Biomedical Engineering Reference
In-Depth Information
TABLE 18.5
Scale-Up Comparison from 75 to 10,000 L Bioreactor with Impeller Size to Fermentor D
i
/D
R
and
Fermentor Shape Factor H/D
R
Remaining Constant
Production fermentor, 10,000 L
Small
fermentor,
75 L
Constant
P
0
/
Constant
u
D
i
Constant
Re
Scale-up criterion
Notation
V
Constant
u
3
i
Energy Input
P
0
fu
D
1
133.3333
3479.8823
26.0991
0.1957
3
i
Energy input/volume
P
0
=Vfu
D
1
1
26.0991
0.1957
0.0015
Impeller rotation number
u
1
0.3371
1
0.1957
0.0383
Impeller diameter
D
i
1
5.1087
5.1087
5.1087
5.1087
i
Pump rate of impeller
QfuD
1
44.9500
133.3333
26.0991
5.1087
Pump rate of impeller/
volume
Q=Vfu
1
0.3371
1
0.1957
0.0383
Maximum impeller speed
(shear rate)
u
D
i
1
1.7223
5.1087
1
0.1957
i
Reynolds number
Re
ΒΌ uD
r=m
1
8.7987
26.0991
5.1087
1
through anaerobic regions. Since many cells have regulatory circuits to respond to
changes from aerobic to anaerobic conditions, these may be constantly altering cellular
metabolism.
Scale-up traditionally is highly empirical and must have no change in the controlling
regime during scale-up, particularly if the system is only reaction or only transport
controlled. Common scale-up rules are the maintenance of: (1) constant power-to-volume
ratios (P
o
/V), (2) constant K
L
a, (3) constant stirrer lade tip speed (
D
i
), (4) combination of
mixing time and Reynolds Number, or (5) constant substrate or product level (usually
DO). Each approach has resulted in successful and unsuccessful examples. Failure of
the rules is related to changes in the controlling regime upon scale-up. The nature of
the practical operating boundaries for an aerated, agitated fermentor can be summarized
in
Fig. 18.7
. The boundaries are fuzzy but must be appreciated for the existence of such
constraints.
Example 18-1. Consider scale-up from a lab fermentor of 1 L working volume to a 30,000 gal
vessel. The small fermentor has a height to diameter ratio of 2.5. The impeller diameter is 30%
of the inside tank diameter. Agitator speed is 400 rpm and Rushton impellers are used. Deter-
mine the dimensions of the large fermentor and agitator speed for:
u
(a) constant P
0
/V;
(b) constant impeller tip speed;
(c) constant Reynolds number.
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