A two-dimensional mathematical model for simulating coupled problems of water flow and heat transport in saturated-unsaturated porous media is presented. The model is composed of two submodels; that is, a saturated-unsaturated water flow submodel and a heat transport submodel. The saturatedunsaturated water flow submodel can take into consideration thermal convection in saturated zone due to temperature gradient, soil water hysteresis accompanied by unsaturated flow, and temperature effect on the density and viscosity of water together with the typical forced convection. The heat transport submodel can handle heat conduction, heat dispersion, and forced and thermal convection in saturatedunsaturated porous media. The numerical method proposed in this paper is based on the finite elements for water flow and the characteristic finite elements for heat transport.
The model was applied to two experimental problems with laboratory and field data. First, water flow in saturated-unsaturated soil column was analyzed under hysteretic and isothermal condition. Then, the model was applied to a problem of coupled transport of water and heat in saturated-unsaturated porous media. The latter problem is accommodated to account for an aquifer thermal energy storage experiment conducted in Sanrihama dune sand area where serial tests of artificial recharge of warm and cold water and recovery for agricultural use have been taken place for several years. Although it was not possible to compare the simulation and experimental results in a strict sense due to the lack of adequate experimental data, it was qualitatively proved that the model can be successfully applied to this type of coupled problems.

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