366
Chapter 9
Finally from Eq (9.48):
k,a =
2540 / (0.8 - 4.67) = 679 h
1
(3)
A mass transfer coefficient of 679 h
'1
can be obtained, also in an industrial reactor designed for good
mass transfer.
Consequently an over all maximum productivity improvement of 27 % compared with the case
D =
0.2
h
'1
,
x =
10
g L
’1
can be obtained by simultaneous optimization of the bioreaction and the mass transfer
process.__________________________________________________________________________________
When the liquid phase concentration of one of the reactants is constrained by a mass transfer
balance one should be wary of using one of the popular rate expressions in which the specific
growth rate is given as the product of two Monod expressions, one for each of the substrates.
Let
S2
be the liquid phase substrate and
S,
the substrate transferred from the gas phase.
The yield coefficients are
Ysl x
and
Ys2x
respectively. The mass transfer coefficient has a known
valued a.
The amount of
St
transferred from the gas phase is
q,1
- k{ a ( s ’- s j
while the rate of the
bioreaction is
qx
=
q,1
Ys!x.
Consequently qxcan be calculated in two ways:
Y$i
xk,a (sj
-
Sj)
Mnax
S
j
+ ^ 2
1
"
(
0
^
2
/
S2
)
(9.51)
Hq (9.51) looks like an equation from which
s2
can be found when the value of S! is given. But
this cannot be true for all values of s, since the right hand side of the equation is zero for s, =
0
.
There is clearly a lower value for Si below which no solutions for
s2
can be found. The right hand
side of (9.51) has-a maximum value determined from Eq(9.34), and consequently we must look
for the lowest value of s( for which the left hand side of (9.51) is smaller than or equal to this
maximum value. If $ / is increased (e.g by increasing the total pressure) then the lowest
permissible Sj value will also increase. I f / w is increased then
also decreases towards zero,
and the process is controlled by mass transfer alone. The two values obtained for
s2
when
ss
is
above its minimum value is no surprise. The same value for
qx
can be obtained both for a small
D
and a large x, and for a large
D
and a small x.
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