Water Quality Management - River Dynamics and Integrated River Management - page 558

The critical deficit is computed by entering the appropriate values into Eq. (9.9) as follows:

40 mg / L e

0.5(0.573)

D

5.44 mg / L

5.52

For a minimum allowable DO concentration of 5 mg/L and a DO saturation concentration of 9.022 mg/L,
the allowable DO deficit is 4.022 mg/L. The allowable upstream CBOD concentration then can be determined
by entering the appropriate values into Eq. 9.10 yielding

^ ` 1/(5.52 1)

* *

L (4.022)(5.52) 5.52 1 ª (5.52 1)(3 / L ) º

¬ ¼

0 0

^ ` 0.2212

L

*

22.2 5.52 1 ª (13.56 / L

*

º

¬ ¼

0 0

Solving this equation by iteration yields L 0 * = 27.98 mg/L. The oxygen-sag curve for this case was also
computed and is shown in Fig. 9.2.
Determination of the deoxygenation-rate coefficient, K d —The value of K d depends on a number of
factors including the nature of the waste (some, such as simple sugars and starches, degrade easier than
others, like cellulose), the ability of the available microorganisms to degrade the wastes in question (it may
take some time for a healthy population of organisms to be able to thrive on the particular waste in the
river), and the temperature (Masters, 1991, p. 126). This relation for K d can be expressed as follows
d = f (nature of the waste, ability of organisms in the system to use the waste, temperature)
The effect of the nature of the waste is summarized in Table 9.1. The decrease in K d from raw sewage
to well-treated sewage and polluted river water probably results from differences in the ease of oxidation
of the materials present, the rate decreasing as more easily oxidized substances are used up (Fair et al.,
1971, p. 645).

Table 9.1 Typical Values for the Deoxygenation-Rate Coefficient (after Davis and Masten, 2004)

K d at 20 ć (day -1 ) Sample

Raw sewage 0.35-0.70

Well-treated sewage 0.12-0.23

Polluted river water 0.12-0.23

As shown in Table 9.1, the value of K d usually is reported for a standard temperature of 20 ć and then
adjusted to other temperatures as follows:

() () . 7 T
dT

x

( )

(9.13)
where T is the temperature of interest. However, Fair et al. (1971, p. 645) note that above 30 ć a decrease
in rate with increasing temperature is observed, probably because of thermal inactivation of the enzymes
responsible for oxidation of CBOD.
The value of K d for use in river modeling and analysis may be determined by calibration of Eq. (9.1)
or (9.2) using measured values of CBOD at several locations along the river of interest, and properly
accounting for the settling of CBOD (which is easier said than done). It is generally assumed that the
demands made on the oxygen resources of polluted waters by living organisms are the same as those
observed in the laboratory when samples are mixed with convenient amounts of synthetic dilution water
and incubated for the CBOD tests, so-called “bottle” estimates of K d . Fair et al. (1971, p. 646) reported
for large and passive streams, the correlation between ķ laboratory observations of the BOD of polluted
waters and ĸ field investigations of the reaction of such streams to pollution is usually high. Wright
and McDonnell's (1979) study of measured in-stream values of K d for 23 river systems primarily in the

K K

d 20