Biot／Squirt Model in Viscoelastic Porous Media

Viscoelastic wave equations are derived for both the Biot flow and squirt-flow involved.The relationship between phase velocity or attenuation of viscoelastic wave and macro parameters of the reservoir is clarified in a porous extensive dilatancy anisotropy medium.Numerical models clearly demonstrate that the viscoelastic property of rocks,not the squirt-flow,causes the dispersion and attenuation in the low-frequency range.The attenuation of the quasi SV-wave,SH-wave and the quasi P-wave depend strongly on the directions of permeabilities.Furthermore,the trends of attenuation of the quasi P-wave fast and the quasi SV-wave are inversed in both the high-frequency and low-frequency ranges.Our numerical result is in agreement with the experimental result that was carried out for the Biot/Squirt model by Jorge [Geophys.65(2000)202].     

Viscoelastic BISQ Model for Low-Permeability Sandstone with Clay

A modified BISQ （Blot/Squirt） model for wave propagation in low-permeability sandstone is developed by introducing the viscoelastic mechanism of a porous skeleton into Dvorkin＇s model. The linear viscoelasticity of the Kelvin Voigt constitutive law is employed to describe the stress-strain relation of a solid frame with clay while the ultrasonic waves propagate through the fluid-saturated sandstone. The phase velocity and attenuation of two p-waves are given based on the present BISQ model. The comparisons between numerical results and experimental data indicate that our viscoelastic model is more realistic and feasible for wave propagation in the low-permeability sandstone, especially with clay, than traditional BISQ models.