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

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, Ψm; solution osmotic pressure head Ψo; 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 DTv first increased as θ increased to0.22 m3/m3 then decreased with furtherincreases in θ. DTv was 3 orders of magnitudegreater than either isothermal vapor Dmv orosmotic vapor Dov, 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. DTvdecreased with increasing C to a greater extent thanDmv and Dov. The effective thermalconductivity decreased slightly with increasing C. Thesolute diffusion coefficient Dd 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.