The present paper is devoted to a micromechanical approach to the non linear elastic behaviour of rocks. It is assumed that the non linear response of the porous medium is entirely due to the existence of a network of microcracks in the solid phase. The micromechanical model provides the quantitative link between the crack closure phenomenon and the macroscopic non linear behaviour. Morphological parameters such as crack porosity and crack density parameter are related to the measurement of the tangent compression modulus. The practical significance of non linear poroelastic behaviour is illustrated by the simulation of the depletion of a pressurized oil reservoir.
This paper presents a micromechanical approach to the non linear elastic behaviour of rocks. The latter is classically attributed to the existence of cracks in the rock matrix, as well as to the non linearity of the contact law between the grains. In the case of sandstones, various experimental data (Bout6ca, 1994) show the increase of the compression modulus as a function of the confining pressure and reveal the existence of an asymptotic value of the compression modulus. For such materials, this suggests that the contribution of contacts to the macroscopic non linear behaviour is negligible with respect to that of cracks. In this work, we therefore explore the hypothesis along which the non linear response of the porous medium is entirely due to the existence of a network of microcracks in the solid phase. The progressive closure or opening of cracks induced by the loading path, is viewed to control the nonlinearity.
At the microscopic scale, the opened cracks are modelled as oblate ellipsoids. We characterize the distribution of aspect ratio by the generalized form of the crack density parameter e initially introduced by Budiansky and O'Connell (1976). We then show that the non linear macroscopic elastic properties can be determined from the knowledge of e. Conversely, e can be determined from a back analysis performed on experimental data giving the compression modulus as a function of the confining pressure.
Finally, the practical interest of these results is illustrated on an example of oil reservoir engineering. We examine the effect of a nonlinear elastic rock compressibility on the depletion phenomenon.
