490
Chapter 11
Example 11.1. Power input to a laboratory bioreactor
In a study of yeast physiology, a 1-L {liquid volume, 800 mL) laboratory bioreactor is used. It is equipped
with one Rushton turbine with
ds
= 47 mm. The density and the viscosity of the medium containing yeast
cells are approximately the same as for water, i.e. 997 kg m'3
and 10'3
kg m s !, respectively. With a stirring
speed of 1200 rpm, the stirrer Reynolds number is therefore (at 25 °C):
Re, =44047
(1)
This is well within the turbulent regime, and a power number of
Np
= 5.2 can be used. The power input is
therefore
P
= 5.2 997 kg rri3
(20 s 1)3
(47 10’3
m)5 = 9.51 W
(2)
For gassed conditions, we assume that the power input is 50% of the power input at ungassed conditions, and
therefore the power input per volume of medium is
P„
= 5.95 W L l
V
(3)
This is a typical figure for laboratory bioreactors. When the bioreactor is used for aerobic yeast fermentation,
it is sparged with air at 1 wm, i.e., 800 mL miri*. The tank diameter is 106 mm, and the superficial gas
velocity is therefore
_ 13.33-10^
~~ ;r*0.1062/4
1.5M 0 “3
m s1
(4)
Assuming that the medium is noncoalescing, we can calculate the volumetric mass transfer coefficient for the
bioreactor using Eq. (10.27) and the parameter values listed in Table 10.4 (try also to calculate
kp
using the
parameter sets specified for noncoalescing media in Table 10.4);
kp
= 0.0018 (1.51 10'3
m s'1)03 (5.95 1 03
Wm’3)07 = 0.113 s 1
(5)
In Example 10.1 it was found that the oxygen requirement of a rapidly respiring yeast culture is
approximately 79.3 mmoles of 02 L 1
h'1
. With the calculated volumetric mass transfer coefficient above, we
therefore find that under steady-state conditions the dissolved oxygen concentration in the medium is
s0 ~ s*0 +
=0.26 mmoles L 1
- 79.3 mmoles L'1
h'‘/(406.8 h 1) = 0.065 mmoles L'1
(6)
k{a
which corresponds to 25% of the saturation value. This will normally not result in oxygen limitation.
However, if the dissolved oxygen concentration is to be maintained at a higher level it is necessary to modify
the bioreactor setup. This is probably done most easily by mounting an additional Rushton turbine on the
impeller shaft. Thereby the power input increases by a factor of approximately 2. This leads to an increase of
approximately 62% in the
kp
value, and the dissolved oxygen concentration can be maintained at around
55% of the saturation value.