Effective thermal conductivity of partially saturated porous rocks

Abstract

The present work is concerned with the determination of the effective thermal conductivity of porous rocks or rock-like composites composed by multiple solid constituents, in partially saturated conditions. Based on microstructure observations, a two-step homogenization scheme is developed: the first step for the solid constituents only, and the second step for the (already homogenized) solid matrix and pores. Several homogenization schemes (dilute, Mori–Tanaka, the effective field method and Ponte Castañeda–Willis technique) are presented and compared in this context. Such methods are allowing: (i) to incorporate in the modellization the physical parameters (mineralogy, morphology) influencing the effective properties of the considered material, and the saturation degree of the porous phase; (ii) to account for interaction effects between matrix and inhomogeneities; (iii) to consider different spatial distributions of inclusions (spherical, ellipsoïdal). An orientation distribution function (ODF) permits simultaneously to incorporate in the modelling the transverse isotropy of pore systems. Appearing as homogeneous at the macroscopic scale, it is showed that the effective conductivity depends on the physical properties of all subsidiary phases (microscopic inhomogeneities). By considering the solution of a single ellipsoïdal inhomogeneity in the homogenization problem it is possible to observe the significant influence of the geometry, shape and spatial distribution of inhomogeneities on the effective thermal conductivity and its dependence with the saturation degree of liquid phase. The predictive capacities of the two-step homogenization method are evaluated by comparison with experimental results obtained for an argillite.