Thermodynamics of Bioreactions
107
When (4.11) and (4.16) are used to calculate
Q
and AG for all three D-values of example 3.5 the following
results are obtained
D
0.15 h
1
0.30 h
*1
0.40 h
1
Q
195.8
86.4
30.0
357
310
172
-AG
208
1 0 2
47
______
m
______
366
______
m
______
the upper numbers are in kJ (C-mole glucose)1, the lower numbers in kJ (C-mole biomass)'1. Both
Q
and
-AG decrease drastically when calculated as kJ (C-mole glucose)'1
, but especially -AG is much less
dependent on D when calculated on a C-mole biomass basis.___________________________________
It is seen in Example 4.5 that the heat of reaction drastically declines when the process becomes
less aerobic
(Yt
„ decreases). According to (4.12), (4.13) or (4.15) the heat of reaction should
decrease to zero in a fully anaerobic process. This is of course not quite true even for an
anaerobic process using a sugar as substrate, and the result is totally wrong in other systems e.g.
when H
2
is used as energy source and
C02
as carbon source - see Example 4.6.
Using a microcalorimeter heat production rates
qQ
=
dQ/dt
of less than 1W per L medium can be
measured quite accurately, and
qQ
can be included in the database as an independent rate
measurement.
qQ
is, however, strongly correlated to
q
0l, and the two measurements should not
be included together in the set of independent rate measurements. Several research groups have
been using microcalorimetry to measure the heat production rate of fermentations, e.g. at
Gothenburg University (Sweden) and at EFPL in Lausanne (Switzerland). A joint publication by
the two groups (von Stockar
et al
., 1993) gives several examples of physiological phenomena
studied by means of microcalorimetry.
Example 4.6 Anaerobic growth on H
2
and C0
2
to produce CH
4
The archae
Methanobacterium thermoautotrophicum
uses methanogenesis as its catabolic pathway, i.e. it
converts H
2
and C0
2
to CH
4
, creating energy in the process. It has an extremely low biomass yield
coefficient of about 0.02 C-mol (mole IL)'1, but a large rate of heat production Tq, up to 13 W (g
biomass)'1. The biomass composition of the organism has been experimentally determined to:
X = CHl.MOo.
39
b U (K = 4.18),
and with
YHlx =
0-02 C-mole (mole H
2)'1
the stoichiometry for a black box model is determined
horn a carbon and a redox balance:
- H
2
- 0.260 C 0
2
- 0.0048 NH
3
+ 0.02 X + 0.240 CH
4
+ 0.511 H20 = 0
(
1
)
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