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FRED H. DEINDOERFER and ARTHUR E. HUMPHREY School of Chemical Engineering, University of Pennsylvania, Philadelphia 4, Pa.
A logical approach to
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Design of Multistage Systems for Simple Fermentation Processes This design procedure can be used to predict operating points and optimum number of stages in a continuous multistage system for fermentation processes which follow simple kinetic and stoichiometric relationships Cowrmuous operation of a fermentation process offers a number of advantages over the conventional batch method from both cost and operational viewpoints. T h e most striking advantage is increased productivity from the same equipment. This carries with it inherent increases in some operating costs. The optimum method of production will depend on a careful analysis of all the cost factors involved. This article points out how the most economical continuous system for simple fermentations can be designed from easily obtainable batch kinetic data and a careful cost analysis. Multistage Systems
Most industrially important fermentations are aerobic, requiring large volumes of air throughout their operation. Therefore, they are carried out best in the conventional stirred-tank type vessel. It is implied that agitation is sufficient for complete back-mixing, ensuring a homogeneous reaction medium. One such vessel, with a continuous feed stream and a n equal-volume continuous exit stream, comprises a reaction stage. A series of these vessels operated continuously (Figure 1) comprises a multistage system. Simple Fermentation Processes
The kinetic character of individual processes differs widely among industrially important fermentation processes -e.g., the different metabolic patterns in streptomycin biosynthesis, the bioconversion of glucose to gluconic acid, and the growth of yeast cell tissue. A number of processes have unifying characteristics which permit arrangement into one of several classes. Simple fermentations display the following kinetic and stoichiometric characteristics: Biocatalytic activity is a function of limiting nutrient concentration and is independent of the age of the cells; and product formed is directly proportional to the cellular concentration attained as well as to the amount of
limiting nutrient utilized. These are usually biosynthetic processes in which the product is intracellular. The definition of simple fermentation processes can be enlarged to include a special type of process not involving growth. These nongrowth processes are essentially suspended cell fermentations, which during continuous operation require preformed cellular material to be separated from the exit stream of a stage and recycled to that stage without accumulation or depletion. T h e material provides the enzymes to convert substrate to extracellular product in a manner analogous to the action of solid catalysts in fluid-bed catalytic processes. These processes are characterized stoichiometrically by a direct proportionality between substrate utilized and product formed. Thus, for processes involving growth, xN-tyM + z C
(1)
where N represents the limiting nutrient concentration, M is cell mass, and C is product concentration. JC, y, and z are stoichiometric coefficients which remain in the constant proportion x:y:t. Also,
where a ( N ) varies as a function of the
limiting nutrient concentration, N . For the synthesis of cell tissue, M and C are identical, and Equations 1 and 2 can be simplified accordingly. For nongrowth processes, XS+ tC (3 1 where S represents substrate concentration. y for these processes is zero. Also,
where a(5) is now a function of the substrate concentration, S. T h e characteristics outlined may appear rather stringent for simple fermentation classification. Actually, however, a large number of processes approximate this type of behavior. Productivity Productivity is synonymous with capacity to produce-Le., the rate at which a unit volume of plant can turn out product. I n Figure 2, the two diagonal lines drawn tangent to the curve at the points shown represent productivities. T h e lesser sloped line is the maximum productivity of the batch fermentation process. Its point of tangency does not correspond, in this case, to the point of maximum product Concentration. At this latter point, the productivity would be lower because the slight increase in
U STAGE I
Figure 1.
STAGE 2
STAGE
n
Vessel arrangement in a multistage system
Each stage is maintained at a constant product concentration level, which becomes progressively higher from one stage to the next
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-DOWN
t
0-
Figure 2.
-
TIME - HR.
Kinetic character of a fermentation process
Continuous operation at full productivity potential eliminates unproductive dawn time but utilizes raw materials less efficiently
tion-aeration control of most fermentation processes. Because of the important effect of pH on metabolic rates, this variable must also be controlled. A number of workers have shown how important oxygen supply is in determining the ultimate concentration and rate of product formation in many processes. An excess of oxygen must always exist in aerobic processes. Factors which affect the rate of oxygen supply demand attention and control. Often overlooked in this respect is the role of antifoaming agents in oxygen transfer. Small amounts of several typical antifoaming agents reduce the rate of oxygen absorption in a fermentation medium by as much as 50%. Kinetic data should be gathered from batch fermentations which contain the amount of antifoam needed to depress foaming during continuous operation and this amount should always be used in continuous operation. Data gathered from batch studies which neglect the above considerations may lead to grossly improperly designed continuous systems. Development of Design Procedure
product concentration is achieved only by an unduly long extension of the process cycle. The batch productivity line takes into account the unproductive parts of the process such as harvesting and rebatching, in a period called down time. This type of analysis was first applied to fermentation processes by Schmitz ( 7 7). The steep sloped line is the maximum instantaneous productivity of the process and represents the full potential of continuous operation. It corresponds to the steepest slope of the reaction curve. Operating the process continuously at the product concentration level corresponding to this slope eliminates unproductive down time. Operating a single stage continuously a t the point of maximum productivity always results in less efficient utilization of nutrient raw materials. Where process economics warrant, second and later stage fermentation vessels can be used to make fuller use of nutrients and arrive a t higher product concentrations in the harvest stream. Productivity
is decreased because of the additional volume. If the continuous operation is to remain most economical, this decreased productivity must exceed or compare favorably with the operating productivity of the batch process. The complete process economic picture must be analyzed thoroughly. Collection of Batch Data
Batch data for kinetic anaIysis must be collected under strictly controlled conditions if they are to be used for designing continuous systems. The continuous process must be operated so that all factors other than limiting nutrient concentration affecting the value of the kinetic variable, Q ( N ) , remain under control. This ensures a common past history for the cell population in a homogeneous stirred-tank vessel. Batch processes used for designing continuous systems should be under identical control. The control requirements extend beyond the normal temperature and agita-
Examples of Typical Simple Fermentation Processes Type of Reaction
Product
hIicroorganism
Growth Processes Cell tissue synthesis Starter culture production Enzyme synthesis Growth factor synthesis
Feed yeast Sausage starter Invertase Vitamin B12
Oxidation
1 1-Hydroxysteroids Gluconic acid Lysine
Torulopsis utilis Pedwcoccus cerevisiae Saccharomyces cerevisiue Bacillus megatherium
Nongrowth Processes
Decarboxylation
810
INDUSTRIAL AND ENGINEERING CHEMISTRY
Rhizopus nigricans Aspergillus niger Aerobacter aerogenes
Continuous reactors in the chemical industry often are designed from batch reaction data. Therefore as a first approach, batch fermentation kinetic data can be used to design continuous fermentation systems in a similar manner. A number of graphical and analytical design procedures for continuous fermentations have been described ( 7 , 3, 4, 8-70). That of -%dams and Hungate (7) is the most general. The method used in the work described here extends their method along lines previously applied to simpler chemical reactions (2, 5, 72). Similar application to fermentation processes was suggested by Luedeking and Piret (6, 7). In a fermentation vessel operating as one stage in a continuous system, the steady-state material balance between input and output streams may be written Input -I-accumulation = output
This can be expressed in mathematical notation VdC', FCn.1 7 - FC, (5)
+
where C, represents the product concentration in the stage under consideration. Subscript n - 1 refers to the incoming stream which has left the previous stage. The rate of change in product concentration, or accumulation, is dC,/dt. F is the volumetric flow rate and V is the operating volume of the stage. The ratio V / F has the units of time and represents the average retention or holding time (sometimes called turnover time) in the stage. Rearrangement of Equation 5 results in a working formula
-
MUL T lSTA 0 E FE R ME NTAT10 N
Equation G is the basis for this design method. A reaction curve of dC/dt us. C is constructed from batch data (Figure 3). Equation 6 represents a family of material balance lines on such a plot, having a slope of F / V and an x- intercept of C&-I. The intersection of a material balance line with the reaction curve locates the operating point of stage n corresponding to the holding time, V/F, and the previous stage concentration, C,-1. The rate of change of concentration, dC/dt, has the units of productivity. C,-l for stage 1 is usually zero and the material balance line passing through the origin with slope F / V , the reciprocal of the average holding time, is chosen so that the first stage is operated at the maximum productivity, corresponding to concentration CI. Subsequent stages can be constructed in a similar manner, the x- intercepts of the operating lines being the concentrations in each previous stage, as shown for stages 2 and 3, respectively. The slopes of the material balance lines need not be identical. When the stages are of different sizes, for instance, the slopes of the operating lines will also be different. Thus, the final product concentration, Ca, obtained from three equally sized stages could also be obtained for this case in two stages, if the second stage were three times the size of the first stage, as drawn for 2’. Possible Deviations from Design Prediction
When a growth-type simple fermentation process is maintained in continuous steady state, the cell population passes through numerous generations. Genetic variations that often occur may result in evolution of strains which enter the reaction described by Equations 1 and 2 in a different manner. T h e proportion, x.y:z, among stoichiometric coefficients, or the functional relationship, a ( N ) , between reaction rate and limiting nutrient concentration, will be altered slightly. If such strains become predominant, a gradual displacement in the steady-stage cell concentration in each stage can occur. If the ratio a(N)/z is larger, a higher cell concentration is established in each stage. The system, then, uses retention times longer than required by the shorter generation time of the predominant strain. O n the other hand, for a smaller a ( N ) / z , the retention time will be too short, and the stages will be depleted of cells. Unless a more favorable genetic variation occurs and a new steady state is established, this depletion leads to complete washout of the system. Such phenomena cannot be predicted from batch
-
C PRODUCT CONCENTRATION
-
G./L.
Figure 3. Representation of reaction curve and material balance line on productivity-concentration plot showing stage location and material balance line construction
kinetic data. They are discovered only through actual continuous operation. Application to Yeast Propagation
The method will now be applied to the propagation of yeast-one of the simplest fermentation processes to analyze kinetically. Data typical of a batch yeast propagation were plotted on concentration-time coordinates, showing the characteristic lag, exponential growth, and decelerating growth phases. The exponential growth phase was characterized by a generation time of 2.0 hours. This hypothetical growth curve is replotted in Figure 4 as a reaction curve
C
- YEAST
with productivity-concentration coordinates, by determining the growth rate (productivity) as a function of concentration using the graphical method of Adams and Hungate. The exponential growth phase is clearly illustrated on a plot of the type shown in Figure 4 by a straight-line relationship, which if extended downward would pass through the origin. The significance of this result is that a simple process involving an exponential growth phase can be operated at any desired point in the exponential phase by employing the same feed rate. The retention time, when operating in the exponential growth phase, is fixed by the generation time of
CONCENTRATION (DRY BASIS)
- G./L.
Figure 4. Graphical design of multistage system for a typical yeast fermentation process A simple process involving an exponential growth phase con be operated ot any desired point in the exponential phase using the same feed rate
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81 1
Table II.
Table 1. Cost of Fermentation Processes Can Be Broken Down to Three Categories yo Process Cost Baker's Cyanocoyeast balamin I. Raw materials 50 10 11. Residence time4 20 20 111. Product isolationb 30 70 a Includes fixed charges such as plant overhead and equipment depreciation, and variable costs such as labor, maintenance, utilities (power, steam, and refrigeration), and waste disposal. Includes all cost factors in I and I1 involved in product isolation.
Relative Costs of Multistage Continuous and Optimum Batch Process Operation
Product Stream Concn.,
Productivity,
G./L.
G./L. X Hr.
Batch
22.0
0.8Sa
0.50
0.20
0.30
1.00
1
16.0 20.0 22.0 23.0 23.4 23.6
5.55
0.69
0.07
0.14
0.90
3.97 2.41 1.90 1.54 1.29
0.55
0.08
0.13
0.50 0.48 0.47 0.47
0.11 0.12 0.14 0.16
0.16 0.18 0.20 0.22
0.76 0.77
No. of
Stages
2 3 4
5 6
Raw materials
Equation 9 is the equation of the aforementioned straight line. T o maximize productivity in the process, the first stage should be operated at a maximum. T h e material balance line is drawn to the peak of the reaction curve. The retention time for this stage and for equal-sized stages in the system is 2.9 hours. T h e second-stage operating point corresponds to the intersection of the material balance line for stage 2, originating a t C1 = 16.0 grams per liter, and dC/dt = 0, with the reaction curve. Later stages are located similarly, leading to a complete system design. Each stage reaches a higher product concentration level, but in so doing decreases the over-all productivity of the system. Economic Considerations
Optimum System Design
Kinetic aspects of a process alone are inadequate in determining the optimum system design. Economic considerations must be included. Estimated fermentation process costs can be broken down into the three categories shown in Table I. Their relative ratio influences the number of stages in the system. T h e estimated cost for cyanocobalamin production are listed to illustrate how widely the relative ratio of the three categories can vary with such factors as degree of asepsis required and complexity of the product isolation operations.
T h e results obtained in the graphical design procedure carried out in Figure 4 are compared in Table I1 with the optimum batch process, to arrive at the ratios of product stream concentration and productivity needed for a n initial cost comparison. T h e decrease in productivity with increased number of stages is apparent. Actually, not until ten stages are used is the productivity of the continuous system less than that of the optimum batch process. Using the cost distribution for the batch process-i.e., 50, 20, and 30%to weight the appropriate ratios obtained
-Ir _-
F
1.45 G
(7 )
where G is the generation time of the microorganism. This expression for the retention time can be substituted in Equation 6, for stage 1. d51 dt
-
Cl-co 1.45 G
For most processes, there is no product in the feed stream, so that Co = 0. (9)
81 2
~
Total
0.78 0.81 0.85
Based on batch downtime of 10 hours and fermentation of 16 hours.
Continuous processing usually increases certain costs, like raw materials and waste disposal; other costs can be expected to decrease. Reasonable approximations for initial cost estimates for comparison with batch operation on a per unit of product basis can be made by assuming that raw materials costs are proportional to the ratio of batch (optimum) to continuous process product stream concentrations; residence time charges are proportional to the productivity ratio of batch to continuous operation raised to the 0.6 power; and product isolation costs, like raw materials costs, tend to be proportional to the ratio of batch to continuous process product stream concentrations, and, to account for benefits of continuous operation, also to the productivity ratio. Therefore the product isolation cost factor is proportional to the product of these two ratios. It is here arbitrarily chosen as equal to the product of the concentration ratio and the productivity ratio raised to the 0.6 power. Actually, in a thorough comparison, product isolation costs are broken down and weighted much more carefully, each isolation operation undergoing its own analysis. Often product isolation operations are already geared for continuous processing, even though the fermentation process is carried out batchwise and little, if any, advantage is gained in this part of the process by continuous fermentation.
the organism. This has been noted by a number of workers. Mathematically the relationship can be expressed as
Relative Costs Residence Product time isolation
INDUSTRIAL AND ENGINEERING CHEMISTRY
from the product stream concentration and productivity columns of Table 11, the relative cost factors listed in the next three' columns are obtained. These factors are added to find the minimum point in the total cost curve, which, for the yeast process, occurs a t approximately two stages, indicating potential savings over optimum batch operation or approximately 24%. Conclusion
Fermentation processes whieh adhere simple kinetic and stoichiometric relationships should be adaptable to continuous processing by proper exercise of control techniques. The design example presented here points out the advantage of operating such processes continuously; the method developed should be of use in designing multistage systems for these processes. LO
Literature Cited (1) Adams, S. L., Hun ate, R. E., IND. ENG.CHEM.42, 1815 fl949). (2) Eldridge, J. W., Piret, E. L., Chem. Eng. Progr. 46, 290 (1950). (3) Finn, R. K., Wilson, R. E., J . Agr. Food Chem. 2, 66 (1954). (4) Golle, H. A., Ibid., 1, 789 (1953). (5) Joncs, R. W., Chem. Eng. Progr. 47,
46 (1951). (6) Luedeking, R., Piret, E. L., 128th Meeting, ACS, Minneapolis, Minn., September 1955. (7) Luedeking, R., Piret, E. L., 134th Meeting, ACS, Chicago, Ill., September 1958. (8) Maxon, W. D., A#pl. Microbiol. 3 , 110 ( 1 9 5 5 ) . (9) Monod, J., Ann. inst. Pasteur 79, 390 (1950). (10) Pirt, S. J., J. Gen. Microbiol. 15, 1V (1956). (11) Schmitz, -4.J., Jr., 12th Intern. Gong. Pure and Applied Chemistry, New York, X. Y . , September 1951. (12) Weber, .A. P., Chem. Eng. Progr. 49, 26 (1953). RECEIVED for review October 1, 1958 ACCEPTED February 27, 1959 Division of Agricultural and Food Chemistry, Symposium on Fermentation Kinetics and Continuous Processes, 134th Meeting, ACS, Chicago, Ill., September 1958.
