Fed-Batch Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 682

Therefore,

K S
m max V=Q 1 ¼

0:5
0:2 ð920=30Þ1

S ¼ g = L ¼ 0:09740 g = L

(c) The concentration of cells can be computed using an appropriate equation from Table
13.1 , which is derived by mass balance of glucose in the reactor. Alternatively, as there is
no cell death, we can directly use yield factor from all the glucose converted in the
reactor. The total amount of glucose fed to the reactor is

QS F t ¼ 30 300 24 ¼ 216; 000

g g

Glucose in the reactor at 24 h ¼ VS ¼ 920 0.09740 g ¼ 89.61 g.

Therefore, the amount of glucose converted is

S 0 V 0 þQS F t VS ¼ 200 þ 216; 000 89:61 g ¼ 216; 110:39 g
which produces 0.3 (YF X/S )

216,110.39 g ¼ 64,833.12 g cells.

Therefore, the total cells in the reactor is

XV ¼ 4000 ðX 0 V 0 Þþ64; 833:12 g ¼ 68; 833:12 g

Finally, the concentration of cells is

XV
V

¼ 6

8 ; 833 : 12 g

X ¼ ¼ 74:8186 =

g L

920 L

(d) Mass balance on the extracellular products,

d ðVPÞ

d t

¼ 0 0 þ r P V

which leads to

d ðVPÞ

d t

¼ m P XðV 0 þ QtÞ

Thus,

V 0 þ 1

P 0 V 0 þ 1

P 0 V 0 þ m P X Qt t

2 m P XðV 0 þ VÞt
V

2

P ¼ ¼

V

P 0 V 0 þ 1

2 m P XðV 0 þ VÞt
V

P ¼

0:1 200 þ 1

2 0:05 74:8186 ð200 þ 920Þ24
920

¼ g = L

¼ 54:67 g = L