Environmental Engineering Reference
In-Depth Information
managers for the Dender thought it was suffering from the classical BOD-DO problem. However, for
navigation purposes, the river has been channelized and regulated by several hydraulic structures. Thus,
the Dender is a series of slow deep pools in which algal processes dominate DO concentrations despite
the low levels of wastewater treatment.
9.2.3.4
Dispersion Effects on BOD and DO
For the case of steady-state flow and a downstream boundary condition of equilibrium between the rate
of oxygen addition by reaeration and photosynthesis and the net rate of removal by oxidation and SOD,
O'Connor (1967) derived a relation for how much error might be involved if the effects of longitudinal
dispersion were neglected in computing the DO and BOD concentrations. He found that the ratio,
R
R
,
between the deoxygenation (or reaeration) rate considering dispersion effects and that ignoring them can
be computed as a function of reach average velocity,
V
, the longitudinal dispersion coefficient,
D
L
, and
the reaction coefficient (
K
r
=
K
d
or
K
a
as appropriate) as follows:
1/ 2
ª
º
§
V
2
·
§
V
2
·
V
2
R
2
(9.28)
«
¨
¸
¨
¸
»
R
2
K D
2
K D
2
K D
«
»
¬
©
¹
©
¹
¼
r
L
r
L
r
L
Brown and Barnwell (1987) listed the
D
L
and
V
values for a wide variety of streams throughout the U.S.
Assuming the 75
th
percentile value for
K
a
from the USGS database (Melching and Flores, 1999), Table
9.5 computes values of
R
R
for several rivers in Brown and Barnwell (1987). For four of six rivers the
error is 1% or less, for the fifth river it is less than 4%, and even for the mighty Missouri River the error only
is 7.6%. Further, these errors result for a relatively high value of
K
a
(although for the South Platte River
the average
K
a
for 6 reaches in the USGS database is 12.9 d
-1
), and the errors for deoxygenation would
be far smaller because
K
d
will be far less than the
K
a
value used. In general, for steady-state conditions the
effect of longitudinal dispersion in natural streams on BOD and DO is negligible.
Table 9.5
The ratio,
R
R
, between the reaeration rate considering dispersion effects and the reaeration rate ignoring
t
hem for several rivers in the U.S. [Dispersion and Velocity Data from Brown and Barnwell (1987)]
River
D
L
(m
2
/s)
K
a
(d
-1
)
U
2
/2
K
a
D
L
V
(m/s)
R
R
Sacramento River
14.96
0.53
12.45
65.25
0.992
South Platte River
16.17
0.66
12.45
93.90
0.995
Missouri River
1486.
1.55
12.45
5.62
0.924
Copper Creek
19.97
0.27
12.45
12.78
0.964
Clinch River
47.01
0.80
12.45
47.07
0.990
Green-Duwamish River
6.77
0.43
12.45
93.29
0.995
9.2.4
Total Dissolved Oxygen Balance
9.2.4.1
Total DO Balance
Because the Streeter-Phelps type functional models are linear system models, the results of Eqs. (9.5),
(9.20), (9.22), (9.24), and (9.27) may be summed to determine the deficit resulting from the combined
effects of the initial DO deficit, CBOD, NBOD, a distributed source of CBOD, SOD, and photosynthesis
and respiration. Further, the effects of a point source of DO such as an in-stream aerator (see Section 9.3.9)
may be computed as follows:
W
D
e
K t
D
(9.29)
PS
Q
l
where
W
D
is the load of oxygen delivered in milligrams per second, and
Q
l
is the flow rate in liters per
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