384
Chapter 9
/= -
D
-D
In
z-
D l)nlZ
Z’
D
1
-z .
(9.94)
z = x/xfl>
and D inai is the wash-out dilution rate
(a + l
) '1
in Eq (9.27).
The parameter z.„ is given by:
z
-
__^ ^max
^0
i9 951
~A> /^max
When n = Z )^ /
D >
1 then z tl is the final value
oix / x0
at the end of the transient. If
n<
1 the
final yalue of
x
is of course zero since the culture is washed out. In that case zx is to be regarded
as just another parameter in the expression for the transient.
For the special case of
n =
1 Eq (9.96) is used instead of Eq (9.95) to calculate the transient.
(9.96)
The final value of
x
is also zero for
n=
1.
Example 9.12 Change of
D
for maintenance-free Monod kinetics
Consider Monod kinetics with the parameters used in Example 9.4:
;
^ = 0 .5
;
* ,= lg L -‘
(
1
)
and the operating parameters
s/=
4 g L '\
D
= 0.4 h
'1
before / = 0, and 0.6,0.8, or 4/3 h
1
after
t
= 0.
First, the steady state before
t
= 0 is calculated:
K rD
10.4
-D
1-0.4
= I gL'! ;
x
0
= 0 .5 (4 -l) = f gL
4
(
2
)
*0
=
3
_ 5
Y«*r
°-5
' 4
6
(3)
Next, we consider the transient where
D =
0.6 h 1
after / = 0. Since
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