Rock physics model for patchy saturated porous media under in-situ stress

In situ stress and wave-induced fluid flow (WIFF) jointly influence the velocities of waves propagating through the formations. However, for partially saturated porous media commonly encountered in the subsurface, the stress- and frequency-dependent characteristics of wave velocity dispersion and attenuation are not yet fully understood. To address this, we propose a new poro-acoustoelasticity model to characterize wave velocities in patchy-saturated porous media under in-situ stress. This model simultaneously accounts for macroscopic global flow arising from wave-induced relative motion between the pore fluid and the solid frame, mesoscopic WIFF associated with patchy fluid saturation, and microscopic squirt flow induced by fluid pressure gradients between pores and cracks. Furthermore, by considering the influence of effective stress on the pore structure, the nonlinear deformation of cracks is incorporated into our rock physics model, thereby extending its stress applicability. The modelling results indicate that two compressional waves (fast P- and slow P-waves) and a shear wave (S-wave) coexist. As the effective stress increases, the velocities of the fast P- and S-wave increase, accompanied by reductions in dispersion and attenuation, which can be attributed to crack closure. In addition, with increasing frequency, the fast P-wave velocity exhibits three successive attenuation peaks, corresponding to the effects of WIFF at meso-, micro-, and macro-scales. In contrast, the slow P-wave velocity appears only at higher frequencies, and its variation is more significantly influenced by water saturation than by effective stress. The validity of the proposed model is demonstrated through comparison with previously published experimental data. Furthermore, our model is used to establish a rock-physics approach to estimate the wave velocities with the well-logging data. The predicted results agree well with the logging measured data, further confirming the feasibility of our approach. Our study and results provide a useful tool for hydrocarbon exploration, CO₂ storage monitoring, and hydrogeology.