Stress path dependence of time-lapse seismic effects in shales: experimental comparison at seismic and ultrasonic frequencies

Changes in pore pressure within geological reservoirs, due to, e.g., hydrocarbon production, CO₂ and energy storage, or wastewater disposal, may cause substantial stress changes in the overburden, altering propagation velocities of elastic waves. The corresponding time shifts are detected and quantified using time-lapse (4D) seismic analysis. To invert seismic time shifts for changes in stress and strains, stress sensitivity of rocks is studied in laboratory experiments on core plugs. Such measurements are typically conducted at ultrasonic frequencies. However, previous studies indicate that the stress sensitivity of velocities at seismic frequencies could be higher than that at ultrasonic frequencies. Therefore, calibration based on laboratory ultrasonic data may lead to inaccurate prediction of stresses and strains when applied to 4D seismic data. To study the influence of frequency on stress sensitivity of acoustic wave velocities, a series of laboratory experiments was performed on two overburden shales with different petrophysical properties. In a low-frequency apparatus—a triaxial pressure cell that combines measurements at low (seismic) and high (ultrasonic) frequencies—the shale samples underwent stress changes with different ratios of horizontal to vertical stress amplitudes to mimic stress variations across the overburden. High-frequency velocity changes were directly recorded, while low-frequency velocity changes were obtained indirectly from the elastic parameters measured at seismic frequency by applying a rock physics inversion using third-order elasticity model. The experiments were conducted at undrained conditions, a representative state for reservoir overburden composed of shales. The results suggest that the stress sensitivities and strain sensitivities (R-factor) of P-wave velocities could be 2-4 times greater at seismic frequencies than at ultrasonic frequencies. Furthermore, it was found that the previously reported linear relation between the stress sensitivity and stress-path parameter (horizontal/vertical stress change) at ultrasonic frequencies also holds for seismic frequencies. We discuss the theoretical background for frequency-dependent stress sensitivity of wave velocities that supports the experimental findings. The effect of frequency when employing laboratory-based calibrations should be taken into account when inverting time-lapse seismic data for changes in stresses and strains.