A micromechanical model for the effective compressibility of sandstones

A self-consistent micromechanical model is proposed to evaluate the effective compressibility of sandstones. The sandstone microstructure is modelled by spherical inclusions with imperfect interfaces embedded in a matrix. Strain localisation coefficients are obtained by extension of the composite sphere model of Herve and Zaoui (1993) to the case of imperfect interfaces between phases. The variations of the effective compressibility and Poisson's ratio of the composite are evaluated as a function of the porosity and the normal and tangential interface compliances. Assuming a stress dependent compliance for the interface between the grains results in a rock compressibility which is decreasing by increasing confining pressure. It is demonstrated that by calibration of a simple stress dependency law for the interface compliances the model results in stress-dependent compressibility which is compatible with the experimental evaluations. The proposed model is compared with the cracks in matrix model of Sayers and Kachanov (1995) and very close results are obtained for modelling the stress-dependent compressibility. This shows that if the isotropic case is considered, it does not matter if cracks are considered to be at grain boundaries or not, as long as their orientation distribution is isotropic and their centers distribution is random.