68
Chapter 3
The kinetics of the fermentation will be discussed in Example 7.3. Here we will analyze the
stoichiometry for different
D
values, observe the sharp change of stoichiometry around An, and make a
consistency test of the data.
The biomass composition is (for simplicity) assumed to be X = CHl,gjO0.»N().i
7
and the ash content 8 wt
% for all /3-values. In a real situation this assumption must of course be checked. The overall
stoichiometry is taken to be:
- C H 20 - Y M№ i - Y „ 0 2 +YKC 0 2 +YtpCH lO1u+YimH 2O + Y a a i iMO0MN M1
= 0
(1)
Equation (1) combines one rate,
q, =
and 6 yield coefficients. The elemental balances supplies four
constraints, and hence 3 rates must be experimentally determined to identify the system. The data shown
in Fig. 3.5 can be used to find the rates of production of glucose, biomass, ethanol,
C 02
and 0 2. Hence
the system is over-determined and we can make a consistency test of the data.
First consider
Ym.
The biomass is - according to reaction (1) - the only sink for the added nitrogen
source.
Ym
can therefore be calculated based on
YM,
but unless we measure
qNHi
there is no way to prove
that
Ym =
0.17
Y„
or whether an unexpected N-containing product is produced. It does not help to include
qNH^
in the set of measurements together with
qx
if we wish to explore the C-mass balances or the degree
of reduction balance since these two measurements form a closed set, separate from the other
measurements of rates which are possible with the stoichiometry in reaction (1).
Mutton rota ( h 1)
Mutton rat* (h 1)
9
8
7 L
1
. 0
0.5
Figure 3.5. Chemostat cultures of
S. cerevisiae.
A. Data for the biomass concentration ( • ) , the specific oxygen uptake rate (■ ), and the specific carbon
dioxide formation rate (A ).
B. Data for the glucose concentration (■ ) and the ethanol concentration (* ).