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7.REACTION MECHANISMS,PATHWAYS,BIOREACTIONS AND
BIOREACTORS
Professional Reference Shelf
R7.2 Oxygen-Limited Fermentation
Oxygen is necessary for all aerobic fermentation (by definition) [cf.Equation (7-98)]. Maintaining the appropriate concentration of dissolved
oxygen in fermentation is important for the efficient operation of afermentor. For oxygen-limited systems, it is necessary to design a
fermentor to maximize the oxygen transfer between the injected air bubble
and the cell. Typically, a fermentor contains a gas sparger, heat transfersurfaces, and an impeller, such as the one shown in Text Figure 7-18 for a
batch reactor. A chemostat has a similar configuration, with the addition ofinlet and outlet streams.
Transport Steps. The overall transport mechanism of oxygen to a cell is
very similar to that described for reactant gas in a slurry reactor and asshown in Figure CD7-3. The corresponding oxygen transport and reaction
steps and equations are analogous to the slurry reactor transport steps
discussed in Chapter 12, that is:
(R7.2-
1)
(R7.2-2)
Generally, the diffusional resistance from the bulk liquid to the cell surfaceis ignored. However, depending on the cell size or cell floc size, the transfer
step from the bulk liquid to the cell surface may be rate-limiting; one suchexample is the oxygenation of a culture ofStreptomyces niveus. The
transport of oxygen into a cell occurs by different mechanisms for yeast and
bacteria. In the case of yeast, an oxygen molecule diffuses across an inertcell membrane before being consumed by the cell. The corresponding rate
equations are:
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Analogousto slurry
reactor
steps
Figure R7.2-1
Oxygen transport to microorganisms.
(R7.2-3)
(R7.2-
4)
where:
ac= cell surface area per mass of cell, m2/g
De effective diffusivity across the cell, m2/s
L = thickness of cell membrane, m
Cc= concentration of cells, g/ m3 (analogous to m in a slurry reactor, Text
Chapter 12)
Ci, Cb, C0, Cc= saturation, bulk, external surface, and internal cellconcentrations of oxygen, respectively
Combining Equations (R7.2-2) through (R7.2-4) and rearranging, we obtain
Yeast
(R7.2-
5)
For many yeast cells, diffusion across the cell membrane can be neglected.
In the case of bacteria, the oxygen begins to be consumed as soon as itdiffuses into the cell membrane. In fact, bacteria consume oxygen primarily
atthe cell membrane, where most of the respiratory enzymes are located.
As is the case of the catalyst pellet in the slurry reactor, the rate of oxygenconsumption can be given by the product of the effectiveness factor and the
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rate of reaction that would occur if the entire interior of the cell wereexposed to the concentration at the external surface, C0
The rate law for oxygen consumption (uptake) generally follows eitherMichealis-Menten or first-order kinetics. In many systems it depends on theparticular growth phase of the bacteria cell. Typical respiration rates for
single-cell yeast and bacteria are on the order of 100 to 600 mg O2/g cellh. For first-order kinetics we have
(R7.2-
6)
where kris the specific reaction rate for oxygen uptake, s-1, and h is the
effectiveness factor for diffusion and reaction of oxygen inside the cell.
Combining equations (R7.2-6), (R7.2-2), and (R7.2-3) gives
Bacteria(R7.2-
7)
We can observe from Equations (R7.2-5) and (R7.2-7) that at low cell
concentrations, transport steps C, D, and E (mass transfer of oxygen to andwithin the cell) become rate limiting.
The main variables affecting kLab are the impeller diameter, Di, and speed,
N(rpm); volumetric flow rate of the gas, Q; tank diameter, DT, and height
LT; and power input to impeller, . Many fermentations produce productsthat cause the broth to exhibit non-Newtonian fluid behavior. Consequently,
a characteristic relaxation time, , is included in the correlation for the
mass transfer coefficient between the gas bubble and the bulk liquid, kLab.Representative correlations for kLab are given in Table R7.2-1.
The power input to the fermentor without gas bubbles present ( ) is afunction of system variables:6,7
where the Reynolds number for this system is defined as
(R7.2-8)
When gas is present, the power input, Pg is reduced for a given propellerspeed 8 and is a function of gas flow rate, impeller speed and diameter, and
the Reynolds number. The ration of the power input with gas present, Pg,
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to that without gas present ( ) is
(R7.2-
9)
Table R7.2-1. Mass Transfer Coefficients In Fermentor
1. Low-viscosity broths Van't Reit (1):
Range
Pure Water2-2600dm3
Electrolytic (Solutions)
2-4400
dm3
where = power input per unit volume of vessel and isin units of W/m3
Q = volumetric flow rate, m3/s
DT= tank diameter, m
Vs = superficial gas velocity
2. Non-Newtonian correlations
Perez and Sandall (2):(R7.2-
10)
Yagi and Yoshida (3):
(R7.2-
11)
Ranade and Ulbrecht (4):
(R7.2-
12)
[Comment: These correlations were obtained in tanks having a volume of12 dm3 or less (5).]
Other parameters in the correlations are:
g = gravitational acceleration, m2/s = fluid viscosity, g/m s
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e = effective viscosity, g/m sw= viscosity of water, g/ms
d= viscosity of dispersed phase,g/m s
= surface tension, N/m
N= impeller rotation speed, s-1 = density, g/m3
DAB = diffusivity, m2/s
3. Effect of solids (6):
(1) K. Van't Reit, Fund. Eng. Chem. Proc. Des. Dev., 18, 357 (1979)
(2) J.F. Perez and O.C. Sandall,AIChE J., 20, 770 (1974)
(3) H. Yagi and F. Yoshida, Ind. Eng. CHem. Proc. Des. Dev., 14, 488(1975)
(4) V.R. Ranade and J.J. Ulbrecht,AIChE J., 24, 796 (1978)(5) D.W. Hubbard, L.R. Harris, and M.K. Wierenga, Chem.Eng. Prog., 84(8),
55 (1988)(6) D.B. Mills, R. Bar, and D.J. Kirwan,AIChE J., 33, 1542 (1987)
The functions F1 and F2 are generally given graphically
for different types of fluids and different geometricconfigurations. 9,10
Fermentation Scale Up
2006 by Pearson Education, Inc.Publishing as Prentice Hall PTR
ISBN 0-13-047394-4
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