Environmental Engineering Reference
In-Depth Information
An error of 13% incurred by neglecting nitrification
is quite significant, and this result indicates that
nitrification is a significant process and should not
be neglected.
ammonium and nitrite, respectively (dimensionless,
go gn −1 ), and k a is the aeration rate constant (T −1 ).
Based on stoichiometric considerations, r oa and r oi
can be estimated as 3.43 and 1.14 go gn −1 , respectively.
For the initial conditions that c o = c o 0 and c a = c ao at
t = 0, the sequential solution of Equations (4.86-4.89)
gives
Applying the nBoD model of nitrification and
assuming that the temporal evolution of nitrification in
a river is similar to the temporal evolution of carbona-
ceous oxygen demand neglects the impact of cofactors
that make nitrification a more delayed process. Specifi-
cally, nitrification requires adequate numbers of nitrify-
ing bacteria, is sensitive to pH, and requires oxygen
levels greater than 1-2 mg/L for Do not to be an inhib-
iting factor.
−
k t
oa
(4.91)
c
=
c e
o
o
0
k c
k
(
)
oa o
0
c
=
c e
−
k t
+
e
−
k t
−
e
−
k t
(4.92)
ai
oa
ai
a
ao
−
k
ai
oa
k c
k
Species Model. A shortcoming of the above nBoD
approach is that it does not account for the time lags
required for oxidizing organic nitrogen to ammonium,
ammonium to nitrite, and nitrite to nitrate, all of which
are affected by the predominant species of nitrogen in
the stream. Also, the influence of pH, oxygen levels,
and other cofactors on the transformation rates are
not taken into account. An alternative, and still rela-
tively simple, model is to consider the concentration of
the nitrogen species separately, which gives (Chapra,
1997)
(
)
ai a
0
c
=
e
−
k t
−
e
−
k t
ai
in
i
−
k
in
ai
(4.93)
k k c
k
e
−
k t
−
e
−
k
t
e
−
k t
−
−
e
−
k t
oa
in
ai
in
ai oa o
0
+
−
−
k
k
−
k
k
k
ai
oa
in
oa
in
ai
k c
k
(
)
oa o
0
c
=
c
+
c
−
c e
−
k t
−
c e
−
k t
−
e
−
k t
−
e
−
k t
oa
ai
oa
ai
n
o
0
a
0
o
0
a
0
−
k
ai
oa
k c
k
(
)
ai a
0
−
e
−
k t
−
e
−
k t
ai
in
−
k
in
ai
k k c
k
e
−
k t
−
e
−
k
t
e
−
k t
−
−
e
−
k t
oa
in
ai
in
ai oa o
0
−
−
−
k
k
−
k
k
k
dc
dt
ai
oa
in
oa
in
ai
o
(4.86)
= −
k c
oa o
(4.94)
dc
dt
a
=
k c
−
k c
(4.87)
The sequential nature of Equations (4.91) to (4.94)
tends to spread out the impact on Do. Using the results
given by Equations (4.91-4.94), the oxygen deficit can
then be calculated by substituting Equations (4.91-4.94)
into Equation (4.90) and solving, which yields the
oxygen deficit associated with nitrification as (Chapra,
1997)
oa o
ai a
dc
dt
i
=
k c
−
k c
(4.88)
ai a
in i
dc
dt
n
(4.89)
=
k c
in i
where c is the concentration of the species indicated by
the subscript (ML −3 ), the subscripts o , a , i , and n denote
organic, ammonium, nitrite, and nitrate, respectively, t is
the travel time in the stream (T), and k is the rate con-
stant for transformation between the species indicated
by the subscripts (T −1 ). The oxygen deficit balance is
given by
C
(
) +
ai
[
(
) −
(
)
]
D t D
N ( )
=
exp
−
k t
exp
−
k t
exp
−
k t
0
a
ai
a
k
−
k
a
ai
C
oa
[
(
) −
(
)
]
+
exp
−
k t
exp
−
k t
oa
a
k
−
k
a
o
a
C
in
[
(
) −
(
)
]
+
exp
−
k t
exp
−
k t
in
a
k
−
k
a
in
dD
dt
=
r k c
+
r k c
−
k D
(4.90)
oa
ai a
oi
in i
a
(4.95)
where D is the oxygen deficit (ML −3 ), r oa and r oi are the
amount of oxygen consumed due to nitrification of
where t is the travel time from the source, and C ai , C oa ,
and C in are defined as
 
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