Environmental Engineering Reference
In-Depth Information
Reaeration and dissolved oxygen deficit—
A first-order process also is used to describe the reduction of
DO deficit,
D
x
, along a flowing stream. The DO deficit is the difference between the saturated DO
concentration,
C
s
, and the actual DO concentration at point
x
,
C
x
, or at travel time point,
C
t
. The saturation
concentration of DO is a function of temperature, salinity, and barometric pressure. The effects of chlorides
usually become significant only in estuarine and oceanic systems, whereas in freshwater systems, DO
saturation is primarily dependent on water temperature (Thomann, 1972, p. 101). This dependence on
temperature is given with sufficient accuracy by the following empirical nonlinear equation:
C
14.652
0.41022
T
0.007991
T
2
0.000077774
T
3
(9.4)
s
where
T
is water temperature in degrees Celsius.
The reaeration and deoxygenation processes are coupled such that the deoxygenation process seeks to
increase the DO deficit while the reaeration process seeks to decrease it. The resulting equation for the
DO deficit derived by Streeter and Phelps (1925) is
LK
D
0
d
e
K t
e
K t
D
e
K t
(9.5)
d
a
a
t
0
KK
a
d
where
K
a
= the reaeration-rate coefficient in 1/day, and
D
0
= the initial dissolved oxygen deficit at
x
= 0/
t
= 0, in milligrams per liter.
The DO concentration at travel time point, t, may be computed as follows:
(9.6)
If the result of the calculation from Eq. (9.6) yields a negative DO concentration, it should be reported as
zero because concentration values cannot be less than zero.
Equation (9.5) is applied to a reach of the river that has a single upstream inflow representing either
the upstream flow of the main channel or a weighted average of the main channel flow and constituent
concentrations and those of a single point source input (tributary stream or wastewater effluent). If several
point sources are close together, they can be aggregated into a single point source. When moving downstream
in the computations, when a new point source input is reached, a new mass balance must be computed to
determine
L
0
and
D
0
for the new reach downstream from the new point source and Eqs. 9.2 and 9.5 are
applied to the new reach. This is repeated until the end of river being studied is reached. A reach should
be homogeneous in its physical conditions including channel shape, bottom composition, slope, and so on.
New reaches can be defined because of changes in physical conditions of the river, and the downstream
concentrations for the upstream reach become
L
0
and
D
0
for the downstream reach.
Several alternative formulations for the DO deficit are available in the literature. One of the most
useful relates the DO deficit, to the self-purification ratio, f, as follows:
CCD
t
s
t
ª
º
§
·
L
D
0
Kt
(
f
)
Kt
0
D
e
1e
1(
f
)
(9.7)
«
¨
¸
»
d
d
t
f
1
L
«
»
©
¹
¬
¼
0
where
. The minimum point in the oxygen sag curve (see Fig. 9.2) can be determined by
setting the derivative of the DO deficit with respect to time equal to zero, i.e.
f
KK
/
a
d
d
D
t
0
d
and solving for the critical time,
t
C
. Doing this the following equation is obtained:
ª
§
·
º
1
D
t
ln
f
1
(
f
1)
0
(9.8)
«
»
¨
¸
C
(
f
)
K
L
«
»
©
¹
¬
¼
d
0
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