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Costanza-Robinson and Brusseau
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for diffusion to occur. This results in larger magnitudes of dispersion. When velocities
are sufficiently large, the contribution of diffusion to dispersion will be negligible.
Under these conditions, while the magnitude of the dispersion coefficient will change
with changes in velocity, the magnitude of dispersion will be velocity-independent.
This is shown by consideration of the Peclet number (Section 2.3). If diffusion is
considered as negligible, the dispersion coefficient in Equation 7.4 can be replaced
with the mechanical mixing term from Equation 7.3. As shown below, this results in
a velocity-independent Peclet number:
vL vL L
P e = = = (7.5)
D αv α
Thus, at high velocities P e , a measure of the magnitude of dispersion, depends
solely on properties of the porous medium, as represented by the dispersivity (α)
and the characteristic length of the system (L). Gas retention in the system (e.g.,
adsorption, dissolution) results in longer residence time and to an increase in apparent
dispersion. However, the magnitude of the dispersion coefficient, a measure of the
dispersion per unit time, does not actually increase (Jury et al., 1991).
Inspection of Equation 7.3 shows that the diffusion contribution to D is solute-
dependent, while that of mechanical mixing is not. Thus, the magnitude of dispersion
will vary as a function of the solute when diffusion provides a significant contribu-
tion, with lower molecular-weight gases exhibiting greater dispersion. Conversely,
dispersion will be solute-independent for larger velocities, when mechanical mixing
dominates dispersion.

7.3 LABORATORY INVESTIGATIONS

7.3.1 Variables Affecting Diffusion
The magnitude of diffusion and its contribution to overall dispersion depends on
properties of the solute and porous medium, as well as transport parameters, such
as carrier velocity, as noted above. Ehlers et al. (1969) found diffusion contributions
to gas-phase dispersion be directly and inversely related to temperature and bulk
density of the medium, respectively. Others have reported similar bulk-density or
total-porosity effects on diffusion rates (Taylor, 1949; Sallam et al., 1984; Karimi et
al., 1987; Shimamura, 1992; Abu-El-Sha’r and Abriola, 1997). Lower bulk densities
correspond to larger pores and less tortuosity; thus, these results are consistent with
the discussion above.
At soil-water contents higher than 4 to 5% (wt), Ehlers et al. (1969) found soil-
water content did not influence effective diffusion coefficients, although the technique
used could not differentiate between gas-phase and aqueous-phase diffusion. Thus,
at higher water contents, the expected decrease in gas-phase diffusion was likely
offset by increased aqueous-phase diffusion. Karimi et al. (1987) examined the role
of soil-water content on diffusion of benzene in a simulated landfill scenario and
was able to isolate the process of vapor diffusion. Increasing soil-water content in