Fed-Batch Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 681

Solution: Initially in the reactor, the amount of glucose, cells, and products are:

Q, S F

S 0 V 0 ¼ 1 200 ¼ 200

g g

X 0 V 0 ¼ 20 200 g ¼ 400 g

P 0 V 0 ¼ 0:1 200 g ¼ 20 g

(a) Overall mass balance of the medium in the fermentor yields

d ðrVÞ

d t

r F Q 0 þ 0 ¼

Assuming that the density of the culture is the same as that of the feed, r F ¼ r , integration

and rearrangement of the overall mass balance equation lead to

V ¼ V 0 þ Qt
V ¼ 200 þ 30 24 L ¼ 920 L

(b) At pseudo-steady state, the concentration of cells remains constant. From the mass
balance of cells in the reactor, we obtain (13.17) ,

d d t ¼ Q

V

0 ¼ m G k d X

Combining with Monod growth equation and negligible death rate, Eqn (13.15) gives the
pseudo-steady state glucose concentration

K S Q=V
m max Q=V

S ¼