Estimates and Rigorous Bounds on Pore-fluid Enhanced Shear Modulus in Poroelastic Media with Hard and Soft Anisotropy

Abstract

A general analysis of poroelasticity for hexagonal, tetragonal, and cubic symmetry shows that four eigenvectors are pure shear modes with no coupling to the pore-fluid mechanics. The remaining two eigenvectors are linear combinations of pure compression and uniaxial shear, both of which are coupled to the fluid mechanics. The analysis proceeds by first reducing the problem to a 2 × 2 system. The poroelastic system including both anisotropy in the solid elastic frame (i.e., with ‘hard anisotropy’), and also anisotropy of the poroelastic coefficients (the ‘soft anisotropy’) is then studied in some detail. In the presence of anisotropy and spatial heterogeneity, mechanics of the pore fluid induces shear dependence on fluid bulk modulus in the overall poroelastic system. This effect is always present (though sometimes small in magnitude) in the systems studied, and can be comparatively large (up to a maximum increase of about 20%) in some porous media - including porous glass and Schuler-Cotton Valley sandstone presented here. General conclusions about poroelastic shear behavior are also related to some recently derived product formulas that determine overall shear response of these systems. Another method is also introduced based on rigorous Hashin-Shtrikman-style bounds for nonporous random polycrystals, followed by related self-consistent estimates of mineral constants for polycrystals. Then, another self-consistent estimation method is formulated for the porous case, and used to estimate drained and undrained effective poroelastic constants. These estimates are compared and contrasted with the results of the first method and a unified picture of the overall behavior is found in three computed examples for polycrystals of grains having tetragonal symmetry.