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


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Abstract

A detailed theory describing the simultaneous transfer of heat, water, and solute in unsaturated porous media is developed. The theory includes three fully-coupled partial differential equations. Heat, water, and solute move in the presence of temperature, T; matric pressure head, Ψm; solution osmotic pressure headΨO; and solute concentration C gradients. The theory can be applied to describe the mass and energy in radioactive waste repositories, food processing, underground energy storage sites, buried electric cables positions, waste disposal sites, and in agricultural soil. Several transport coefficients for heat, water, and solute are included in the theory. The coefficients are evaluated for a silty clay loam soil to clarify their dependence on water content (Θ), T, and C. The thermal vapor diffusivity DTv first increased as Θ increased to 0.22 m3/m3 then decreased with further increases in Θ. DTv was 3 orders of magnitude greater than either isothermal vapor Dmv or osmotic vapor Dov, diffusivities at Θ of 0.20∼m3/m3, T of 50ˆC, and C of 0.001 mol/kg. All of the liquid and vapor water transport coefficients increased with increasing T. DTv decreased with increasing C to a greater extent thanDmv and Dov. The effective thermal conductivity decreased slightly with increasing C. The solute diffusion coefficient Dd was 6 to 7 orders of magnitude greater than the thermal solute and salt sieving diffusion coefficients at Θ of 0.20∼m3/m3, T of 50ˆC, and C of 0.001 mol/kg.

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