52
Chapter 3
q{
is the volumetric production rate, i.e. the mass of compound i produced per volume reactor and
per unit time. Sj and
p\
are the concentrations of the ith substrate and metabolic product,
respectively, x is the concentration of the biomass. Subscript / indicates the concentration of the
variable in the liquid feed to the bioreactor.
For a gaseous substrate or product Eqs. (3.2) and (3.3) are slightly modified
( < + ^ ) ^ + Ч*л/_ О = 0
(3.5)
+ O
r + vO v " ^ ) = 0
(3.6)
In Eqs. (3.5) and (3.6)
q,
is again the rate of production of the component by the biochemical
reaction, whereas
q\
is the rate at which the component is transferred from the gas phase to the
liquid medium, which is given by:
<
(3.7)
q!pi ~ k,a[p* ~ p i)
(3.8)
kp
is a mass transfer coefficient which may depend on the fermentation medium and on the
component being transferred, but certainly depends on the agitation of the liquid medium or the
construction of the sparger used to introduce the gas.
and
p<
are the concentrations of the
component in the liquid which is in equilibrium with the gas phase. Both depend on the partial
pressure of the component in the gas phase, on the medium temperature, pH etc. as will be further
discussed in Chapter 10.
»
'
P i= H Pl7tpi
(3-9)
In Eq. (3.9)
nt.
and
it Pt
are the partial pressures in the gas phase and
H,
is a so-called Henry’s law
coefficient, which as described above is dependent on the medium and on the operating conditions.
A typical unit for
H
is mol (L atm)'1.
Finally the gas phase partial pressures are given from mass balances for the gas phase over the
whole system:
~Vs,)=kASi ~s) v
(З.Ю)
where Vgj and vg are the inlet and head space volumetric gas flow rates, respectively. v^f is different
from vg if the volumetric production rate of gaseous products is different from the consumption rate
of gaseous substrates or if liquid phase components, typically water are stripped off from the
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