Anisotropic effective-medium modeling of the elastic properties of shales

Abstract

Shales are complex porous materials, normally consisting of percolating and interpenetrating fluid and solid phases. The solid phase is generally comprised of several mineral components and forms an intricate and anisotropic microstructure. The shape, orientation, and connection of the two phases control the anisotropic elastic properties of the composite solid. We develop a theoretical framework that allows us to predict the effective elastic properties of shales. Its usefulness is demonstrated with numerical modeling and by comparison with established ultrasonic laboratory experiments. The theory is based on a combination of anisotropic formulations of the self-consistent (SCA) and differential effective-medium (DEM) ap proximations. This combination guarantees that both the fluid and solid phases percolate at all porosities. Our modeling of the elastic properties of shales proceeds in four steps. First, we consider the case of an aligned biconnected clay-fluid composite composed of ellipsoidal inclusions. Anisotropic elastic constants are estimated for a clay-fluid composite as a function of the fluid-filled porosity and the aspect ratio of the inclusions. Second, a new processing technique is developed to estimate the distribution of clay platelet orientations from digitized scanning electron microphotographs (SEM). Third, the derived clay platelet distribution is employed to estimate the effective elastic parameters of a solid comprising clay-fluid composites oriented at different angles. Finally, silt minerals are included in the calculations as isolated spherical inclusions.