Page 276 - Soil and water contamination, 2nd edition

Gas exchange 263

per °C. Usually a value of 2.4 percent per °C is adopted (Thomann and Mueller, 1987)
(compare Equation 13.20):

k (T ) k ( 20o ) . 1 ( 024 ) T 20 (14.22)
L L
where T = the water temperature (°C).
Example 14.2 Reaeration

In a small lake at an altitude of 100 m above sea level, the dissolved oxygen concentration
-1
is 4 mg l , the water temperature is 13 °C, and the wind speed 10 m above the water
-1
surface is 7.5 m s . Estimate the oxygen flux density during a rain shower with an
-1
intensity of 10 mm h .
Solution
First, calculate the oxygen exchange coefficient at 20 °C due to wind. As the wind speed
-1
at 10 m is greater than 1.82 m s , use Equation (14.17):
k L ,W . 0 0864 . 8 5 . 7 5 . 0 . 3 67 5 . 7 . 0 43 5 . 7 2 43 . 1 706 m d -1

Second, calculate the oxygen exchange coefficient at 20 °C due to precipitation, using
Equations (14.19) and (14.20):
B 10 6 . 0 103 100 2390 10 . 1 26 . 0 0437
k L ,P 24 . 45 . 0 0437 . 1 068 m d -1

Thus, wind contributes more to the reaeration than precipitation. The resulting oxygen
exchange coefficient at 20 °C is estimated using Equation (14.21):

k . 1 706 . 1 068 . 0 047 . 1 706 . 1 068 . 2 689 m d -1
, L 20oC
The oxygen exchange coefficient at 13 °C is calculated using Equation (14.22):

k . 2 689 . 1 024 7 . 2 277 m d -1
, L 15oC
Then estimate the saturated dissolved oxygen concentration at 13 °C, using Equation
(14.14):

3
-3
-1
DO sat 14 . 652 . 0 41022 13 . 0 007991 13 2 . 0 0000777774 13 10 5 . mg l (=g m )
Finally, determine the oxygen flux density across the air–water interface (see Equation
14.10):
-2
-1
-1
-2
J k L (DO DO sat ) . 2 277 7 ( 10 ) 5 . . 7 97 g m d = 0.092 mg m s .
14.4 GAS EXCHANGE CONTROLLED ON THE WATER SIDE
The empirical relationships presented above can, in principle, also be used for gases
other than oxygen, provided that the gas exchange is controlled on the water side (K’ >>
H
0.01) and the gas is non-reactive. The gas exchange coefficient k must be corrected for

L

10/1/2013 6:45:18 PM
Soil and Water.indd 275
Soil and Water.indd 275 10/1/2013 6:45:18 PM