Page 49 - gas transport in porous media

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may be significant when compared to Fickian diffusion around liquid islands. The
following sections present more detailed numerical models and experimental results
that confirm this finding.
3.5.2 Numerical Model
Numerical, mechanistic models of the pore-scale processes associated with enhanced
vapor diffusion were developed by Webb and Ho (1997) and subsequently applied by
Webb (1998, 1999). The Dusty-Gas Model was used to simulate air–vapor advection
and diffusion in a pore network including Knudsen and ordinary (Fickian) diffu-
sion. Kelvin’s equation was used to estimate vapor-pressure lowering effects at the
liquid-island gas/liquid interface, and the Young-Laplace equation was used to eval-
uate gas–liquid pressure differences at both ends of the liquid island. Concentration
gradients were applied to the pore-scale model to calculate the vapor and air flow rates.
The porous media was conceptualized to be a series of randomly-arranged spheres.
Heat transfer was simulated to occur between the spheres by particle-to-particle con-
tact, while flow of gas occurred around the spheres and around liquid islands. The
liquid saturation was assumed to be sufficiently low such that the liquid was confined
to pendular rings, or liquid islands. Bulk flow of liquid was not simulated. The numer-
ical code TOUGH2 (Pruess, 1991) was employed for the simulations. Figure 3.9
shows an example of the simulated water-vapor-diffusion mass flow vectors using
the numerical model.
Results of the numerical studies showed that significant enhancement of vapor
diffusion in porous media was possible in the presence of liquid islands. The enhance-
ment increased dramatically as the length of the liquid islands increased. In contrast,
gas (air) diffusion was found to decrease slightly in the presence of liquid islands. The
concentration gradient was found to have a dominant effect on enhancing the vapor
diffusion. This contrasted previous modeling results of Philip and deVries (1957) that
postulated enhancement would only occur due to temperature gradients. Although the
concentration gradient and temperature gradient are often related (e.g., vapor pressure

Y-Dimension (microns) 100

50

0

0 100 200 300
X-Dimension (microns)
Figure 3.9. Simulated water-vapor-diffusion mass flow vectors in a pore network with a liquid island
above the middle particle (from Webb and Ho, 1997, reprinted with permission)