Biotechnol. Prog. 1990,6,349-356
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Growth and Fermentation Model for Alginate-Entrapped Saccharomyces cere visiae Betty J. M. Hannount and Gregory Stephanopoulos* Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
A model of growth and fermentation for alginate-entrapped Saccharomyces cerevisiae is presented. The model is based on Peringer’s rate equations (Peringer, P.; et al. Biotechnol. Bioeng. Symp. 1973,4,27-42), developed for glucose-repressed cultures of suspended cells a t varying dissolved oxygen concentrations, and was fitted to estimates of growth and fermentation rates for immobilized cells obtained through a combination of experimental measurements and reaction-diffusion analysis. Immobilized cell fermentation data with alginate beads in suspension compared well with simulations of reaction and diffusion in a similar system incorporating the proposed growthfermentation model. In view of these findings, the model was further applied to the simulation of transient and steady-state operation of a packed-bed immobilized cell bioreactor. Results about the effect of operating parameters on bioreactor performance are presented, and implications regarding system design and operation for optimal overall performance are discussed.
Introduction In the preceding paper ( 2 ) ,the theory of reaction and diffusion was applied to the analysis of growth and fermentation data obtained with Saccharomyces cereuisiae cells entrapped in an alginate membrane. Under the assumption of constant specific rates of growth and metabolism, the corresponding boundary value problems were solved explicitly to yield analytical expressions for the fluxes of glucose and ethanol through the membrane. Upon comparison with direct flux measurements, values of the specific growth rate and specific rates of glucose uptake and ethanol production were obtained, intrinsic to immobilization conditions in alginate. The above rate values were compared to the rates measured for cells in suspension and several important differences noted. In order to satisfy the constant rate assumption, experiments were conducted under anaerobic conditions and at high glucose concentrations. Under aerobic conditions, however, due to low oxygen solubility and high oxygen uptake rate, intramembrane oxygen gradients develop and the constant rate assumption is no longer valid. In this case, the determination of the intrinsic growth and fermentation rates under immobilization conditions becomes a very involved problem, which is further complicated by the lack of local intramembrane metabolite concentration measurements. The absence of such rate data and models that can account for oxygen, glucose, and ethanol effects and that are valid under immobilization conditions prevents transmembrane distribution analysis and rational immobilized bioreactor design. A different approach to the above problem is presented in this paper. It begins with the postulation of a metabolic model expressed in the form of rate equations for growth, glucose uptake, ethanol production, and oxygen consumption. By use of these rate models, the boundary value problems of diffusion and reaction in the cell-occupied membrane are solved numerically to yield intramembrane concentration profiles and predictions of glucose and
* To whom correspondence should be addressed.
+ Present
CA 92121.
address: Mycogen Corp., 5451 Oberlin Dr., San Diego,
ethanol fluxes through the membrane. These predictions are compared with the corresponding flux measurements under aerobic conditions; furthermore, both simulated and measured flux data are analyzed, in a procedure similar to that applied in ref 2 with constant rate assumption, to produce metabolic rate estimates characteristic of the intrinsic immobilized metabolic rates. Upon comparison of simulated and measured values of fluxes, as well as rate estimates, model parameters are adjusted to maximize the agreement between model predictions and experimental measurements. The metabolic model obtained by the previous approach is applied to simulate fermentation data for S. cereuisiae immobilized in alginate beads. Satisfactory agreement between the simulations and experimental results provides further support for the validity of the model. The latter is finally applied to the analysis of an immobilized cell packed-bed bioreactor, yielding interesting results about the design and operation of such systems for biochemical transformations.
Growth and Fermentation Model There are few models in the literature with sufficiently broad applicability for the effect of dissolved oxygen on the rates of growth and metabolism of S. cereuisiae. Peringer et al. (1)have proposed a relatively simple model for glucose-repressed suspension cultures applicable for a broad rate of dissolved oxygen concentrations. The model is based on balancing cellular ATP requirements with ATP synthesis rate; ATP-wasting reactions are not accounted for in the model. Since the amount of glucose metabolized by oxidative phosphorylation is small compared to that metabolized by glycolysis, glucose uptake rate is modeled by the latter. Due to an observed linear relationship between the inverse of the respiration rate and the inverse of the dissolved oxygen tension, the rate of oxidative phosphorylation is modeled as a Michaelis-Menten reaction with oxygen as the substrate. The growth rate of S. cerevisiae is taken to be proportional to the ATP utilization rate, which equals the sum of ATP production rate via glycolysis and oxidative phosphorylation. Although the model developed by Peringer et al. has some biochemical basis,
8756-7938/90/3006-0349$02.50/0 0 1990 American Chemical Society and American Institute of Chemical Engineers
Biofechnol. Prog., 1990, Vol. 6,No. 5
350
Table I. Parameter Values for Peringer’s and Proposed Models
parameter
units h-l h-‘ ( % air saturation)-’ g/L 9t air saturation g/(g.h)
g/(g.h)
% .g:l.h % air saturation 91air saturation
Peringer’s model 0.208 0.103 4.93 x 10-4 0.1 1.36 2.08
8.19 X lo2
air saturation g/L %t
proposed model 0.24 0.12 5.0 x 10-4 0.1 5.8 2.2 8.19 X lo2 14.0 1.36 14.0 93.0
it is still a phenomenologicalmodel. As such it is described by the following set of equations:
a=[&IE3
respiration rate of immobilized cells compared to free cells probably does not increase more than the glucose uptake rate increases. Therefore, in assuming an immobilized cell oxygen uptake rate expression identical with the suspended cell rate expression,there is limited potential for error. The sensitivity of the immobilized cell model to the oxygen uptake rate expression is further discussed later. The effect of glucose concentration on the rate expressions was also assumed to be identical with that of eqs 1-3. This assumption is supported by the experimental data under anaerobic conditions, which indicate that the growth rate and ethanol production rate of immobilized cells are not affected by the presence of a glucose gradient from 50 to 1 g/L or by symmetric glucose concentrations of 25 g/L on the two sides of the membrane. The specific growth rate and specific glucose uptake rate measured under anaerobic conditions were used to determine p~ and am,respectively. Furthermore, due to saturation kinetics, an upper limit is approached by the growth rate at high oxygen concentrations. The maximum specific growth rate, measured a t high aeration rates, is approximated by p~ p~ for small values of K,, p , and KL. This then allows the determination of parameter p ~ An additional modification of eqs 1-3 was necessary in order to achieve reasonable parameter fit. Experimental data obtained under aerobic conditions indicated that the glucose uptake rate decreases with dissolved oxygen concentration and asymptotically approaches a minimum rate at high dissolved oxygen concentrations. Therefore, the following expression was substituted for glucose uptake rate in Peringer’s model:
+
S
(3) From batch and continuous culture experiments, the values of Table I were obtained for the model parameters by Peringer et al. ( I ) . Due to diffusional transport limitations, ethanol may accumulate significantlyinside the alginate matrix. Hence, the first step in adopting Peringer’s model to immobilization conditions was to add a term to the rate expressions (eqs 1-3) for ethanol inhibition. Although there is agreement in the literature about the inhibitory effect of ethanol on growth and fermentation, the quantitative description of this effect is somewhat more controversial. Linear (349, exponential (6, 7), and hyperbolic functions (8,9),have been used. A linear relationship was chosen in this work, with maximum allowed ethanol concentration equal to 93 g/L (IO). Growth, glucose uptake, and ethanol production all cease above this level, and immobilization has not been shown to alter the ethanol tolerance of S. cereuisiae significantly. The ethanol production rate was taken to be proportional to the glucose uptake rate, with the proportionality constant determined from the anaerobic ethanol yield data. This is supported by metabolic rate data obtained under aerobic conditions (2) and is probably due to the high glucose concentrations used. The oxygen utilization rate of immobilized S. cereuisiae was taken to be identical with that of eq 3 for suspended cells. Macipar et al. measured approximately a 7-fold increase in the oxygen utilization rate of yeast adsorbed onto ceramic (11). Entrapped cells may behave quite differently than adsorbed cells, however, so it is impossible to extrapolate this rate increase to calcium alginate immobilized cells. At the glucose concentrations employed in this investigation, the respiration rate of 5’. cereuisiae remains low for all dissolved oxygen concentrations. Oxygen is utilized for biosynthetic reactions, such as sterol and fatty acid synthesis, and for residual respiration. Since immobilized cells take up glucose faster than suspended cells, there may be a concomitant increase in the oxygen uptake rate of immobilized cells if some of the excess glucose is oxidized to carbon dioxide and water. However, the high ethanol yield of immobilized cells a t all dissolved oxygen concentrations indicates that the
I-”
[ a 1 - K L%02 , a + 0 2K , + s T h e maximum specific glucose uptake rate is still determined from the experiments conducted under anaerobic conditions. Equations 4-7 summarize the proposed model:
Y
=0.43~~
8 = L[ 8m02 K , + s KL,O, + 0
,] [ l - e/e,]
(6) (7)
In order to evaluate the parameters of eqs 4-7 and to also partially validate the proposed model, the procedure outlined below was followed. Further details of the procedure can be found elsewhere (12). The unsteadystate partial differential equations describing reaction and diffusion in the alginate membrane were integrated numerically by using the rate equations 4-7 and appropriate boundary conditions. The Crank-Nicholson method of finite differences with a time step of 0.001 h and a distance step of 0.008 cm was employed for this purpose (12). From the obtained time-dependent concentration profiles, the glucose and ethanol fluxes through the membrane were determined as a function of time for different bulk dissolved oxygen concentrations. These simulated fluxes were compared to those experimentally measured under the same bulk dissolved oxygen concentrations. Both simulated and experimentally measured fluxes were analyzed by a method described in ref 12 for constant reaction rates ( F , a, v) (2) to yield
.
35 1
Biotechnol. Prog., 1990, Vol. 6, No. 5 3.0
0.35
1
p
-
Y
0.20
o
20
40
60
100 120 140 160
a0
180
zoo
Bulk Dissolved Oxygen Concentration (% air saturation)
Figure 1. Comparison of simulated (0)and measured (0) estimates of the average specific growth rate, ~ D R of, immobilized S. cereuisiae in alginate membrane at varying bulk dissolved
oxygen concentrations.
1.01 0
I
I
I
20
I
40
I
I
60
I
I
00
I
I
100
I
I
120
I
I
I
140
I
160
4
I
I
100
I
200
Bulk D i s s o l v e d Oxygen Concentration (% air saturation)
Figure 3. Comparison of simulated (0) and measured (0) estimates of the average specific ethanol production rate, VDR, of immobilized S. cereuisiae in alginate membrane at varying bulk
dissolved oxygen concentrations.
3.00+e0
io
3
1ho
1~
1
1 . ~
d
Oullc D i s s o l v e d O x y g e n C o n c e n t r a t i o n ("4, a i r s a t u r a t i o n )
Figure 2. Comparison of simulated (0)and measured (0) estimates of the average specific glucose uptake rate, (YDR, of immobilized S. cereuisiae in alginate membrane at varying bulk
dissolved oxygen concentrations.
estimates of the values of p, a, and v, denoted by MDR, CYDR, and UDR, respectively. Due to oxygen gradients, p, a, and u vary throughout the matrix and ~ D R (, Y D R , and VDR represent average values. Model parameters were adjusted in order to yield the best possible agreement between experimental and simulated values for ~ D R CYDR, , and UDR. Model parameters so determined are summarized in Table 1. Figures 1-3 compare simulated and experimental values , and UDR for different bulk dissolved oxygen of ~ D R (YDR, concentrations. The agreement between PDR, (YDR,and VDR from measured and experimental fluxes is deemed very satisfactory. The sensitivity of model predictions to model parameters was investigated by varying each parameter individually. A detailed presentation of the obtained results is given in ref 12; the main conclusion of the sensitivity analysis studies is that no single parameter has a determining effect on model response, nor is the model very sensitive to small variations of any of the parameters. These observations underline the phenomenological nature of the model but also its relative robustness in design and control studies.
Average measured growth rates are compared in Table I1 to average growth rates obtained by simulations making use of the model (eqs 4-7) and solving the appropriate boundary value problem. The close agreement of the values of Table I1 provides further support to the model. The model was further tested by comparing its predictions against experimental measurements made in the course of fermentation runs with S. cereuisiae cells immobilized in calcium alginate beads suspended in a wellstirred and aerated batch reactor. Alginate beads occupied approximately 5 % of the reactor's working volume, allowing complete mixing in the liquid phase. Alginate beads of 3.4-mm diameter were used, and uniform fluid concentrations through the bioreactor were assumed. Model predictions for bulk glucose and ethanol concentrations were obtained as functions of time by integrating the corresponding mass balances in the liquid phase:
The concentration gradients on the bead surface in eqs 8 and 9 were evaluated after the radial concentration profiles for glucose and ethanol were first determined by solving the corresponding boundary value problems of reaction and diffusion in the alginate phase:
Model Validation As part of the flux measurement experiments discussed in the previous section and in ref 2, total biomass concentrations in the alginate matrix were also measured at the beginning and end of the fermentation. These biomass measurements allowed the calculation of an average biomass growth rate under immobilized conditions.
with the following boundary and initial conditions:
& =o ar
at r = 0,
s = sb
at r = R
(1la)
ae=O -
at r = O ,
e =eb
at r = R
(llb)
ar
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Biotechnol. Prog., 1990,Vol. 6, No. 5
Table 11. Average Specific Growth Rate from Experiments and Model DO concn, 5% air satn 0 50 100 200
experiment" 0.26 0.29 0.29
modelb 0.24 0.26 0.28
0.30
0.30
*
Determined from final biomass concentration. Predicted by mathematical model. 0
Time (hours)
and
b = bo for all r a t t =O for all r a t t = 0 e = 0 for all r at t = 0 0, = 0 2 , b for all r at t = 0 s = sb
(124 (12b)
F i g u r e 4. Bulk glucose and ethanol concentrations as a function of time for S. cereuisiae immobilized in alginate beads in a batch Glucose concentration; (A)ethanol concentration. reactor. (0) Initial biomass concentration is 11.0 g dry weight/L. Solid and dashed lines represent model predictions for glucose and ethanol concentration, respectively.
(124 (12d)
The integration of the above system of equations was carried out with the Crank-Nicholson method of finite differences to yield predictions for the bulk glucose and ethanol concentrations versus time. These predictions were compared to experimentally measured values.
Materials and Methods Cell Cultivation, S. cereuisiae ATCC 18790was grown in defined glutamate medium as described in ref 2. Preculture medium (1 mL) was transferred to each of two flasks with 250 mL of growth medium and 50 g/L glucose. Cells were incubated for approximately 10 h at 30 "C and were growing exponentially at a rate of 0.42 h-l when the cell density reached the desired level. At that point, a 1-mL sample was removed from each of the growth flasks (originally 250-mL volume) and put on ice for cell counting with a Levy-Hausser counting chamber. The biomass concentration in the liquid culture was determined from a correlation between the cell number and dry weight, which was previously established. Biomass was harvested by centrifugation for immobilization in alginate. Alginate Bead Preparation. Alginate-cell mixture, prepared as described elsewhere (2,12),was stirred well and pumped slowly through a Pasteur pipette into 2 % calcium alginate. Alginate beads, of average diameter 3.4 mm, were hardened for 1.5 h at 4 "C. Analyses. Glucose was assayed enzymatically (Sigma Chemical Co., St. Louis, MO). Ethanol concentrations were measured by alcohol dehydrogenaseassay (Sigma Chemical Co.). Absorbance measurements were made on a Hitachi Model 100-30 spectrophotometer. ImmobilizedCell Experiments. The immobilized cell experiments were carried out in a 250-mL flask closed with a rubber stopper. There were ports in the stopper for aerating the medium, removing gas, and taking samples. The reactor was stirred magnetically and maintained at 30 " C in a water bath. The experiments started with the addition of calcium alginate beads (approximately5 % v/v) to defined glutamate medium already in the reactor. Samples (0.5 mL) were withdrawn periodically with a sterile needle and syringe and then filter-sterilized. The samples were analyzed for both glucose and ethanol at a later time. The initial glucose concentration in the reactor was close to 25 g/L.
Time (hours)
Figure 5. Bulk glucose and ethanol concentrations in a batch reactor as a function of time for S. cerevisiae immobilized in alginate beads. ( 0 )Glucose concentration; (+) ethanol concentration. Initial biomass concentration is 5.9 g dry weight/L. Solid and dashed lines represent model predictions for glucose and ethanol concentrations, respectively.
Experimental Results Results are shown in Figures 4 and 5 for two runs, one of low (5.9 g dry weight/L) and one of high (11.0 g dry weight/L) initial biomass concentration in the alginate beads. Lines in the figures represent the time trajectories predicted by the immobilized cell diffusion-reaction model for the experimental conditions. Experimental data from both runs follow the trends predicted by the model. Although the growth-fermentation model was developed from experiments conducted with final biomass concentrations of 8 g/L alginate or less, in the alginate bead experiments final biomass reached 150 g/L alginate. Thus, the model developed at low biomass concentrations applies to higher biomass concentrations as well.
Packed-Bed, Immobilizer Bioreactor Model In light of the relative success of the growth-fermentation model in predicting glucose and ethanol fluxes and cell biomass concentrations in a flat matrix configuration, as well as the time profiles in a fermentation with beadimmobilized s. cereuisiae cells, the model was applied to the simulation and analysis of a packed-bed, immobilized cell bioreactor. Neglecting axial and radial diffusion in a high Peclet number operation, the mass balance for any of the three compounds of interest (glucose, ethanol, and dissolved oxygen) can be written as
with boundary (reactor inlet) and initial conditions defined
BiotechnoL Pmg., 1990, Vol. 6, No. 5
353
by the feed stream concentrations: c(o,t) = c(z,o) = Cfeed
I
(14)
Equation 13 is coupled to the boundary value problem of eqs 10-12 through the surface concentration gradient. The Crank-Nicholson method of fiiite differences was used for the solution of the latter problem. The boundary conditions a t the bead surface change with time and position in the reactor as determined by eq 13. Therefore, at each time step, intrabead concentration profiles are computed by iterating for the bulk fluid concentrations. A time step size of 0.005 h was used. Due to steep concentration gradients in the alginate beads, the bead radius was divided in 500 steps. Equations 13and 14 were solved by the Keller box finite difference method (13) together with eqs 10-12. For each step in time, the bulk fluid concentrations in the reactor were calculated by using the bead concentrations at the previous time step. Then the bead concentration profiles were updated and the bulk fluid concentrations were computed again for the same time step. The iteration proceeded until the bulk fluid concentrations changed by less than 1.0 X 10" g/L. Equations 13 and 14 were solved for a time step of 0.005 h and a reactor step size of 6.08 cm. More information about the procedure and the computer programs used can be found in ref 12. An immobilized cell plug flow reactor (PFR) was designed to produce approximately 500 g of ethanol/h at maximum biomass concentration. In all of the reactor simulations, it was assumed that alginate beads containing 10.0 g dry weight/L are available at the start of the reactor operation. Alginate occupies 50% of the PFR volume. The maximum biomass concentration permitted anywhere in the alginate beads was 200 g dry weight/L. The PFR volume is 2.17 L, with a diameter to length ratio of 0.25. Reactor performance was evaluated on the basis of ethanol productivity, ethanol yield, and effluent ethanol concentration. The effects of four operating conditions on the reactor performancewere investigated the diameter of the alginate beads, the reactor residence time, the glucose feed concentration, and the concentration of dissolved oxygen during start-up. Three types of operation were analyzed: completely anaerobic operation, oxygenated feed, and a decreasing residence time during the first 8 h of operation to improve yield and productivity during start-up. Each simulated run was of 20 h duration, after which a steadystate operation was reached. Effluent ethanol concentrations for bead diameters of 1 , 2 , and 5 mm and a volumetric flow rate of 12.7 l/h are shown in Figure 6 for a glucose feed concentration of 100 g/L. The area under the curves is proportional to the reactor productivity, since a constant flow rate and reactor volume were used. The ethanol yield is also proportional to the area under the curve since the yield is based on feed glucose, not on the amount of glucose utilized in the reactor. For the first 2 h of operation, the bead size does not affect the reactor performance because initially the beads contain 100 g/L glucose. However, after 2 h the effluent ethanol concentration, ethanol productivity, and ethanol yield decrease when the bead diameter is increased from 1 to 5 mm. As the biomass concentration in the reactor increases and the bulk glucose concentration decreases, the effect of the bead size becomes more pronounced. At steady state, a 5-mm-diameter bead results in 66% of the ethanol productivity and yield achieved with a l-mmdiameter bead. A 2-mm-diameter bead has 95% of the ethanol productivity and yield of a 1-mm-diameter bead.
d = l mm
30 v
c
4
25-
5
20-
+.2 0
0
5 15-
Time (hours)
Figure 6. Effect of bead diameter on effluent ethanol concentration of an immobilized cell PFR with a feed glucose concentration of 100 g/L and a residence time of 0.17 h.
Increasing the feed concentration to 200 g/L yields similar results, although the effect of bead size becomes less pronounced. At steady state, a 5-mm-diameter bead results in 75 % of the yield or productivity obtained with a 1-mm-diameter bead. Similarly, a decreased flow rate brings the curves in Figure 6 closer together while a slower approach to steady state is also observed. Further reactor simulations were performed with 1- and 2-mm-diameter beads. Beads with a 2-mm diameter are probably optimum because smaller alginate beads are more difficult to produce and are weaker mechanically. The decrease in the reactor performance caused by the bead size is relatively small for 2-mm-diameter beads. Figure 7 shows the effects of varying the reactor residence time for a 2-mm-diameter bead in a plug flow reactor with glucose feed concentrations of 100 g/L. As the residence time increases, the effluent ethanol concentration also increases during both the initial and steadystate reactor operation. Doubling the reactor residence time results in a 69% increase in the ethanol yield but a 17% decrease in the ethanol productivity. Changing the bead diameter to 1mm does not affect the above results to any significant degree. The behavior of productivity, yield, and effluent concentration at steady state and for varying operating conditions is presented in Figures 8-10. Under all conditions examined, productivity decreases monotonically with residence time, while yield and effluent concentration increase monotonically. Again, bead size seems to have marginal effects for sufficiently small diameters. On the other hand, the effect of feed concentration is significantly more pronounced. Increasing feed concentration yields increased effluent concentration and reactor productivity but decreased overall yields. Finally, operation performance seems to become insensitive to residence time for sufficiently large residence times. On the basis of these results, a well-balanced operation should employ a feed concentration of 100 g/L a t a residence time of 0.22 h and a bed packed with 2-mmdiameter beads. With a residence time of 0.22 h, reactor productivity is 175 g/(L.h) and the effluent concentration is 38 g/L. The ethanol yield based on glucose feed is 0.38. Further increases in the residence time above 0.22 h result in slightly higher effluent concentrations and yields but significantly lower productivities. Decreasing the residence time below 0.22 h will produce an unacceptably low effluent ethanol concentration and ethanol yield. If the reactor is operated with a feed stream containing 200 g/L glucose, higher residence times are required for efficient glucose utilization. A t a residence time of 0.54
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Biotechnol. hog.., 1990, Vol. 6, No. 5
3
I
100,
0
0.2
0.4
0.6
0.8
1.0
Residence Time (hours) Time (hours)
Figure 7. Effect of residence time on effluent ethanol concentra-
tion of an immobilized cell PFR with a feed glucose concentration of 100 g/L and a bead diameter of 2 mm.
0' 0
I
0.2
I
0.4
I
0.6
I
0.8
I
1.0
Residence Time (hours)
Figure 8. Effect of residence time on ethanol productivity of an immobilized cell PFR at its maximum biomass loading. (0) sf = 100 g/L and d = 2 mm; (x) sf= 100 g/L and d = 1mm; (0) sf = 200 g/L and d = 2 mm; (A)sf = 200 g/L and d = 1 mm. 0.5
2
0.4
0
-
. ol
m
0.3
ol
v
P
;0.2
-
c 0
2
0.1
w
0 Residence Time (hours)
Figure 9. Effect of residence time on ethanol yield of an immobilized cell PFR at its maximum biomass loading. (0) sf = 100 g/L and d = 2 mm; (x) sf = 100 g/L and d = 1 mm; (0) sf = 200 g/L and d = 2 mm; (A)sf = 200 g/L and d = 1 mm. h, the ethanol yield has reached only 0.34 when the glucose feed concentration is 200 g/L and 2-mm-diameter beads are used. Ethanol productivity is 125 g/(L.h), which is 28% less than that achieved with a residence time of 0.22 h and 100 g / L glucose feed. The effluent ethanol concentration, however, is 68 g/L for the reactor with a 200 g/L glucose feed stream. The higher effluent ethanol concentration simplifies downstream processing. By increasing the feed glucose concentration, the effluent ethanol concentration can be increased proportionally, but the residence time must be increased as well, leading to a lower reactor productivity. The choice between a 100
Figure 10. Effect of residence time on effluent ethanol concentration of an immobilized cell PFR at its maximum biomass loading. (0)sf= 100 g/L and d = 2 mm; (X) sf= 100 g/L and d = 1mm; (0) sf= 200 g/L and d = 2 mm; (A)sf= 200 g/L and d=lmm.
and a 200 g/L feed stream will depend on the cost of the feed streams and the cost of ethanol separation. The distribution of biomass in the alginate beads at various times after reactor start-up is shown in Figure 11. The reactor simulations were carried out for 5-mmdiameter beads and a feed glucose concentration of 200 g/L with a reactor residence time of 0.54 h. Five hours after start-up, biomass was uniformly distributed throughout the alginate beads at both the reactor inlet and outlet. Ten hours after start-up, biomass had begun to increase more rapidly at the bead surface compared to the center of the beads. Also at 10 h, the beads near the reactor outlet had less biomass than the beads near the reactor inlet. After 20 h of operation, biomass was distributed nonuniformly in the alginate beads. For beads close to the reactor inlet, the outer region of the beads contained the maximum biomass concentration. Approximately 97 96 of the alginate bead volume contained the maximum allowed biomass. Beads close to the reactor outlet also had a nonuniform distribution of biomass, but the maximum biomass had been reached in only 12 96 of the alginate bead volume. Average biomass concentrations are shown in Figure 12 as functions of the distance from the reactor inlet, for 5, 10, and 20 h after start-up in a similar reactor operation. Five hours after start-up, the biomass concentration was uniform throughout the reactor for residence times of both 0.17 and 0.54 h. After 10 h, the biomass became unevenly distributed, with higher concentrations obtained closer to the reactor inlet. The concentration of dissolved oxygen in the feed stream can affect the PFR performance. Figure 13 shows the effluent ethanol concentration versus time in a PFR with a 100 g/L glucose feed stream, 2-mm-diameter beads, and a residence time of 0.25 h. Supplying oxygen in the feed stream at 50 or 100% of air saturation enhances the reactor performance during the first 4-8 h of operation compared to the performance for an anaerobic feed stream. After the first period, however, an anaerobic feed stream yields the highest ethanol productivity, yield, and effluent concentration. Oxygen increases the growth rate of S. cerevisiae but decreases the specific ethanol production rate of the organism. Thus, the reactor performs better initially when oxygen is supplied, but as the maximum biomass concentration is approached, oxygen decreases reactor performance by decreasing the specific ethanol production rate. The effect of supplying oxygen during the first 8 h of operation and then switching to anaerobic feed is shown in Figure 14. Higher ethanol productivity, yield, and
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Biotechnol. Prog., 1990, Vol. 6, No. 5 250 -
0.04
0
0.08
0.12
0.16
}
1=20
I
1=10
}
1=5
0.24
0.20
Distance (cm)
Time (hours)
Figure 11. Biomass concentration profile in alginate bead of an immobilized cell PFR at t = 5, 10, and 20 h after start-up for 5-mm-diameterbeads located at the reactor inlet (t= 0)or reactor outlet ( z = L) and a residence time of 0.54 h.
Figure 14. Effect of supplying oxygen during the first 8 h of
reactor operation on effluent ethanol concentration for feed dissolved oxygen concentrations of 0,50, and 100%air saturation. 45
2
m 40 v
.-
m
T = 0.17
a
2
r = 0.54 r = 0.17 r = 0.54
50
L
>
0)
4
0
}
1=10
}
1.5
w 0
2
4
6
8
10
12
14
16
18
20
Time (hours)
beads at t = 5, 10, and 20 h after start-up and residence times of 0.17 and 0.54 h.
Figure 15. Effect of increasing residence time during start-up on effluent ethanol concentration from immobilized cell PFR.
Conclusion
451
.L
.z? 3 5 -
5
30-
$
25-
ri)
0
a
20-
C
2w 1 5 7 10-
:
cl
5
0
0
2
4
6
8
10
12
14
16
18
20
Time (hours)
Figure 13. Effect of dissolved oxygen concentration in the feed stream of an immobilized cell PFR on effluent ethanol concentration for feed dissolved oxygen concentrations of 0,50, and 100% air saturation.
effluent concentration are reached by using a feed stream with a dissolved oxygen concentration of 100% air saturation during the initial 12-h period and switching to anaerobic conditions at all later times. In another simulation, the residence time of the PFR was increased during the start-up period in an attempt to increase the ethanol effluent concentration during startup. The results are shown in Figure 15 for a glucose feed concentration of 100 g/L and 2-mm-diameter beads with a final residence time of 0.25 h. Increasing the reactor residence time from 0.25 to 0.83 h during the initial 8-h period causes the ethanol effluent concentration to double without affecting the effluent ethanol concentration at later times.
A growth-fermentation model, originally developed for S. cerevisiae cultures in suspension, was modified to describe experimental observations with alginateentrapped s.cerevisiae glucose fermentations. The model performed satisfactorily in predicting the behavior of other immobilized cell systems. In view of the close agreement between model predictions and experiments, the model was further applied to the simulation of a packed-bed immobilized cell bioreactor. Besides insights obtained into the operation of such systems, the developed model can provide a useful tool in deriving an optimal set of operating conditions, after some key performance criteria have been decided upon.
Notation A b C
D d e em
F
f K 0 2
P
cross-sectional area of packed-bed reactor biomass concentration, g/L general metabolite concentration in packed-bed model diffusion coefficient (9, glucose; e, ethanol; 0, oxygen) bead diameter, mm ethanol concentration ethanol concentrationafter which cell growth ceases (eq 4) volumetric flow rate in packed-bed reactor reactor volume fraction occupied by beads Michaelis constant (s, glucose; L, oxygen) dissolved oxygen concentration, % air saturation measure of Pasteur effect in model (eq 1)
358
R r S
t X
z
Biotechnol. Prog., 1990,Vol. 6, No. 5
alginate bead radius radial distance in alginate bead glucose concentration, g/L time intramembrane distance distance from reactor inlet
Greek Symbols a specific glucose uptake rate, g/(gh) maximum specific glucose uptake rate (eq 2) ffm U specific ethanol production rate, g/(gh) 0 specific oxygen utilization rate, % satn L/ (gh) maximum specific oxygen utilization rate (eq 3) ,8 P specific growth rate, g/(gh) maximum specific growth rate from glycolysis (eq 1) PG maximum specific growth rate from respiration PR (eq 1) 7 reactor residence time, h Subscripts b bulk DR obtained through the application of diffusionreaction analysis m maximum
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Acknowledgment Financial support for this research provided by the National Science Foundation (PYI Grant CBT-8514729), the Monsanto Co., and Merck & Co., Inc., is gratefully acknowledged. This work was carried out in part at the California Institute of Technology Department of Chemical Engineering. The authors are also indebted to Prof. Pao Chau of t h e Department of Chemical Engineering, University of California, San Diego, for providing his laboratory for the alginate bead fermentation experiments. The packed-bed immobilized cell bioreactor simulations were performed at the UCSD Supercomputing Center.
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Accepted August 8, 1990. Registry No. Ethanol, 64-17-5.
