How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 578

As shown in Fig. 11.6 , the dependence of DO for aerobic and facultative organisms on cell
growth follows the Monod growth equation. For aerobic organisms

m max DO
K DO þ

m ¼ (11.42)

DO

and for facultative organisms,

m ¼ m max0 þ ðm max m max0 Þ

DO

(11.43)

K DO þ DO

where m max0 is the maximum specific growth rate in anaerobic conditions. Facultative organ-
isms grow with or without oxygen. For anaerobic organisms, there is no growth if oxygen is
present.
The critical oxygen concentration is about 5% to 10% of the saturated DO concentration
for bacteria and yeast and about 10% to 50% of the saturated DO concentration for mold
cultures, depending on the pellet size of molds. Saturated DO concentration in water at
25 C and 1 atm pressure is about 7 ppm. The presence of dissolved salts and organics
can alter the saturation value, while increasingly high temperatures decrease the saturation
value.
Oxygen is usually introduced to the fermentation broth by sparging air through the broth.
Oxygen transfer from gas bubbles to cells is usually limited by oxygen transfer through the
liquid film surrounding the gas bubbles. The rate of oxygen transfer from the gas to liquid
phase is given by

N O 2 ¼ k L a C C L ¼

OTR (11.44)
where k L is the oxygen transfer coefficient (m/h), a is the gas e liquid interfacial area (m 2 /m 3 ),
C* is saturated DO concentration (g/L), C L is the actual DO concentration in the broth (g/L),
and the N O 2 is the rate of oxygen transfer (g/L/h). Also, the term oxygen transfer rate (OTR) is

used.
The rate of oxygen uptake is denoted as OUR and

m G X
YF X=O 2

OUR ¼ m O 2 X ¼ (11.45)

where m O 2 is the specific rate of oxygen consumption (g g-cells/h), YF X=O 2 is the yield factor
on oxygen (g-cells/g-O 2 ), and X is cell concentration (g-cells/L). When oxygen transfer is the
rate-limiting step, the rate of oxygen consumption is equal to the rate of oxygen transfer. If the
maintenance requirement of O 2 is negligible compared to growth, then
m G X

YF X=O 2 ¼ k L aðC C L Þ

(11.46)

or in the batch reactor with negligible medium volume loss (due to air sparging),

dX
dt ¼

YF X=O 2 k L aðC C L Þ

(11.47)

Growth rate varies nearly linearly with the OTR under oxygen-transfer limitations. Among
the various methods used to overcome DO limitations are the use of oxygen-enriched air or