Revisiting numerical validation of Gassmann’s equations: Open-pore boundary condition

Abstract

Gassmann’s equations are widely used to predict the effective moduli of fluid-saturated rocks from dry properties and basic petrophysical parameters, yet pore-scale validations that explicitly demonstrate numerical convergence remain limited. Furthermore, recent publications have questioned the logical consistency of the derivation of Gassmann’s equations, arguing instead for the consistency of the Brown and Korringa (1975) formulation with a “mean” compressibility. A pore-scale validation of Gassmann’s relations was performed under an open-pore boundary geometry, where the pore network intersects the external surface and the imposed macroscopic displacement acts simultaneously on solid and fluid at the boundary. Three-dimensional finite-element simulations were used that couple linear elasticity of the solid skeleton with the quasistatic, compressible Navier–Stokes equations that govern fluid flow. Direct relaxation tests on monomineral, isotropic (cubic) models with generic pore topology (narrow throats linked to a wider pore body) were conducted across a sequence of mesh refinements. In the low-frequency limit, the numerically evaluated undrained bulk modulus converged to the Gassmann prediction to within numerical precision. Comparisons with the Brown and Korringa (1975) formulation indicated that the “mean” compressibility converges to the grain compressibility, causing the formulation to collapse to the classical Gassmann result as resolution increases. Together with earlier closed-pore analysis, the results confirmed that for such models, Gassmann’s equations remain valid for open- and closed-pore boundary conditions, provided that uniform pore pressure is achieved in the quasistatic limit.