Fluid Substitution in Porous and Fractured Solids: The Non-Interaction Approximation and Gassmann Theory

摘要

We establish an exact equivalence of the non-interaction approximation (NIA) and Gassmann theory in describing the changes in effective elasticity due to variations in the bulk modulus of fluid infill of isolated inclusions that have identical shapes and orientations. If the sizes of inclusions (pores or fractures) are equal, the fluid pressures in all inclusionsare equal too regardless of their hydraulic connectivity. This fact makes Gassmann theory rigorous; therefore, other effective media schemes should comply with it when applied to such microstructures. While the NIA satisfies this requirement, other effective media schemes (e.g., self-consistent and differential) do not.