450
Chapter 10
of the oxygen content as well as of the gas flow rates are necessary and the solubility of oxygen in the
medium must be known. Furthermore, the dissolved oxygen tension should not change during the
measurement, since the assumption of a steady-state (or pseudosteady-state) is a strict requirement. See also
problem 3.1 for experimental errors due to evaporation of e.g. water from the medium {v” ^ v°ut).
The dynamic method
The dynamic method is also based on measurement of the dissolved oxygen concentration in the medium.
However, it does not require measurement of the gas composition and is therefore cheaper to establish. The
dynamic mass balance for the dissolved oxygen concentration is:
t
f *
\
~ c 0 ) + q0
(3)
If the gas supply to the bioreactor is turned off, <?o is zero and the first term on the right hand side of the
equation immediately drops to zero. The dissolved oxygen concentration decreases at a rate equal to the
oxygen consumption rate,
-q0,
which can therefore be determined from measurement of the dissolved
oxygen concentration
c0(t).
If
q„
is independent of
c0
the dissolved oxygen concentration decreases as a
linear function of time. When the gas supply is turned on again, the dissolved oxygen concentration
increases back to the initial level, and by using the estimated (average) value for
qo,
the value of
kp.
can be
determined from the measured profile of dissolved oxygen.
This method is simple, and it can be applied during a real fermentation. It is, however, restricted to
situations in which
q0
can be determined correctly when the gas supply is turned off. Most available probes
for measuring the dissolved oxygen concentration do, unfortunately, have a response time close to the
characteristic time for the mass transfer process, and the measured concentrations are therefore influenced
by the dynamics of the measurement device, e.g., an oxygen electrode.
The dynamic method can also be applied at conditions where there is no reaction, i.e.
q0
= 0. This is
interesting when studying the influence of operating parameters, e.g., the stirring speed and the gas flow
rate, on the volumetric mass transfer coefficient in model media. After a step change in the concentration in
the inlet gas, there are dynamic changes both in the dissolved oxygen concentration and in the oxygen
concentration of the exhaust gas. Because of the slow dynamics of oxygen electrodes, it is preferable to
apply the exhaust gas measurements for determination of the mass transfer coefficient. (Here a mass
balance for oxygen in the gas phase should be used.) However, before this approach is applied, it is
important to make a careful check of the dynamics of the gas analyzer.
The sulphite method
It is also possible to determine the oxygen transfer rate by using a model oxygen consuming chemical
reaction. The traditional sulphite method is based on the oxidation of sulphite to sulphate by oxygen (see
Eq.4).
so;--sor-|o2=o
(4)
This reaction is catalyzed by a number of metal ions, which may occur as impurities. However, one
normally adds a known amount of copper (e.g. 10'3 M Cu2+) or cobalt salt to the medium in order to make
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