Anisotropy of elastic wave velocities in deformed shales: Part 2-Modeling results

This study was devoted to the interpretation of the evolution of elastic wave velocities in anisotropic shales that are subjected to deformation experiments in the laboratory. A micromechanical model was used to describe the macroscopic effective elastic properties and anisotropy of the rock in terms of its microscopic features, such as intrinsic anisotropy and crack/pore geometry. The experimental data (reported in Part 1) were compared quantitatively with the micromechanical model predictions to gain some insight into the microstructural behavior of the rock during deformation. The inversion of the experimental data using the micromechanical model was carried out by means of a numerical minimization of the least-squares distance between data and model in terms of effective compliances. Under isotropic mechanical loading, the overall behavior of the dry shale is consistent with the closure of crack-like pores, which are aligned in theplane of symmetry of the transversely isotropic background matrix. Those cracks represent a low fraction of the total porosity, but they have a strong effect on elastic wave velocities. The data are consistent with an initial (horizontal) crack density of 0.07. Crack closure also is evidenced at early stages of axial loading applied perpendicular to the shale bedding plane, whereas crack density increases significantly as axial stress is increased. Interpretation of the wet experiment is less straightforward, although some preliminary conclusions could be drawn. Under isotropic stress, crack closure also is evidenced, whereas crack density remains constant at the early stages of deviatoric loading. When axial peak stress is approached, crack density increases drastically, which likely indicates onset and development of vertical cracking. Wet experiments probably are more complex because water is likely to be expelled from crack-like pores toward equant pores in response to the mechanical loading.