Sonic Dispersions of P-Waves of Two Types: Fractured Safaniya Sandstone

Abstract

As P-waves propagate in fractured porous rock, fluid pressure in fractures may be distinct from that in the contiguous matrix; the fluid pressure differential can drive a viscous squirt between them, which substantially attenuates the waves. A double porosity model of P-waves is constructed based on this mechanism and under the major assumption of isotropic fractures. As a second assumption, matrix permeability between two neighboring rock units is set to zero, whereas fracture permeability is not vanishing to allow the existence/propagation of slow P-wave. The resulting wavenumber equation has two eigenvalues representing two types of P-waves. The P-wave of the first type is the fast P-wave in acoustics, whereas the P-wave of the second type is the slow P-wave in hydrogeology. Safaniya sandstone of the Wasia Formation is used for illustration. The parameters of the sandstone are calibrated by the phase velocity and quality factor of the fast/acoustic P-wave, measured at 10 kHz from a sonic log in Saudi Arabia. Thus, the dispersions/attenuations of P-waves of the two types are determined. The results reveal that fast P-wave dispersion in the low-frequency (seismic) regime is small, whereas that in the high-frequency (sonic) regime is extraordinarily large. The small fracture Biot dispersion at low frequencies arises from interfracture viscous flow, whereas the large dispersion at high frequencies arises from fracture–matrix squirt. The clear separation of the two mechanisms in the frequency domain is the novelty of this study.