Velocity and attenuation of ultrasonic S-wave in Berea sandstone

Abstract

In Biot theory, the relative velocity between fluid and solid and their relative acceleration, via Darcy permeability and the coupling factor, respectively, are used to quantify stress between the phases. In this paper, the relative velocity via variable permeability is used to improve the quantification of the stress. The modeling quantities are the S-wave velocity ratio of brine saturated Berea sandstone to the dry sandstone and the (viscous-flow-induced) attenuation. Although skeleton shear modulus depends on differential pressure (the confining pressure minus pore pressure), the two quantities are conservative at small differential pressures. The modeling results reveal that Berea sandstone has a permeability of 0.02–0.03 Darcy for S-wave at 1 MHz, much smaller than Darcy permeability (0.075 Darcy). The cause is that with the increase of frequency, the thinning of Stokes boundary layer decreases permeability. Moreover, the total porosity of 0.23 is better than the effective porosity of 0.20 in the simulation, because S-wave does not discriminate connected pores or occluded pores.