386
Chapter 9
t
(
8
)
The three transients illustrating the approach to a new nonzero steady state
(n -
4/3), for the washout
dilution rate
D
=
Dmai,
and for
D
in excess of
D ^ n
= 3/5) are shown in Fig. 9.7. The three curves approach
the new steady state at very different rates, the smallest rate being that corresponding to
n
= 1. Although the
kinetics used here are too simple to imitate a real transient, the observed difference in the approach to a new
steady state after a change in D is found also with other kinetics expressions. Whereas an approach to within
90% of the new steady state is reached after about 4-6 hours for
D
= 0.6 h
'1
and
D
= 4/3 h'1, 56 hours is
required for
D
=
0.8
h
1
._______________________________________________________________
A comparison of the relative magnitude of the two terms in Eq. (9.94) results in an accurate method
for determination of
from transient wash-out experiments. Thus for
n<
1
the first term
eventually dominates when
x/x
0
0
.
f°r
n<‘
°r
ln( t ) =(Z>”“ ' I>>' +c’
(9'97)
The slope of the straight line In
(x/x0)
vs.
t
is the difference between
and the
D
value chosen in
the wash-out experiment. When using (9.97) to find
one must keep in mind that the basis for
the method is an unstructured kinetic model. Results such as those shown in Figure 7.14 are
obtained if the initial state of the biomass is far from that of a fully active biomass.
b
Change of the feed concentration from*?/ to
sf.
Although
x
and
s
can be separated using (9.88 a) the resulting differential equation cannot be
solved analytically, and as is almost always the case the dynamic mass balance must be solved
by numerical integration.
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