Page 21 - gas transport in porous media

Webb
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configuration diffusion is qualitative at best. However, it should indicate the approx-
imate permeability where configurational diffusion should at least be considered to
be as the possible diffusion mechanism.
2.3 COMBINED MECHANISMS
The interaction between advection and diffusion in porous media can be significant.
Consider two separate volumes connected by a tube containing a light gas and a
heavy gas. Diffusion of the light gas is faster than the heavy gas because of the higher
molecule velocity. The net flow of molecules is toward the heavy gas volume, so the
pressure rises in the heavy gas volume and decreases in the light gas volume. In turn,
this pressure difference causes advection from the heavy gas volume to the light gas
volume. Thus, diffusion directly leads to advection. Only in the case of equimolar
gases will diffusion not result in advection.
As mentioned earlier, this scenario was implicitly included in the diffusion formu-
lation discussed by BSL in that diffusion is relative to the molar-average velocity.
However, this effect has generally been ignored. Coupling of the advection and diffu-
sion mechanisms has been formalized with the development of the Dusty Gas Model
by Evans, Mason and colleagues (Evans et al., 1961; Evans et al., 1962a; Mason et
al., 1963; Mason et al., 1964). The Dusty Gas Model (DGM) takes the gas trans-
port equations a step further by including the effect of the porous media as a “dusty
gas” component of the gas mixture. The “dusty gas” is assumed to consist of large
molecules fixed in space that is treated as a component of the gas mixture. The kinetic
theory of gases is applied to this dusty-gas mixture. One of the key aspects of the
DGM is the combination of diffusion (ordinary and Knudsen) and advection. Ordi-
nary and Knudsen diffusion are combined through addition of momentum transfer
based on kinetic-theory arguments, and diffusive fluxes (ordinary plus Knudsen) are
added to advective fluxes based on Chapman-Enskog kinetic theory.
The DGM, including numerous data-model comparisons, is discussed in detail
by Mason and Malinauskas (1983) and by Cunningham and Williams (1980). Other
excellent references on application of the Dusty Gas Model for porous media are
Thorstenson and Pollock (1989a, 1989b) and Jackson (1977).
The exclusive presentation of the DGM in this chapter does not imply that the DGM
is the most comprehensive gas-phase diffusion model available for porous media.
There are a number of other models available including Feng and Stewart (1973), who
extended the DGM to more complicated pore networks, a mean transport pore model
as presented byArnost and Schneider (1995) (see Šolcová and Schneider (Chapter 14
of this book)), and Shapiro (1993), who developed a model for heterogeneous
anisotropic porous media. Altevogt et al. (2003a, b) present an alternate approach for
binarygasdiffusion. Rather, theDGMisthemostwidelyusedmodelforamechanistic
approach to combine gas advection and diffusion in porous media at the present time.
Ignoring thermal diffusion, which is typically small, the DGM can be written
D
either in terms of the diffusive molar flux, N , or the total molar flux (diffusive plus
T
advective), N , which are relative to fixed coordinates (Thorstenson and Pollock,