Page 73 - gas transport in porous media

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of the dimensionless Henry’s constant vary widely. For example, values for a number
2
of trace organics range from 3.7 × 10 −9 for bromacil to 1.4 × 10 for n-octane (Jury
et al., 1984).
A simplified approach to calculating the effective ordinary diffusion coefficient of
gas under unsaturated conditions including dissolved gas diffusion was developed by
Jury et al. (1983a). The model neglects advection and only considers ordinary (con-
tinuum) diffusion. The Millington and Quirk (1961) tortuosity expression is assumed
to apply to both phases based on the saturation of that particular phase. The resulting
expression for the unsaturated porous media diffusion coefficient can be written as

10/3
D ∗ = φ 4/3 S 10/3 D AB,g + S D AB, /K H
AB g
This expression uses the same approach presented by Jury et al. (1983a, 1991) but is
slightly different. The above expression is based on the gradient of the concentration
in the gas phase rather than the total concentration (gas, liquid, and solid phases). Note
that the approach ignores the coordinate system issue discussed in Section 2.2.1.1.
The above equation is a simple way to estimate the importance of dissolved gas
diffusion in the liquid phase.
Figure 5.4 shows the results of an example calculation of the unsaturated porous
medium diffusion coefficient for a porosity of 0.5, dimensionless Henry’s constant of
2
10 −4 , clear fluid gas diffusivity of 1.0×10 −5 m /s at 1 bar, and a clear fluid dissolved
2
gas diffusivity of 1.0 × 10 −9 m /s. The figure shows the clear fluid gas diffusivity
value as well as the reduction in the porous medium diffusivity due to the porous
media. Diffusion in the gas phase dominates at low liquid saturation values, while
dissolved gas diffusion in the liquid phase dominates at higher liquid saturations.
Jury et al. (1991, 1984a) show that diffusion in the gas, liquid, or both phases
may dominate depending on the dimensionless Henry’s constant and the liquid
saturation value.

10 –4
Clear fluid–Gas phase
–5
10
Diffusivity (m 2 /S) 10 –6 D AB
*

10 –7 Liquid phase Gas phase

10 –8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Liquid saturation

Figure 5.4. Unsaturated porous media diffusion coefficient