Double-porosity acoustoelasticity for rocks with penny- and wedge-shaped cracks incorporating bubble vibration

Abstract The fluid-saturated pressured (or stressed) cracked (FSPC) rocks containing a small amount of bubbles are frequently encountered in the subsurface. However, the wave propagation in such rocks is poorly understood. To address this issue, we proposed a double-porosity acoustoelasticity (DPAE) theory for wave dispersion and attenuation in FSPC rocks containing a small amount of bubbles by means of the theories of classic poro-acoustoelasticity (PAE), bubble vibration, and squirt flow. The dispersion and attenuation induced by global fluid flow and squirt flows between stiff pores and compliant cracks are incorporated, wherein the penny- and wedge-shaped cracks coexist. The pressure dependence of rock elasticity and wave propagation is characterized by the classic PAE theory. Modelling results show that the addition of bubbles leads to a notable vibration in P-wave dispersion and attenuation, thus influencing the frequency and pressure dependence of P-wave dispersion. However, the bubble amount has little effect on S-wave dispersion and attenuation. By comparing the results with the experimental measurements of two rock samples at different frequencies and effective pressures, we confirm the feasibility of our theory. Our theory and results may provide the theoretical basis for many practical applications, including in-situ pressure prediction and hydrocarbon exploration.