Asymptotic analysis of the equilibrium equation of a fluid-saturated porous medium by the homogenization method

Abstract

The homogenization of static elasticity equations describing the stress strain state of fluid-saturated porous medium is considered. In this paper, the homogenization method is used to determine the pore pressure transfer tensor, which (a coefficient in the isotropic case) is an important parameter influencing the stress-strain state of fluid-saturated rocks. It shows what a part of the pressure in the fluid is “active” in the formation of macroscopic strains.

The pore pressure transfer tensor is calculated for model and real geological specimens. The dependence of this tensor on the porosity, pore shape, and Poisson ratio is investigated. The use of the computational technique for determining the effective properties of rocks shows that it is practically important in the engineering geology.