140 BIOLOGICAL TREATMENT OF WASTEWATER
Combining Eqs. 4, 6 and 7 yields:(^)
q
Y
(8)
and
(^)
qq
S
KS
max
.
(9)
Under conditions of rate limited growth, i.e., nutrient
exhaustion or auto-oxidation, Eq. 6 becomes:
(^)
d
d
d
d
X
t
Y
S
t
bX
(10)
where b is the auto-oxidation rate or the microbial decay rate.
In absence of substrate, this equation is reduced to:
(^)
d
d
X
t
bX.
(11)
Several kinetic equations have been suggested for analy-
sis and design of biological wastewater treatment systems
and the following have been applied frequently: 10 – 13
(^)
d
d
S
t
qSX
KS
max
( )
(12)
(^)
d
d
S
t
qSX
(13)
(^)
d
d
S
t
qX
S
S
2
0
(14)
where S 0 is the initial substrate concentration. Combining
Eqs. 10 and 12 gives the net specific growth rate:
(^)
d
d
X
Xt
qYS
KS
max b
(15)
A similar kinetic relationship can be obtained by combining
Eq. 10 with Eqs. 13 and 14.
Effect of Temperature
One of the significant parameters influencing biological
reaction rates is the temperature. In most of the biologi-
cal treatment processes, temperature affects more than one
reaction rate and the overall influence of temperature on the
process becomes important. The applicable equation for the
effect of temperature on rate construct is given by:
k T = k 20 u T – 20 (16)
where u is the temperature coefficient. This equation shows
that reaction rates increase with increase in temperature.
Methods of BOD Removal
In wastewater treatment processes, the microorganisms are not
present as isolated cells, but are a collection of microorganisms
such as bacteria, yeast, molds, protozoa, rotifers, worms and
insect larvae in a gelatinous mass.^13 These microorganisms
tend to collect in a biological floc, called biomass, which is
expected to possess good settling characteristics. The bio-
logical oxidation or stabilization of organic matter by the
microorganisms present in the floc is assumed to proceed in
the following sequence: 13,14
(a) An initial high rate of BOD removal from waste-
water on coming in contact with active biomass
by adsorption and absorption. The extent of this
removal depends upon the loading rate, the type of
waste, and the ecological condition of the biomass.
(b) Utilization of decomposable organic matter in direct
proportion to biological cell growth. Substances
concentrating on the surface of biomass are
decomposed by the enzymes of living cells, new
cells are synthesized and end products of decom-
position are washed into the water or escape to the
atmosphere.
(c) Oxidation of biological cell material through
endogenous respiration whenever the food supply
becomes limited.
(d) Conversion of the biomass into settleable or oth-
erwise removable solids.
The rates of reactions in the above mechanisms depend upon
the transport rates of substrate, nutrients, and oxygen in case
of aerobic treatment, first into the liquid and then into the
biological cells, as shown in Figure 5.^15 Any one or more of
these rates of transport can become the controlling factors in
obtaining the maximum efficiency for the process. However,
most often the interfacial transfer or adsorption is the rate
determining step.^14
In wastewater treatment, the biochemical oxygen demand
is exerted in two phases: carbonaceous oxygen demand to
oxidize organic matter and nitrogenous oxygen demand
to oxidize ammonia and nitrites into nitrates. The nitroge-
nous oxygen demand starts when most of the carbonaceous
oxygen demand has been satisfied.^15 The typical progression
of carbonaceous BOD removal by biomass with time, during
biological purification in a batch operation, was first shown
by Ruchhoft^16 as reproduced in Figure 6. The corresponding
metabolic reactions in terms of microorganisms to food ratio,
M/F, are shown in Figure 7. This figure shows that the food
to microorganisms ratio maintained in a biological reactor is
of considerable importance in the operation of the process.
At a low M/F ratio, microorganisms are in the log-growth
phase, characterized by excess food and maximum rate of
metabolism. However, under these conditions, the settling
characteristic of biomass is poor because of their dispersed
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