Biotechnol. Prog. 1990, 6,362-369
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Mathematical Modeling and Simulations of Membrane Bioreactor Extractive Fermentations D. E. Steinmeyert and M. L. Shuler' School of Chemical Engineering, Cornel1 University, Ithaca, New York 14853-5201
A model of extractive ethanol fermentation within a membrane bioreactor has been constructed by using a structured, nonsegregated model of Saccharomyces cereuisiae. The model has been tested by comparing actual and simulated reactor fermentations. The time-dependent approach to steady-state operation is well predicted. The model has also been used to examine an array of alternative operating strategies.
Introduction Bioreactors, based on membrane entrapment of cells, have been reported as early as 1947 (Harmsen and Kolff, 1947). Reviews of developments with membrane-based bioreactors are available [e.g., Vick Roy et al. (1983) and Cheryan and Mehata (1986)l. Unmodified membrane bioreactors do not work well with either reactions that produce large amounts of gas or products that cause feedback inhibition. Gas evolution can lead to high pressures that disrupt membranes or exclude nutrient from the cell compartment. Feedback inhibition due to product accumulation, exacerbated by diffusional limitations, can reduce reaction rates to unacceptably low levels. Membrane bioreactors that include solvent extraction can potentially eliminate the problems with feedback inhibition [e.g., Cho and Shuler (1986) and Frank and Sirkar (1986)l. This report is based on the reactor design suggested by Cho and Shuler (1986), which divides the reactor into four separate compartments: a gas layer, a cell layer, a nutrient layer, and a solvent layer. Such a design facilitates gas removal, and the correct choice of membrane and solvent prevents phase toxicity in a system where glucose is converted to ethanol by the yeast Saccharomyces cerevisiae. Efthymiou and Shuler (1988) have used a pressure swing operation, termed pressure cycling, to significantly improve mixing between the cell and nutrient layers of the reactor and therefore improve reactor performance. Steinmeyer and Shuler (1990) have demonstrated that the reactor may be operated continuously for long periods of time. Given the complexity of the reactor system, it has been difficult to explore experimentally the range of possible operating conditions and system configurations. This survey could be more efficiently carried out with a reliable mathematical model of the system, and this paper describes such a model. The heart of the model is a flexible model of the "catalyst", the structured nonsegregated model of S. cereuisiae described by Steinmeyer and Shuler (1989). A larger model, describing the operation of a pressurecycled membrane reactor system, has been built around the cell model. The model allows the simulation of reactor experiments with a given set of initial conditions. The veracity of the model has been tested by comparing actual and simulated reactor fermentations. T h e model
* Corresponding author. t Current address: Kinetek Systems,11802Borman Dr., St. Louis,
MO,63146. 8756-7938/90/3006-0362$02.50/0
has also been used to examine an array of alternative operating strategies.
Model Description The model has been constructed to describe the operation of the reactor system as it existed in the continuous experiments presented in a recent paper (Steinmeyer and Shuler, 1990). A flow schematic of such a system is illustrated in Figure la. A diagram of the reactor alone is given as Figure lb. As described previously (Steinmeyer and Shuler, 1990), the reactor as operated in the current work contained a gas space (gas layer) above a high-density cell suspension (cell layer) and a nutrient layer separated from the cells by a hydrophilic membrane. A pressure swing operation (pressure cycling) convectively mixed the cell and nutrient layers. In separate units, solvent extraction of ethanol from the rapidly recycled nutrient stream occurred across a hydrophobic membrane. A structured nonsegregated cell model (Steinmeyer and Shuler, 1989) describes the actions of the cells within the cell layer, i.e., the conversion of substrates to cell mass and products. Around this model has been built a description of a reactor system, including pressure cycling of nutrient and liquid-liquid extraction of the product from the nutrient. A geometrically specific design is not inherent to the mathematical description of the system, although a number of parameters, such as mass transfer coefficients, are dependent upon geometry and must be specified a priori. The volume exchange caused by the pressure cycle is mimicked in the model with a time-dependent exchange of suspension medium between the cell and nutrient layers. Given the time- and direction-dependent rate of flow at any point in a simulation, a proportional amount (depending upon the phase of the cycle and the time step of the numerical integration) of medium is removed from either the cell or nutrient layer and added to the other layer. The mixing of the volume increment with the layer to which it is being added is assumed to be instantaneous. The masses of the various components in the exchanged medium are therefore added to those already existing in that layer, and the concentrations of each component are recalculated at the end of each step of the integration as the sum of the existing and incrementally added masses divided by the existing and added volume of the layer. Inherent to this description of the cycle is the assumption that the cell and nutrient layers are well mixed. Volume is moved from one layer to another until the volume in the cell layer reaches a prespecified high or low
0 1990 American Chemical Society and American Institute of Chemical Engineers
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a
a
Nutrient Recycle
&-I Nutrient Bleed
b GaS
T
F1
FO
1
Nutrient
S
P
-
Figure 1. (a) Flow schematic of the flat-plate reactor system. Nutrient flow is continuous while the solvent is replaced on a periodic basis. (b) Diagram of reactor unit.
limit, at which point the cycle is reversed. The rate of exchange is prespecified to decrease after start-up to simulate the slowing that is a result of membrane fouling and cell polarization effects in actual experiments. As the amount of suspending medium in the cell layer changes over the course of the cycle, the concentration of cells in that layer rises and falls, but the mass of cells is affected only by the changing environmental conditions resulting from the rate of the cycle, not by the cycle itself. The cells are assumed to be evenly suspended throughout the cell layer, and the volume that they occupy is neglected. Ethanol is removed from the nutrient through the extraction system into the solvent. The rate of recycle of the nutrient through the extraction system in past reactor experiments has been very rapid, so it is assumed in the model that the concentration drop per pass is negligible and that the extraction takes place at the concentration of ethanol in the nutrient recycle. The hydrodynamic effects of the ethanol-laden nutrient being pumped from the recycle vessel through the extractors and back to the recycle are reflected only in the extractive mass transfer coefficient, which has been determined for ambient operating conditions. The partial changes of TBP (tributyl phosphate) with fresh solvent typical of the continuous experiments were modeled as periodic (the frequency was varied so that the changes would fall at roughly the same times as in the experiments) stepwise dilutions of the solvent with fresh solvent. In the simulations of alternative operating strategies, the concentration of ethanol in the TBP is assumed to be controlled a t designated levels and is therefore maintained at a preset value. The feed of fresh concentrated nutrient solution has been included with flow rates modulated to achieve prespecified control objectives. The flow rates that were used in the model for the simulation of reactor experiments were those that were measured in the actual experiment. In simulations of alternative operating strategies, the feed rate was controlled to meet specific objectives, typically a residual concentration of glucose in the nutrient recycle of 100 g/L. The bleed (overflow) rate from the nutrient recycle was set to maintain a maximum value on the amount of nutrient in the nutrient recycle vessel. For simulations of experiments, the rate was maintained to keep the total amount of nutrient medium comparable to that at the start-up of an experiment. For the simulation of hypothetical operating strategies, the bleed rate was manipulated
Figure 2. Schematic of mass flow in the yeast model [from Steinmeyer and Shuler (1989)l. The symbols are defined as follows: CP1, extracellular amino acids; CAI, extracellular ammonium; CA2, extracellular glucose; CP2, extracellular nucleic acid bases; AI, ammonium; A2, glucose; P1 and P11, amino acids; P2, nucleotides; M1, protein; M2, RNA; Ms, DNA; M4, cell envelope; Mg, storage carbohydrate; El, amino acid biosynthetic enzymes; W1, ethanol + C02; W2, glycerol.
to control the volume of the nutrient at the level of our long-term continuous experiments. The small volume changes caused by the conversion of glucose to COz and ethanol are assumed to be minimal and do not change the total volume of nutrient in the system or the bleed rate in the model. However, the volume changes associated with the extraction of ethanol and water into the solvent have been included where appropriate. Oxygen is assumed to enter the cell layer through the gas layer above the cells and as a component of the nutrient entering the layer during the fill phase of the pressure cycle. Evaporative stripping of ethanol in the gas overhead is considered negligible and is not included. The reactor model is based on a detailed model of S. cerevisiae that has been described earlier [see Steinmeyer and Shuler (1989)l. A schematic of the cell model is given as Figure 2. The rate expressions and parameter values have been described elsewhere (Steinmeyer and Shuler, 1989). Equations have been added to the cell model to describe the rates of extraction of ethanol and cellular oxygen uptake. The unsteady-state mass balances are then written for each component of the model shown in Figure 2 (Steinmeyer and Shuler, 1989). Table I depicts the overall mass balances to calculate the concentrations of ethanol, glycerol, nucleic acid bases, oxygen, glucose, amino acids, and ammonium for both the cell layer fluid and the nutrient layer fluid. In addition, the number of viable and nonviable cells and the volume of fluid in the cell layer and nutrient layer are calculated. A copy of the program is available (Steinmeyer, 1990). Reactor fermentations were simulated by numerically integrating these equations over time given a set of initial conditions and disturbances. The integration was carried out with an algorithm of our own, using the Euler predictor-corrector method with variable step size. The step size was automatically increased or decreased after each time step as a function of the number of iterations required to reach convergence. The minimum and maximum steps allowed were 0.002 and 10 s, respectively.
Simulation of Reactor Experiments The reactor model has been tested by comparing its simulation of a continuous reactor fermentation to the data obtained in the actual experiment. The initial conditions (concentrations,initial volumes, and state and amount of inoculum) and disturbances to the system (feed and bleed
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Table I. External Mass Balances of the Reactor Model dCEC/dt = FI(CEN - CEC)/VCELL + 46 [-RATP - (PO)(RESP)]/VCELL dCA2C/dt = FI(CA2N - CABC)/VCELL - RA2/VCELL dCGC/dt = FI(CGN - CGC)/VCELL + RG/VCELL dCPlC/dt = FI(CP1N - CPlC)/VCELL - (RANA + RCATA)/ VCELL dCP2Cdt = FI(CP2N - CPBC)/VCELL - (RNBE RNBU)/VCELL dCAlC/di = FI(CA1N - CAlC)/VCELL - RAl/VCELL dO2Cldt = FI(O2N - 02C)lVCELL + KCELUP(O2S 02C)/VCELL - 6RESPTVCELL dVCELL/dt = FI - FO dCXVldt = CXV(F0 - FUNCELL + (RM - RD)/VCELL dCXD)dt = CXD(F0 - FI)'/VCELL + RD/VCELL dCEN/dt = [(FO)(CEC) - (BLE + FI + dVNUT/ dt)CEN = RMCE[(KD)(CEN) - CES]]/VNUT
CEC CAPC CGC CPlC GP2C CAlC 02c VCELL
cxv
CXD CEN CA2N CGN CPlN CP2N CAlN 02N VNUT CA2NO CP2NO CPlNO CAlNO
cell layer ethanol cell layer glucose cell layer glycerol cell layer amino acids cell layer bases cell layer ammonium cell layer oxygen cell layer volume viable cells nonviable cells nutrient layer ethanol nutrient layer glucose nutrient layer glycerol nutrient layer amino acids nutrient layer bases nutrient layer ammonium nutrient layer oxygen nutrient layer volume feed glucose feed bases feed amino acids feed ammonium
RMCE KD KCELUP KNUTUP 02s RATP PO RESP RA2 RG RANA RCATA RNBE RNBU RAI RM RD SPVE ERSW FI FO FE BLE
rates and solvent changes) of the experiment were preprogrammed into the simulation. The experimental materials and methods are described in Steinmeyer and Shuler (1990). The base experiment for model verification and comparison to alternative operating strategies used yeast (S.cerevisiae) and a defined feed medium with 350 g/L glucose, 10 g/L yeast extract, and salts. The initial charge of medium in the recycle vessel had 175 g/L glucose. A diagram of the experimental apparatus is depicted in Figure 1. Solvent extraction was performed outside the reactor by pumping the nutrient medium from the recycle vessel through an extraction unit and back to the reservoir. A Millipore 0.22-pm Duropore membrane was selected for the cell/nutrient membrane, and Celanese Celgard K442 was used for the extraction membranes. The surface area of the cell/nutrient membrane was 100 cm2,and the surface area in the extraction system was 300 cm2. The reactor was inoculated with a 250-mL inoculum containing 0.81 g of cells. An initial volume of 1100 mL of fermentation medium was used, and the initial volume of TBP was 1 L. The feed was started at 25 h (6.3 mL/ h) and was readjusted at 91 h to 3.6 mL/h. Spent TBP was replaced with fresh solvent at 25 (500 mL), 50 (500 mL), and 73 (760 mL) h. The final mass of cells at the end of the experiment (3000 h) was 3.4 g. The experiment was conducted at 35 OC, corresponding to the values of the kinetic parameters in the base yeast model (Steinmeyer and Shuler, 1989).
Simulation of the Experiment The initial conditions and operational disturbances of the experiment, described above, were preprogrammed into
dCGN/dt = [(FO)(CGC)- (BLE + FI + dVNUT/ dt)CGN]/VNUT dCA2Nldt = [(CA2NO)(FE) + (FO)(CAPC) - (BLE + FI + dVNUT/dt)CAON]/VNUT dCPlN/dt = [(CPlNO)(FE) + (FO)(CPlC)- (BLE + FI + dVNUT/dt)CPlN] /VNUT dCP2Nldt = [(CP2NO)(FE) + (FO)(CPZC) - (BLE + FI + dVNUT/dt)CPBNl /VNUT dCAlN/dt'= [(CAlNO)(FE)+ (FO)(CAlC) - (BLE + FI + dVNUTldt)CAlNl/VNUT dO2N/dt = FO(02C :OZN)/VNUT + KNUTUP(O2S OZN)/VNUT dVNUTldt = FO - FI + FE - BLE - (SPVE)(RMCE)[(KD)(CEN)- CES)] - ERSW dCES/dt = RMCE[(KD)(CEN) -. CES]/VSOL ethanol extraction mass transfer coefficient solvent/medium ethanol distribution coefficient cell layer oxygen uptake mass transfer coefficient systemic oxygen uptake mass transfer coefficient nutrient oxygen solubility phosphate bond consumption rate P:O ratio oxygen consumption rate glucose uptake rate glycerol product rate anabolic amino acid uptake rate catabolic amino acid uptake rate nucleic acid base efflux rate nucleic acid base uptake rate ammonium uptake rate rate of cell growth rate of cell death ethanol specific volume water extraction rate flow into cell layer from nutrient layer flow out of cell layer into nutrient layer flow of feed into nutrient recycle flow of bleed from the nutrient recycle
the model, and with these operating conditions, the experiment was simulated for 94 h. The concentrations of glucose and ethanol in the cell, nutrient, and solvent layers from the simulation (lines) are compared to the data from the experiment (points) in Figure 3. The predicted mass of cells at the end of the simulation was 2.9 g. As is evident from Figure 3, simulated and experimental results are quite similar, diverging gradually with time as expected (in separate simulations, the course of the model's simulation was not significantly altered by subtle variation of the initial conditions within the range of physiological relevance, except through propagation of error). The best comparison (for reasons that will be discussed shortly) is made between the predicted and actual concentrations in the nutrient layer. The residual concentration of glucose in the nutrient layer is a function of the rate of glucose consumption by the cells and addition by the feed. In the experiment, the glucose feed was manipulated to roughly equal the consumption rate, after the residual concentration of glucose had dropped to about 100 g/L. The feed rate preprogrammed into the model corresponded exactly to the measured feed rate. Assuming that the error in measuring the experimental rate is negligible, the difference between the experimental and simulated residual concentration of glucose in the nutrient layer at any time is indicative of the cumulative difference between the experimental and simulated glucose consumption rates. The dilution rate of the nutrient recycle stream resulting from the addition of the concentrated nutrient feed was on the order of 0.5% (v/v)/h, so the residual concentrations of ethanol in the nutrient and cell layers are not affected as noticeably by
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of the layer. These measured concentrations of glucose and ethanol would be expected to be somewhat lower and higher, respectively, than those of the bottom element and the layer average concentrations that the model would predict if mixing was incomplete. Thus the experimental concentration differences across the cell/nutrient membrane were expected to be slightly higher than the simulated differences. The closeness of the simulated to the experimental results strongly suggests that the major variables which govern the course of a reactor experiment are correctly described in the model, giving is predictions of the effects of changes in the operating strategy credulity. Comparison of model predictions to other yeast reactors gives similarly good agreement.
Simulation of Alternative Operating Strategies A substantial improvement in the rate at which volume
the feed. The sawtooth pattern of the concentration of ethanol in the solvent is the result of periodic partial replacement of solvent with ethanol-free solvent. The drop in the concentration of residual glucose in the nutrient recycle over the first day of operation is similar in both experiment and simulation, suggesting that the predicted rate of glucose consumption over this period is comparable to that of the experiment. Thereafter, the model appears to overpredict the rate slightly (the simulated glucose concentration does not rise as rapidly as in the experiment and is roughly 10 g/L lower than the measured value at the end of the simulation). Since a total of approximately 294 g of glucose was consumed during the experiment, this 11-gcumulative difference represents only a 4 73 divergence of prediction from the experiment after 4 days of simulation. The concentration of ethanol in the nutrient layer was also comparable in both experiment and simulation, as was the concentration of ethanol in the solvent. The residual level of ethanol in the nutrient layer is a result of the difference between the rate of production and the rate of removal of ethanol into the extractant. The rate of increase in the concentration of ethanol in the solvent is similar in both experiment and simulation, and the concentration of ethanol in the nutrient is also similar to the data. One aspect of the simulation that differs from the experiment is the magnitude of the concentration differences of glucose and ethanol across the cell/ nutrient membrane, which are smaller in the simulation than suggested by the experimental data. These bear upon the assumption that the cell layer is well mixed. The cell layer might be throught of as containing two volume elements, the bottom element being the increment of fluid that is exchanged with the nutrient layer via the pressure cycle and the top element being the volume of the cell layer at the end of the empty (or beginning of the fill) phase of the cycle, which is not exchanged with the nutrient layer. These two elements are mixed by diffusion and by the combined convective effects of the turbulence caused by the gas flowing into and out of the gas layer at the change of cycle phases, the rising of COz up through the layer, and the eddies caused by the movement of the fluid elements up and down in the cell layer chamber. The data on cell layer concentrations were obtained by meaurements of concentrations in samples removed from the top element
is exchanged between the cell and nutrient layers would be realized with the use of a membrane with a bigger pore size. The potential benefits of a hypothetical suitable membrane may be simulated by appropriately increasing the rate of volume exchange in the model. Increases in the rate of production necessitate comparable increases in the rate of extraction. The rate of the extraction with a given driving force may be increased by increasing the amount of surface area between the phases (increasing the amount of extractive membrane) or by decreasing the resistance to mass transfer (such as by using a thinner membrane or decreasing the thickness of the diffusion layers on both sides of the membrane). The rate of extraction may further be increased by increasing the driving force, the difference between the equilibrium concentrations of the solute in the two phases in contact. Increasing the concentration of ethanol in the nutrient layer is constrained because such increases lower the productivity of the cells through feedback inhibition. Lowering the residual concentration of ethanol in the solvent or using a solvent with a higher equilibrium partition coefficient for the solute are more attractive alternatives. Table I1 summarizes the effects of various strategies on reactor productivity. All values are relative to the base case described in Figure 3. Figure 4 illustrates the effects of increasing the rate of volume exchange on the productivity of the reactor, when other conditions are comparable to those of the longterm continuous experiment (the base case). In the simulation, the concentration of ethanol in the solvent was controlled at 10 g/L (the concentration varied between 5 and 15 g/L in the continuous experiment as a result of batchwise rather than continuous replacement of the solvent), and the amount of membrane used in the extractive part of the system was 3 times the amount used to retain the cells in the cell layer, as in the experiment. The feed rate (of 350 g/L glucose feed medium) was varied to keep the residual concentration of ethanol in the nutrient recycle at 100 g/L. A 485 mL/h exchange, the rate at the beginning of the long-term experiment (with the 0.22pm-pore membrane), was used as the base line. A 26 500 mL/h exchange was measured with a Millipore 0.45-bm Duropore membrane. Each of the exchange rates was held constant over the course of the simulation. The four curves illustrate the increase in production as the rate of exchange increases. Over the course of each pressure cycle, the concentration of ethanol in the cell layer rises and falls, and since cellular productivity is to a large extent limited by ethanol inhibition, the productivity of the cells also varies over the cycle. The ethanol production
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Table 11. Summary of Predicted Relative Productivities of Various Scenarios with Continuous Recvcle Reactor Case ratio of extractive solvent membrane exchange membrane to residual distribution pore size, rate, nutrient/cell ethanol concn in relative case coefficient wm mL/h membrane nutrient layer, g/L productivity ~
0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.5 5.0 10.0 1.5 5.0
10
2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21
0.22 0.45 0.22 0.22
485 22500 485 485 970 970 970 22500 22500 22500 485 485 970 970 970 485 485 485 485 485 485
0.45 0.45 0.45 0.22 0.22
0.22 0.22 0.22 0.22 0.22 0.22
~~
3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 19.0 19.0 19.0 19.0 19.0 1.0 1.0 1.0 1.0 3.0 3.0
10 10 0 20 0 10 20 0 10 20 0 5 0 5 10 10 10 10 10 30 30
1.0 1.9 1.3 0.8 1.6 1.2 1.0 2.4 1.7 1.4 3.1 2.0 4.2 2.8 2.3 0.8 1.2 1.9 2.8 1.4 2.8
Experimental base case; actual productivity is 1.1 g of ethanol/h.
"1 Effect of varying residuol ethonol in TBP on production
Effect of increoting cycle rot? on production R e i i d ~ o lClhmol ~n TEP E.lroc!lrc IYd.CC 0r.a
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25
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Figure 4. Effect on the rate of ethanol production of varying the rate of medium exchange between the cell and nutrient layers.
rate data shown in this and subsequent figures are of cellular productivity at random points of the cycle, so the magnitude of the scatter illustrates the degree of variability. The initial surges in production are the result of the system's extractive capability at start-up acting as through it is greater than it actually is, since ethanol that is produced is diluted more rapidly from the cell layer into the nutrient than it will ultimately be able to be extracted into the solvent, allowing more cells to be produced and a higher level of production than will ultimately be able to be maintained. As is seen from the four curves, a limit is approached beyond which production may be increased no more by mixing. This limit is the point at which the concentrations of nutrients and products in the cell and nutrient layers are equal. A roughly 2-fold improvement in production is possible by increasing the exchange rate from the basal level to 26 500 mL/h, which brings mixing close to this limit. Figure 5 illustrates the effects of changing the residual concentration of ethanol in the solvent on the productivity of the system for conditions comparable to the base case. Allowing the ethanol residual concentration to increase to 20 g/L decreases production by 20 % However, such an increase would reduce separation costs. If the residual concentration were decreased to 0 g/L, the productivity would increase 30 % . Doubling the rate of medium exchange between the cell
.
Figure 5. Effect on the rate of ethanol production of varying the residual concentration of ethanol in the solvent for a volume exchange rate of 485 mL/h.
and nutrient layers, as illustrated in Figure 6, diminishes the concentration gradients across the cell/nutrient membrane, lowering the concentration of ethanol in the cell layer and ethanol inhibition and thereby increasing the productivity of the system. This effect is illustrated in the relative positions of the 0, 10, and 20 g/L residual ethanol production curves in the figure, each of which is higher than the corresponding case in Figure 5. The rate of production in the 10 g/L case, for example, is improved about 20 % As the rate of mixing between the cell and nutrient layers increases, the limit of negligible concentration differences is approached and productivity becomes limited by the rate of extraction. Figure 7 illustrates the effect of varying the residual concentration of ethanol in the solvent when the mixing rate is increased to 26 500 mL/h, which brings the reactor close to this limit. Lowering the residual concentration to 0 g/L increases the rate of production by roughly 25% over the 10 g/L case and 75% over the 20 g/L case. Each of these represents a roughly 100% increase over the comparable case when the rate of mixing is 485 mL/h. Figure 8 illustrates the effect on the rate of production of increasing the amount of extractive membrane to roughly 19 times the amount within the reactor (6 times that of Figures 3-6). Despite the 6-fold increase in extractive
.
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"1
Effect of vorying residuol ethonol in TBP on production Effect of vorying residual ethonol in TBP on production
- -
Lxlrocti*. surloc* arm 3 uembron. flux 970 ml/h,
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F i g u r e 6. Effect on the rate of ethanol production of varying the residual concentration of ethanol in the solvent for a volume exchange rate of 970 mL/h. mEffect of vorying reslduol ethonol in TBP on production
- -
Effect of vorying dis:rlbution coefflcients of hypothetical solvents on production
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F i g u r e 7. Effect on the rate of ethanol production of varying the residual concentration of ethanol in the solvent for a volume exchange rate of 26 526 mL/h.
F i g u r e 10. Effect on the rate of ethanol production of hypothetical solvents with large distribution coefficients for ethanol.
Effect of varying residual ethonol in TBP on production u.mbrw IU. I 485 r m h r Exlroclb wrloce arm
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Figure 8. Effect on the rate of ethanol production of increasing the amount of extractive membrane to 19 times the amount retaining the cells within the cell layer a t a volume exchange rate of 485 mL/h.
capacity, the increase in the steady-state ethanol production rate of each of the three cases is less than 3-fold over the comparable cases in Figure 5, confirming that, with a 485 mL/h exchange, the rate of production and transport of ethanol out of the cell layer partially limits the overall productivity of the system. Doubling the exchange rate to 970 mL/h (Figure 9), with other conditions the same, increases productivity by a factor of about one-third over the rates shown in Figure 8. Figures 10 and 11illustrate the potential advantages that might be afforded by a solvent with an equilibrium distribution coefficient for ethanol greater than that of TBP. (The distribution coefficient with TBP is 0.5 in aqueous solution but appears to be slightly higher in fermentation broth.) Increasing the distribution coefficient drives the two phases further from equilibrium for a given
485 M / h i
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0
50
75
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Figure 11. Effect on the rate of ethanol production of varying the residual ethanol concentration in hypothetical solvents.
concentration difference, thereby increasing the driving force of the extraction. In Figure 10, the rate of medium exchange between the cell and nutrient layers is 485 mL/h (the base case level). The amount of extractive membrane has been decreased to equal the amount of membrane used to retain the cells within t h e cell layer, a n d t h e residual concentration of ethanol in the solvent was controlled at 10 g/L. The four curves illustrate the production rates expected from hypothetical solvents with distribution coefficients of 10, 5, 1.5, and 0.5. Increasing the coefficient from 0.5 to 5 results in a 2.3-fold increase in productivity, and from 0.5 to 10.0, a 3.4-fold improvement. In these simulations the amount of extractive membrane used was one-third of that used in Figure 5, but the production rates in the simulations with coefficients of 5 and 10 (2.2 and 3.2 g/h, respectively) still represent 1.9- and 2.8-fold increases over the 10 g/L residual ethanol case in Figure 5.
Biotechnol. Prog., 1990, Vol. 6,No. 5
'0
50
100
150
260
260
360
Time ( h r s )
Figure 12. Rate of ethanol production in each unit of a cascade of three individual recycle systems in series.
The effect of changing the residual concentration of ethanol in hypothetical solvents with distribution coefficients of 1.5 and 5 is illustrated in Figure 11. The amount of extractive membrane has been increased to 3 times the amount of membrane between the cell and nutrient layers. Increasing the residual ethanol concentration from 10 to 30 g/L results in about a 25% decrease in productivity. The rates of production are greater in the current set of simulations than in the corresponding cases in Figure 10 because the amount of extractive membrane has been increased 3-fold. I t should be noted that these simulations are for a temperature of 35 "C, where the cells are particularly sensitive to ethanol inhibition. At a lower temperature, the absolute values of residual ethanol concentration and extractive membrane area to obtain a given reaction rate would differ from these predictions. The conclusions concerning relative strategies would not change. In a practical system the recycle mode with approach to a continuous flow stirred tank reactor (CFSTR) would not be used. A much more tenable approach would be a system approaching plug flow reactor (PFR) behavior because nearly complete conversion of substrate could be obtained while maintaining high average substrate levels. A cascade of an infinite number of CFSTR units in series approaches PFR behavior. We have simulated the behavior of the system with three of the recycle reactors in series. In the simulation of a cascade of three reactor systems in series, the initial conditions of each system were nearly the same as those for the base case. The concentration of glucose in the feed to the first unit was reduced to 200 g/L (as it would be for a perfect PFR to avoid substrate inhibition). The overflow from the first system was the feed to the second, and the overflow from the second was the feed to the third. The solvent was assumed to be presaturated with water, and the change in volume of the nutrient streams in each of the systems resulting from extraction of ethanol and water was assumed to be negligible. The feed rate to the first unit was adjusted to maintain a residual glucose concentration in the nutrient of 100 g/L (the steady-state concentrations in the second and third units were 36 and 2.5 g/L, respectively). As is evident from Figure 12, the productivities of the second and third units were lower than that of the first. At 300 h, the second was roughly one-third lower and the third was roughly two-thirds lower. These lower rates of production are the result of increased ethanol inhibition (the diluent effect of the feed to the first unit is less in the second and third) and glucose concentration limited uptake, especially in the third. The predictions concerning the third stage should be received with caution, since at
the low steady-state concentration of glucose in the cell layer, the cells would probably exhibit a glucose derepression response (not currently included in the model), which would affect both the uptake and respiration rates. After 100 h of simulation, the rate of production of ethanol in the second unit was comparable to, and that of the first unit was somewhat higher than, the productivity predicted for a single system with a 350 g/L feed (and other conditions comparable to those of the current simulation). This result is a product of each unit having the same production and extraction capacity up to 38 h after startup. Since the feed to the first unit is less concentrated than in the base case, the feed and overflow rates are significantly higher, and since ethanol is also removed in the overflow, the higher effective product removal rate increases overall productivity.
Conclusions The faithfulness of the model of the system to the actual process is suggested by the closeness of the data from the continuous reactor experiment to the model's simulation of it. Given the uncertainty in the measurement of the values of the various parameters (initial conditions and disturbances) that initialize the model to describe the experimental, the similarity between experiment and simulation is even more remarkable. The survey of alternative operating strategies through model simulations suggests that no single aspect of reactor performance limited the productivity of the system for the experimental base case. Rather, productivity was limited by both the rate of mixing of the cell and nutrient layers and the rate of extraction of the ethanol into the solvent. The simulations suggest that individual changes in the operating strategy would have varied effectiveness in improving productivity. Increasing the rate of mixing between the cell and nutrient layers would significantly improve performance without deleteriously limiting other aspects of system operation. Rates of flow much higher than the basal rate used in the simulations would be realized with alternative membranes. Such membranes exist, but cell retention is incomplete. Incomplete retention may be acceptable in a commercial system. Additional extractive capability could be added to accommodate the increased productivity. Adding this extra capacity to the system could be done by using more extractive membrane or by using a given amount of extractive surface area more efficiently by altering the driving force for extraction. Decreasing the residual concentration of ethanol in the solvent from the level used in the continuous experiment improves the rate of production, but any such increase must be justified along with probable increases in the difficulty and cost of recovering the ethanol from the solvent and solvent handling. As a result, the modest improvements in productivity possible by decreasing the residual concentration probably do not represent a significant operational advantage. Alternative solvents with higher distribution coefficients for ethanol clearly have the potential to markedly improve the productivity of the system. Unfortunately, solvents with distribution coefficients for ethanol significantly greater than that of TBP are not available at this time.
Acknowledgment We gratefully acknowledge support, in part, for this work from a contract from DOE'S Energy Conversion and Utilization Technology Project in Biocatalysis managed by the Jet Propulsion Laboratory.
Biotechnol. Prog., 1990, Vol. 6, No. 5
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Registry No. Ethanol, 64-17-5.
