Mass Transfer
441
Similarly, we find from the correlation for the influence of the stirring speed
f
J 2
V'523
kta =
4.5 • 1 (H i ï Æ -
N ym =
9.1 ■
1 (T V 523;V3-146
'
l 4 *
10_
J
(
5
)
Thus the value of the numerical constant found for each of the two sets of experiments is slightly different.
The correlation in Eq. (1) holds only for
N<
15 s'1, whereas the correlation in Eq. (2) is based on
N=
16.7
s'1. From Fig. 10.6 it is observed that for
N=
16.7 s'1
the measured
kfi
value is lower than predicted by the
correlation in Eq. (1), and this may explain the lower value for the constant in Eq. (4) compared with Eq.
(5). Thus the correlation in Eq. (5) is probably the best, and to test the correlation another series of
experiments was performed, with varying
at
8.33 s'. The results of this comparison are shown in Fig.
10
.
8
.
If we compare the correlation derived in this example with Eq. (10.27), we see that the structure is the same
since the power input is correlated to the stirring speed. For the examined bioreactor it was found that the
power input (measured as the power drawn by the motor) is correlated with the stirring speed to the power
3, i.e.
P
N 7
,
(6)
This indicates that the influence of the power input is stronger in the present system than reported in the
literature (see Table 10.4). The influence of the superficial gas flow rate is also larger than reported in the
literature (see value of a for noncoalescing medium in Table 10.4). The correlation derived here is based on
measurement of
kfi
using the sulphite method, and since the sulphite concentration must be quite high
(around 0.5 M) to obtain accurate measurements of the rate of sulphite consumption, the medium is strongly
noncoalescent. This may explain the deviation between the correlation of the present example and similar
correlations based on other measurement methods.
Figure 10.8. Double logarithmic plot of the influence of the aeration rate
vg
(L min"1) on the volumetric
mass transfer coefficient
kfi
(s'1). The stirring speed is 8.33 s'1. The line is the regression line for the
correlation in Eq. (5).
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