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Biological Reactors 735

The range is Tchobanoglous and Burton (1991, p. 550), 0.3 <
For conventional activated sludge, the F=M range is 0.2
3
F=M 0.4 kg BOD applied=kg MLVSS=day (Tchobanoglous VL < 0.6 (kg BOD=day)=(m reactor) or [20 < VL < 40 (lb
3
and Burton, 1991, p. 550). If S o and X are expressed as BOD=day)=(1000 ft reactor)].
concentrations, the volumes cancel. As seen by the definition,
the lower the F=M ratio, the more the organisms are in a 23.2.4.1.6 Design Parameters
‘‘starved’’ condition. A larger tank size gives lower values The F=M and u c are the recommended parameters for design
of F=M ratio. and operation Tchobanoglous and Burton (1991, p. 534). The
empirical parameters u and VLF have been long used and may
23.2.4.1.3 Specific Substrate Utilization Rate be useful for an approximate confirmation of results from
The ‘‘specific substrate utilization rate,’’ U,isdefined F=M and u c .
(Tchobanoglous and Burton, 1991, p. 533) as
23.2.4.1.7 Cell Production Rate
From Section 22.4.5, Table 22.8, the Y 0.94 g cells=g
(S o S)
(22:43)
uX
U substrate, or Y(COD=COD) 0.64 g cell COD=g substrate
COD. In terms of BOD, the ‘‘rule of thumb’’ is Y(g cells=g
where BOD) 0.5 g cells synthesized=g BOD degraded (Ecken-
U ¼ (F=M) E felder, 2000, Figure 19). Example 23.1 illustrates the calcula-
tion of the mass flux of cells leaving the system.
E (S o S)=S o
The F=M parameter is used most often in practice while the U Example 23.1 Cell-Wasting Rate
is seen more frequently in texts, since U is an identity with
m=Y (Equation 22.45). As seen by comparing F=M and U,if Given
S << S o , then F=M U. Also for reference, U m=Y; in other S o 280 mg BOD=L or 0.280 kg BOD=m 3
words, m=Y is the ‘‘independent variable’’ and U is the S 30 mg BOD=L
3
‘‘dependent variable’’; U is determined by m=Y. But this is Q ¼ 18,925 m =d (5.0 mgd)
not strictly true. To expand on this statement, for a given
system, if u is determined by Q and V, and if S o depends on Required
the influent flow value, and if X is determined by operation, S is Rate of cell wasting, WX r
a dependent variable. But actually, since m ¼ ^m [S=(K s þ S)], a Solution
quadratic equation is involved to solve for S. Assume X r 10,000 mg=L ¼ 10.0 kg cells=m 3
Y(g cells=g BOD) 0.5 g cells synthesized=g BOD
23.2.4.1.4 Sludge Age, u c
degraded
The sludge age is used in operation and is defined (Section Therefore, the mass rate of cell synthesis is
22.5.7.5) as WX r ¼ Q(S o S)Y
3
3
¼ (18,925 m =day) (0.280–0.030) kg BOD=m )
V(reactor) X
(22:52)
u c ¼ (0.5 g cells synthesized=g BOD degraded)
WX r
¼ 2,366 kg cells=day
3
where W (2,366 kg cells=day)=(10.0 kg cells=m )
3
3
V(reactor) is the volume of aeration basin (m ) ¼ 237 m =day
X is the cell concentration, usually measured using the Discussion
3
surrogate, MLVSS (kg=m ) The cells wasted are usually mixed with the sludge under-
W is the waste sludge flow as taken as a sidestream from flow from the primary settling tank and sent to the anaer-
3
the return sludge flow (m =s) obic digester. A more accurate calculation would account
X r is the cell concentration as ‘‘underflow’’ from the final for endogenous respiration, which means that about b
3
clarifier, recycled (kg=m ) fraction of the cells synthesized decay. The calculation
1
is, DX(decay) bX; let b 0.1 day ; therefore, DX(decay)
1
m
Also, keep in mind that u ¼ 1=(m b), and for design, (0.1kg cellsdecayed=day=kg viable cells=day ) (2366kg
c
m viable cells)¼ 237 kg cells decay=day. Net cell wasting
c
u c >> u . From operating data in U.S. plants, u c ranges, 3 rate 2366–237 2129 kg cells=day.
u c 15 day (Tchobanoglous and Burton, 1991, p. 534).
Oxygen demand:
23.2.4.1.5 Volumetric Loading The oxygen demand for a wastewater in a reactor has
three parts: substrate oxidation, cell oxidation (as
The volumetric loading has been used for many decades; it is
endogenous respiration), and ammonia oxidation.
given here for reference, and is defined as
Substrate oxidation: The oxygen demand for substrate oxi-
dation may also be calculated from stoichiometry (Section
kg BOD=day
22.4.5, Table 22.8) based on the equation for the conver-
m reactor volume sion of domestic wastes to cells. As seen, the conversion is
VLF ¼ 3