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. Further, recent publications have questioned the logical consistency of the derivation of Gassmann’s equations arguing instead the consistency of the Brown and Korringa (1975) formulation with a “mean” compressibility. Here. a pore-scale validation of Gassmann’s relations is 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 are employed that couple linear elasticity of the solid skeleton with the quasi-static, compressible Navier--Stokes equations that govern fluid flow. Direct relaxation tests on mono-mineral, isotropic (cubic) models with generic pore topology (narrow throats linked to a wider pore body) are conducted across a sequence of mesh refinements. In the low-frequency limit, the numerically evaluated undrained bulk modulus converges to the Gassmann prediction to within numerical precision. Comparisons with the Brown and Korringa (1975) formulation indicate that the “mean” compressibility converges to the grain compressibility, causing this formulation to collapse to the classical Gassmann result as resolution increases. Together with earlier closed-pore analysis, the results confirm that for such models Gassmann’s equations remain valid for both open- and closed-pore boundary conditions, provided uniform pore pressure is achieved in the quasi-static limit.