Design of Fermentation Processes
419
the model. Derive the following relation between the steady state value of
D
and the
corresponding value of
p
:
D
=
k,
+
kn
-
u
^
*
2
-M
(
1
)
Show that
D
is always larger than M
for realistic values of
k,
and
k2.
b.
Let
p ~
0.5
s
/
+ 2) h 1,
sy=
10 gL '1,
Y„
= 0.5 g g~',
k,=
2 h'1
and
k3 ~
1.5 h'1.
The dilution rate is
D
= 0.2 h‘\
Calculate
s, x
, and
x,
and compare with the corresponding values for
k}~
0.
Assume that the above data were obtained with a small laboratory reactor of volume
V
= 1 L,
height
h -
1.3 diameter
d.
The inner surface of the reactor is 550 cm2. For a film density
p=
1 g
cm3 calculate the film thickness
A.
(Answer: 123 l1 m which is likely to go undetected in the experiments)
Make a simulation of
x
g L 1
as a function of D, both in the case of biomass adhesion and for
kj=
c.
Consider a 50 m3 industrial reactor for the same process,
h =
3
d.
The internal surface, including
baffles, heat exchangers etc. is 100 m2.
What would the film thickness be if
k{
and
k2
have the same values as in (b)? In reality a film of
this thickness would never be stable. It is more likely that the film thickness
A
is also 123 P m in
the industrial reactor. The adhesion mechanism is probably the same in both scales (
k2
2 h'1),
but
k2
is much larger for the industrial reactor.
Determine the “effective” large scale value of
k2
and the relation between
x
and
D.
You will
conclude that a serious underdesign of the large scale operation would result if the laboratory
data were used uncritically as the design basis.
The data was taken from a real process, the production of lipases by a microorganism that
hydrolyzes linseed oil in an aqueous emulsion of the vegetable oil. Some oil sticks to the reactor
surface and part of the culture adheres to this film.
Problem 9.12 Plug flow reactor with recycle
The recycle reactor of Fig. 9.5 also functions for a sterile feed because part of the effluent from the plug
flow reactor is recycled to the inlet. In Fig. 9.4, the operation of a chemostat is improved because part of the
effluent is returned to the inlet with a higher cell concentration
xR
=
fix
than that which exists in the reactor.
It is appealing to combine the two procedures by the installation of a cell separator (e.g., a cyclone) at the
exit from the plug flow reactor and return cell-enriched medium to the inlet.
With reference to Fig. 9.5, let the exit concentration from the plug flow reactor be
xr
while the cell
concentration is
xR
~ p xr
in the recycle stream
vR
= vR.
As in Fig. 8.4, it is assumed that the substrate
concentration is s in all streams leading to or from the separator.
xf =
0, i.e., the feed stream is sterile.
a.
Derive algebraic expressions for
xr, xh
and
s2
in terms of
sfi s, R,
and
p
for maintenance-free
Monod kinetics.
b.
Show that Eq. (9.76) can be used to calculate 1 if
xr
is used in place of
x
and
a ’
is used in place of
af =KJ sf\
1
-R(p-l)s/sf f
(1)