A new squirt coefficient to simulate P‐wave attenuation

Abstract

ABSTRACTIn double‐permeability models, the squirt coefficient representing the fluid mass equation came from mathematical parameterization that was inconsistent with physics, resulting in the prediction of an infinitely large squirt coefficient at an infinitely high frequency. This was a drawback of the models, as an infinitely large squirt flux rate means unrealistic infinite large velocity and kinematic energy (velocity and energy must be bounded). This paper is motivated by solving the problem. At first, when P‐wave compresses a porous rock, the contact of grains (the normal of which is the wave direction) is very compliant, which generates a strong squirt transverse to the wave direction. In contrast, the squirt along the wave direction is relatively small. Based on such a transverse squirt mechanism, a new squirt coefficient is derived, which yields a vanishing value at infinite high frequency. Secondly, the squirt coefficient is put into a previous model to predict velocity and attenuation of ultrasonic P‐wave. Two core samples (Berea sandstone and Boise sandstone) are used for illustration; both the measured velocity and quality factor are well simulated. It is notable that there is an interesting shoulder on the velocity dispersion curves before the asymptotical behaviour of velocity at high frequency.