Ind. Eng. C h e m . Res. 1989,28, 231-236
23 1
Study of Transport Phenomena in an Immobilized Yeast Membrane Bioreactort Yong S. Jeong and W. R. Vieth Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, N e w Jersey 08854
Takeshi Matsuura" Division of Chemistry, National Research Council of Canada, Ottawa, Canada K I A OR6
A transport study has been conducted for a multilayer UF membrane/dead cell layer/RO membrane system in order to isolate the permeation phenomena of solvent (water) and glucose solute occurring during the bioreaction. It has been found that the transport can be described considering the above system as a series of four barrier layers, including a concentrated boundary layer, a UF membrane, a cell layer, and a RO membrane. While convective and diffusive transport mechanisms are combined in the first three barrier layers, the convective transport of solvent water and the diffusive transport of glucose solute are separate in the last barrier layer. T h e concentration polarization of glucose solute is lessened by the insertion of the cell layer between UF and RO membranes due to a significant solvent flux decrease and a high mass-transfer coefficient in the cell layer. The need for immobilized whole cell reactor systems is widely recognized. Many reactor configurations have been tried using one or more semipermeable membranes to perform bioreaction and separation simultaneously (Cho and Shuler, 1986; Tharakan and Chan, 1986; Vieth et al., 1972). The major problems faced by such systems are high diffusional resistances, substrate depletion, and product inhibition. Over the past few years, many membrane reactors have been proposed which address these problems individually (Karel et al., 1985; Venkatasubramanian et al., 1983). We have proposed in our earlier reports a bioreactor in which living yeast cells are sandwiched between an ultrafiltration (UF) membrane and a reverse osmosis (RO) membrane (Vasudevan et al., 1987, 1988). A solution containing glucose substrate and nutrients is in contact with the ultrafiltration membrane, and pressure is applied on the feed substrate solution. The substrate permeates through the UF membrane freely together with solvent (water) and arrives at the cell layer, where the bioreaction starts to occur, leading to product ethanol. When the solution is forced by pressure out of the cell layer from the side which is in contact with the RO membrane, permselection between substrate glucose and product ethanol occurs. While ethanol permeates almost freely through the RO membrane, the latter is practically impermeable to glucose substrate (de Pinho et al., 1988). Therefore, one is able to obtain product ethanol solution without much contamination from glucose and nutrients. The advantages of such a bioreactor over conventional membrane bioreactors are (a) high cell concentration within a limited reactor space; (b) forced convective flow of substrate to the cell layer, which is much faster than diffusive transport; (c) removal of product ethanol and COz from the cell layer and prevention of the product inhibition. A similar device for membrane immobilization has been proposed by Michaels (1980) as membrane-moderated immobilized cell bioreactors. Though the above bioreactor system has been successfully demonstrated (Vasudevan et al., 1987) and the effect of some operational variables such as operating pressure, feed glucose concentration, and porosities of UF and RO membranes on the reactor performance has been studied (Vasudevan et al., 1987), the entire bioreactor system has not been fully understood since the transport character+ Issued
as NRCC No. 29791. 0888-5885/89/2628-0231$01.50/0
istics of cell layers were not known for both substrate and product. Therefore, it is most urgently needed to establish the transport mechanism and to produce associated parameters, particularly with respect to cell layers. There are several reports found in the literature on the diffusion coefficients of substrate glucose and product ethanol in the cell-immobilized calcium alginate membranes (Hannoun and Stephanopoulos, 1986) and of glucose in the cell-immobilized beads (Chotani, 1984). Though it might be interesting to compare transport parameters of the sandwiched membrane system with those in the more conventional form of the cell immobilization, it is, however, out of the scope of this work. Another interesting view on the transport characteristics of this bioreactor system is to look at the whole membrane reactor system as a series of permeation barriers, including a UF membrane, a cell layer, and a RO membrane. Since there have already been theoretical studies on the transport through a series of membranes particularly for the gas transport (e.g., Sirkar (1977, 1978)), it would be interesting to study both theoretically and experimentally liquid transport through a series of barrier layers. The objective of this work is, therefore, to establish a transport theory which describes the permeation of solvent and substrate glucose through a series of transport barriers. Then, the theory is tested experimentally by using a bioreactor system in which dead cells are sandwiched between UF and RO membranes, so that the transport alone can be isolated. It should be noted that clogging effects of dead cells are different from those of living cells. However, the transport through a dead cell layer seems to be the best approximation of that through a living cell layer. The reason why substrate glucose was chosen for the transport study is because RO membranes show semipermeable characteristics to glucose solution. On the other hand, RO membranes allow free passage of ethanol solute. Both the development of transport equations and experimental results are presented in this paper.
Materials and Methods The materials used in the experiment and the experimental methods were described in detail in our previous paper (Vasudevan et al., 1987,1988). The cellulose acetate membranes, both for RO and UF experiments, were laboratory prepared. The details of the membrane preparation are shown in Table I. It should be noted that UF-1 membrane was gelled in a gelation media which is higher 0 1989 American Chemical Society
232 Ind. Eng. Chem. Res., Vol. 28, No. 2, 1989 Table I. Details of Cellulose Acetate Membrane Preparation membrane UF-1 UF-2 RO casting soln composition, wt % 1. cellulose acetate (E-398-3) 17.0 2. acetone 69.2 1.45 3. magnesium perchlorate 12.35 4. water 4 temp of casting soln, "C room temp of casting atm room humidity of casting atm 60 solvent evaporation period, s ethanol/water vol ratio in gelation 50150 40/60 0/100 medium 0 temp of gelation medium, "C 72 shrinkage temp, "C shrinkage period, min 10
in ethanol content than UF-2 membrane. Saccharomyces Cereviciae ATCC 4126 was employed as the biocatalyst in this study since extensive immobilization studies have been done in the past on this cell. Inoculum was prepared using YM Broth. A measured volume (20-60 mL) of known concentration (in the exponential phase, about 2 X lo7 cells/mL) was centrifuged. The cells were then brought into 20-60 mL of 50 vol % ethanol solution and stirred with a Vortex-Genie for half an hour to homogenize and to kill the yeast. The solution was then centrifuged to remove liquid, and the cells were washed with pure water. Staining with methylene blue proved cell death without the lysis of cells (Hannoun and Stephanopoulos, 1986). The dead yeast cells were filtered through a 0.2-pm microfilter and then sandwiched between UF and RO membranes. The total number of sandwiched cells was controlled to lolo,and the volume of the sandwiched cell layer is about 1 cm3. The bioreactor used in this experiment is the same as that illustrated in the previous report (Vasudevan et al., 1987,1988). The membrane was mounted at the bottom of the reactor, the feed solution was loaded, and the pressure was applied by nitrogen gas on feed solution. A magnetic stirrer was driven in close proximity of the membrane surface so that the development of the concentrated boundary layer was minimized. All reverse osmosis experiments were carried out at laboratory temperature (23-26 "C), at operating pressure of 2758 k P a g (400 psig) and feed glucose concentration of 0.27-0.76 m. In each experiment, the fractional solute separation, f , was determined as f = (feed glucose concentration - permeate glucose concentration) /feed glucose concentration and the product permeation rate (PR), which represents the flux in the presence of glucose in the feed, and pure water permeation rate (PWP) in kilograms/hour for a given area of the membrane surface (19.64 cm2 in this work) were determined under the specified experimental conditions. The data on PR and PWP were corrected to 25 "C using the relative viscosity data for pure water. The glucose concentration was determined by using a glucose analyzer (YSI Model 27 industrial analyzer).
Theoretical Section In order to facilitate understanding of the transport equations developed below, the symbols shown in Figure 1 will be used throughout this paper as subscripts. The letters a, b, c, and d indicate the four barrier layers involved and the numbers 1 and 5 indicate feed and permeate, respectively. The numbers 2, 3, and 4 indicate
1
2
3
4
5
feed
F)ermeate
Figure 1. Schematic illustration of barrier layers involved in a sandwiched UF membrane/dead cell layer/RO membrane system.
1
2,4
5
feed
'meate
Figure 2. Schematic illustration of barrier layers involved in RO membrane separation.
barrier boundaries. Capital letters A and B are also used throughout this paper as subscripts to indicate solute (glucose) and solvent (water), respectively. Furthermore, the transport equations given below have been developed on the basis of the following assumptions: both convective and diffusive transports are combined in barrier layers a-c, while the solvent convective flow induced by the effective pressure difference hp-A.rr and the solute diffusive flow induced by the solute concentration difference Ac are separate at barrier d. By use of the symbols defined in Figure 1 and on the basis of the assumption stated above, the transport equations have been developed for the following three cases. (1)Transport through Reverse Osmosis Membrane Alone. Figure 2 describes the system. The system consists of barriers a and d alone. The feed (l), the surface of contact between concentrated boundary layer and RO membrane (2 or 4),and permeate ( 5 ) are considered. The transport equations describing such a system are (Sourirajan and Matsuura, 1985)
NB = Ad(P2 - P 5 cA2
-
cA5
-
cA5
+
~ 5 )
(1)
(3)
Equation 1 shows that solvent flux is proportional to the effective pressure drop at barrier d (reverse osmosis membrane). Equation 2 shows that the solute flux through barrier d is proportional to the concentration difference
Ind. Eng. Chem. Res., Vol. 28, No. 2, 1989 233 1
(3) A Dead Cell Layer Sandwiched between Reverse Osmosis and Ultrafiltration Membranes. This system is schematically represented by Figure 1 and consists of barriers a-d. The feed (l),the surface of contact between barriers a and b (2), between barriers b and c (3), and between barriers c and d (4), and the permeate (5) are all included in this system. The transport equations describing this system can be written as (11) NB= Ab(P2 - p3) (12) NB = AC(P3 - p 4 ) N B = Ad(P4 - P5 - ~4 + ~ 5 ) (13) (14) NA= (DAM/K8)d(CA4 - cA5)
5
3,4
2
feed
oermeate
(15) Figure 3. Schematic illustration of barrier layers involved in a combined UF/RO membrane system. Table 11. Some Reverse Osmosis and Ultrafiltration Performance Dataa feed PWP, PR, solute membranes concn, m g/hb g/hb sep, % 99.4 0.484 61.6 35.7 RO 0.497 1137.4 730.0 1.5 UF-1 0.425 30.3 5.10 95.7 UF-1/RO 15.2 3.18 94.5 UF-l/dead cell layer/RO 0.407 4.2 UF-2 0.470 370.7 258.9 0.409 23.8 3.84 95.3 UF-2/RO 2.94 87.6 0.394 9.5 UF-2/dead cell layer/RO "Operating pressure = 2758 kPag (=400 psig). bPWP = pure water permeation rate; PR = product permeation rate in the presence of glucose in the feed; effective membrane area = 19.64 cm2;1 g/h = 1.418 X lo-' m3/(m24.
on both sides of barrier 5, and eq 3 is the concentration polarization equation by which the boundary layer concentration cA2 can be calculated. The quantity k, is the mass-transfer coefficient in barrier a (the concentrated boundary layer) and is equal to Dm/8, according to the film theory. The quantity u is the permeation velocity through barrier d and can be written as u =
NA+NB
NB
I -
C
C
cA2
- cA5
-= exp( C A l - cA5 cA3 - cA5
-= exp( cA2
-
t) t)
Equations 4 and 5 are valid in this system, too.
cA3 - cA5
a)
Equations 4 and 5 are valid in this system, too. Under the conditions of the pure water permeation experiment, there is no solute involved in the feed and all terms associated with the osmotic pressure disappear in eq 1 , 6 , 7 , and 11-13. Using the above equations and eq 5, the following equations can be derived: for pure water permeation through RO membrane alone:
for pure water permeation through combined UF/RO membranes: from eq 5-7
(4)
or
where c is the total molar concentration including solute and solvent and is almost constant in the entire solute concentration range under study. Of course P1 = P2 (5) (2) Combined Ultrafiltration and Reverse Osmosis Membranes. Figure 3 represents the system. This system consists of barriers a, b, and d. The feed (1) the surface of contact between barriers a and b (2) and between barriers b and d (3 or 4) and the permeate (5) are considered in this system. In analogy to case 1, the transport equations describing the system can be written as NB= Ab(P2 - p3) (6) N B = Ad(P3 - p5 - X3 + 7 5 ) (7)
NA= (DAM/K6)d(CA3 - cA5)
cA4 - cA5 -= ex.(
(8)
NB(1/Ab) = PI- p5
(20)
when there is no RO membrane attached. for pure water permeation through a sandwiched UF/dead cell layer/RO membrane system: from eq 5 and 11-13
Results and Discussion Typical performance data for glucose separation by the reverse osmosis membrane alone, the ultrafiltration membrane alone, a combined UF/RO membrane, and a sandwiched UF/dead cell layer/RO membrane system are shown in Table 11. All flux data are considered as steady-state data. The experiments were conducted under the operating pressure of 2758 W a g (=400psig) and from 0.4 to 0.5 m glucose concentration. The data show that the pure water permeation rate decreases significantly from UF membrane to RO membrane, but the decrease is less remarkable from RO membrane to a combined UF/RO membrane, indicating that RO film resistance is dominant
234 Ind. Eng. Chem. Res., Vol. 28, No. 2, 1989 Table 111. Some TransDort Parameters Obtained from RO and UF ExDeriments dimension step 1 step 2 Combination of UF-1and RO Membranes Ab kmol/ (m2.s.kPa) 3.24 X lo6 A C kmol/(m2.s-kPa) 5.54 x 10-8 Ad kmol/(m2.s.kPa) 1.75 x 10-7 1.30 X lo4 k, m/s kb m/s k C m/s 0.6 X (DAM/K6)d m/s Ab
A, Ad
k.3 kb k C
(DAM/K6)d
kmol/ (m2.s.kPa) kmol/(m2.s.kPa) kmol/(m2.s.kPa) m/s m/s m/s m/s
step 3
step 4
1.16 X lo6 1.33 X
3.04 X lo4 1.28 X
Combination of UF-2 and RO Membranes 10.55 X 3.30 X lo-* 1.75 x 10-7 1.30 X lo4
in the latter system. The pure water permeation rate decreases further from a combined UF/RO membrane to a sandwiched UF/dead cell layer/RO membrane system. As for the product permeation rate, which is the permeation rate in the presence of glucose in the feed, there has been a significant decrease from UF membrane to RO membrane. The decrease from RO membrane to a combined UF/RO membrane is also remarkable, reflecting a strong concentration polarization caused by the UF membrane. The decrease in the product permeation rate from a combined UF/RO membrane to a UF/dead cell/RO membrane system is not so significant because the increase in concentration polarization by the presence of the cell layer is not very large as explained later. As for glucose separation data, the latter value decreases from RO membrane to a combined UF/RO membrane and a sandwiched UF/dead cell layer/RO membrane system progressively, while UF membrane alone shows pratically no separation to glucose solute. By use of eq 1-21, the transport parameters necessary to describe the transport phenomena of a sandwiched UF/dead cell layer/RO membrane system are calculated by the following steps from a given set of reverse osmosis experimental data. Step 1. First, we consider the pure water permeation rate data for an RO membrane alone, a UF membrane alone, and a sandwiched UF/dead cell layer/RO membrane system. In the last experiment, both UF and RO membranes are considered to be the same as those used in the first two experiments. Then, parameters Ab, A,, and Ad are obtainable from eq 18, 20, and 21, since N B values involved in the foregoing equations are all known from the pure water permeation experiments. P1-P5 is equal to the applied gauge pressure. Step 2. Then, we consider the reverse osmosis experimental data of glucose solution obtained from the reverse osmosis membrane alone. Equations 1-3 are used for the analysis of the data. Since we know the operating gauge pressure, solvent permeation rate, solute permeation rate, feed solute concentration, and product solute concentration from experiments, P2-P5, NB,NA, cAl, and cA5 are all known. The quantity u can be calculated from eq 4. The osmotic pressures 1r2 and 1r5 are uniquely related to the concentration cA2 and cA5. Therefore, the only unknowns involved in eq 1, 2, and 3 are c A 2 , (DAM/Kfdd for glucose solute, and k,. Since there are three equations involved, these three unknowns can be solved. (DAM/K6)d and k , are thus obtainable as parameters associated with the solute transport through barriers. Step 3. Next, we shall consider the reverse osmosis experimental data of glucose solution obtained from a
5.01 x 10-7 0.6 X
1.03 X
1.05 X 10” 3.05 X loa 2.91 X
combined UF/RO membrane. In order to analyze the data, eq 6-10 are used. Among quantities involved in these equations, P3,cA2, cA3, and kb are unknown. The numerical values are known for the rest of the quantities. There are, however, five equations to solve for the above four unknown quantities. We are going to consider the quantity (DAM/K6)das another unknown quantity and solve for a total of five unknowns, simultaneously by using five equations. This calculation is reasonable since the reverse osmosis membrane laminated onto the ultrafiltration membrane is not necessarily the same membrane as used in the experiment with RO membrane alone, although both RO membranes have been prepared under the same conditions. Of course, (Dm/K6)dvalues calculated from steps 2 and 3 have to be close to each other. The parameters associated with the barrier transport of the solute and obtainable in this step are (DAM/K6)d and kb. Step 4. Finally, we shall consider the reverse osmosis experimental data of glucose solution obtained from a sandwiched UF/dead cell layer/RO membrane system. In order to analyze the data, eq 11-17 are used. Among the quantities involved in these equations, P3,P4,cA2, cA3, cA4, and k, are unknowns. The numerical values are all known for the rest of the quantities. Again, we are going to consider the quantity ( D A M I K 6 ) d as another unknown quantity and solve for seven unknowns, simultaneously, by using seven equations. The parameters associated with the barrier transport of the solute and obtainable in this step are, therefore, ( D A M / K 6 ) d and kc. All numerical quantities obtained are listed in Table I11 with respect to the combinations of UF-l/RO and UF2/RO membranes, all of which have been laboratory made under conditions given in Table I, together with steps involved in the calculation of the numerical values. Looking into Table 111, reproducibility of (DAM/K6)d values from steps 2-4 is reasonably good when considering that RO membrane samples used in each step are not exactly identical, though they are all from the same batch. As for ( D A M / K b ) d values obtained for the UF-2/RO membrane combination, the value from step 4 was greater than those from other steps. This is probably because the RO membrane used in a sandwiched UF-Bldead cell layer/RO membrane was more permeable to glucose than those used in other experiments. Similarly, 1.05 X lo4 m/s was used as kb for UF-2 film in step 4 instead of 5.01 X lo-’ m/s obtained as kb from step 3. The change in kb value of step 4 from that of step 3 was necessary in order to obtain reasonable agreement in kc’s from UF-1/RO and UF-2/RO combinations. Table I11 is informative about the contribution of the individual barrier component to the overall mass transport.
Ind. Eng. Chem. Res., Vol. 28, No. 2, 1989 235 If A values of each barrier component are compared, then Ab
a
T
> A d > A,
indicating a more intensive resistance against solvent flow from the cell layer than that either from UF membrane or RO membrane. As for A values of two different UF membranes, AUF-l
> AUF-P
indicating that UF-1 membrane has pore sizes larger than those of UF-2 membrane. This result is in agreement with those reported earlier (Sourirajan and Matsuura, 1985). Comparing the mass-transfer coefficients k,, kb, and k, listed in Table 111,
1
2
1
2
3
5
kc >> k, > k b for both UF-l/RO and UF-2/RO combinations. It is understandable that the mass-transfer coefficient of the high concentration boundary layer, k,, is greater than that of the UF membrane, kb, since the solute diffusion in the UF membrane is more restricted than in the boundary layer solution. The significantly greater mass-transfer coefficient of the dead cell layer, k,, than both k, and k b values seems, on the other hand, very puzzling. It may probably be due to agglomeration of cell particles and generation of local turbulence in the convective flow occurring between cell particle agglomerates, which results in a higher masstransfer coefficient in the cell layer. Furthermore, the order in the pure water permeation constant is Ab >> A,, while the order in the mass-transfer coefficient is k, >> kb, which seems contradictory at a first glance. Besides, A, is calculated to be about 3 orders of magnitude higher than the experimental value on the basis of 1-mm thickness of closely packed yeast cells. This may, however, be understood by considering that the high resistance (1/AJ against the solvent flow is not due to the cell layer itself but due to the blocking of UF membrane pores by cell particles. Remember that the porous sublayer of the UF membrane is in contact with the cell layer. The sizes of the pores on the porous sublayer are sufficiently large to accommodate cell particles, and therefore, blocking of UF membrane pores from underneath is possible. The resistance against the solvent flow expressed as that from the cell layer ( l / A J is therefore not necessarily contributed from the cell layer itself but it is in fact the resistance contributed from the boundary between UF membrane and the dead cell layer. Figure 4 shows the pressure profile and the concentration profile across barrier layers calculated using the parameters shown in Table 111. Profiles for the combined UF-1/RO membrane and the sandwiched UF-l/dead cell layer/RO membrane system are shown to demonstrate the effect of the inserted cell layer. The pressure and concentration profiles illustrated in Figure 4a for the combined UF-1/RO membranes show that the pressure drop takes place primarily at the RO membrane and the concentration polarizations at both the concentrated boundary layer and the UF membrane are very severe. The profiles illustrated in Figure 4b for the sandwiched UF-l/dead cell layer/RO membrane system indicate that the pressure drop takes place also in the cell layer (or UF membrane/cell layer boundary) and the concentration polarization is less severe than that for a combined UF-1/RO membrane. The less severe concentration polarization is primarily due to a lower permeation velocity of solvent because of a high resistance against solvent flow resulting from the presence of the cell layer and the high mass-transfer coefficient in the cell layer.
3
4
5
NUMBER OF BARRIER BOUNDARY
Figure 4. Pressure and glucose concentration change at different barrier boundaries. (a) Combined UF-l/RO membrane, u = 7.23 X lo-' m/s. (b) Sandwiched UF-l/dead cell layer/RO membrane, u = 5.45 x m/s.
-
0.95
I
a t ad , ,
t r a m reference experiments
=
O
0901
UF-lidead cell IayeriRO
5.
d a t a f r o m reference experiments
n
-
0.2
0.3
0.4
0.5
0.6
0.7
0.8
F E E D GLUCOSE MOLALITY
d a t a tram reference experiments
0.90r
0.80
UF-Z/dead cell IayeriRO
02
03
04
05
06
07
08
F E E D GLUCOSE MOLALITY
Figure 5. Comparison of calculated (line) and experimental (symbol) values for the RO performance of sandwiched UF/dead cell layer/RO membranes: f = solute separation; [PR] = product permeation rate; feed molality of the reference experiment, 0.4; operating pressure = 2758 kPa-g (=400 psig); effective film area = 19.64 m3/(m2.s). cm2; 1 g/h = 1.418 X
236 Ind. Eng. Chem. Res., Vol. 28, No. 2, 1989
Figure 5 shows some performance data of sandwiched UF-l/dead cell layer/RO and UF-2/dead cell layer/RO membrane systems. The solid line is the calculated data on the basis of the numerical values listed in Table 111, while the open circles are the experimental data points. The difference between calculated and experimental data are within experimental error range (solute separation, &2%, product rate, i 0 . 3 g/h) except for separation data of UF-2/dead cell layer/RO system at 0.76 m. It should be noted that all transport parameters were generated on the basis of reference experiments, the data from which are also shown in Figure 5. The calculated values for experimental conditions other than reference experiments have, therefore, to be considered as purely predicted values. The agreement between the predicted and experimental values shown in Figure 5, therefore, testifies to the validity of the transport equations developed in this work and to the associated parameters.
Conclusion From the experimental observations and the subsequent analysis of the experimental data, we have drawn the following conclusions with respect to glucose transport through a sandwiched UF membrane/dead cell layer/RO membrane system. 1. The transport of solvent (water) and solute (glucose) through the above system can be described by a series of four barrier layers. 2. Convective and diffusive transports are combined in the concentrated boundary layer, UF membrane, and cell layer. 3. The solvent convective flow and solute diffusive flow are separate in the RO membrane. 4. The presence of the dead cell layer decreases the water permeability significantly, probably due to partial closing of pores of the UF membrane which is in contrast with the cell particles. 5. The mass-transfer coefficient in the cell layer is very high, which results in a small concentration gradient in the dead cell layer. 6. A useful extension of the work would be to use a glucose/ethanol system to demonstrate the separation effects of the bioreactor. When the sandwich system is used as a bioreactor, the biocatalytic reaction is combined with the transport phenomena investigated in detail in this work. The analysis of the bioreactor system is currently under way. Nomenclature A = pure water permeability constant, kmol/(m2.s-kPa)
c = molar concentration of solution including solute and
solvent, mo1/m3 cA = molar concentration of solute A, mol/m3 D A B = diffusivity of glucose in water DAM/K~= solute permeability constant, m/s f = fractional solute separation
K = partition coefficient of solute between solution and membrane phases 112 = mass-transfer coefficient, m/s N A = solute flux, mol/(m2.s) N B = flux of solvent water, mol/(m2.s) P = pressure, kPa PR = product permeation rate, g/h PWP = pure water permeation rate, g/h u = permeation velocity through membrane, m/s Greek Symbols 6 = effective membrane thickness, m ?r = osmotic pressure, kPa
Subscripts 1-5 = as illustrated in Figure 1 a-d = as illustrated in Figure 1 A, B = substrate (glucose) and solvent (water),respectively Registry No. H20, 7732-18-5; glucose, 50-99-7.
Literature Cited Cho, T.; Shuler, M. L. Biotechnol. Prog. 1986, 2, 53. Chotani, G. K. Ph.D. Thesis, Rutgers University, Piscataway, NJ, 1984. de Pinho, M.; Nguyen, T. D.; Matsuura, T.; Sourirajan, S. Chem. Eng. Comm. 1988,64, 113. Hannoun, B. J. M.; Stephanopoulos, G. Biotechnol. Bioeng. 1986,28, 829. Karel, S. F.; Libicki, S. B.; Robertson, C. R. Chem. Eng. Sci. 1985, 40, 1321.
Michaels, A. S. Desalination
1980,35, 329. Sirkar, K. K. Chem. Eng. Sci. 1977,32, 1137. Sirkar, K. K. Sep. Sci. Technol. 1978, 13, 175. Sourirajan, S.; Matsuura, T. Reverse Osmosis1Ultrafiltration Process Principles; National Research Council of Canada: Ottawa, Canada, 1985. Tharakan, J. P.; Chan, P. C. Biotechnol. Bioeng. 1986,28, 329. Vasudevan, M.; Matsuura, T.; Chotani, G . K.; Vieth, W. R. Sep. Sci. Tech. 1987, 22, 1651. Vasudevan, M.; Matsuura, T.; Chotani, G. K.; Vieth, W. R. Proceedings Biochemical Engineering V, New York Academy of Science, New York, 1988; p 345. Venkatasubramanian, K.; Karkare, S. B.; Vieth, W. R. Appl. Biochem. Bioeng. 1983,4, 312. Vieth, W. R.; Wang, S. S.; Gilbert, S. G. Biotechnol. Bioeng., Symp. Ser. 1972, 3, 285.
Received f o r review April 28, 1988 Accepted July 25, 1988
