Page 435 - Elements of Chemical Reaction Engineering Ebook

406 Nonelementary Reaction Kinetics Chap. 7

An inspection of Equation (7-128) reveals that the specific growth rate of the
cells can be controlled by the operator by controlling the dilution rate D.
Using Equation (7-101) to substitute for p in terms of the substrate concentra-
tion and then solving for the steady-state substrate concentration yields

(7- 129)

Assuming that a single nutrient is limiting, cell growth is the only process con-
tributing to substrate utilization, and that cell maintenance can be neglected,
the stoichiometry is
-rs = r&/c (7-130)

cc = ~C/S(CSO - C,) (7-131)
Substituting for C, using Equation (7-129), we obtain

(7- 132)

7.5.7 Wash-out

To learn the effect of increasing the dilution rate, we combine Equations
(7-123) and (7-100) and Set rd = 0 to get

(7-133)

We see that if D > p, then dCcldt will be negative and the cell concentration
will continue to decrease until we reach a point where all cells will be washed out:
c, = 0
The dilution rate at which wash-out will occur is obtained from Equation
(7-132) by setting C, = 0.

Flow rate at which (7- 134)
wash-out occurs
We next want to determine the other extreme for the dilution rate, which
is the rate of maximum cell production. The cell production rate per unit volume
of reactor is the mass flow rate of cells out of the reactor (i.e., liz, = C,u,)
divided by the volume V, or

Substituting for C, yields

(7-135)