The heterogeneous spatial distribution of fluids induced by capillarity leads to the difficulty to accurate describe seismic wave dispersion and attenuation in partially saturated rocks, affecting the precision of hydrocarbon reservoir exploration. In this work, based on the Santos framework, a modified Santos-Rayleigh model was developed for partially saturated double-porosity medium by reformulating the Biot-Rayleigh equations to incorporate capillarity and kinetic energy effects within fluid inclusions. Numerical analysis reveals that the presence of capillarity induces an additional enhancement of P-wave velocity within low-frequency. Furthermore, under varying configurations of water, oil and gas, the P-wave velocities in the low-frequency band fall below the Gassmann-Wood limit due to coupled capillarity and mesoscopic flow. Significant dispersion and attenuation occur when gas serves as the inclusion, and a smaller modulus contrast between the host and inclusions leads to weaker low-frequency dispersion. The internal kinetic energy of inclusion gives rise to a shift of both dispersion and attenuation toward lower frequencies. Comparison with the experimental data confirms that the modified model exhibits a good low-frequency agreement, providing reliable velocity predictions under varying water saturation levels.

Source rocks (shales) exhibit different geometric pore types and considerable anisotropy caused by the preferential orientation of the clay and kerogen layers, which is not accounted for in classical rock-physics models. Pore geometry can be effectively studied through the aspect ratio, and in this study, we use the aspect ratio to characterize different pore geometries. Then, we consider a pore connectivity index as well as a lamination index associated with these orientations. An inclusion-based theory (differential effective medium and self-consistent approximation) and the Brown-Korringa equations are used in the modeling approach. The results show that the indices as well as the aspect ratio of the connected pores significantly affect the elastic properties. We propose an inversion method to invert these three parameters simultaneously from experimental vertical P- and S-wave velocities using a global optimization algorithm. The method is applied to well log and seismic data from the Longmaxi shale reservoir in southwest China to verify its predictive ability.

Understanding the effects of cracks on the elastic and electrical properties of tight carbonates is crucial for the exploration and development of deep and ultra-deep carbonate reservoirs. In this work, the porosity, electrical conductivity and ultrasonic velocities of two brine-saturated carbonate samples (where the pore space is dominated by cracks) are measured jointly at different effective pressures (5-90 MPa), as well as the velocities with saturating nitrogen at the same pressure conditions. The results show non-linear changes in the measured values, indicating a correlation with the presence of cracks. To analyze the pressure-dependent elastic and electrical properties, an approach combining a multiphase Kachanov model with a multiphase reformulated electrical differential effective medium (REDEM) model is proposed. This approach agrees well with the pressure-dependent experimental results of brine-saturated carbonate samples. The crack aspect ratio spectra are estimated using the experimental porosity as a constraint to improve the accuracy of the inverted crack geometry. The spectra from the elastic (electrical) inversion are input into the multiphase REDEM (Kachanov) model to predict the electrical conductivity (wave velocities). Comparisons with laboratory measurements show the ability of the proposed approach to estimate elastic wave velocities from the electrical conductivity using the inverted crack geometry, and vice versa.