Dissipation factor and phase velocity approximate formulas for P-waves in fluid-saturated porous media

Actual sedimentary rocks are generally homogeneous porous media saturated by fluid, which are described by poroelastic media. Wave velocity and dissipation factor in poroelastic media provide essential information about rock and fluid properties and are widely used in many fields. The exact wave velocity and dissipation factor can be obtained from wavenumbers determined by dispersion equation through complex mathematic operations. Reported approximate formulas are most given under the assumption that the characteristic angular frequency (ωc) is far larger than the angular frequency (ω) and becomes invalid for high frequency. Thus, this paper derived phase velocity and dissipation factor approximation of the two P-waves in poroelastic media for the whole low-frequency range. Based on the Geertsma–Smit approximation, we modified the infinite-frequency limiting velocity for fast P-wave approximation and removed the ω/ωc<<1 assumption for slow P-wave approximation. Numerical analysis shows that the proposed approximate formulas for P-waves in porous media can reveal the exact variations of phase velocity and dissipation factor in the low-frequency range, which is from zero frequency for isotropic media to the characteristic frequency. Phase velocity approximations of the two P-waves in poroelastic media are very close to exact values, with maximum relative errors being far less than 1%.