WATER QUALITY - Water Quality Engineering in Natural Systems - page 13

(CBOD), illustrated in Figure 2.4b, can be approxi-
mated by the following first-order model:

ultimate carbonaceous BOD

NBOD

BOD u

dL
dt

5-day BOD

= − k L (2.9)

1

nitrification
begins

BOD 5 CBOD

where L is the CBOD (Ml −3 ) remaining at time t (T)
and k 1 is a rate constant (T −1 ). If L 0 is the CBOD remain-
ing at time t = 0, equal to the ultimate CBOD , Equation
(2.9) can be solved to yield

0 5

Time (days)

(a)

L L e k t =

−

1

BOD u (2.10)

0

L

Since the CBOD at time t is related to L by

L 0

CBOD = L L

0

(2.11)

0

Time (days)
(b)

the CBOD as a function of time is given by combining
Equations (2.10) and (2.11) to yield

Figure 2.4. (a) Typical BOD curve; (b) carbonaceous BOD
remaining versus time.

CBOD = L ( 1 − e k t

−

) (2.12)

1

0

The CBOD is exerted by heterotrophic organisms
that derive their energy for oxidation from an
organic carbon substrate, and NBOD is exerted by nitri-
fying bacteria that oxidize nitrogenous compounds in
the wastewater. The carbonaceous demand is usually
exerted first, with a lag in the growth of nitrifying bac-
teria. Normally, nitrogenous oxidation of raw sewage is
only important after 8-10 days of oxidation in the pres-
ence of excess oxygen; for treated sewage, however,
nitrification may be important after 1-2 days, due to the
large number of nitrifying bacteria typically found in
treated sewage (Tebbutt, 1998).
BOD tests are conducted using 300-ml glass bottles
in which a small sample of polluted water is mixed with
(clean) oxygen-saturated water containing a phosphate
buffer and inorganic nutrients. The mixture is incubated
in a stoppered bottle in the dark at 20°C, and the dis-
solved oxygen in the mixture is measured as a function
of time, usually for a minimum of 5 days. Since the
sample is incubated in the dark, there is no possibility
for photosynthesis to occur, so the oxygen concentra-
tion must either remain constant or decline. Since both
biological and chemical processes may cause a decline
in oxygen concentration, BOD should be understood to
refer to biochemical oxygen demand rather that simply
biological oxygen demand. If a problem with nitrifica-
tion is suspected in the BOD test, a specific nitrification
inhibitor can be added to the water sample so that only
the carbonaceous BOD is measured.
The cumulative oxygen demand of the polluted water
after 5 days is called the 5-day BOD , and is usually
written as BOD 5 . The kinetics of carbonaceous BOD

The ultimate CBOD, L 0 , can be expressed in terms of
the 5-day CBOD, CBOD 5 , as

CBOD

5

(2.13)

L =

0

− 5 k

1 − e

1

where both CBOD 5 and k 1 are derived from the BOD
test data. The value of k 1 depends on a number of factors,
such as the nature of the composition of the waste, the
ability of available microorganisms to degrade the waste,
and the temperature. For secondary-treated municipal
wastewaters, k 1 is typically in the range 0.1-0.3 d −1 at
20°C, which gives a L 0 /CBOD 5 ratio of approximately
1.6. Schnoor, (1996) suggests a value of 1.47 for L 0 /
CBOD 5 in municipal wastewater, and data reported by
lung (2001) indicate that 2.8 may be more typical for the
L 0 /CBOD 5 ratio. On average, biological oxidation is
complete in about 60-70 days for most domestic waste-
waters (lung, 2001), although little additional oxygen
depletion occurs after about 20 days (Vesilind and
Morgan, 2004). Municipal wastewater discharges with a
CBOD 5 less than or equal to 30 mg/l are typically con-
sidered acceptable, and it is recommended that commu-
nities discharging treated domestic wastewater into
lakes or pristine streams reduce their CBOD 5 to less
than 10 mg/l to protect the indigenous aquatic life
(Serrano, 1997).
It is interesting to note that the 5 days used in the
BOD measure was originally chosen as the standard
duration for expressing BOD because the BOD test
was devised by sanitary engineers in England where the