A supplementary analytical model for the stagnant effective thermal conductivity of low porosity granular geomaterials

Abstract

A cylindrical unit cell model for predicting stagnant effective thermal conductivity of two-phase or three-phase low porosity granular geomaterials was proposed in this paper. In the present model, the cylindrical unit cell is made of a quasi-hemispherical/cylindrical solid particle, and the solid grain is surrounded by water or air or the mixtures of two phases. In addition to the thermal conductivity of each phase, the effects of porosity and saturation degree on the stagnant effective thermal conductivity of geomaterials were investigated by introducing the coefficients α and β that control the porosity and saturation degree, respectively. The stagnant effective thermal conductivity of cylindrical unit cell was obtained via lumped parameter method and a further spatial correction was then conducted. Comparisons with some empirical models and experimental data for three types of selected geomaterials indicate that this theoretical model successfully captures the stagnant effective thermal conductivity with variation of saturation degree and thus provides the stagnant effective thermal conductivity of granular geomaterials with acceptable accuracy in the porosity range [0, 0.33] at most degrees of saturation.