Excluded‐volume expansion of Archie's law for gas and solute diffusivities and electrical and thermal conductivities in variably saturated porous media

Abstract

Describing and predicting gas and solute diffusivities and electrical and thermal conductivities under variably saturated fluid conditions are necessary for simulating gas, solute, and heat transport in soils. On the basis of comprehensive data for gas (Dp) and solute (Ds) diffusivities and electrical (EC) and thermal (TC) conductivities for differently textured and variably saturated soils, we investigated analogies and differences between the four parameters. At fluid (water or air) saturation, relative parameter values for Dp, Ds, and EC were all well described by an excluded‐volume expansion of Archie's first law. The cementation exponent in Archie's first law was close to 1.5 for all parameters. At fluid‐unsaturated conditions, relative values of Dp, Ds, and EC (normalized at fluid saturation) were well described by an excluded‐volume expansion of Archie's second law. In the case of relative TC, the saturation exponent in Archie's second law was substituted by the inverse of it for the three other parameters since water bridge effects dramatically enhance the TC with increasing moisture contents in relatively dry porous media. If appropriate but different expressions for a percolation threshold in Archie's second law were applied for the four parameters, a saturation exponent value of around 2.0 generally gave accurate predictions of all four parameters for differently textured soils. Finally, the excluded‐volume expansion of Archie's second law was modified to also represent porous media with bimodal pore size distribution and well‐described data for Dp and Ds in aggregated soil.