Biochemical Reactions - A First Look
69
YiW
is - as mentioned earlier - uninteresting and it can probably not be measured accurately enough to be
of any value. Water is therefore excluded from the analysis, and hereby all four elemental balances
cannot be used. However, through using a carbon balance, a nitrogen balance and a degree of reduction
balance the degrees of freedom is still 3, i.e. 3 rates must be experimentally determined to identify the
system. Thus, when water is excluded from the stoichiometry one yield coefficient disappear, but also
one of the constraints cannot be used.
By excluding water and assuming that
is directly determined from
the remaining variables in the
system are
YK,
7SC
,
Y
sp and
together with
qs.
Two constraints, the carbon - and the redox balances can
be set up and three out of the five rates
q0, qx, qc, qp
and
qr
must be used to identify the stoichiometry
(except for
Ym
and
Ytv/
as explained above). All five rates are available from Fig. 3.5. Three values of
D
are chosen for further studies,
D
= 0.15 h'1
(or any D < 0.25 h'1, at least within the accuracy of Fig. 3.5),
D
= 0.30 If1
and
D =
0.40 h l.
D
< 0.25 IT
At these dilution rates we have:
x
= 14 g L’1,
s = p lss
0, r f= 28 g L 1,
xf=
0.
14 g/L • 0.92
30 (g/C - mole)
25.17 (g/C- mole)
28 g/L
= 0.548 C-moles DW (C-mole glucose)'1
(
2
)
From a carbon balance, we find
Ysc —
1 —
YSI
= 0.452 moles C02 (C-mole glucose)'1
(3)
and from a generalized degree of reduction balance
4
- 4
4.20yjx =>
Yso
=
\
(4 - 4.20• 0.548) = 0.425 moles 0 2 (C-mole glucose)'1
(4)
With these values for
YK
and T„, RQ is calculated to be 1.06, which corresponds well with the data in
Fig. 3.5. In the considered range of dilution rates it is observed that
rQ
and rc both increase linearly with
D
and the slope is 30.0 mmoles of C 02 per gram DW. This corresponds to
Yxc
= 0.82 moles of CO; per
C-mole of biomass, or
Ysc
=
YSXYXC
=
0.45 moles C 03 (C-mole glucose)'1
(5)
This value is nearly the same as that found from the carbon balance in (3), where the calculation is based
on measurements of glucose and the biomass concentrations. Again it is concluded that there is a
consistency in the experimental data. Observe that
ra
and rc are both larger than zero when
D =
0. This is
due to a consumption of glucose for maintenance purposes (see Section 5.2.1).
D >
0.25 h 1
At the two dilution rates we find the following data from Fig. 3.5:
D = 0 .3 h ':
jc = 7.1 gL"1
and/> = 4.2 g L 1
D
= 0.4 h'1
:
x ~ 4.4 g L'1
and
p
= 8.3 g L'1
No attempt is made to smooth the biomass and the ethanol data, and the accuracy is not better than 0.1 -
0.2 gL l.
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