Scale and Boundary Effects on the Effective Elastic Properties of 2-D and 3-D Non-REV Heterogeneous Porous Media

Abstract

A digital 3-D representation of a heterogeneous medium can be used as an input to physics-based numerical methods to obtain an estimate of the effective physical properties of the composite, such as transport, electrical, and elastic properties. These properties can then be used to simplify large-scale numerical simulations of physical processes by considering the constitutive equations of the heterogeneous composite as if it was a homogenous continuum. By definition, effective physical properties do not depend on the boundary conditions applied to a medium during an experiment. In finite-sized media, computing effective properties for a medium may not be feasible due to the boundary effects on the computed parameters. Through numerical experiments, we developed a methodology to minimize the boundary effects by considering a subdomain within a sample onto which the experiment was performed. Specifically, we analyzed the boundary effects on the computed elastic properties of 2-D and 3-D subdomains located within a digitized sample of a Berea sandstone and a compacted random pack of identical spherical particles. As the parent sample size increases while the size of the subdomain remains fixed, the elastic properties of the latter converge to constant values. These values correspond to the effective elastic values of the subsample, though they depend on the immediate region surrounding the subdomain. In addition, we propose a method to relate the effective elastic properties of rock samples to another microstructural parameter to be used in prediction of elastic properties of other samples having the same type and geological conditions.