Page 125 - Materials Chemistry, Second Edition

108 Practical Design Calculations for Groundwater and Soil Remediation

where D is the free-air diffusion coefficient, G is the COC concentration in
the gas phase, ϕ is the air-filled porosity, and ξ is the air-phase tortuosity
a
a
factor. The ξ term accounts for the diffusion taking place within a porous
a
medium rather than in an open air space. It can be estimated from empirical
equations such as the Millington-Quirk equation [9]:
a φ 10/3
a ξ= 2 (3.40)
t φ

where ϕ is the total porosity, which is the sum of the air-filled porosity and
t
the volumetric water content (ϕ = ϕ + ϕ ). The air-phase tortuosity factor
t
w
a
varies from zero, when the entire pore space is occupied by water (saturated
condition), to about 0.8, when the porosity is high and the medium is dry.
The values of free-air diffusion coefficients for selected compounds can
be found in Table 2.5. The free-air diffusion coefficient is generally 10,000
times higher than that in a dilute aqueous solution. The diffusion coefficient
can also be estimated from the diffusion coefficient of another compound
of similar species and their molecular weights by the following relationship
(same as that for liquid in Equation 3.27):

= (3.41)
D 1 MW 2
D 2 MW 1

The diffusion coefficient is inversely proportional to the square root of its
molecular weight. The heavier the compound, the harder it is for it to diffuse
through the air. Temperature can have an influence on the diffusion coef-
ficient. The diffusion coefficient increases with temperature, and the follow-
ing relationship applies:

D @ T 1 =  T 1  m (3.42)
0
D @ T 2   T 2  
0

where T is the temperature in Kelvin. Theoretically, the exponent, m, should
be 1.5; however, experimental data indicate that it ranges from 1.75 to 2.0.

Example 3.24: Estimate the Air-Phase Tortuosity Factor
A subsurface soil is relatively sandy and has a porosity of 0.45. Estimate its
air-phase tortuosity factor:

1. When the volumetric water content is 0.3
2. When the volumetric water content is 0.05.