Mass Transfer
425
10.1 Gas-Liquid Mass Transfer
In aerobic processes, oxygen is a key substrate and because of its low solubility in aqueous
solutions a continuous transfer of oxygen from the gas phase to the liquid phase is decisive for
maintaining the oxidative metabolism of the cells (see Example 10.1). A few minutes without
aeration of the medium has for example a serious impact on the ability of a culture of the mold
Penicillium chrysogenum
to produce the desired penicillin,
whereas
facultatively aerobic
organisms, such as the yeast
Saccharomyces cerevisiae
or the bacterium
Escherichia coli,
will
drastically change their product formation when deprived of oxygen.
However, oxygen gas-liquid mass transfer, is not the only important phase transfer process in
fermentation processes. Carbon dioxide is formed during respiration, and also in most fermentative
processes. A too high concentration of carbon dioxide may act inhibitory on the microorganism,
and a continuous removal of the carbon dioxide formed is therefore needed (Jones and Greenfield,
1982). Methane and other light hydrocarbons can be used for the production of single-cell protein.
In these processes, both oxygen and the sparingly soluble hydrocarbon must be transferred to the
liquid phase at a rate sufficient to meet the requirements of the cells. Methane may also be a
product gas in anaerobic wastewater treatment processes. In this case the necessary gas-liquid
transfer involves removing the methane and carbon dioxide from the liquid phase.
Example 10.1 Oxygen requirements of a rapidly respiring yeast culture
To illustrate the requirements for a high gas-liquid mass transfer of oxygen, we consider the experimental
data for
S. cerevisiae
analyzed in Example 3.5. For dilution rates below 0.25 h'1, where the metabolism is
purely respirative, we have
YSB
~
0.425 moles
0 2
(C-mole glucose)'1
(1)
For a dilution rate of 0.2 h;1
there is virtually no glucose in the outlet from the chemostat (see Fig. 1), and
the volumetric glucose uptake rate is therefore calculated to be
-q, =
0.2 h'1
28 g L 1
= 5.6 g L'1
h'1
= 0.1867 C-moles L'1
h'1
(2)
Thus the volumetric oxygen uptake rate is
q ‘^ -q 0
=
0.425 0.1867C-moles l / 1
h'1
-79.3 mmoles0: L'1
h'1
(3)
If the dissolved oxygen concentration is at its maximum (approximately 0.26 mmoles 0 2 L'1
when sparging
with air, see Table 10.1) oxygen will be depleted within 12 s if the supply of oxygen is stopped. This
illustrates the requirement for a continuous transfer of oxygen to the liquid medium. In Example 10.2, we
will quantify the mass transfer necessary to keep the dissolved oxygen concentration constant.____________
Gas-liquid mass transfer is normally modeled by the two-film theory (see Fig. 10.2), which was
introduced by Whitman (1923). The flux
JA
of compound A through each of the two films is
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