Double Shell As a Directly Solvable Model of aMicro-inhomogeneous Poroelastic Medium

Abstract

We consider pore pressure and fluid compressibility effects on rock properties in the case of inhomogeneous solid matrix. For this purpose we propose a model amenable to exact analytical. It consists of similar double-layered spherical shells with a fluid inside. We show how could be realized different values of effective stress coefficient for porosity, give clear interpretation of it. In addition we validate Brown-Korringa approach. Its predictions exactly coincide with the exact solution. At the same time some new theories of poroelasticity gives predictions deviating from the double-shell model results. These theories claim that the porosity perturbation must be incorporated explicitly in the theory of porous media deformation. We give some possible explanation why this conception is not correct.