Excluded-Volume Expansions of Archie's Law for Gas and Solute Diffusivities and Electrical and Thermal Conductivities in Variably-Saturated Porous Media.

Abstract: Knowledge of each of the gas and solute diffusivities and electrical and thermal conductivities is necessary for understanding and simulating gas, solute and heat transport phenomena in soils. Interrelations between these four transport parameters are highly useful for understanding the interacting soil-pore and soil-particle network dynamics as well as for developing improved predictive models for each parameter. Based on comprehensive literature data sets for gas (D_p) and solute (D_s) diffusivities and electrical (EC_a) and thermal (TC_a) conductivities for differently-textured and variably-saturated sands and soils, the analogies between those parameters were investigated. At fluid (water or air) saturated conditions, we considered different threshold fluid contents (F_th^*) for each parameter, and subsequently found that the relative parameter values for D_p, D_s and EC_a were all well described by a simple power function of F_sat- F_th^* (excluded –volume expansion of Archie’s First Law), where F_sat is the total porosity. At fluid-unsaturated conditions, relative D_p, D_s and EC_a values were described by a excluded-volume expansion of Archie’s Second Law and showed similar trends for all three parameters, but different trends for sandy versus loamy-clayey soils. In the case of relative TC_a, the pore connectivity parameter C in Archie’s Second Law needed to be taken as the inverse of the C for the three other parameters, since water forming liquid bridges between soil particles dramatically increases TC_a at lower water contents. Finally, the exclusion-volume expanded Archie’s Second Law was also modified to represent porous media with bimodal pore-size distribution and tested against data for D_p (gaseous phase) and D_s (liquid phase) in differently-textured soils (sand, loam, aggregated volcanic soils) where both parameters were measured on the same soils at different soil-water contents and matric potentials.