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

Thermal conductivity of unsaturated clay-rocks

“…The solid phase being composed by several minerals with different thermal conductivities, the equivalent grain thermal conductivity is unknown. It can be computed from classical mixing law or homogenization (see Gruescu et al, 2007;Giraud et al, 2007). In the present work, we choose to optimize directly λ S to limit the uncertainties due to additional computations.…”

How interface size, density, and viscosity affect creep and relaxation functions of matrix-interface composites: a micromechanical study

“…Specification of the concentration-influence relations (8) and (9) for (22), and consideration of the viscous interface behavior according to (4), deliver the following set of coupled, linear, inhomogeneous, first-order, ordinary differential equations (with constant coefficients) for the dislocation histories of the two interface families: (23) and (24). This underlines the coupled nature of Eqs.…”

“…Specification of the concentration-influence relations (12) and (13) for (14), as well as consideration of the components of the involved influence tensors according to the "Appendix," and of the viscous interface behavior according to (4), deliver the following two differential equations for the time evolutions of the in-plane dislocation functions…”

“…Matrix-inclusion composites are known to exhibit interaction among the inclusions [1][2][3][4][5][6][7]. When it comes to the special case of inclusions in form of flat interfaces, i.e., to that of matrix-interface composites, interaction among interfaces would be clearly expected as well; however, the two-dimensional nature of interfaces is responsible for particularly surprising interaction properties [8,9], reminiscent of the situation encountered with micro-cracked materials [10,11].…”

Thermal conductivity measurement in clay dominant consolidated material by Transient Hot-Wire method.

“…This hot-wire method has been developed for measurements in electro-conducting liquid [3][4][5][6] and in highly corrosive liquids [7][8][9]. Actually, the use of the transient hot-wire method is extended to granular materials [10,11], in solid geomaterials [12][13][14][15], and in soils by pedologists [16][17][18][19]. The texturemoisture and thermal conductivity relationship have been studied firstly on a model material composed of glass bead assemblages to demonstrate the role of porosity and saturation index.…”