Page 279 - Soil and water contamination, 2nd edition

266 Soil and Water Contamination

zero and the gas concentrations are small (less than 5 volume percent), the gas flux due to
diffusion can be calculated using:
C( C ) z)
0
(
J D* (14.25)
z
-2
-1
where J is the gas flux across the soil–air interface [M L T ], D* = the effective diffusion
2
-3
-1
coefficient [L T ], z = soil depth [L], C(z) = the gas concentration at depth z [M L ], and
-3
C(0) = the gas concentration at the soil–air interface (z = 0) [M L ]. The flux J is positive for
the chemical moving from soil to air. If the gas concentration becomes larger than 5 volume
percent, the diffusion process itself leads to a significant apparent velocity in the gas-filled
pores. In this case the gas flux can be calculated using (Thibodeaux, 1996):
MW P T P T P (z )
J D * ln (14.26)
z R T P T ) 0 ( P
-1
where MW = the molecular weight of the chemical (g mol ), P = the total pressure (atm),
T
R = the gas constant (= 0.082058 (l ⋅ atm)/(mol ⋅ K), and T = the absolute temperature
(K), P(z) = the partial vapour pressure of the gas at depth z (atm), and P(0) = the partial
vapour pressure of the gas at the depth z (atm). The effective diffusion coefficient D* is
derived by correcting the chemical specific molecular diffusion coefficient D for effects
a
of the temperature, effective porosity of the soil, and soil water content. The porosity and
water content of the soil reduce the flow area and increase the flow path length (tortuosity ).
A useful model for describing these effects on the effective gas diffusion coefficient is (see
Thibodeaux, 1996):
n 10 3 /
D* 2 D a (14.27)
n
where n = the total soil porosity [-] and θ = the volumetric soil water content [-]. Note that
n – θ represents the volumetric air content of the soil. This empirical Equation (14.27) does
not have calibration constants and gives only a rough estimate (accurate within a factor
of about 5). One use of the vapour transport models for gas exchange across the soil–air
interface (Equations 14.25 and 14.26) is for estimating volatile gas emissions from landfills.
As mentioned before, the concentration of anthropogenic chemicals in the free atmosphere is
approximately zero, so the flux can be estimated using the chemical concentration in the soil
air at a given depth, the chemical specific diffusion coefficient (and molecular weight in some
cases), and the porosity and volumetric water content of the soil.

Example 14.3 Gas exchange across the soil–air interface.
The soil vapour concentration of tetrachloroethene (perchloroethylene or PCE ) at 5 m
3
below the soil surface is 150 mg m . Given a soil porosity of 0.30 and a volumetric
soil water content of 0.12, estimate the PCE flux across the soil–air interface due to
diffusion. The molecular weight of PCE is 165.83 and its diffusion coefficient in air is
-2
2 -1
7.2·10 cm s .
Solution
The effective gas diffusion coefficient in soil can be estimated using Equation (14.27):

. 0 ( 30 . 0 12 ) 10 3 /
2
-1
-7
2 -1
3
2
2
D * 2 . 7 10 . 0 037 2 . 7 10 7 . 2 10 cm s = 2.7·10 m s
. 0 30 2

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Soil and Water.indd 278 10/1/2013 6:45:20 PM