Design of Fermentation Processes
417
where
a * J / A )
(4)
d.
On a diagram with
Ysxs f
on the abcissa and
fii
on the ordinate, find the region in which the
solution
X2
= 0,
Xi
> 0,
S >
0 is the only stable steady state.
e.
On the same diagram, calculate the curve
ffo
versus
YsxSyt
which separates the region with
exponentially damped oscillations from the region with pure exponential decay of a perturbation
(Xj, X2,
*S) > 0. Make the numerical calculations with Pi = 0.02 L g'1
and
a
=
0.2.
f.
Describe in your own words how you would plan the production of a valuable microorganism
Xj
which can be attacked by a parasite or a phage. Can you choose any value of the dilution rate? of
feed stream concentration
sf!
g.
Illustrate with a few examples, using suitable values for the
true
kinetic parameters
etc.)
and operating variables
(sf, D,
etc.). This last part of the exercise is intended to help in the
back-translation from the dimensionless variables and parameters, which are very helpful in the
theoretical development but may be difficult to relate to an actual physical situation.
Answers to (d) and (e) are shown graphically in the figure below. The horizontal line below which washout
is the only stable solution is given
by p, = \ + a =
1.2. Since in the figure
sf
appears both in the abscissa and
the ordinate, there may be some confrision if the figure is compared with Fig. 8 in Tsuchiya
et al.
(1972),
who treated the same model. For
sf *
0, the parameter
a—>
<
x>
and the horizontal line in the figure will bend
upward and approach the ordinate axis asymptotically, as in the corresponding figure in the original paper,
where 1 /
D
is used as ordinate.
Ysx Sf
Problem 9.10 Production of a protein that is degraded by the action of proteases.
A valuable protein is produced by a growth associated process using a microorganism for which the
volumetric growth rate is given by
0.2
5
.
qx ~
——
x
g biomass (L medium h)
(1)