Page 130 - gas transport in porous media

Chapter 7: Gas-Phase Dispersion in Porous Media
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−1
), T is temperature (K), m is the solute mass
where k is Boltzmann’s constant (J·K
(M), and v rms is the root-mean-square velocity of the gas particles (L·T −1 ). Thus,
given thermal equilibrium and consequent equal kinetic energy, lower molecular
weight gases will exhibit higher average velocities relative to higher molecular weight
gases. This higher velocity translates into larger diffusion coefficients and larger
contributions to overall dispersion.
Diffusion processes often dominate transport in low permeability zones, such as
within aggregates or fine-textured lenses. In the case of volatile organic compounds
(VOCs), the occurrence of diffusion can both aid and present additional challenges to
remediation efforts. Specifically, the larger spatial distribution of the VOC caused by
diffusion may increase the probability of detecting the VOC in the subsurface, such
that a remediation plan can be implemented. Conversely, it is this same diffusion
processthatisoftenlargelyresponsibleforthetransportofVOCsinthevadose-zoneto
the water table resulting in groundwater contamination (e.g., Lupo, 1989). Moreover,
contaminant diffusion can influence the fate of contamination in a system by altering
its bioavailability. Diffusion largely governs gas-exchange between the atmosphere
and soil, including the exchange of carbon dioxide and oxygen, and atmospheric
pollutants, such as fluorocarbons (Weeks et al., 1982). Jury et al. (1991) estimate that
only 0.5%, 1%, 0.1%, and 7–9% of the overall subsurface gas exchange is induced by
temperature and barometric pressure changes, wind, and precipitation, respectively.
Thus, they conclude that diffusion is the primary gas transport mechanism in soil
systems. Little et al. (1992) review the critical role diffusion plays in transporting
subsurface VOCs into homes and buildings.

7.2.2 Mechanical Mixing
Mechanical mixing is a solute-independent component of dispersion, governed by the
physical properties of the porous medium and carrier gas velocity. Mechanical mixing
is a lumped term, incorporating a number of sources of velocity variations that result
in solute mixing and dilution. Such velocity variations may be caused by (A) non-
uniform velocity profiles along the cross section of individual pores (e.g., velocities
are higher in the center of the pore relative to near-wall velocities); (B) distributions in
pore sizes (e.g., large pores promote higher velocities than smaller pores); and (C) the
tortuosity of flow paths, as shown in Figure 7.2. The effective pore-size distribution
and tortuosity are influenced by the presence of soil-water.At larger scales, dispersion
may be caused by the presence of lenses of material with different permeabilities.
Larger-scale differences in permeability may further influence capillary forces and
the resultant large-scale water saturation, although much less is known about large-
scale mechanical mixing processes (Freeze and Cherry, 1979; Selker et al., 1999).
Because the magnitude of mechanical mixing depends on the degree of heterogeneity,
it is expected that the magnitude of gas-phase dispersivity will be proportional to the
system-scale as has been demonstrated for aqueous-phase dispersion (Pickens and
Grisak, 1981; Gelhar et al., 1992).