E N O I N E E R I N G A D V A N C E S IN FERMENTATION PRACTICE 0.1
mal collection efficiency of a particular filter is that estimated solely from interception effects calculated a t a velocity just below which inertial effects are zero. The theoretical expression for the collection efficiency of a single isolated fiber, due solely to interception effects, can be estimated from Equation 3 (2).
-
no = 0.5 [1/(2 In N R ~ )X] [2(1 R ) In (1 R) (1 R) 1/(1
+
+ +
+
-
+ R)1
0.000l
(3)
where no = collection efficiency of a single isolated fiber, R = d,/d,, and N R = ~ Reynolds number. If 1 micron unit density bacterial particles are selected as the basis for design, the air velocity at the point of minimal efficiency is 0.066 dt and the single fiber efficiency, Equation 3, can be simplified to an expression in terms of a single variable, d,. Figure 2 is a plot of this relation. From experimentation with aerosols (7), it has been found that the effectiveness of a filter can be expressed by 1.27 no (1 4.5 a)aL In N1 -= (4) Nz (1 where N1 = total number of particles entering the filter, Nz = total number of particles penetrating the filter, L = filter
+
I
2 4 IO dt fiber diameter in microns
20
Figure 2. Single fiber efficiency, direct interception from
1
-t R ) + i T R 1
[2(1 +R)In(l + R ) - ( l
where R = d,/d/
and N R ~= d/Vp CL
calculated at V = 0.066df
thickness, and a = volume fraction of fibers in the filter. Equation 4 is a reasonable basis for air sterilizing filter design. The proper single fiber efficiency, no, to use in this
Fermentation Kinetics and Model Processes
S-IES of batch fermentation processes in nearly all development programs involve periodic observations of growth, carbohydrate utilization, and product formation throughout the course of the fermentation. The fermentation literature abounds with such data for a large number of processes, and often also for a wide variety of operating conditions for a particular process. Kinetic analysis is the interpretation of these data and the factors which influence them, to shed light on proposed reaction schemes or fermentation patterns. Analyses carried out to date have followed mainly three
Limiting Nutrient Concentration, N Figure 1. Relation of specific growth rate to nutrient concentration
avenues of approach-phenomenological ( 5 , 8 ) , thermodynamic (7), and kinetic (2, 7, 73). The crux of any kinetic analysis lies in determining how the rate of product formation and its stoichiometric coefficient vary with respect to the chemical and physical factors that influence them. Really meaningful quantitative knowledge here is lacking for practically all fermentation processes. An exception is processes where the primary product is cellular tissue. Progress has been made in this area notably in the analysis of continuous propagation of unicellular organisms where the only factor of concern is a single limiting nutrient (6, 70-72, 74-76). Usually a hyperbolic rate equation similar to that commonly encountered in enzyme kinetics is employed to relate the specific growth rate, k, with nutrient concentration, N :
This equation (Figure 1) shows that the specific growth rate is linearly dependent upon the limiting nutrient concentration in the low concentration range and approaches a maximum rate, k,, at high nutrient concentrations. K is a constant characteristic of the enzyme
equation when experimental data are lacking is that based on collection due solely to interception effects estimated at an air velocity where minimal filtration efficiency is expected. T o design an economical filter utilizing this equation it is necessary to assess the filtration job to be accomplished (for a sterilizing filter a logical design basis might be that which would permit only a 1-in-1000 chance of a single contaminant’s penetrating the filter during the period of its operation), determine the filter thickness required for such a job from Equation 4,and select the filter size in terms of superficial area which results in minimal capital and operating expenditures. literature Cited ( 1 ) Chen, C. Y.,Chem. Reus. 55, 595 fl955). ,---,(2) Davies, C. N., Prod. Inst. Mech. Engrs. (London) B1,185 (1952). (3) Humphrey, A. E., Gaden, E. L., IND. ENC.CHEM. 47, 924 (1955). (4) Langmuir, I., Blodgett, K. B., General Electric Research Lab., Schenectady, N. Y., Rept. RL-225 (1944). ARTHUR E. HUMPHREY School of Chemical Engineering, University of Pennsylvania, Philadelphia 4, Pa.
FermentationOver-all “Type” Reactions Type Simple
Simultaneous
Consecutive
Stepwise
Description Nutrients converted to products in a fixed stoichiometry without accumulation of intermediates Nutrients converted to products in variable stoichiometric proportion without accumulation of intermediates Nutrients converted to product with accumulation of an intermediate Nutrients completely converted to intermediate before conversion to product or Nutrients selectively converted to product in preferential order
systems involved in the growth process. That an equation as simple as Equation 1 relates growth rate with nutrient concentration in continuous cell cultivation under idealized conditions is fortuitous. Almost any examination of complicated enzyme reaction schemes indicates that a number of important conditions must be met before a hyperbolic rate equation can be justified. The more fundamental of the three approaches to kinetic analysis is offered through available background in chemical kinetics. This background suggests VOL. 52, NO. 1
0
JANUARY 1960
63
a classification scheme for apparent or over-all “type” reactions, which can be described easily by simple volumetric observations made during the course of most fermentations. Figure 2 shows an example of a simultaneous reaction which obviously involves an “overflow” or “shunt” metabolism ( 4 ) . Figure 3 is one example of the stepwise reactions unique to enzymatic processes. Similar reactions occur in a number of fermentation processes. Mostly, however, the processes involve a combination of several over-all type reactions. Kinetic information, coupled with biochemical evidence, provides a sound basis for studying reaction mechanisms in a fermentation process. Such studies can eventually lead to improvements in batch
fermentations through a program of control that optimizes the rate-determining steps occurring during a fermentation, once they are established, and can also lead to the successful design and operation of multistage continuous systems. Analytical support for such studies is now available in the form of commercial automatically operated analytical instruments. Electronic analog computers permit rapid process simulation and can aid greatly in the interpretation of kinetic results previously difficult to analyze. By a judicious combination of the engineer’s interpretation of reaction kinetics, the biochemist’s understanding of reaction chemistry, and the microbiologist’s ability to maintain active cells, which provide the catalysts for the numerous reactions occurring, fermentation technology can realize a substantial advance in process understanding and control over the next decade. literature Cited
!ICE
Figure 2. Simultaneous conversion of sugar into cell protein and cell fat during Rhodoforula glutinis growth (3)
(1) Calam, C. T., Driver, N., Bowers, R. H., J . Appl. Chem. 1,209 (1951). (2) Deindoerfer, F. H., Humphrey, A. E., IND.ENG.CHEM.51, 809 (1959). (3) Enebo, L., Anderson, L. G., Lundin, H., Arch. Biochem. 11,383 (1946). (4) Fosfer, J. W., “Chemical Activities of Fungi,” Academic Press, New York, 1949. (5) Gaden, E. L., Jr., Chem. and Ind. (London) 1955, p. 154. (6) Herbert, D., Elsworth, R., Telling, R. C.. J. Gen. Microbiol. 14, 601 (1956). (7) Luedeking, R., Piret, E. L., Division of Agricultural and Food Chemistry, 134th Meeting, ACS, Chicago, Ill., September 1958. (8) Maxon, W. D., Appl. Microbiol. 3, 110 (1955). (9) Monod, J., Ann. Rev. Microbiol.3, 371 (1949).
i
n u
Phase of Glucose Utilization
L
Figure 3. Diphasic utilization of energy sources during the growth of Escherichia coli ( 9 ) (10) Monod,
J., “Recherches sur la croissance des cultures bacteriennes,” Herman & Co., Paris, 1942. (11) Moser, H., “Dynamics of Bacterial Populations Maintained in the Chemostat,” Carnegie Inst. of Wash., Publ. 614 (1958). (12) Novick, A,, Szilard, L., Proc. Natl. Acad. Sci. U. 5‘. 36, 708 (1950). (13) Piret, E. L., Luedeking, R., Division of Agricultural and Food Chemistry, 128th Meeting, ACS, Minneapolis, Minn., September 1955. (14) Pirt, S. J., J . Gen. Microbiol. 16, 59 (1957). (15) Spicer, C. C., Biometrics 11, 225 (1955). (16) Teissier, G., Rev. xi.,Extrait du No. 3208, 209 (1942).
FRED H. DEINDOERFER School of Chemical Engineering, University of Pennsylvania, Philadelphia 4, Pa.
Continuous Fermentation
THE
major emphasis in this discussion of continuous fermentation is on the single-stage homogeneous fermentation or stirred-tank reactor, where feed and product streams are continuous and equal and the fermentor contents, cell3 and liquid, are kept homogeneous by agitation. The modifications of this basic system-multistage, recycle, two-phase, etc.-are considered to a lesser extent. The table a t right gives some material balance relationships for the basic system. The complete balance given in Equations l and 2 reduces to Equation 3 when steady state is assumed. Then a t steady state each synthetic or degradative rate is simply equal to the appropriate concentration term multiplied by the dilution rate as shown in Equations 4,5, and 6 (X“ = substrate concentration, X p = production concentration). To relate the concentration of one material (such as the substrate) to that of another (such as the cells) the yield
64
The batch growth curve can be used directly, appropriate equations can be developed, or a graphical analysis can be used.
Material Balance Relationships
IUPJT t GROWTH
(-341 = OUTPUT t ACCJMULAT
S O E C I F ’ C GROWTH
RATE CONSTON? l k l =
Mechanism for Culture Control
Oh (1 )
$ = DILUTIOW R A T E 13)
- - - - - - - - - - - - -RATE
OF
CE! L SYUTHESIS = X3
(I!
F 4 T E OF S U E S T R A T E U T , L I Z A T ’ O N = [ X i - X ‘ ! R A T E OF F P 3 D U C T F O R M A T I O N = -
-
f ELD C 3 \ S T A N T
-
IY1 =
Xi-X
(6
kPD
_
4
D
1
(6 ) _
-
_
(7
constant, J‘, is employed as in Equation 7. T o design a continuous fermentor for cell production it is necessary to have kinetic data, to evaluate k. This can be done to some extent with batch fermentation data.
INDUSTRIAL AND ENGINEERING CHEMISTRY
There are two mechanisms for control of continuous cultures. One is exemplified by the Turbidostat of Bryson; the other, by the Bactogen of Monod and the Chemostat of Novick and Szilard. I n the Turbidostat the cell population is held constant by a device which measures the culture turbidity and regulates the feed accordingly. In the Chemostat the feed and withdrawal rate are held constant at a value less than the maximum growth rate. Under these conditions the growth rate is regulated by a limiting nutrient concentration. This can be shown to constitute a self-regulating and stable steady state. The Chemostat principle is more widely applied to continuous fermenta-
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