How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 567

S

10

X

1

t L

0 10 20 30 40

t , h

FIGURE E11-2.1 Semi-log plot of the biomass concentration (and substrate concentration) variation with time.

Equation (11.25) also shows that a lower initial substrate concentration gives rise to a lower
apparent yield for a given finite specific death rate in the growth kinetics. Usually, S 0 >>

K S ,
the effect of initial substrate concentration on the apparent biomass yield is negligible as indi-
cated by Eqn (11.25) .

Example 11-2 . Using Monod equation of growth and a constant biomass yield factor to corre-
late the data in Example 11-1. Determine the maximum growth rate m max , saturation constant
K S , and yield factor YF X/S.
Solution. The Monod equation of growth is only applicable for balanced growth, i.e. when
pseudosteady state inside the cells has been established. Therefore, it is not applicable in the
lag phase. To be certain of the time to start for using Monod equation of growth, we plotted
out the cell growth data on semi-log scale as shown in Fig. E11-2.1 . A straight line (dashed
line) is drawn as a guide on the cell biomass data. From Fig. 12.2-1, we can observe that there
is an apparent lag time of t L ¼

5.5 h. The cell concentration changes with time becomes expo-

nential after t ¼ 10 h. Thus, we correlate the data starting from t ¼ 10 h.

Mass balance of the cell biomass in the batch reactor leads to
d X

d t ¼ m G X ¼ m max S K S þ S X

(E11-2.1)

Mass balance on the substrate in the batch reactor leads to

dS

dt ¼ m G X YF X=S ¼ m max S

X
YF X=S K S þ S

(E11-2.2)

Using the OdexLims in Excel to solve the two differential equations, (E11-2.1) and
(E11-2.2) , while correlating the experimental data, we obtain the kinetic parameters: