Page 25 - gas transport in porous media

18
given below
Webb
k b g
∗
F g =− 1 + ρ g (∇P g − ρ g g) − ρ g D ∇x
12
µ g P g
The DGM and the ADM results presented in this section were calculated by the
TOUGH2 code (Pruess, 1991), which was modified to incorporate the DGM by Webb
(1998). Pruess (Chapter 12 of this book) summarizes the flux expressions in many
commonly used porous media codes including TOUGH2.
2.4.1 Zero Pressure Difference
The first data-model comparison considers zero pressure difference across the porous
media. In this case, there is diffusion but no advection. From Graham’s laws, the
ratio of the mole fluxes (not the magnitude) for Knudsen diffusion and for ordinary
diffusion is the same. Graham’s laws give a mole flux ratio of helium to argon of 3.2
based on the molecular weights of helium (m = 4.00) and argon (m = 39.944).
Data-model comparisons are given in Figure 2.1 as a function of the average pres-
sure. Helium mole flux is positive, and argon mole flux is negative. The data for both
gases increase with increasing pressure. The DGM data-model comparison is quite
good. In addition to the individual values, the ratio of the mole fluxes is consistent
with the theoretical value given above. In contrast, the model predictions of theADM
show a constant mole flux value independent of pressure for each component, which
is not consistent with the data. The ADM predicts that the mass fluxes of the two
components are equal. The mole flux ratio (helium/argon) is simply the inverse of the
ratio of the molecular weights, or about 10, which is not consistent with the data. The
ADM, which for zero pressure difference reduces to Fick’s law, does not match the
experimental data very well. Knudsen diffusion is not included because there isn’t
any advection in the ADM predictions.

2.4.2 Zero Net Mole Flux

The second case is for zero net mole flux. This case simulates what would occur in
a closed volume, where the total mole fluxes of the two components are equal. The
sum of diffusion and advection of each component are equal to each other resulting in
a zero net mole flux. The predicted flux of each component and the pressure difference
across the experiment are compared to the experimental data.
Figure 2.2a gives the data-model comparison for the mole flux as a function of the
average pressure. The data-model comparison for the DGM is very good including
the variation of flux with pressure. For the ADM, the predicted mole flux is constant,
unlike the data.
The data-model comparison for pressure difference across the porous media is
shown in Figure 2.2b. The pressure difference results in equal and opposite mole
fluxes across the graphite. The data-model comparison for the DGM is very good.
TheADM data-model comparison is poor, similar to the zero pressure difference case.