Mass Transfer
439
than in bubble columns, and stirred tanks are therefore traditionally used in aerobic fermentation
processes where there is a high oxygen demand, e.g., antibiotic fermentations. New bioreactor
designs based on cleverly designed static mixers or gas injection nozzles can, however, outperform
the stirred tanks. A very high
kp
value (up to 0.5 s‘l) can be obtained, but the corresponding power
input is usually also very high.
When the range of process variables for which the correlation in Eq. (10.27) holds is studied in
more detail, it is observed that the mass transfer coefficient
kp
for a noncoalescing medium is
greater by about a factor of 2 than that for a coalescing medium under the same operating
conditions. These overall correlations are, however, very rough simplifications since they are made
to fit data obtained in many different bioreactors. For a specific agitator system, e.g., a six-bladed
Rushton turbine (see Section 11.2), the situation is more complex. Here it is found that the
influence of the power input is larger in the noncoalescing medium, whereas the influence of the
superficial gas velocity is smaller compared with a coalescing medium (e.g., pure water) (see Table
10.4).
In the derivation of Eq. (10.23), it was assumed that the dynamic shear stress caused by eddies was
much larger than the viscous stress. This will not be true for highly viscous media, and the very
simple correlations of the type given by Eq. (10. 27) will therefore no longer be valid. In general,
the
kp
value is found to decrease with increasing liquid viscosity, but the effect is small until
"H
> 50 101 kg m 1
s '. For an in-depth review of mass transfer in highly viscous media see e.g.
Schiigerl (1981).
Example 10.4 Derivation of empirical correlations for
kp
in a laboratory bioreactor
Pedersen (1992) examined the gas-liquid mass transfer in a stirred laboratory bioreactor. The volumetric
mass transfer coefficient
kp
was determined by the sulphite method (see Note 10.3), and the influence of
aeration rate and stirring speed on
kp
was examined. Data for the bioreactor and the operating conditions
are summarized in Table 10.5.
The results of the measurements investigation using the sulfite method are shown as double logarithmic
plots in Figs. 10.6 and 10.7. The volumetric mass transfer coefficient increases with increasing gas aeration
rate
vg
and with increasing stirring speed
N,
but there is an upper limit to the
kp
value for the considered
system. From each of the two series we find the correlations
Table 10.5. Data for a standard laboratory bioreactor and the ranee of operating conditions examined1.
Variable
Value
Meaning
V,
15 L
Tank volume
V,
10 L
Liquid volume
d,
0.20 m
Tank diameter
dt
0.07 m
Stirrer diameter
N
4-25 s'1
Stirring speed
vs
2.2-25-10'5 m V
Gas flow rate
"The bioreactor was equipped with two Rushton turbines. For details of the design see Pedersen (1992).
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