Page 277 - Soil and water contamination, 2nd edition

264 Soil and Water Contamination

the appropriate molecular diffusion coefficient. As mentioned above, the gas exchange
coefficient is proportional to the molecular diffusion coefficient or the square root of the
molecular diffusion coefficient, depending on the gas exchange model adopted (thin film
model versus surface renewal model , respectively). The molecular diffusion coefficient in
turn is approximately proportional to the square root of the molecular weight (Hemond and
Fechner-Levy, 2000). This implies that:

D MW
k ( A) k ( O ) w, A k ( O ) O 2 (14.23)
L L 2 L 2
D MW
w, O 2 A
-1
where k (A) = the gas exchange coefficient for gas A [L T ], k (O ) = the oxygen exchange
L L 2
-1
-1
2
coefficient [L T ], D = the molecular diffusion coefficient of gas A in water [L T ], D =
w,A w,O2
-1
2
the molecular diffusion coefficient of oxygen in water [L T ], MW = molecular weight of
O2
-1
-1
oxygen (= 32 g mol ), MW = molecular weight of gas A (g mol ), and β = an exponent [-]
A
between 0.5 (surface renewal model ) and 1.0 (thin film model ). Usually a value of 0.7 is used
for β.
Example 14.3 Gas exchange controlled on the water side
Estimate the gas exchange coefficient at 20 °C for carbon tetrachloride (CCl ) for a 3.5 m
4
-1
deep river with an average flow velocity of 73 cm s .
Solution
First, estimate the gas exchange coefficient for oxygen using the Churchill et al.
relationship (Equation 14.16):
k L . 5 05 . 0 73 . 0 97 5 . 3 . 0 67 . 1 61 m d -1
Then, the gas exchange coefficient for carbon tetrachloride can be estimated using
Equation (14.23). The molecular weight of carbon tetrachloride is 154 and that of
oxygen is 32 (see Table 14.1). Thus,
7 . 0
32
k L . 1 61 . 1 61 . 0 577 . 0 93 m d -1
154

14.5 GAS EXCHANGE CONTROLLED ON THE AIR SIDE

If the gas exchange is controlled on the air side (K’ << 0.01), the gas exchange coefficient
H
can be estimated using (Lijklema, 1991):
0. 5
D A , a
k L ( A ) 1. 607W 10
D H , a 2 O (14.24)
-1
where k (A) = the gas exchange coefficient for gas A in m d , W = the wind speed at
L 10
-1
10 m above the water surface (m s ), D = the molecular diffusion coefficient of gas A in
a,A
2
-1
2
-1
air [L T ], and D a,H2O = the molecular diffusion coefficient of water vapour in air [L T ]
-1
2
-5
(= 2.4·10 m s at 20 °C). Other empirical expressions for gas exchange controlled on the
air side are given by Schwarzenbach et al. (1993), Schnoor (1996), and Thibodeaux (1996).
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