Acoustic waves in a borehole penetrating a double-porosity formation

The focus of hydrocarbon reservoir exploration and development has increasingly shifted toward unconventional reservoirs, particularly tight formations. These reservoirs are distinguished by their low porosity and permeability, as well as a complex pore structure comprising numerous pores and fractures. Conventional poroelasticity-based rock physics models, which typically assume single-scale pore structures, are insufficient for characterizing acoustic wave responses. Consequently, establishing the relationship between acoustic waves and pore-scale heterogeneity remains a critical challenge. To address this problem, this study focused on acoustic logging in double-porosity formations described by Biot–Rayleigh theory. A semianalytical method was proposed for calculating the full-waveform acoustic responses in boreholes penetrating double-porosity formations, and numerical simulations were conducted to investigate the properties of acoustic logging response. To capture the frequency-dependent behavior of borehole waves, the dynamic permeability was incorporated into the double-porosity model. Synthetic signal analysis revealed distinct waveform characteristics in a double-porosity medium compared to the results in a single-porosity medium. In high-permeability formations, the inclusions volume ratio had a frequency-dependent impact on wave behavior: (1) at low frequencies, Stoneley wave amplitude increased with inclusions volume ratio, and (2) at high frequencies, pseudo-Rayleigh waves experienced amplitude attenuation and velocity reduction as the inclusions volume ratio increased. In tight formations, changes in inclusions radius and volume ratio continued to influence acoustic fields, causing the shifts in arrival times and changes in wave amplitudes. The results highlighted the essential role of incorporating pore-scale heterogeneity in effective reservoir characterization.