358
Chapter 9
When maintenance kinetics is coupled to a Monod expiession for
n
=
D:
qs = -D (sj-s)~-
D
+
ms) x
or
X=x
S (l-S )
S
+
b (S + a)
where the new parameter
b = m j (n ^ Y™)
.
U)
(
2
)
When maintenance is added to any kinetics
fi(S)
the biomass concentration decreases to zero for
D —>
0,
whereas
X
=
1 - S
for maintenance free kinetics.
For the kinetics of figure (9.3.D) the largest value of
X
that can be obtained is:
VT-Tu*"
~ \a
b
+ 1
for
S
=
-a* +
va* +
a
*
where a*=ab/(l+b)
(3
)
The value of
qx
or of
Px - qx /(fi^ sf Y™e)
can always be found as the product of
D
and
x
(or ,¥):
Monod:
P
=
S(\-S)
S + a
Where the explicit solutions for
and for
Sopi
are shown in eq (9.34).
Substrate inhibition:
S (l-S )
(4)
P,
=
where
b = sf Ki
.
Product inhibition:
1
S + a + &S2
Sop, = - c + (c2 + c/'1
and
c = a / (1+b)
J d - s ) ( i - r f ( i - 5 ) )
.
.
,
Tr = ---------------------------
where
d= Y sp
S f
/pm
S
+ a
(5)
(6)
Maintenance:
P,
=-
^ ( l - S )
(5 + ü)
(S +
b(5 + a))
(figure 9.3 D)
(
7
)
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