Numerical modeling of effective elastic properties for heterogeneous porous media. Application to a case study of a carbonate reservoir rock sample

Abstract

An application of an open-access software destined for fast calculation of the contribution of an individual inhomogeneity of one of two types (cracks or inclusions/pores) to calculation of the effective elastic properties of an oil reservoir rock sample extracted from a wellcore fragment containing isolated pores is presented. We obtained the pore geometries by a 3D image from an X-ray tomography processed and converted into stereolithography (.stl) format. The data required for the calculations besides the shapes of the inhomogeneities are the Young’s modulus and the Poisson’s ratio of the matrix (in the isotropic case); these data were found by geological analysis. After we had calculated the contribution of each pore to the elastic properties of the rock sample, we obtained the overall effective elastic properties by the Mori–Tanaka scheme. The proposed methodology is straightforward and it was possible to detect even a slight anisotropy (less than 5%) of the effective elastic properties. We found experimentally the effective elastic properties of the sample from the measurement of the acoustic wave velocities. The results obtained show a good agreement in terms of anisotropy and porosity detection; however, the effective elastic properties diverged by a large margin (up to 200%). This may be explained by the presence of microcracks undetected by the tomography. As a future work, we consider a more thorough study of the microstructure of the sample to verify the hypothesis about the presence of microcracks.