ANISOTROPIC EFFECTIVE-MEDIUM MODELING OF THE ELASTIC PROPERTIES OF SHALES

Shales are complex porous materials, normally consisting of percolatin g and interpenetrating fluid and solid phases. The solid phase is gene rally comprised of several mineral components and forms an intricate a nd anisotropic microstructure. The shape, orientation, and connection of the two phases control the anisotropic elastic properties of the co mposite solid. We develop a theoretical framework that allows us to pr edict the effective elastic properties of shales. Its usefulness is de monstrated with numerical modeling and by comparison with established ultrasonic laboratory experiments. The theory is based on a combinatio n of anisotropic formulations of the self-consistent (SCA) and differe ntial effective-medium (DEM) approximations. This combination guarante es that both the fluid and solid phases percolate at all porosities. O ur modeling of the elastic properties of shales proceeds in four steps . First, we consider the case of an aligned biconnected clay-fluid com posite composed of ellipsoidal inclusions. Anisotropic elastic constan ts 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 cla y platelet orientations from digitized scanning electron microphotogra phs (SEM). Third, the derived clay platelet distribution is employed t o 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.