Effective medium methods and a computational approach for estimating geomaterial properties of porous materials with randomly oriented ellipsoidal pores

摘要

The role of effective medium approaches and the differential scheme in estimating the overall elastic moduli of a porous medium with randomly oriented pores is examined. The analytical estimates of the elastic moduli are compared with approximations available in the literature that are valid for small pore aspect ratios. Accuracy of the analytical estimates is further established by performing finite element simulations. Finite element estimates are obtained for a model of a porous medium containing three families of spheroidal pores arranged in a mutually orthogonal configuration. This model is regarded as a close approximation to a porous medium with randomly oriented pores. Also, experimental data available for several sandstones and granites was used to analytically examine the influence of the aspect ratio of pores on overall properties. This information is also used to provide an estimate for the permeability of the porous medium.