Effective elastic properties and thermal conductivity of isotropic rocks containing concave pores. Application to oolitic limestones

Abstract

This paper focuses on effective elastic properties, and thermal conductivity of materials constituted by an isotropic homogeneous solid matrix containing both ellipsoidal and non-ellipsoidal pores. In the frame of Effective Media Theory (EMT), property contribution tensor approach extended to non-ellipsoidal inhomogeneities are used to estimate effective elastic properties and thermal conductivity. On the basis of recent results obtained by the authors, a reference 3D shape is considered: supersphere characterised by a concavity parameter and being convex or concave. Related compliance contribution tensors verifying cubic symmetry have been characterised thanks to 3 D finite element modelling and analytical approximation formula have been derived and are used in this paper. Analysis is focussed on the effect of the parameter characterising concavity on both effective elastic coefficients and thermal conductivity. Application to isotropic porous rock with two separated classes of pores, such as oolitic limestones, is considered. Numerical results are presented for a reference oolitic rock, Lavoux limestone. Maxwell, Self-Consistent and Differential schemes are compared. It is shown that concavity parameter is of major importance as may be aspect ratio of spheroidal pores, and that the three reference schemes may conduce to comparable results for the particular investigated microstructure, characterised by a high volume fraction of porous grains (oolites)