Design of Fermentation Processes
35?
In (4) and (5) relatively simple algebraic expressions are obtained for
Sopt.
This is not so for (6) and (7),
but algebraic solution of these problems is hardly worth the effort since an automatic calculation of
q f
as in figure 9.3 gives the answer for any given values of the parameters if only an expression for
qx
as a
function of
S
can be set up.
The productivity problems solved here for unstructured kinetics may also have limited value in practice.
Thus, in aerobic fermentation of yeast
qx
increases practically proportional to
D
for any reasonable value
of
Sf
since
Ks
is in the mg L'1
range. At
D = Dcrit
the stoichiometry changes abruptly with the onset of
ethanol production. To obtain maximum productivity of biomass and of a growth associated protein
product it is desirable to work at
D
only slighter lower than
Dcrit.
This mode of operation leads to severe
control problems as discussed by Andersen et al. (1997)._________________________________________
9.1.3 Biomass Recirculation
In the preceding discussion it has been shown that for given fermentation kinetics (with or without
maintenance) and for a given feed composition it is possible for a steady state continuous reactor to
calculate the complete effluent composition based on a single measured quantity. This may be
either the dilution rate or the concentration of substrate, biomass, or product in the effluent. If in Eq.
(9.20) an extra degree of freedom is introduced by relaxation of the assumption that the biomass
concentration
xe
in the effluent is equal to the biomass concentration
x
in the reactor, then a new set
of design problems arises. For all other reactants and products the assumption of ideal homogeneity
of the stirred tank reactor is maintained, but the value of
D
that corresponds to given feed and
effluent concentrations will now depend also on
x.
When
x > x
e, the reactor is able to process more
feed than in the basic situation with
x = xe
since the rate of biomass formation is proportional to
x.
Enrichment of the reactor medium relative to the effluent stream can be achieved by means of a cell
centrifuge installed after the reactor and
recirculation of cells
to the inlet of the reactor through an
exterior loop. The same effect can also be obtained by means of a filter installed inside the
reactor—typical on-line probes for removal of cell free jnedium to analysis are extreme cases of
complete cell-medium separation. The cells may undergo a partial sedimentation in the reactor—
here, cells immobilized on granules of inactive carrier material such as sand particles or floes of
microorganisms are typical examples. Finally, a more-or-less loose wall growth of cells leads to
enrichment of cells in the reactor, although cells growing on the walls or on granules may exhibit
different kinetic behaviour than do freely suspended cells.
With maintenance-free Monod kinetics, the modification of Eq. (9.21) to Eq. (9.23) reads
D xe = fix
(9.36)
D(sf -s) = Yxsjux
(9.37)
Dp = Y^pM x
(9.38)
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