Page 29 - gas transport in porous media

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Webb
(1, 10, and 100 atmospheres). The b DGM correction factor depends on the trace gas.
If the trace gas is heavier than the bulk species (air), the correction factor is less than
1.0. Conversely, if the trace gas is lighter than the bulk gas, the b DGM correction
factor is greater than 1.0. The values have a generally small range, varying between
about 0.5 and 2.7 for the trace gases evaluated. The τ DGM correction factor can be
viewed as the ratio of ordinary diffusion flux predicted by the DGM divided by the
Fick’s law value. For example, if the value of τ DGM is 0.01, Fick’s law without the
correction factor would overpredict the ordinary gas diffusion flux by two orders of
magnitude compared to the DGM prediction. The value of τ DGM is about unity for
2
higher permeabilities (> 10 −13 m ) at all pressures. For lower permeabilities, Fick’s
law may dramatically overpredict the gas diffusion flux. The value of τ DGM decreases
2
dramatically to about 0.01 at a permeability of 10 −18 m . The variation of the ratio
for different trace gases is small. Therefore, the difference between the DGM and
2
ADM becomes important for permeabilities < 10 −13 m , with larger differences for
lower permeabilities and lower pressures.

2.6 APPLICABILITY OF DGM TO REAL POROUS MEDIA
There are questions and concerns about the applicability of the DGM to real porous
media and the appropriate parameter values. While a number of authors (Abu-El-
Sha’r and Abriola, 1997; Fen and Abriola, 2004; Cunningham and Williams, 1980,
pg. 220; Mason and Malinauskas, 1983, pg. 50) address this point, it must be pointed
out that the DGM (or the other coupled models as discussed earlier), are the best
models to date and are vastly superior to the ADM, which was used for a number of
years and is still used today.
While the DGM is widely used, there are modifications to improve its applicability.
For example, modifications have been made to the DGM to include things such as
mass transfer (e.g., Chen and Rinker, 1979) and chemical reaction (e.g., Veldsink
et al., 1995). Note that these references are just representative and do not necessarily
represent the latest information on these modifications.

ACKNOWLEDGMENTS

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed
Martin Company, for the United States Department of Energy’s National Nuclear
Security Administration under Contract DE-AC04–94AL85000.

NOMENCLATURE
b Klinkenberg coefficient
c concentration
c F constant in Forchheimer equation
D ordinary diffusion coefficient
D iK Knudsen diffusion coefficient