Page 746 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Biological Reactions and Kinetics 701

22.5.7.4 Relating Monod Kinetics to U m 1
u _ (22:54)
c
Going back to the stoichiometric relationship between cell m b
synthesis and substrate reacted, i.e., dX=dt ¼ Y(dS=dt), Equa-
m
tion 22.29, and since dX=dt ¼ mX, Equation 22.30, then if we where u is the minimum cell residence time.
c
equate mX ¼ Y(dS=dt), we may rearrange to give Notes on the foregoing are:
m dS=dt . u c is an operating parameter and is controlled by the
(22:48)
¼
Y X W, the rate of wasting, which is based approximately
on a routine. Usually the operator monitors the
In other words, (dS=dt)=X is a micro-version of the ‘‘specific
MLSS, a surrogate for X, and fine tunes W, based
substrate utilization rate,’’ and is an identity with U the macro-
on whether the MLSS trend is increasing or decreas-
version. Importantly, it shows that
ing. W may be an intermittent flow, rather than
m continuous. A centrifuge test is used, as a rule, in
¼ U (22:49)
Y practice as a surrogate for MLSS.
m
. In operation, u c u ; otherwise the cells will leave
c
It means that the plant loading equals the capacity of the the system at a rate that exceeds their generation rate.
microorganisms, m=Y, to process the substrate. See also Tcho- . The waste flow, W, is taken from the recycle flow, R,
banoglous and Burton (1991, pp. 371, 388). with concentration, X r .
. As a guideline, 3 < u c < 15 day (Tchobanoglous
22.5.7.5
Sludge Age, u c
and Burton, 1991, p. 534). From Example 22.3, for
1
1
Another parameter common in practice is ‘‘sludge age,’’ or ^ m ¼ 5 day , and m ¼ 1.25 day , and if b 0.1,
‘‘mean cell residence time,’’ or ‘‘solids retention time,’’ u 0.2 day and u c 0.9 day, respectively. In oper-
m
c
defined as (Lawrence, 1975, p. 224) ation, they recommend that u c u .
m
c
m
. As b ! 0, then m ! bm, and 1=bm ¼ u .
c
total-active-mass-in-system
(22:50) 22.5.7.7
u c ¼ Relationship between U and u c
total-active-mass-leaving-system-per-day
The relationships between u c , F=M and U are (Tchobanoglous
V(reactor) X and Burton, 1991, p. 534)
(22:51)
u c ¼
½ WX r þ (Q W)X e Š
1 F
E b (22:55)
As a rule, for conventional activated sludge, X e X r . and so u c M
¼ Y
Equation 22.51 may be approximated as
By definition, F=M S o =uX and E (S o S)=S o ; with the
V(reactor) X substitutions,
(22:52)
u c ¼
WX r

1 S o S o S
where ¼ Y b (22:56)
u c uX S o
u c is the mass of viable cells in system=rate of cell synthe-

sis (kg viable cells in system=kg cell synthesized=day) S o S
b (22:57)
W is the waste flow (removed from recycle flow in an uX
¼ Y
3
activated-sludge reactor) (m =s)
¼ YU b (22:58)
X r is the concentration of viable cells in recycle flow (kg
3
cells=m )
X e is the concentration of viable cells in flow leaving final
3 22.5.8 NITRIFICATION=DENITRIFICATION
clarifier, i.e., (Q W) (kg cells=m )
The Monod equation is applicable to any substrate in a
For reference, and as may be seen from Section 22.5.3 Net
biochemical reaction. In nitrification, the substrate is NH 3
Growth, X=[dX=dt] net ¼ 1=(m b), as N; in denitrification, the substrate is NO 3 as N. Values

for the yield coefficient, Y, and the kinetic constants bm, K s ,
1 and b, are given in Table 22.9, as obtained from the litera-
(22:53)
m b
u c ture.
22.5.7.6 Minimum Cell Regeneration Time, u m 22.5.8.1 Nitrification: NH 4 to NO 3
þ
c
m
The time for cell generation is designated, u and is defined The nitrification rate depends upon several factors including
c
further as ammonia concentration; cell concentration, X(nitrifiers);