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.

[1]  J. Letey.  MOVEMENT OF WATER THROUGH SOIL AS INFLUENCED BY OSMOTIC PRESSURE AND TEMPERATURE GRADIENTS , 1968 .

[2]  L. Boersma,et al.  Thermal Conductivity of Soils as a Function of Temperature and Water Content1 , 1979 .

[3]  J. W. Biggar,et al.  Simultaneous Transport of Chloride and Water During Infiltration , 1973 .

[4]  W. Kissling,et al.  The influence of airflow on the vertical infiltration of water into soil , 1992 .

[5]  E. Bresler,et al.  Simultaneous transport of solutes and water under transient unsaturated flow conditions , 1973 .

[6]  D. D. Vries,et al.  The theory of heat and moisture transfer in porous media revisited , 1987 .

[7]  J. R. Philip,et al.  Moisture movement in porous materials under temperature gradients , 1957 .

[8]  J. Bear,et al.  Migration of salts in the unsaturated zone caused by heating , 1995 .

[9]  Bridget R. Scanlon,et al.  Water and heat fluxes in desert soils: 2. Numerical simulations , 1994 .

[10]  Robert Horton,et al.  Water Transport in Unsaturated Nonisothermal Salty Soil: I. Experimental Results , 1989 .

[11]  T. L. Jones,et al.  Enhancement of thermal water vapor diffusion in soil , 1984 .

[12]  E. C. Robertson.  THERMAL PROPERTIES OF ROCKS , 1988 .

[13]  Robert Horton,et al.  Simultaneous Transfer of Heat, Water, and Solute in Porous Media: II. Experiment and Analysis , 1992 .

[14]  Robert Horton,et al.  Simultaneous Transfer of Heat, Water, and Solute in Porous Media: I. Theoretical Development , 1992 .

[15]  R. Horton,et al.  SIMULTANEOUS SOIL HEAT AND WATER TRANSFER , 1992 .

[16]  J. W. Biggar,et al.  Simultaneous Solute and Water Transfer for an Unsaturated Soil , 1971 .

[17]  Gaylon S. Campbell,et al.  A SIMPLE METHOD FOR DETERMINING UNSATURATED CONDUCTIVITY FROM MOISTURE RETENTION DATA , 1974 .

[18]  J. Bear,et al.  Advective fluxes in multiphase porous media under nonisothermal conditions , 1989 .

[19]  Omar T Farouki,et al.  Thermal properties of soils , 1981 .

[20]  D. D. Vries,et al.  Simultaneous transfer of heat and moisture in porous media , 1958 .

[21]  C. Dirksen,et al.  Hydraulic Conductivity and Diffusivity: Laboratory Methods , 2018, SSSA Book Series.

[22]  W. D. Kemper,et al.  Osmotic Efficiency Coefficients Across Compacted Clays 1 , 1966 .

[23]  Robert Horton,et al.  Water Transport in Unsaturated Nonisothermal Salty Soil: II. Theoretical Development , 1989 .

[24]  W. D. Kemper,et al.  Diffusion of Salts in Clay-Water Systems1 , 1966 .

[25]  D. E. Kissel,et al.  Temperature Effects on Urea Diffusion Coefficients and Urea Movement in Soil , 1988 .

[26]  W. D. Kemper,et al.  Movement of Water as Effected by Free Energy and Pressure Gradients III. Restriction of Solutes by Membranes1 , 1963 .

[27]  C. C. Tanner.  The Soret effect. Part 2 , 1927 .

[28]  W. Piver,et al.  Vertical transport and fate of low-water-solubility chemicals in unsaturated soils , 1985 .

[29]  J. Cary.  SOIL MOISTURE TRANSPORT DUE TO THERMAL GRADIENTS: PRACTICAL ASPECTS , 1966 .

[30]  Gaylon S. Campbell,et al.  Soil physics with BASIC :transport models for soil-plant systems , 1985 .

[31]  P. Milly,et al.  A Simulation Analysis of Thermal Effects on Evaporation From Soil , 1984 .

[32]  R. Horton,et al.  THE EFFECT OF COLUMN WETTING ON SOIL THERMAL CONDUCTIVITY1 , 1984 .

[33]  Jacob Bensabat,et al.  Heat and mass transfer in unsaturated porous media at a hot boundary: I. One-dimensional analytical model , 1991 .

[34]  H. D. Scott,et al.  Thermal Diffusivity and Conductivity of Moist Porous Media 1 , 1979 .

[35]  R. Horton,et al.  Tillage Effects on Soil Water Retention and Pore Size Distribution of Two Mollisols1 , 1985 .