Mass Transfer
449
According to the conclusion of Example 10.2, a very high
kp
value is required to maintain the
dissolved oxygen concentration at 60% of the saturation value in a rapidly respiring culture of
S.
cerevisiae.
This high
kp
value for oxygen can be obtained in a laboratory bioreactor (and perhaps in
small-scale pilot-plant bioreactors), but will be difficult to obtain in a large-scale bioreactor.
However, a substantially lower dissolved oxygen concentration than 60% is normally acceptable in
industrial applications of S.
cerevisiae.
The simplest possible way to describe oxygen uptake
kinetics is by using a Monod expression. The saturation constant,
Ka,
is in the range 1-10 pM,
which corresponds to approximately 0.4-4.0% of the saturation concentration (at 25 °C and 1 atm
of air). As long as the dissolved oxygen concentration is maintained well above this value, the
oxygen consumption rate will therefore be zero order with respect to the dissolved oxygen
concentration, i.e. oxygen limitation does not occur.
Note 10.3. Methods for determination of the volumetric mass transfer coefficient for oxygen
There are several different methods for measuring the volumetric mass transfer coefficient
kp
for oxygen.
Some of these methods can also be applied for other components, but others are specific for oxygen. Here a
few of the best-known methods are described:
The direct method
Most bioreactors used for aerobic fermentation processes are equipped with exhaust gas analysis for oxygen
and probes for measuring the dissolved oxygen concentration. From the measurement of oxygen content in
the inlet and exhaust gases together with measurement of the gas flow rate it is possible at steady-state
conditions, as already discussed in Chapter 3.1, to determine the volumetric oxygen transfer rate,
, which
at steady-state, is equal to the volumetric oxygen uptake rate,
-q0.
We have from Eq. (3.10)
Po
v g
R T in
g r p out
(
1
)
where
R
is the gas constant (= 8,314 J (mol K)'1
= 0.08206 L atm (mol K)1), Tis the temperature (K),/?0 the
partial pressure of oxygen,
the gas flow rate.
Most gasanalyzers will give the result in terms of mole fraction of oxygen in the gas. When normal air is
used, it is sufficient to analyze only the outlet gas composition. However, for large bioreactors it is
important to take the pressure difference over the reactor into account. If also at the same time the dissolved
oxygen concentration,
c0,
is measured in the medium, it is possible to calculate the volumetric mass transfer
coefficient from:
k}a
(
2
)
Eq. 2 assumes that the saturation concentration,
c0\
is the same throughout the reactor,
i.e.
that the pressure
difference is small and that the decrease in partial pressure of oxygen in the gas phase is small. If that is not
the case, a better option is to use Eq. 10.8 for the concentration driving force. This is a simple method, and
has the major advantage that is can be applied during a real fermentation. However, accurate measurements
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