350
Chapter 9
Table 9.2. Changes in the distribution of a given amount of consumed substrate between biomass and
producta for various values of
m,.
M h '1)
X** - X ,
Anal
A
Aina!
0
1
I
5.303
0.08
0.961
1.0096
5.264
0.16
0.926
1.0186
5.227
0.32
0.862
1.0344
5.156
a H is assumed to be equal to
, and m ,= nip.
Using Eqs. (3) - (6), it is possible to relate the changes in the total biomass yield and product yield to the
dimensionless maintenance parameter. Table 9.2 shows the calculation for some reasonable parameter
values
^r*e = 0-2,
Y£ul=0.Bt
= 0.4h'' ,
and
=mP
0.08,0.16 and
0.32h"1)
respectively. Other parameter values are taken from Example 9.1.
From the first two rows of the table it is easily checked that when T,f“ +
=
1, the sum of produced
biomass and product is
s0
irrespective of the value of
-m
p . When the maintenance requirement
increases, more substrate is directed toward product formation._____________________________________
The higher degree of complexity of biochemically structured kinetic models as compared with
unstructured models usually makes batch reactor mass balances based on structured kinetics
intractable by analytical methods— but again it must be stressed that computer solutions are easy to
find, and a study of the numerical solution for various operating conditions may certainly reveal
characteristic features of the model. The lactic acid fermentation kinetics of Eqs. 3 to 5 in Example
7.6 will be used to illustrate how a structured kinetic model can be coupled to an ideal batch reactor
model. The final model becomes
dx
~dt
= fjx = \y2Xr2
—(1 —
s
s
/21*2—
— “ G
~ Y n ) k 3
s + K
,
s + Ki
3 J
SN +
X Ax
ds
— = (-rt
~ a 2r2)x =
s
,
S
S
j
+ a,fc,--------------- -----
\XjX
s + K }
2 2 s + K2 sN +Ks
— = r,x = k, — -—
X Ax
dt
1
l s + Kl
dt
s
+
K2 s
+ K
(9.15a)
(9.15b)
(9.15c)
(9.15d)