Page 429 - Elements of Chemical Reaction Engineering Ebook

400 Nonelementary Reaction Kinetics Chap. 7

Product formatiqn
in the stationary (7-1 14)
phase
where kp = specific rate constant with respect to product, (dm3/g s”
C,, = concentration of the secondary nutrient, g/dm3
C, = cell concentration, g/dm3
K, = constant, g/dm3
rp = Yp/sn(-rm)

The net rate of substrate consumption during the stationary phase is

-rsn = mCc + Ysniprp

(7-115)

Because the desired product can be produced when there is no cell growth, it
is always best to relate the product concentration to the change in substrate
concentration. For a batch system the concentration of product, Cp, formed
after a time t can be related to the substrate concentration, C,, at that time.
In the stationary
phase the concentra- (7-1 16)
tion of live cells is cp = Y,i,<CsQ - CS)
constant
We have considered two limiting situations for relating substrate con-
sumption to cell growth and product formation; product formation only during
the growth phase and product formation only during the stationary phase. An
example where neither of these situations apply is fermentation using lactoba-
cillus, where lactic acid is produced during both the logarithmic growth and
stationary phase.

7.5.4 Mass Balances

There are two ways that we could account for the growth of microorgan-
isms. One is to account for the number of living cells and the other is to
account for the mass of the living cells. We shall use the latter. A mass balance
on the microorganism in a CSTR (chemostat) (shown in Figure 7-15) of con-
stant volume is

rate of rate of rate of net rate of
accumulation cells cells generation
of cells, entering, leaving, of live cells, (7- 1 17)
gfs B/S g/s

dCc
V- uo cco ucc + (rg - Td)V
dt