and 500 cm'. The second series of simulations was developed to investigate the influence of the substrate feed rate on the performance of the reactor. The substrate feed rates used in these simulations were 0-0.022 cm3 min-l. The third series of simulations, only for the case of the fedbatch-bleed operation, was conducted to study the influence of the receiver solvent bleed rate on the performance of the reactor. The bleed rates used in these simulations were 0-0.5 cm3 min-' and the substrate feed rate was maintained constant a t 0.01 1 cm3 min-'.
RESULTS AND DISCUSSION
4
In order to demonstrate the importance of product inhibition phenomena during enzymatic hydrolysis of olive oil in AOT-iso-octane reversed micelles, two types of reaction mechanisms were considered. One is that no inhibition mechanism operated; the second is with a competitive inhibition mechanism. If the product was removed as formed, there would be no inhibition. The simulated time course of the reaction for batch operation without separation ( A = 0) is shown in Fig. 2. This graph shows that the reaction would proceed much faster if the product were removed as it was formed (indicated by dotted line). After approximately five hours, the substrate conversion is 60 % where inhibition is assumed and 95 YO for the situation where no inhibition is simulated. Thus, the strong inhibitory effect of oleic acid on lipase would appear to be an important factor to consider in the design of a large scale process. With this in mind, it is quite reasonable to assess the influence of the various
96
c
I
/
/
Value 67.1 pmol min-' mg-' e:nzyme 0.505 mg 0.7 17 mol dm-3 0.089 rnol dm-3 3.87 x lo-' m s-' 3.57 x m s0-500 cm2 0-0.022 cm3 min-l 0 0 5 cm3 min-' 0.683 mol dm-3 0 rnol dm-3 16.7 h
/
I
_ _ _ _ NO
INHIBITION
__ INHIBITION
0' 0
"
200
"
400
'
I
800
"
800
i "
1000
t (min) Fig. 2. Comparison of time course of substrate conversion between product inhibition and no product inhibition mechanism, using AOT-iso-octane reversed micelle model system under batch operation without separation ( A = 0). (----) No product inhibition; (-) product inhibition.
252
Chen-Li Chiang, Shau- Wei Tsai
parameters on the performance of a reactor for different operational strategies. Figure 3 illustrates the effects of effective membrane area on substrate conversion at different substrate feed rates. The common belief is that a large membrane area is more productive since inhibitory products would then be removed faster when formed. Such is not the case, as shown in Fig. 3, which indicates the decrease in conversion as membrane area increases. The effects of membrane area on the product yield trend similarly, as shown in Fig. 4. In order to investigate these unexpected results, the effects of the membrane area on substrate leakage and on product removal were examined as shown in Figs 5 and 6 , respectively. These graphs clearly
'""L
'
'
'
indicate that an increase of membrane area resulted in both increased substrate leakage and increased removal of inhibitory products. While increased substrate leakage has an adverse effect on the conversion of substrate, an increased removal of inhibitory product has a positive effect on the conversion of the substrate. In this case, the increase of effective membrane area would only marginally alleviate product inhibition and would actually intensify substrate leakage. Overall, an increase of effective membrane area does not improve the process. Figure 3 also demonstrates the effects of substrate feed rate on substrate conversion. With the smaller membrane areas (less than 150cm2), conversion decreases as the substrate feed rate increases. Conversely, when larger membrane areas are used (greater than 300 cm2),
7
0.040
~
J
1 MI= 0.0 ___...
mL/min MI= 0.0055 mL/min M,= 0.0110 mL/min MI= 0.0220 mL/min
F 2 0.018 PI F4
a
MI= 0.0 mL/min MI= 0.0055 mL/min --__ MI= 0.0110 mL/min --- MI= 0.0220 mL/min
0.008
0
100
200
,300
400
500
A (cm)
0.000
Fig. 3. The effects of membrane area of an RDMR on substrate conversion at different substrate fecd rates using an AOT-iso-octane reversed micelle model system. (-) M , = 0 cms min-'; (----) M , = 0.0055 cm3 min I ; (----) M , = 0.01 1 cm3 min (---) M I = 0022 cm3 min-I.
'
0
'
'
100
'
I
200
'
I
d 500
400
300
A (crn2)
Fig. 5. The effects of membrane area of an RDMA on substrate leakage at different substrate feed rates using an AOT-isooctane reversed micelle model system. Key as Fig. 3.
0.096
- M____ MI1 &
0.0
ml/min
._____ 0.0055 mL/min
M,= 0.0 mL/min ___._. M,= 0.0055 mL/min
0.024
----
Mi= 0.0110 ml/&
_ _ _ &= 0.000
k
0
-
100
d
-
200
0.0220 mL/min -
,300
d
400
i
500
A (cm) Fig. 4. The effects of membrane area of an RDMR on product yield at diffcrent substrate feed rates using an AOT-iso-octane rcvcrscd micelle model system. Key as Fig. 3.
--0.00' 0
'
I
100
'
0.0110 mL/mjn
MI= 0.0220 mL/mm
I
200
I
,300
'
'
400
'
J
500
A (cm)
Fig. 6. The effects of membrane are of an RDMR product concentration in the receiver phase at different substrate feed rates using an AOT-iso-octane reversed micelle model systcm. Key as Fig. 3.
Evaluation of a recycle dialysis membrane reactor
conversion increases as the substrate feed rate increases. However, the effects are less significant for the larger membrane areas. Figure 4 shows the potential advantage of higher product yield which might be gained by increasing the substrate feed rate. A higher substrate feed rate corresponds to a higher substrate leakage. The extra cost of substrate leakage should be amply compensated for by higher product yield-a compromise between high product yield and high substrate leakage should be found. Theoretically, inhibitory products may be continuously removed by the bleed stream during the conversion process and this may accelerate the dialysis rate. Thus, the fed-batch-bleed operation seems to permit development of an inherently more efficient continuous process. Figure 7 demonstrates the effects of the receiver solvent bleed rate on substrate conversion. With smaller membrane area (less than 100 cm2),conversion increases as the bleed rate increases. However, the effects are not significant. With a larger membrane area (greater than 100 cm2), conversion decreases as the bleed rate increases (except R = 0 1 cm3min-'). The case of R = 0.1 cm3min-l is particularly interesting since the curve is intermediate between the curves for R = 0 and R = 0.3 cm3 min-'. These unexpected results may also be explained by substrate leakage, including leakage in receiver and bleed phase, as shown in Fig. 8. Substrate leakage increases as the bleed rate increases, except for R = 0.1 cm3min-', with larger membrane area. The product concentration in source phase, Pl,is plotted against membrane surface area for a variety of R values in Fig. 9. From the figure, PI is observed to decrease as R increases. As described above, the removal of inhibitory products
253 could be responsible for higher substrate conversion, but not in the RMDR system. Losses are more likely due to substrate leakage since, inevitably, both the molecules of substrate and product are of low molecular weight and therefore easily permeate. Of particular significance to the present study is that the permeability coefficient of the substrate is almost the same as the permeability coefficient of the product. Which of the three mode is preferable may only be decided by careful consideration of the particular situation. In order to reduce substrate leakage, an alternative method of operation was investigated. First, reaction medium was initially operated in batch mode for 16.7 h, then recirculated through the dialysis cell, using an effective membrane area of 500 cm2.The receiver solvent
t
--
w / ,
0.03
3 F
2
,,/
0.02
rn
B
R= 0.0 mL/min R= 0.1 mL/min R= 0.3 mL/min R = 0.5 mL/min
(0
--0
.
Y 0
0
0
U 100
'
I
200
'
'
I
300
I
400
'
'
500
A (cm')
Fig. 8. The effects of membrane area of an RDMR on product yield at different receiver solvent bleed rates using an AOT-isooctane reversed micelle model system. Key as Fig. 7.
R= 0.0 mL/min R= 0.1 mL/min R= 0.3 mL/min R= 0.5 mL/min
0.64
L?i
0.48
- R= 0.0 mL/min -.-.__ R = 0.1 mL/min ___-
20
--_
R= 0.3 mL/min R= 0.5 mL/min
0.161
,
,
