Bioreactor Design and Operation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 926

Increasing
agitation

Cell damage

Foaming

Permissible
operation
range

Decreasing
aeration

Increasing
aeration

O 2 limitation

Poor mixing

Decreasing
agitation

FIGURE 18.7 Practical operating boundaries for aerated, agitated fermentor.

Solution. Assume geometric similarity and the reactor are cylindrical. The dimensions of
the small reactor can then be obtained as follows:

V ¼ 4 D

R H ¼ 4 D

5 8 D

2 R 2:5D R ¼ R

(E18-1.1)

8 5p 3

D R ¼ (E18-1.2)

0.02396 m.
The large reactor is of 30,000 gal and geometrically similar to the small reactor. Therefore,
the scale factor in reactor dimensions is the cubic root of the volume ratio. That is
(30,000

D R ¼ 0.07986 m; H ¼ 0.19965 m; D i ¼ 0.3 m; D R ¼

3.785412 O 1) 1/3 ¼ 48.42595. Therefore, the dimensions of the large reactor are

D R ¼

¼

9.668 m; D i ¼ 3.867 m; H 1.1602 m.

(a) For constant P 0 /V;

3 i Þ small ¼ðu 3 i Þ large

ðu D D (E18-1.3)

!

2
3

D i small
D i large

¼ 40048:42595

2
3 rpm

u large ¼ u small ¼ 30:1 (E18-1.4)

(b) For constant impeller tip speed;

ðuD i Þ small ¼ðuD i Þ large (E18-1.5)