How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 577

0, the product would be only
growth associated, and consequently a would then be equal to YF P/XG .
As we have already observed from Fig. 11.5 that the growth- and endogenous metabolism-
associated product formation may be more general and the three cases listed above can be
simplified from it, i.e. Eqn (11.38) . Only when the substrate limiting the product generation
is the same as that limiting the cell growth, the three simplified cases prevail. In most indus-
trial applications, this is not the case.

If a ¼ 0, the product is only nongrowth associated, and if b ¼

11.8. O XYGEN DEMAND FOR AEROBIC MICROORGA NISMS

Dissolved oxygen (DO) is an important substrate in aerobic fermentations and may be
a limiting substrate, since oxygen gas is sparingly soluble in water. At high cell concentra-
tions, the rate of oxygen consumption may exceed the rate of oxygen supply, leading to
oxygen limitations. When oxygen is the rate-limiting factor, specific growth rate varies
with dissolved-oxygen concentration according to Monod equation,

just like any other

substrate-limited case.
Above a critical oxygen concentration, the growth rate becomes independent of the dis-
solved-oxygen concentration. Figure 11.6 depicts the variation of specific growth rate
with dissolved-oxygen concentration in a rich medium (no other substrate limitation).
Oxygen is a growth rate-limiting factor when the DO level is below the critical DO concen-
tration. In this case, another medium component (e.g. glucose, ammonium) becomes
growth-extent limiting. For example, with Azotobacter vinelandii at a DO 0.05 mg/L, the

growth rate is about 50% of maximum even if a large amount of glucose is present.
However, the maximum amount of cells formed is not determined by the DO, as oxygen
is continually resupplied. If glucose were totally consumed, growth would cease even if
DO

¼

0.05 mg/L. Thus, the extent of growth (mass of cells formed) would depend on
glucose, while the growth rate for most of the culture period would depend on the value
of DO.

¼

(a) (b)

1.00

0.35

0.30

0.95

0.25

0.90

0.20

µ
µ max

0.85

0.15

0.80

0.10

0.75

0.05

0.00 0.70

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.1 0.2 0.3 0.4 0.5

DO, mg/L DO, mg/L

FIGURE 11.6 Growth-rate dependence on DO for aerobic (a) and facultative organisms (b). The lines are Monod
equation fit to the data (symbols). Data source: J. Chen, A.L. Tannahill and M.L. Shuler, Biotechnol. Bioeng., 27: 151, 1985.
(a) Strictly aerobic organism: Azotobacter vinelandii. (b) Facultative organism (Escherichia coli).