Page 425 - Elements of Chemical Reaction Engineering Ebook

396 Nonetementary Reaction Kinetics Chap. 7

just their metabolic path to allow them to consume the nutrients in their new
environment.
Exponential growth Phase I1 is called the exponential growth phase owing to the fact that the
phase cell’s growth rate is proportional to the cell concentration. In this phase the
cells are dividing at the maximum rate because all of the enzyme’s pathways
‘for metabolizing the media are in place (as a result of the lag phase) and the
cells are able to use the nutrients most efficiently.
Phase I11 is the stationary phase, during which the cells reach a minimum
biological space where the lack of one or more nutrients limits cell growth.
During the stationary phase, the growth rate is zero as a result of the depletioa
of nutrients and essential metabolites. Many important fermentation products,
Antibiotics including most antibiotics, are produced in. the stationary phase. For example,
Produced during penicillin produced commercially using the fungus Penicillium chrysogenum is
the stationary
phase formed only after cell growth has ceased. Cell growth is also slowed by the
buildup of organic acids and toxic materials generated during the growth
phase.
Death phase The final phase, Phase IV, is the death phase where a decrease in live cell
concentration occurs. This decline is a result of either the toxic by-products
.
and/or the depletion of nu&ent supply.
7.5.2 Rate Laws

While many laws exist for the cell growth rate of new cells, that is,
cells + substrate __j more cells + product

the most commonly used expression is the Monod equation for exponential
growth:
Monod equation rg = bCC (7-100)
where rg = cell growth rate, g/dm3 - s
Cc = cell concentration, g/dm3
p = specific growth rate, s-l
The specific cell growth rate can be expressed as

IJ. = bmax - (7-101)
CS
S-1
K, + CS
where pmax = a maximum specific growth reaction rate, s-l
Ks = the Monod constant, g/dm3
Cs = substrate concentration, g/dm3
For a number of different bacteria, the constant K, is small, in which case the
rate law reduces to
rg = PmaXCc (7-102)

The growth rate, rg, often depends on more than one nutrient concentration;
however, the nutrient that is limiting is usually the. one used in Equation
(7-101). Combining Equations (7-100) and (7-101) yields