Wave propagation in fluid-saturated porous rocks under stress: An integrated approach

ABSTRACT Under stress, fluid-saturated porous rocks progressively undergo crack closure, stress accumulation, and crack growth leading to mechanical failure, significantly changing crack density, permeability, and fluid pressurization. The understanding of the stress-dependence of elastic wave propagation in such rocks has great potential applications to infer stress states as well as predicting physical properties such as permeability at depth. It however involves understanding physically the complex coupling processes at play for the observed nonlinear stress-dependence of elastic properties in poroelastic rocks, and finding convenient comprehensive modeling strategies to capture it. In parallel to modeling cracks nonlinear closure or growth, various piecewise modeling approaches such as nonlinear elasticity, hyperelasticity or inelasticity, have been proposed to encompass that complex behavior. Because the nonlinear Padé acoustoporoelasticity theory provides such an unified tensor-based framework to capture these coupling processes, it is of interest to investigate the physical meaning of involved elastic constants for stressed fluid-saturated cracked rocks. This knowledge gap is addressed by experimental validation using low- and high porosity Fontainebleau sandstone samples, saturated with water and glycerin. The results show that (1) the acoustoelastic 3oeCs account for hyperelastic strains due to stress accumulation in the background (comprising grains and stiff pores) and should be estimated from the dry-rock experimental data in the high-pressure regime, (2) Padé coefficients account for strong nonlinear strains due to crack closure, showing a clear power-law correlation with the normalized crack indicator expressed as a function of crack density and aspect ratio, (3) Fitting with the physics underlying Eshelby-type inclusion modeling approaches, Padé coefficients show no dependence to the saturating fluids, and (4) the solid–fluid coupling described by Biot’s poroelasticity is significantly affected by acoustoelastic effects.