4X6
Chapter 9
Problem 9.8 Providing an experimental foundation for the design of a fermentation process.
Vara
et al,
(2002)
made an experimental
study of Teicoplanin production by
Actinoplanes
teichomyceticus
in order to obtain design data for an industrial production of the antibiotic in continuous
a.
You are required to make a short review of their experimental plan and to compare it with the
experimental plan used in Example 6.1. The kinetic parameters used to construct table 6.1 were
in fact extracted from the results of the above reference, thus illustrating the resemblance
between mechanistically based kinetic expressions for enzymatic reactions and empirical rate
expressions for cellular reactions. Which experimental plan is likely to lead to the best values for
the kinetic parameters?
b.
Figure 6 of the reference shows simulations of the concentrations of substrate (glucose =
5
),
biomass (x) and product (teicoplanin
=p)
as functions of dilution rate in a continuous cultivation.
You are required to check the simulations using the kinetic model (including maintenance). Why
does
x(D)
decrease for small
D
while
p(D)
continues to increase?
c.
Table 1 of the reference shows results of continuous experiments in a stirred tank with
recirculation according to Figure 9.4 B. Find the connection between the parameter
c
in the
reference and
Q
used in Eq (9.46). Why are the data in the last column of the table almost
independent of £>? Confirm the conclusion of the paper that continuous operation with cell
recirculation is the best mode of operation, and that an increase of productivity by a factor 3
compared to straight continuous operation is achieved.
d.
The microorganism gradually looses the ability to produce teicoplanin. Compare the deactivation
model (10)-(11) used by the authors with that used in Example 9.15, and confirm that the model
simulates the data in figure 8 of the reference with a high accuracy. Why could a simpler model
taken from Example 9.15 not be used?
Problem 9.9
Prey-predator interaction
Consider the prey predator model of Eqs. 1 to 3 of Example 9.16, but with a general substrate limitation for
growth of
Xi,
i.e.,
p j D=
instead of
p l /D = fi].
a.
Let
cf idS - f S)
and show that the steady state
have negative real part.
b.
Can undamped oscillations occur?
c.
Take/ =
S / (S + a),
and show that (1) all eigenvalue of Eq. (2) have negative real part, and (2)
x,
and x2 coexist for
culture.
X ,= liP J ^ S f-
X 2 = ( P J - \) ip 2xw
;
S ^ - P J X ,
0
)
is stable if the zeros of
(2)
A >
a + l- X j
1 -X ,
(
3
)
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