An Exact Expression for the Effective Bulk Modulus for Acoustic Wave Propagation in Cylindrical Patchy-Saturation Rocks

Hydrocarbon reservoirs often contain partially gas-saturated rocks that have attracted the attention of exploration geophysicists and geologists for many years. Wave-induced fluid flow (WIFF) is an effective mechanism to quantify seismic wave dispersion and attenuation in partially gas-saturated rocks. In this study, we focus on the local fluid flow induced by variations in fluids in different regions and present a new model that describes seismic wave propagation in partially gas-saturated rocks, namely, the cylindrical patchy-saturation model. Because the seismic wave velocity and attenuation oscillate at high frequencies, it is not ideal for studying dispersion and attenuation caused by WIFF. To avoid the high-frequency oscillation in the cylindrical patchy-saturated model, we use an approximation to the Newman function instead of the full Newman function to calculate the effective bulk modulus. We then calculate the P-wave velocity and attenuation of the proposed model and interpret the lab-measured data. The proposed model is an alternative patchy-saturation model that can explain the problem of high-frequency oscillation and low-frequency attenuation.