Acoustic response characteristics of unsaturated porous media

By employing the plane wave analysis method, the dispersion equations associated with compressional and shear waves using Santos’s three-phase poroelastic theory were driven. Considering the reservoir pressure, the high frequency corrections and the coupling drag of two fluids in pores, the influences of frequency and gas saturation on the phase velocities and the inverse quality factors of four body waves predicted by Santos’s theory were discussed in detail. The theoretical velocities of the fast compressional and shear waves were compared with the results of the low and high frequency experiments from open publications, respectively. The results showed that they are in good agreement in the low frequency case rather than in the high frequency case. In the latter case, several popular poroelastic models were considered and compared with the experimental data. In the models, the results of White’s theory fit the experimental data, but the parameter b in White’s model has a significant impact on the results. Under the framework of the linear viscoelasticity theory, the attenuation mechanism of Santos’s model was extended, and the comparisons between the experimental and theoretical results were also made with respect to attenuation. For the case of water saturation less than 90%, the extended model makes good predictions of the inverse quality factor of shear wave. There is a significant difference between the experimental and theoretical results for the compressional wave, but the difference can be explained by the experimental data available.