418
Chapter 9
In (1) the concentration of the growth limiting substrate is s g L 1.
x
is the biomass concentration in g If1.
The yield of biomass on the substrate is
Ya =
0.5 g g'1.
Production of the protein is severely catabolite repressed and the volumetric production rate is
1
.
qp
=
qz
g protein (L medium h)
(2)
Production of the protein is to take place in a continuous, steady state stirred tank, and the glucose feed
concentration is
sf =
10 g L'1.
a.
Determine the largest value of
D
for which the steady state process will work. Thereafter
determine the yield coefficient
Ysp.
For which value of
D
(or r) is
at its maximum? Is that the
same value for which
qp
is at its maximum? Why is the continuous stirred tank process better
than a batch reactor process?
b.
Make a sketch of
qp
as a function of
s
for
y < 10 g L“1. Calculate the largest productivity
{<&)ma* which can be obtained and determine the corresponding value of
D.
c.
Equation (2) is an idealization of the real situation. The microorganism also produces proteases
that to a considerable degree destroy the desired protein. The correct expression for
qp
is:
1
1 + 10j
qx-kx
(
3
)
Determine the maximum value of
k
above which no net production of the protein will be
obtained for any operating conditions. Derive an approximate relation between
k
and the
maximum protein productivity. You should not attempt to obtain an algebraic solution, but use a
graphical representation in which
qp
given by (2) is plotted together with
kx
and make your
approximate solution based on this graph.
d.
It is contemplated to install a cell separator at the exit of the reactor and recirculate cells to the
inlet.
Discuss whether an increase of productivity (given by (3)) can be obtained in this way. Is there
any difference between the two cases (A): The protein product is secreted 100 % to the medium
and (B): The protein product remains quantitatively inside the cells? What is the potential
increase in maximum productivity if a recirculation ratio
R
= 0.5 and a cell separation factor
p -
1.5 (Eq (9.43)) is used?
Problem 9.11 Adhesion of cells can lead to serious underdesign of an industrial reactor.
In a continuous stirred tank reactor operating at a given dilution rate
D
and with sterile feed the
concentration of biomass in the medium (the suspended culture) is
x
g L'1. Some biomass adheres to the
inner surface of the reactor. The concentration of adhering biomass (converted from a more “natural”
unit g (m2 reactor surface)1) is x, g L'1.
Suspended and adhering biomass grow with the same yield
coefficient
Ysx
and the same specific growth rate
jj.
Suspended and adhering biomass are exchanged by
first order rate processes :
k} x
(adhesion) and
k2 x,
(attrition of biofilm).
a.
Write mass balances for the suspended and for the adhering biomass. Add a substrate balance to
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