Fluid-solid substitution in rocks with disconnected and partially connected porosity

It is usually believed that Gassmann fluid substitution can be performed only for a fully interconnected portion of the pore space. While this is certainly true, the presence of disconnected porosity does not necessarily invalidate Gassmann's predictions. This unconventional view is supported with an analytic proof of the equivalence of Gassmann theory and the noninteraction approximation for the effective elasticity of solids with isolated self-similar pores. Numerical tests for more realistic microgeometries, where pores have diverse shapes and the pore space is partially disconnected, demonstrate that errors in Gassmann-type infill substitution are typically small and unlikely to exceed a few percent as long as the aspect ratios of pores are greater than approximately 0.2. If the fracture-like pores are aligned or elasticities of the substituted infills are close, Gassmann theory remains accurate for isolated pores with smaller aspect ratios.