Acoustic waves attenuation and velocity dispersion in fluid-filled porous media: theoretical and experimental investigations

Abstract

New model of acoustic wave propagation in saturated porous media is developed. Like the Biot/Squirt flow (BISQ) theory it combines both the Biot and Squirt flow mechanisms. The novelty in this model is that the expression of average pore fluid pressure is independent of the characteristic squirt flow length introduced in the BISQ theory. Taking advantage of t he analytical relation between velocity (attenuation) and measurable rock physical parameters such as permeability, porosity, Pore fluid viscosity and compressibility, velocity and attenuation dispersion versus frequency is modelled for different permeability values: 1.25 md, 5 md, 10 md and 20 md. The results using the proposed model and the earlier BISQ theory show the same order of magnitude in attenuation and velocity dispersion versus frequency but reverse behaviour with respect to permeability change. An attempt to determine permeability using both theories on experimental data from highly permeable beach sands (unlithified) material shows good agreement with laboratory measured values. Ultrasonic data acquired on two different sets of sandstone samples are compared to velocity and attenuation prediction from the Biot/Squirt flow (BISQ) model and our newly proposed model. Our model better resolves measured velocity from the first set of sandstone samples. The attenuation however is highly underestimated by both models. In the second set of samples, the Gassmann's velocity is calculated from measured dry P- and S-wave velocities at different confining pressures and is compared to the result of low-frequency velocity prediction from the previous models. It was expected that velocity predicted by both models converges to the Gassmann's velocity at confining pressure high enough to suppress the squirt flow effect. Despite evidence (from the velocity vs. confining pressure curves) of the closure of microcracks that enhance the squirt flow effect the Gassmann's velocity was still much larger than other models prediction. We argue that evidence of clay inclusion in the sandstone matrix might be responsible for the poor resolution of attenuation in the former set of samples, and the misfit between velocities in the second set. Qualitative agreement was observed between velocity dispersion estimated from field experimental data and theoretical prediction using the reformulated BISQ model.