452
Chapter 10
rate of oxygen transfer from the liquid phase to the gas phase:
<7/AO,
2
(
10
)
The volumetric decomposition rate of hydrogen peroxide is calculated from the volumetric addition rate and
the concentration of hydrogen peroxide in the added liquid according to
*7
»-fii ~
J
r f
K
(
11
)
The interfacial concentration of oxygen is calculated from the gas phase partial pressure of oxygen. (Note
that both terms in Eq. 10 are negative, since oxygen is generated in the liquid and thus DOT=
c0l c*>
1). An
assumption concerning the mixing of the gas phase is necessary to determine the interfacial concentration of
oxygen. Hickman used the assumption of complete backmixing of both the liquid and the gas phase, which
gives
c
exit
vf
r f
and
k,a
= -----HlQl—
H 0
2VjC0 {DOT -
1)
(
12
)
The hydrogen peroxide method is easy to implement All that is needed to estimate the
k/a
value is to
measure the addition rate of hydrogen peroxide and the oxygen concentration (or DOT) in the liquid phase.
An independent (but much less accurate) measurement of <3o is obtained from the difference in oxygen
content between Vg and v°ut as in the “direct method”. In comparison to the sulphite method, a significant
advantage of the hydrogen peroxide method is that the
k/a
value is not enhanced by the catalase
concentration over a rather wide range (Hickman, 1988). The risk of enhancing the mass transfer by
reaction in the liquid film is smaller, and the effect on coalescing properties by the catalase is apparently
also smaller. The method has been applied with good results for
k/a
measurements in large industrial
reactors also with viscous, non-Newtonian media (Pedersen, 1997).
Tracer methods
85Kr is a volatile isotope emitting beta and gamma radiation. By injecting the isotope into the medium and
then measuring the radioactivity in the exhaust gas, it is possible to determine the volumetric mass transfer
coefficient for Kr (see Problem 10.3). Since it can be assumed that constant ratios exist between
k/a
values
for different gases at the same conditions, the estimated
k/a
value for Kr can be used to calculate
k/a
for
oxygen. Pedersen
et al.
(1994), used the ratio
(k/a)xr_
_ o
(13)
(k/a)0
Approximately the same value is found if one uses the ratio between the molecular diffusion coefficients for
the two species (see Eq. 10.33). This method is easy to implement, and it is well suited for measurement
both in model media and under real fermentation conditions [see, e.g., Pedersen
et al
(1994)]. The main