Scale-up of Bioprocesses
511
Table 11. 9.
Characteristic times for important processes in fermentations
Process
Variable
Circulation
tc
Mixing
tm~ 4 tc
Gas flow
tgas
(1
-
&
)
T/Ug
Gas-liquid mass transfer
U = 1/kfl
Biomass growth
t
bio
~~
Substrate consumption
t$c ~ s/(J5
Substrate addition
II
!
The
fundamental method
is based on actually solving the governing equations of flow(see
section 11.3.5) in combination with the reaction kinetics. In a strict sense this is not even
theoretically possible, since in particular the microbial kinetics is not fully known (see section
11.4). Assumptions concerning both the kinetics and flow modeling (see Note 11.5) are thus
necessary.
In the
semifundamental methods
, simpler flow models are applied, e.g., the compartment models
described in Section 11.3.5. When such a model is combined with a suitable kinetic model, a
reasonably precise description of the process may be obtained. However, despite the extensive
simplification
of the problem
when one
moves
from
the
fundamental
models to
the
semifundamental models, the complexity of the model is still substantial if e.g. a structured kinetic
model is applied.
Regimen analysis
is based on a comparison of characteristic times for the different mechanisms
involved in the overall fermentation process. The characteristic time for a certain process, which is
modeled as a first-order process, is defined as the reciprocal of the rate constant. For processes,
which are not first order, the characteristic time can be calculated as the ratio between capacity (e.g.,
the volumetric content of the considered species) and the flow (e.g., the volumetric consumption
rate of the species). Table 11.9 lists the most important characteristic times in fermentation
processes. By analyzing the characteristic times, it is possible to identify potential problems such as
oxygen limitation in the large-scale process. The regimen analysis may also suggest further scale-
down studies, such as repeated exposure to substrate depletion.
Example 11.5. Regimen analysis of penicillin fermentation
In the literature, one finds many applications of time-scale analysis to identify the limiting regime in a given
process (see Sweere
et al,
1987 for a review). Here we will consider the penicillin fermentation for which
Pedersen (1992) found the characteristic times listed in Table 11.10. The characteristic times are given for the
two different phases of a typical fed-batch fermentation (i.e., the growth phase and the production phase),
carried out in a 41-L pilot plant bioreactor. The smallest characteristic time is certainly
tmix
(which was
experimentally determined using isotope techniques). This indicates that no mixing problems arise during the
fed-batch fermentation in the pilot plant bioreactor. Thus there will not be any concentration gradients for the
substrates (glucose and oxygen). This conclusion will, however, definitely be different in a large production
vessel, where the mixing time may approach 20-50 s. The characteristic mixing time for mixing in the gas,
tga
„ is high, indicating that this mechanism is slow. The characteristic times for glucose addition,
tsa,
and
glucose consumption,
tSC
i
are of the same order of magnitude. This is quite obvious, since it
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