RIVERS AND STREAMS - Water Quality Engineering in Natural Systems - page 95

(de)oxygenation, S 1 (ML −3 T −1 ), is commonly described
by a first-order reaction of the form

nesota, discharged primary effluent into the Upper
Mississippi River, the in-stream value of k d was 0.35 d −1 ,
when the plant was upgraded to secondary treatment,
k d decreased to 0.25 d −1 , and further upgrading all the
way up to installing a nitrification process dropped the
value of k d to 0.073 d −1 .
Aside from the reduction of BoD by first-order
decay of dissolved organics, BoD reduction can also
occur as a result of settling of suspended sediments
when a portion of the BoD is associated with the sus-
pended material. In such cases, the total BoD removal
rate, k r , can be expressed in the form

S

1 = −

k L
d

(4.56)

where k d is a reaction rate constant (T −1 ), and L is the
BoD remaining (ML −3 ). The reaction rate constant, k d ,
depends primarily on the nature of the waste, the ability
of the indigenous organisms to use the waste, and the
temperature; typical values of k d at 20°C are shown in
Table 4.4. For temperatures other than 20°C, the values
of k d given in Table 4.4 must be adjusted, and the fol-
lowing adjustment is generally used:

k = k + k (4.58)

r d s

k = k θ

T − 20

(4.57)

d d

T 20

where k d is the reaction rate constant associated with
the dissolved BoD, and k s is the rate constant associated
with sedimentation. The rate constant k d can be approxi-
mated by the rate constant derived from BoD bottle
tests; however, this relation is only approximate since
the types and distribution of consuming microorganisms
in rivers can be different than in bottles. For example,
in rivers microorganisms attached to the bottom can be
sufficiently effective in removing BoD that the rate
constant in the river becomes a function of the depth of
flow (Bowie et al., 1985).
There are some indications that small-scale velocity
fluctuations have an impact on BoD decay rates that
are usually estimated under stagnant laboratory condi-
tions (Al-Homoud et al., 2007). However, such effects
are generally neglected in practice. Wastewaters other
than domestic sewage do not all follow first-order reac-
tions for the rate of (de)oxygenation. For example,
wastewaters with high sugar content can be expected to
have BoD reaction orders less than one (Roider et al.,
2008). The most notable difference between wastewa-
ters with first-order reaction rates and those with less-
than first-order reaction rates is that in the first-order
case, the oxygen demand asymptotically approaches
zero at large times, while in the less-than first-order case,
the oxygen demand is complete at a finite time.

where T is the temperature of the stream (°C), k d T and
k d 20 are the values of k d at temperatures T and 20°C,
respectively, and θ is a dimensionless temperature coef-
ficient. There are variations in the value for θ used in
practice, with Thomann and Mueller (1987) recom-
mending θ = 1.04, Tchobanoglous and Schroeder (1985),
Chapra (1997), and novotny (2003) recommending
1.047, and Schroepfer et al. (1964) recommending
θ = 1.135 for typical domestic wastewater at tempera-
tures in the range of 4-20°C, and θ = 1.056 for tempera-
tures in the range of 20-30°C. The latter values are
widely accepted in practice (Mihelcic, 1999), and the
fact that θ > 1 in Equation (4.57) means that BoD reac-
tions occur more rapidly at higher temperatures. Tem-
perature conditions selected for waste assimilative
capacity evaluation should correspond to the average
temperature of the warmest month of the year (novotny,
2003). The reaction rate constant, k d , sometimes called
the in-stream deoxygenation rate , is inversely propor-
tional to the level of treatment provided prior to efflu-
ent release into the river or stream, as indicated in Table
4.4. The lower rate constants for treated sewage com-
pared with raw sewage result from the fact that easily
degradable organics are more completely removed than
less readily degradable organics during wastewater
treatment. Lung (2001) reported that when the Metro-
politan Wastewater Treatment Plant in St. Paul, Min-

4.4.2 Reaeration

The rate at which oxygen is transferred from the atmo-
sphere into a stream, defined as the reaeration rate , S 2
(ML −3 T −1 ), is commonly described by an equation of the
form

TABLE 4.4. Typical Deoxygenation Rate Coefficients

Type of Water k d at 20°C (d −1 )

Untreated wastewater 0.35-0.7

Treated wastewater 0.10-0.35

S = k c ( − c ) (4.59)

2 a s

Polluted river 0.10-0.25

Unpolluted river <0.05

where k a is the reaeration constant (T −1 ), c s is the dis-
solved oxygen saturation concentration (ML −3 ), and c is
the actual concentration of Do in the stream (ML −3 ).

Sources of data : Kiely, 1997; Thomann and Mueller, 1987; Davis and
Masten (2004).