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Network Modeling of Diffusion Coefficients for Porous Media: I. Theory and Model Development

Dep. of Agricultural Engineering, North Dakota State Univ., Fargo, ND 58105-5626

J. L. Nieber

Dep. of Agricultural Engineering, Univ. of Minnesota, 1390 Eckles Ave., St. Paul, MN 55108

*Corresponding author (steele{at}plains.nodak.edu).

ABSTRACT

Gas diffusion often dominates constituent transport in porous media and is dependent on pore geometry, water content, and water distribution in a porous medium. Network models of porous media offer the ability to investigate the influence and interaction of pore-scale porous media properties and fluid properties on macroscopic properties of the medium. This study was conducted to investigate the macroscopic relative gas diffusion coefficient vs. air-filled porosity relationship (diffusion characteristic) of porous media using a network modeling approach. A cubic sphere-and-tube network model of porous media was adapted from petroleum engineering using Fick's law and the principle of conservation of mass to simulate one-dimensional, steady-state, isothermal, isobaric, molecular diffusion of a dilute binary gas in a nonadsorbing porous medium containing a single nonwetting fluid (air) and a single wetting fluid (water). The network model simulates hysteresis in air and water distributions in porous media for boundary drying and wetting curves of the soil water characteristic and demonstrates the effect of air-filled porosity, Henry's law liquid-gas partitioning coefficient, the ratio between gas- and liquid-phase diffusion rates, and pore geometry on the diffusion characteristic.

Contribution from the Minnesota Agric. Exp. Stn., Scientific Journal Series, Paper no. 19889.

Received for publication January 4, 1993.

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