productivity with oxygen transfer for 5-liter, 200-gallon, and 15,000-gallon fermentors. The data correlate well. For both the streptomycin and penicillin fermentations, there is a sharp decrease in productivity below a threshold level and a broad range of good productivity which permits fairly easy scale-up. Roxburgh, Spencer, and Salans ( 3 ) demonstrated a similar scale-up is possible for the ustilagic acid fermentation, and Strohm, Dale, and Peppler (6) obtained a good correlation for yield of baker’s yeast us. oxygen transfer in agitated and nonagitated vessels ranging from laboratory sizes to a 30,000-gallon yeast propagator. About seven years ago, bacterial fermentation for the production of vitamin B ~ Q was scaled up at Pabst Laboratories. This bacterial fermentation was affected by excessive agitation. T h e translation from 110-gallon operating volume to the production scale in the 6000- and 12,000-gallon tanks was excellent. The prediction of process results from the bench scale 2-gallon fermentors is clear, but the curve is displaced (see figure). This is probably due to the fact that an order of magnitude of about two to three times the power
Air Sterilization
SUBMERGED
aerobic fermentation processes require a continuous supply of large quantities of air. Sterilization of this air is mandatory in many fermentations. For pure culture operation, incomplete destruction or inadequate removal of the microorganisms carried in the air may preclude successful operation. Many ways have been suggested for sterilizing air. Only adiabatic compression and filtration through bed of fibrous and granular materials have found widespread usage on an industrial scale. Of these, filtration through beds of fibrous materials such as glass wool is by far the more common method. I n recent years sufficient research has been carried out to permit the design of these fibrous filters on a rational basis. Major requirements which every air sterilization system must satisfy are: The system should be simple in design. I t should not be inordinately costly to operate. I t should remove or destroy air-borne contamination to the extent necessary for satisfactory fermentation performance. I t should be stable to repeated steam or chemical vapor sterilization. I t should condition the air. Its ability to maintain a sterile air supply should not be jeopardized by power failure or compressor surges.
62
Oxygen Adsorption Coefficient Can Be Used to Relate Fermentor Physical Performance to Productivity
Gage T’ol.,
Gal. 110 6000
Press. on Tank, R.P.M. P.S.I.G. 140 0 5 100 0
5
Av . Press., Atm. 1.04 1.38
Air Flow, C.f.m. Ft./hr. atm. sparger
press.
level
x 104
x
1.17
6 8 190
1.51
240
61 61 135 134
2.52 3.39 3.64 4.66
4.70
per unit of volume is required in the 2gallon tanks above that required for the 110- to 12,000-gallon sizes over an equivalent gas transfer range. I t is possible that there is a sparing action of power, which can be considered a measure of liquid turbulence, on the gas transfer requirement. A satisfactory scale-up can be accomplished without getting completely involved in the complicated nature of the fermentation process itself. The most usable concept is on the basis of oxygen transfer. literature Cited
(1) Cooper, C. M., Fernstrom, G. A,,
This latter requirement is frequently overlooked. Its consideration is paramount in the design of filters compounded from fibrous materials. Typical performance data for the removal of bacteria from air streams by fibrous filters are illustrated in Figure 1. For a particular filter, there is an intermediate air velocity at which filtration efficiency is a minimum. If the filter design is based upon a performance observed a t an operating velocity other than that a t which minimum efficiency occurs, surges or brief power failures could create periods of operation a t lower than designed for efficiencies. Minimal efficiency at an intermediate air velocity occurs because different forces act to collect air-borne particles a t difference velocities. At low velocities, gravitational, diffusional, and electrostatic forces act on the particle.
I
Air Velocity
INDUSTRIAL AND ENGINEERING CHEMISTRY
Typical filter performance
104
... 3.35 ...
Miller, S. A., IND.ENG.CHEM.36, 504 (1944). (2) Karow, E. O., Bartholomew, W. H., Sfat, M. R., J. Agr. Food Chem. 1, 302 11953).
(3j-ROXburgh, J. M., Spencer, J. F. T., Salans, H. R., Zbid.,2, 1121 (1954). ( 4 ) Rushton, J . H., Chem. Eng. Progr. 47, 485 (1951). (5) Rushton, J. H., Oldshue, J. Y.,Zbid., 49. 161 (1953). (G) Strohm, J.; Dale, H. F., Peppler, H. J., Appl. Microbiology 7,235 (1959). (7) Wise, W. S., J. Gen. Microbial. 5, 167 (1951).
W. H. BARTHOLOMEW’ Pabst Laboratories, Milwaukee, Wis. 1 Present address, International Minerals and Chemical Corp., Skokie, Ill.
Their effect is inversely proportional to air velocity. At high velocities, inertial forces come into play, which are directly proportional to air velocity. The nature of inertial effects is such that below a certain air velocity, collection due to inertial forces is zero. One set of workers (3)has shown this velocity to be approximately that at which the filtration efficiency is a minimum. I t has been suggested (4) that this velocity could be estimated by the following relation Vminimurn eiiioienoy
*
Vinertial eiieota
-+
0
1.125 1.1 d / CPPdPZ
(1)
where ,u = air viscosity, d, = fiber diameter, C = Cunningham correction factor, p p = particle density, and d, = particle diameter. For the collection of unit density, 1-micron bacterial particles from air streams at room temperature and pressure, this velocity is equal to
dr (2) where velocity Vis in feet per second and the fiber diameter, d,, is in microns. Regardless of air velocity, some collection always occurs, because air-borne particles possess a finite size and will be intercepted by some fiber blocking an air stream along which a particle moves. Collection must always be greater than that due to interception, as it represents the minimum collection physically possible. In the absence of experimental data, a reasonable estimate of the miniV i n e r t l a l eifeots
Figure 1.
Calcd. Kd, X P Kdw X P
-+
0 = 0.066
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 a t 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 a t 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
