Calculation of matrix permeability from velocity and attenuation of ultrasonic S-wave

Abstract

Abstract Previously, hydrogeologists and petroleum engineers use seepage experiments to measure permeability. This paper develops a novel method to calculate matrix permeability from velocity and attenuation of an ultrasonic S-wave. At first, permeability is derived as a function of frequency when an S-wave scans a fluid-saturated rock. Substituting the permeability into a previous S-wave model gives theoretical velocity and attenuation, in which the nexus parameter is the average distance of aperture representing pores. Fitting the predicted velocity and quality factor against the measured counterparts yields permeability in the full frequency range. For Berea sandstone, the inverted permeability at low frequency (0.0376 Darcy) is comparable to Darcy permeability (0.075 Darcy), confirming that Berea sandstone is homogenous. For Boise sandstone, the inverted permeability at low frequency is 0.0457 Darcy, much lower than Darcy permeability (1 Darcy). When S-wave scans the rocks, its velocity and attenuation are dominated by matrix pore throats and the inverted permeability represents matrix permeability. Unlike Berea sandstone, Boise sandstone has fractures and widely distributed grain diameters. The fractures and the large pores (due to large grain diameter) are preferential pathways that increase Darcy permeability far more than matrix permeability.