Pore-Scale Model for Thermal Conductivity of Unsaturated Sand

A new framework is proposed for predicting thermal conductivity dry out curves (TCDC) quantifying the relationship between soil thermal conductivity and degree of saturation at non-elevated temperatures. Pore-scale expressions are derived to quantify water retention and corresponding conductive heat transport for an idealized contacting-sphere geometry approximating that of granular (sand-sized) porous media. Measured water retention behavior is used to constrain a simulated soil–water characteristic curve and corresponding TCDC by differentiating pores containing water in the form of inter particle liquid bridges from pores containing water in the form of saturated pockets. Modeled TCDCs compare well with experimental measurements for representative fine-, medium-, and coarse-grained sands. Predicted thermal conductivity is within 5–10 % of the full scale range for saturations greater than 20 %. Model predictions perform as well as or better than predictions made using many existing empirical approaches. Because the model directly incorporates basic soil properties and process variables in its formulation, including grain size, grain size distribution, and wetting direction, it becomes a potentially useful framework to improve understanding of fundamental controls on soil thermal conductivity.