Page 275 - Soil and water contamination, 2nd edition

262 Soil and Water Contamination

derived based on data from natural streams (see Jha et al., 2001). Since oxygen concentration
is one of the most important ecological parameters in surface water, most relationships focus
on oxygen transfer (reaeration ). A commonly used relationship for estimation of the gas
exchange coefficient for oxygen is the Churchill et al. (1962) relationship:

k . 5 05 u . 0 97 H . 0 67 (14.16)
L
-1
-1
with the gas exchange coefficient in m d , the flow velocity u in m s , and the water
depth H in m. This Equation (14.16) is valid in the range 0.6 < H < 3.35 m and 0.6 < u <
-1
1.52 m s . In lakes , the turbulence is mainly induced by wind. The mechanisms that drive
the reaeration are the shear stress at the water surface, wave formation, drop formation,
and wave breaking. The latter two mechanisms only occur at high wind speeds. Banks
(1975) derived the following relationship for the oxygen exchange coefficient from field
studies:
k . 0 0864 . 8 5 . 0 . 3 67 W . 0 43W 2 43W (14.17)
L ,W 10 10 10
-1
where k = the oxygen exchange coefficient due to wind (m d ), and W is the wind speed
L,W 10
-1
at 10 m above the water surface (m s ). According to this equation, the reaeration of the
lake water stops if the wind speed is zero. Ruys (1981) disputed this and replaced Banks’s
-1
-1
equation in the range from W = 0 m s to W = 1.82 m s by:
10 10
k L ,W . 0 37 . 0 09W 10 (14.18)
-1
which represents the tangent of Equation (14.17) at W = 1.82 m s . So, this equation
10
-1
predicts a gas exchange coefficient for oxygen of K = 0.37 m d at zero wind speed.
L
Banks and Herrera (1977) demonstrated that rain can also contribute considerably to
oxygen exchange in a lake through an increase of turbulence and a large dissolved oxygen
concentration in the raindrops. They related the gas exchange coefficient to the energy that a
rain shower adds to the lake water:
B 10 6 . 0 103 Z 2390 i . 1 26 (14.19)
k L, P 24 . 45 B (14.20)

-1
where k = the oxygen exchange coefficient due to precipitation (m d ), B = the energy
L,P
-2
added to the water body per unit time per unit area in W m , Z = the altitude of the
-1
lake surface above sea level (m) and i = the rainfall intensity in mm h . The gas exchange
coefficient for oxygen at 20 °C in a lake in the case of both wind and rain can be estimated
by:
k k k . 0 047 k k (14.21)
L L, W L, P L, W L, P
Besides flow velocity, wind speed, and rainfall intensity, the gas exchange coefficient
is also affected by water temperature and the presence of contaminants. Contaminants in
the water generally cause a decrease of the gas exchange coefficient, particularly if surface-
active substances (e.g. detergents), or floating film-forming substances (e.g. oil) are involved.
However, at present we lack the knowledge to be able to quantify these effects for a general
situation. A rise in the water temperature results in an increase of the molecular diffusion
coefficient and a decrease of the stagnant film thickness at the water surface. This in turn
results in an increase in the gas exchange coefficient of between 0.5 percent and 3.0 percent

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