Page 428 - Elements of Chemical Reaction Engineering Ebook

Sec. 3.6 Bioreactors 399

The yield coefficient Yils accounts for substrate consumption for maintenance:

mass of new cells formed
y' =
c/s mass of substrate consumed
Product formation can take place during different phases of cell grciwth.
When product is produced only during the growth phase, we can write

mass of product formed
where YprC =
mass of new cells formed
However, when product is produced during the stationary phase, we can relate
product formation to substrate consumption by

rrateof ] = [" ] i" ] i"
We now come to the difficult tasg of relatin8 the rate of nutrient con-
sumption, -rs, to the rates of cell grow@, product generation, and cell main-
tenance. In general,'we c~ln write

]
. accounting Substrate
substrate consumed + consumed to + consumed for (7 - 1 1 1)
consumption by cells form product maintenance

- = &/Crg + K/prp . +
'S
In a number of cases extra attention must be paid to the substrate balance. If
produlct is produced during the growth phase, it may not be possible to sepa-
rate out the amount of substrate consumed for growth from that consumed to
produlce the product. Under these circumstances all the substrate consumed is
1umpe:d into the stoichiometric coefficient, YTlC, and the rate of substrate disap-
pearance is
Product formation
in the growth phase -r, = Yslcr, + mCc (7-1 12)
The corresponding rate of product formation is
The stationary
Phase rp = rgyp/c (7-1 13)
Because there is no growth during the stationary phase, it is clear that
Equation (7-1 12) cannot be used to account for substrate consumption, nor can
the rate of product formation be related to the growth rate [e.g., Equation
(7-113)]. Many antibiatics, such as penicillin, are produced in the stationary
phase. In this phase, the nutrient consumed for growth has become virtually
exhausted and a different nutrient, called the secondary nutrients, is useld for
cell maintenance and to produce the desired product. Usually, the rate law for
product formation during the stationary phase is similar in form to the Monod
equation, that is,