Scale-up of Bioprocesses
507
where
Na
is the aeration number defined by Eq. (11.9). To make a balance for the gas phase, the gas-hold
ups in the different compartments are needed. This was estimated from the power input in the impeller
region and from the superficial gas velocity in the well-mixed region according to
(!-*„)=
0
.
1 3 ^ 1
u f
(
6
)
(1-.?„)= 0.6«,17
(7)
Steady-state conditions requires
+
+
=0
(8)
r m
for the well mixed regions and
kfi
b(4 "
c0 b)
+
{cG
m
- c0il) + qOJ>
=
0
(9)
Vb
for the bubble regions.
The oxygen concentration predicted by the compartment model in the non-coalescing case as well as the
measured oxygen concentration are shown in Fig. 11.14.
Obviously, this simple compartment model will not be able to predict the observed gradually changing
oxygen concentration in the axial direction. However, qualitatively, the increased dissolved oxygen
concentration close to the impellers is indeed predicted. With respect to the overall oxygen transfer rate, a
better agreement was found using the compartment model than the application of either Eq. 1 or 2 for the
entire reactor volume (Fig. 11.15).
Figure 11.14. Calculated oxygen concentration for coalescing case compared to measured oxygen
concentration as a function of axial position in the reactor (data from Oosterhuis and Kossen, 1983).
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