Scale-up of Bioprocesses
491
Example 11.2 Maintaining mixing times at different scales.
A process in the lab-scale reactor described in Example 11.1 is to be scaled up to a 1
m3
reactor, with the
same aspect ratio and the same impeller diameter to tank diameter ratio. It is desirable to maintain the
same mixing time in the large-scale reactor as in the lab-scale reactor. Since the mixing time is inversely
proportional to the stirrer rate, N, (cf. Eq 11.2) the stirrer rate in the large reactor need to be the same as in
the small scale, i.e. N= 20 s'1.
The impeller diameter in the 1
m3
reactor is 0.047 10 = 0.47 m. For the large scale reactor we get
997 ■
20 ■
(0.47)2
6
Re
----------- i---- — = 4.4 106
1
HT3
(
1
)
This is clearly in the turbulent regime, and the power number can be considered constant,
Np
= 5.2. The
power consumption can be calculated to
P
= 5.2 997 kg m'3
(20 s'1)3
(0.47 m)5
= 951 kW
(2)
If we assume that the power consumption falls with 50% at gassed conditions, we get
P
=595 kWm'3
(3)
V
This power consumption is far too high to be acceptable for a large-scale bioreactor. As a rule of thumb,
the power consumption should be about 1-5 kW m'3
for large-scale bioreactors. The important conclusion
from this calculation is that
it is not possible to maintain the same m ixing time in a large-scale bioreactor
as in a well-mixed laboratory scale reactor if the scale-up is made using geom etrically sim ilar reactors.
If instead the same power consumption per volume is maintained during scale-up, the mixing time can be
shown fromEq. (11.2) and (11.8) to increase approximately according to
J
(4)
where
tmJ
and
tmj
are the mixing times for the large scale reactor and small scale reactors, and
dsJ
and
dSJ
are the respective stirrer diameters. In the current example, it can be estimated that the mixing time in the
1
m3
reactor is approximately 5 times that in the 1
L reactor if the power consumption of 5.95 kW m'3
is
maintained.
11.3.3. Heat transfer
Biological reactions are very temperature sensitive and a careful temperature control is therefore
absolutely essential. Heat is generated by agitation of the medium and —
as discussed in Chapter
4 - by the large heat of reaction, which often accompanies bioreactions. Hence cooling is
required, and removal of heat is done by heat exchange.