Page 431 - Elements of Chemical Reaction Engineering Ebook

402 Nonelementary Reaction Kinetics Chap. 7

dCS
The mass balances V - r,V = YslC(-rs)V - mC,V (7- 120)
=
dt
Dividing by V yields

Growth phase

For cells in the stationary phase, where there is no growth, cell maintenance
and product formation are the only reactions to consume the substrate. Under
these conditions the substrate balance, Equation (7-1 1 S), reduces to

Stationary phase v- dCs 5 (7-121)
dt
Typically, rp will have the same form of the rate law as rg [e.g., Equation
(7-1 14)].
Batch stationary
growth phase
The rate of product formation, rp, can be related to the rate of substrate con-
sumption through the following balance:

(7- 122)

Dcring the growth phase we could also relate the rate of formation of product,
rp, to the cell growth rate, rs. The coupled first-order ordinary differential
equations above can be solved by a variety of numerical techniques.

Example 7-9 Bacteria Growth in a Batch Reactor

Glucose-to-ethanol fermentation is to be carried out in a batch reactor using an
organism such as Saccharomyces cerevisiae. Plot the concentrations of cells, sub-
strate, and product and growth rates as functions of time. The initial cell concentra-
tion is 1.0 g/dm3 and the substrate (glucose) concentration is 250 g/dm3.
Additional data [partial source: R. Miller and M. Melick, Chem. Eng., Feb. 16,
p. 113 (1987)l:
C; = 93 g/dm3 Ycls = 0.08 g/g

n = 0.52 Ypls = 0.45 g/g (est.)

pmax = 0.33 h-' Yplc = 5.6 g/g (est.)
K, = 1.7 g/dm3 kd = 0.01 h-'

m = 0.03 (g substrate)/(g cells * h)