RIVERS AND STREAMS - Water Quality Engineering in Natural Systems - page 101

the BoD is specified as a second-order process (with
two rate constants) rather than a first-order process
(with one rate constant), appropriate expressions for
evaluating the oxygen sag can be found in Mamedov
(2006) and Adrian and Sanders (1998). Alternatively,
when the BoD is specified as a less-than first-order
process (such as wastewaters with high sugar content),
appropriate expressions for evaluating the oxygen sag
can be found in Roider et al. (2008).

8

7 mg/L

7

6

5

4

3

2

anoxic conditions

1

4.4.4 Other Considerations

0

0 5 10 15 20 25 30 35 40

Aside from assuming complete transverse mixing and
neglecting longitudinal dispersion, several additional
assumptions are implicit in the Streeter-Phelps model,
the most important of which are (1) that mixing occurs
rapidly over the cross section of the channel, and (2)
that biochemical oxygen demand and reaeration are the
only significant oxygen sources and sinks. If mixing does
not occur rapidly, as measured by the length scale for
cross-sectional mixing (Eq. 4.17), significant oxygen
depletion may occur prior to cross-sectional mixing, and
Equation (4.22) will not give an accurate measure of the
initial concentration for the one-dimensional oxygen
sag model. Under these circumstances, a more detailed
two- or three-dimensional numerical model of cross-
sectional mixing is necessary.

distance from source (km)

Figure 4.7. variation of dissolved oxygen downstream of
source.

When using the Streeter-Phelps Do sag curve to
determine the adequacy of wastewater treatment prior
to discharge, it is important to use the river conditions
that will result in the least Do concentration. Usually,
these conditions occur in the late summer when river
flows are low and temperatures are high. A frequently
used criterion is the 10-year 7-day low low, which is
equal to the conditions in which the 7-day average low
flow has a return period of 10 years. This is typically
called the 7 Q 10 flow. In extreme circumstances, rivers
can become iced over in the winter, reducing surface
aeration to zero. In such cases, breaking the ice cover to
expose the water surface or injecting oxygen into the
effluent diffuser might be necessary to maintain ade-
quate Do levels in the river.
The Streeter-Phelps model, Equation (4.71), assumes
that the river is mixed completely and uniformly in the
transverse directions (i.e., over the width and the depth),
and the longitudinal dispersive flux (of Do) is negligible
compared with the advective flux. The relative impor-
tance of advection to dispersion is measured by the
Péclet number, Pe (dimensionless), which is defined as

4.4.4.1 Nitrification. In some streams, nitrification
exerts a significant demand on Do and so the ultimate
BoD, L 0 , in the Streeter-Phelps equation (Eq. 4.71),
must include both carbonaceous and nitrogenous
demand. In these cases, it is sometimes assumed that L 0
(mg/L) can be calculated as

L a = ( CBOD ) + b ( TKN ) (4.81)

0 5

where CBoD 5 is the 5-day carbonaceous BoD (mg/L),
TKn is the total Kjeldahl nitrogen (= organic nitro-
gen + ammonia) (mg/L), and a and b are empirical con-
stants. TKn is a measure of total oxidizable nitrogen,
and typical values for a and b are 1.2 and 4.0, respec-
tively. In some cases, the contribution of nitrogenous
BoD to the ultimate BoD is taken as 4.33 TKn
(Krenkel and novotny, 1980; novotny, 2003) or 4.57
TKn (Chapra, 1997) rather than 4.0 TKn; therefore,
a midrange value of 4.33 TKn for the ultimate
nitrogenous BoD might be appropriate. Under usual
circumstances, the ultimate carbonaceous BoD is of
approximately the same magnitude as the ultimate
nitrogenous BoD.
In order to predict the oxygen consumption in a
stream due to nitrification, it is necessary to describe
the variation of oxygen demand (due to nitrification)

= VL
K

Pe

(4.80)

L

where V is the stream velocity (LT −1 ), L is the charac-
teristic length scale (L), and K L is the longitudinal dis-
persion coefficient (L2T−1). 2 T −1 ). The assumption that
longitudinal dispersion can be neglected is justified
when Pe > 10, and dispersion cannot be neglected when
Pe < 1. For intermediate values of Pe, both advection
and dispersion must be taken into account. Most river-
ine flows are advection dominated, and Pe >> 10 (Rubin
and Atkinson, 2001).
For wastewaters other than domestic sewage, BoD
reaction rates are not always first order. In cases where