Porosity perturbations and poroelastic compressibilities

摘要

The Biot-Gassmann (BG) poroelasticity theory is based on the assumption of a microhomogeneous solid frame. This means that it considers the solid frame to be homogeneous at the porescale level. If the solid frame is built out of two or more solid constituents at the pore-scale level, then the porous rock can be considered microinhomogeneous. Although in a macroscopic sense, it still is homogeneous. Porosity changes during deformation of microinhomogeneous rocks lead to poroelastic compressibilities that are not compatible with the BG theory. The key to modeling the compressive response of microinhomogeneous rocks is the porosity perturbation equation known from the volume-averaging-based poroelasticity framework. This porosity perturbation equation entails an effective stress coefficient that can be different from unity. Only if this porosity effective stress coefficient equals unity can the porosity perturbation equation implicit to Biot's theory be recovered. The porosity perturbation equation was reconciled with the poroelastic compressibility definitions suitable for pressure-cell experiments. These compressibilities were parameterized in terms of the porosity effective stress coefficient. The results provide a means to consistently interpret pressure-cell experiments on Berea sandstone samples in which a difference between the unjacketed bulk and pore compressibilities has been found.