Page 272 - Soil and water contamination, 2nd edition

Gas exchange 259

-3
-3
the water–air interface [M L ], C = the chemical concentration in water [M L ], and C =
w sw
-3
the chemical concentration in water at the water–air interface [M L ]. The thickness of the
gas and water films cannot be measured directly, so the gas exchange coefficients should be
determined empirically. Subsequently, the thickness of the films can be estimated from the
gas exchange coefficient and independent knowledge of the molecular diffusion coefficients.
Typical vales for δ range between 20 and 200 μm and typical values for δ are in the order of
w a
1 cm (Hemond and Fechner-Levy, 2000).
If Henry’s law applies exactly at the water–air interface, then:
k a J H C sw C a K' (14.8)
From Equation (14.5), it appears that:
J
C C (14.9)
sw w
k
w
By combining the Equations (14.8) and (14.9), we can solve for the mass flux J across the
water–air interface in terms of the bulk phase concentrations, Henry’s law constant , and the
gas exchange coefficients for water and air:
1 C C
J C w a k L C w a k L w C eq C (14.10)
/ 1 k / 1 k K' K' K'
w H a H H
-1
where k = the overall gas exchange coefficient [L T ], C = the equilibrium concentration of
L eq
-3
the chemical in solution [M L ]. The equilibrium concentration C is an important term if
eq
the chemical under consideration is a constituent of the atmosphere, like oxygen , nitrogen ,
or carbon dioxide . In the case of anthropogenic contaminants, this term often approximates
zero.
For the vertically averaged concentration in a surface water body, which is influenced by
gas exchange between the surface water and the atmosphere, we may formulate the following
mass balance :
dC J k C
w
L C w a (14.11)
dt H H K'
H
where H = the water depth [L]. Note the similarities between Equation (14.11) and
Equations (13.15) and (13.25). Analogous to electrical resistance, the reciprocal of the overall
gas exchange coefficient k represents the overall resistance against gas exchange. This overall

L
resistance consists of two components (see Equation 14.10):
1 1 1 (14.12)

k k K' k
L w H a
The first term of the right-hand side of the equation represents the liquid phase resistance

of the water film, the second term represents the gas phase resistance of the air film. If the
gas is soluble in water, then the dimensionless Henry’s law constant K’ is small and the gas

H
exchange is controlled by the gas phase resistance. This is the case if K’ is much smaller
H
than 0.01. In this case, the resistance of the water film may be ignored. Examples are H O
2
evaporation , SO , NH , H O, most pesticides , PAHs , and long chain organic molecules. If
2 3 2
the gas is hardly soluble in water (e.g. O , N , most volatile organic solvents), then K’ is
2 2 H
large and the water film resistance controls the transfer (Schnoor, 1996). This is the case if
K’ is much greater than 0.01. If the value of K’ is in the order of 0.01, both resistances
H H

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Soil and Water.indd 271
Soil and Water.indd 271 10/1/2013 6:45:16 PM