472
Chapter 10
c.
With the estimated
k&
value, find the largest possible oxygen consumption rate when
vg =
1 w m
and
Pg
= 3000 W. During penicillin fermentations it is found that the dissolved oxygen
concentration should be above 30% of the saturation value if the penicillin production is not to be
inhibited. Assume that the oxygen uptake rate can be described by Monod kinetics with
- 0.015
mmoles L
'1
and
= 0.65 mmoles (kg DW
)"1
s '. Calculate the maximum biomass concentration
that can be sustained without inhibition of the penicillin production.
Problem 10.4. Mass transport into pellets
The concentration profile for a solute A, which reacts as it is transported by molecular diffusion in a
spherical pellet is given as the solution to Eq. (1)
1
d ( 2dS^
^
qA(sA)
X 2
d z{
d x )
qA{5A = saJ
(
1
)
where the dimensionless concentration, SA
, and the dimensionless radial coordinate, X, are given by
S A = —
and
(
2
)
SAj
K
and the Thiele modulus,
is given by Eq. (3)
<P =
<?(saJ R 2
9
D ^ s
'ff^ A 'S
(3)
-qA
is the volumetric consumption rate (unit: mol m
'3
(pellet) s ') ,
R
is the pellet radius, and
Deg
is the
effective diffusion coefficient in the pellet for the species being considered.
ch
is the bulk concentration of
the species. For zeroth-order kinetics the pellet size that gives a zero concentration precisely at the center of
the pellet is given by (see Note 10.7)
R
=
~9a{sAj )
(4)
We now consider oxygen diffusion into a pellet of
Penicillium chrysogenum.
For this microorganism, the
oxygen uptake rate can be approximated by
= *
x
(5)
So+Ko
with
k ~
4.0 mmol Oz (g DW
) 1
h
'1
and
Ko
= 58 dmol 0
2
L'1. The biomass concentration in the pellet is
approximately 99 kg DW m
'3
of pellet (this corresponds to a void volume of around 70% and a water
content of 67% in the cells) and the concentration of oxygen in the bulk medium is 17.4 Mmole L 1.
Calculate the critical pellet radius when it is assumed that Eq. (4) can be used. Discuss the application of Eq.
(4). Calculate the effectiveness factor using the generalized Thiele modulus (Eq. 10.55) as a function of the
pellet radius (25 Mm
<R<
500 Mm).
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