Chapter 9
ini —
J o a -1
Of eXp(Cj 0
+ exp(c,
d(c, t)
= In
- 1 + exp(c, 0
x _ of -1 + exp(ct Q
Finally, the solution of the product mass balance is
p - p 0
[exp(c, Q -l]
The calculations on a greatly simplified structured model demonstrate that these models can give an
insight into the fermentation process far beyond what is offered by the unstructured models:
Exponential growth of both biomass and product is eventually obtained. The time constant
is determined by the net rate of formation of active component in the cell, i.e., the constant
Cj in the substrate-independent model.
A time lag is introduced in a biologically reasonable way. Cells with a low initial activity—
e.g., taken from a stirred tank reactor with a very small dilution rate—have a low initial
value of
and a large time lag, as seen from the horizontal shift between the growth curves
in Fig. 9.2.
9.1.2 The Continuous Stirred Tank Reactor
The mass balance for a continuous, ideally mixed, constant-volume tank reactor is
~ = q ( + q(c) +
(c/ - c)
The influence of mass transfer on the operation of the steady state stirred tank reactor is considered
in section 9.1.4, while the dynamics of stirred tank continuous reactors is deferred to Section 9.3.
Thus, in the present section the accumulation term and
are both zero.
Monod kinetics will again be used to illustrate some general features of the steady-state stirred tank
reactor model. The feed to the stirred tank reactor is sterile and contains no product. In accordance
with the major assumption of the ideal tank reactor, the concentration
of any substrate or
metabolic product is constant at every point of the reactor. In most cases the effluent concentration
is also Cj, but this is not necessarily correct, e.g., if the reactor system contains some kind of
separation equipment as will be discussed in section 9.1.3.
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