The Effect of Dynamic Permeability on Velocity and Intrinsic Attenuation of Compressional Waves in Sand

Stress waves contain useful information about the properties of porous materials; they can be recovered through different non-destructive testing methods such as crosswell, vertical seismic profile, borehole logging as well as sonic tests. In all these methods, it is crucial to assess the effects of frequency on wave attributes including velocity and intrinsic attenuation. The dependency of permeability on frequency which is known as dynamic permeability and its effects on wave attributes of compressional waves are investigated in the present paper. Utilizing the dispersion relation derived for compressional waves, it is shown how the velocity and intrinsic attenuation of waves propagated in water saturated sand may be influenced by dynamic permeability. In low frequency range (viscous dominated flow regime), the dynamic permeability behaves like Darcy steady-state permeability and its effects on wave attributes are negligible. However, deviations from Darcy permeability start to occur at higher frequencies. Therefore, it is important to know how dynamic permeability controls the behavior of wave velocity and intrinsic attenuation in relatively high frequencies.  For example, it is demonstrated that neglecting dynamic permeability results in overestimation of velocities of fast and slow waves in high frequency ranges (inertia dominated flow regime).