Page 134 - gas transport in porous media

Chapter 7: Gas-Phase Dispersion in Porous Media
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the range 8 to 11% (wt) was observed to decrease the effective benzene diffusion
coefficient. Similar inverse relationships between soil-water content and diffusion
are reported for graded (Taylor, 1949) and aggregated porous media (Millington and
Shearer, 1971; Arands et al., 1997). Shimamura (1992) presented similar results for
a number of sandy soils with controlled grain-size distributions.
Taylor (1949) presented diffusion rates as a function of matric potential, a variable
that is inversely related to soil-water content. The plot of effective diffusion distance
(inversely proportional to tortuosity) versus matric potential displayed significantly
less variability for the four natural and graded porous media studied, as compared to
the plot of effective diffusion distance versus soil-water content. Viewing diffusion
as a function of matric potential, incorporates both the effects of soil-water content
and pore- and grain-size distributions, thereby allowing more general conclusions to
be drawn for a variety of porous media.

7.3.2 Variables Affecting Mechanical Mixing and
Total Dispersion

The total magnitude of dispersion depends on several factors, including physical
properties of the porous medium, physicochemical properties of the gaseous solute,
and flow conditions. Edwards and Richardson (1968) measured dispersion coeffi-
cients by varying argon velocity in a dry packed system, demonstrating that the
dispersion coefficient is relatively constant at low Reynolds numbers (e.g., 0.01–0.5)
and increases approximately linearly for higher Reynolds numbers. The Reynolds
number is a measure of the turbulence of flow and for the same fluid and porous
medium is directly proportional to average linear velocity. Thus, for the low velocity
experiments, the magnitude of dispersion remained relatively constant, but increased
linearly at higher velocities. The authors interpret this as indicating that molecular
diffusion, a velocity-independent term (see Equation 7.3), dominates dispersion at
low velocities (e.g., low Reynolds numbers).At higher velocities, mechanical mixing,
which is directly proportional to velocity, dominates dispersion. Using expressions
similartoEquation7.3, EdwardsandRichardson(1968)definethreeregionsofdisper-
sion: (1) low Reynolds numbers where the mechanical mixing term (in Equation 7.3)
is negligible; (2) intermediate Reynolds numbers where both mechanical mixing and
diffusion terms are significant; and (3) high Reynolds numbers where the diffusion
term becomes negligible. This three-region approach had been previously applied to
the case of saturated flow.
Popovi˘cová and Brusseau (1997) also examined the role of carrier gas velocity on
the magnitude of dispersion and the relative contributions of diffusion and mechan-
ical mixing to methane transport in a dry, homogeneous, glass-bead column. At
low velocities, virtually all methane dispersion was due to diffusion, while at larger
pore velocities, mechanical mixing contributed more than 80% of the observed dis-
persion. Similar velocity-dependence of dispersion-contributions was observed for a
heterogeneous glass-bead column, and total dispersion increased relative to the homo-
geneous system. The heterogeneous column had a macropore located in the center of