Volumetric Deformation, Ultrasonic Velocities and Effective Stress Coefficients of St Peter Sandstone During Poroelastic Stress Changes

Abstract

A suite of hydrostatic compression tests in a St Peter sandstone core was performed to characterize its static and dynamic poroelastic response. The pore pressure cycles under constant confining pressure simulated scenarios of reservoir depletion and injection. The volumetric deformation and axial ultrasonic velocities (Vp and Vs) were recorded and the corresponding effective stress coefficients were derived. As expected, the variations of pore pressure under constant confining pressure induce poroelastic deformation and velocity changes, which is generally consistent with the exact effective stress law. Data discrepancy between depletion and injection was observed throughout the cycles, which is considered to be a result of material hysteresis. The dynamic elastic moduli were calculated based on the velocities by assuming isotropy, which are in qualitative agreement with the static values. The static and dynamic effective stress coefficients were derived with respect to volumetric deformation and Vp and Vs. It is found that the static effective stress coefficient is consistently less than unity, and decreases from an average of ~ 0.6 with pressure difference to as low as ~ 0.35. The pore pressure has a measurable positive influence on the coefficient for the same pressure difference. The dynamic effective stress coefficient is generally around unity when the pressure difference is low (< 30 MPa), but deviates significantly from unity as the pressure difference further increases. The trend of such deviation highly depends on the wave type and loading path. Despite possible experimental artifacts, the derived dynamic effective stress coefficient is quite distinct from the static counterpart. This corroborates previous findings that the effective stress coefficients of different physical quantities are fundamentally different. It emphasizes that the estimation of static effective stress coefficient based on correlation with dynamic data is not fully warranted and can incur significant errors.