Page 427 - Elements of Chemical Reaction Engineering Ebook

398 Nonelernentary Reaction Kinetics Chap. 7

substance, respectively. Representative values of kd range from 0.1 h-l to less
’than 0.0005 h-I. The value of k, depends on the nature of the toxin.
Doubling times Microbial growth rates are measured in terms of doubling times. Dou-
bling time is the time required for a mass of an organism to double. Typical
doubling times for bacteria range from 45 minutes to 1 hour but can be as fast
as 15 minutes. Doubling times for simple eukaryotes, such as yeast, range
from 1.5 to 2 hours but may be as fast as 45 minutes.

7.5.3 Stoichiometry

The stoichiometry for cell growth is very complex and varies with micro-
organisdnutrient system and environmental conditions such as pH, tempera-
ture, and redox potential. This complexity is especially true when more than
one nutrient contributes to cell growth, as is usually the case. We shall focus
our discussion on a simplified version for cell growth, one that is limited by
only one nutrient in the medium. In general, we have

cells + substrate - more cells + product
cells (7- 109)
’ yc/sc + yp/sp
where the yield coefficients are

mass of new cells formed
YCIS = mass of substrate consumed to produce new cells

with

The stoichiometric yield coefficient that relates the amount of product
formed per mass of substrate consumed is
mass of product formed
= mass of substrate consumed to form product
In addition to consuming substrate to produce new cells, part of the sub-
strate must be used just to maintain a cell’s daily activities. The corresponding
maintenance utilization term is

mass of substrate consumed for maintenance
Cell maintenance m=
mass of cells * time
A typical value is
gsubstrate 1
m = 0.05 - = 0.05 h-’
g dry weight h
The rate of substrate consumption for maintenance whether or not the cells are
growing is