Heat, Water, and Solution Transfer in Unsaturated Porous Media: I -- Theory Development and Transport Coefficient Evaluation

Abstract

A detailed theory describing the simultaneous transfer of heat, water, and solute in unsaturated porous mediais developed. The theory includes three fully-coupledpartial differential equations. Heat, water, andsolute move in the presence of temperature, T; matricpressure head, Ψ m ; solution osmotic pressure head Ψ o ; and solute concentration C gradients. Thetheory can be applied to describe the mass and energyin radioactive waste repositories, food processing,underground energy storage sites, buried electriccables positions, waste disposal sites, and inagricultural soil. Several transport coefficients forheat, water, and solute are included in the theory. The coefficients are evaluated for a silty clay loamsoil to clarify their dependence on water content (θ),T, and C. The thermal vapor diffusivity D Tv first increased as θ increased to0.22 m3/m3 then decreased with furtherincreases in θ. D Tv was 3 orders of magnitudegreater than either isothermal vapor D mv orosmotic vapor D ov , diffusivities at θ of0.20~m3/m3, T of 50°C, and C of 0.001mol/kg. All of the liquid and vapor water transport coefficients increased with increasing T. D Tv decreased with increasing C to a greater extent thanD mv and D ov . The effective thermalconductivity decreased slightly with increasing C. Thesolute diffusion coefficient D d was 6 to 7orders of magnitude greater than the thermal soluteand salt sieving diffusion coefficients at θ of0.20~m3/m3, T of 50°C, and C of 0.001 mol/kg.