Overcoming Gassmann's equation limitations in reservoir rocks

Abstract

Velocities of low-frequency seismic waves and, in most rocks, sonic logging waves depend on the compressibility of the undrained rock, which is conventionally computed from the drained rock compressibility using Gassmann's equation. Although more comprehensive and accurate alternatives exist, the simplicity of the equation has made it the preferred fluid substitution model for geoscience applications. In line with recent publications, we show that Gassmann's equation strictly applies only to rocks with a microhomogeneous void space microstructure that is devoid of cracks and microcracks. We use a rock physics model that separates the respective compliance contributions of pores and cracks on dry (drained) moduli and show that Gassmann's model does not apply to rocks with measurable crack density. A fourth independent bulk modulus (in addition to the bulk moduli of the mineral matrix, dry frame, and saturating fluid) is required to take the effect of cracks into account and perform fluid substitution modeling for rocks with pores and cracks more accurately than prescribed by Gassmann's equation. Therefore, we propose combining the Vernik-Kachanov model with Brown-Korringa's equation for more reliable modeling of undrained bulk compressibility for reservoir rocks with measurable crack density. To conclude, a practical quantification of the applicability of Gassmann's equation based on the combined effects of crack density and stress sensitivity is proposed.