RIVERS AND STREAMS - Water Quality Engineering in Natural Systems - page 102

with time. In this regard, two alternative approaches
have been used in practice. In the first approach, called
the NBOD model , the nitrification process is assumed
to be mathematically similar to the biochemical oxygen
demand process for carbonaceous material. Using this
approach, the ultimate nitrogenous BoD (nBoD) is
substituted for the ultimate carbonaceous BoD, a
decay coefficient for nitrification is substituted for the
decay coefficient for carbonaceous BoD, and the
Streeter-Phelps equation is then used with these sub-
stituted parameters to simulate the oxygen deficit due
to nitrification. In the second approach, called the
species model , the reaction rates of the nitrogen species
participating in the nitrification process and their con-
sumption of oxygen are described separately, and this
system of equations is combined to predict the overall
consumption of oxygen due to nitrification. of these
two approaches, the latter approach is more represen-
tative of the actual nitrification process and better
describes the temporal variation of oxygen demand,
while the former approach is still commonly used and
is easier to deal with mathematically, but less realistic
and not recommended. In both approaches, the oxygen
deficit caused by nitrification, Δ D n ( x ), is added to the
(Streeter-Phelps) oxygen deficit caused by carbona-
ceous oxygen demand, D SP ( x ), to yield the total oxygen
deficit, D ( x ), such that

(Ruane and Krenkel, 1975), where values of k n of 0.1-
0.5 d −1 are typical of deeper waters, and values of
k n > 1 d −1 are typical of shallower waters (Chapra,
1997). Temperature affects nitrification differently than
other processes, and the thermal factor for nitrification,
θ , is around 1.1.

EXAMPLE 4.13

Treated domestic wastewater is discharged into a river
with an average stream velocity of 30 cm/s and an esti-
mated reaeration coefficient of 0.5 d −1 . The TKn of a
mixed wastewater discharge is 0.8 mg/L, and the nitrifi-
cation rate constant is estimated to be 0.6 d −1 . (a) Esti-
mate the oxygen deficit due to nitrification 15 km
downstream of the wastewater discharge. (b) If the the-
oretical oxygen deficit neglecting nitrification is
6.2 mg/L, what is the percent error incurred by neglect-
ing nitrification?

Solution

(a) From the data given, V = 30 cm/s = 0.30 m/s =
25,920 m/d, k a = 0.5 d −1 , TKn = 0.8 mg/L, and k n =
0.6 d −1 . The ultimate nitrogenous BoD, L 0n , is given
by Equation (4.84) as

L 0N = 4.33 × TKN = 4.33 0.8 × = 3.5 mg/L (4.85)

D x D x ( ) = ( ) + ∆ D x ( ) (4.82)

SP N

Substituting into Equation (4.83) yields the oxygen
deficit due to nitrification at x = 15 km = 15,000 m
as

Both the nBoD model and the species model for deter-
mining Δ D N ( x ) are described below.

NBOD Model. In this model, the oxygen demand is
assumed to follow the same process as for the biochemi-
cal oxidation of carbonaceous material, and hence
Δ D N ( x ) is given by

k L
k

k x
V

k x
V

N 0 N N a

∆ D = exp −

−

exp −

N

− k

a N

(0.6)(3.5)
0.5 0.6

(0.6)(15 000)
25 920

,

= exp −

− ,

∆ D x
k L
k

( )

N

k x
V

k x
V

−

(0.5)(15 000)
25

,
,920

N 0N N a

exp − exp − k ≠ k

− exp −

a N

− k

a N

=

x
V

k x
V

a

k L exp − k = k .

= 0.9 mg/L

N 0N a N

(4.83)

(b) The incremental oxygen deficit due to nitrification
is 0.9 mg/L. Since the theoretical oxygen deficit
obtained by neglecting nitrification is 6.2 mg/L,
the actual oxygen deficit is 6.2 mg/L + 0.9 mg/L =
7.1 mg/L, and the error incurred by neglecting nitri-
fication is given by

where k n is the first-order nitrification rate (d −1 ), and L 0n
is the ultimate nitrogenous BoD (mg/L), which can be
taken as

L 0 = 4.33 × TKN (4.84)

N

0.9
7.1

The magnitude of the nitrification reaction rate con-
stant, k n , has been reported in the range of 0.1-15.8 d −1

error = × 100 = 13%