Velocity field of wave-induced local fluid flow in double-porosity media

Abstract

Under the excitation of elastic waves, local fluid flow in a complex porous medium is a major cause for wave dispersion and attenuation. When the local fluid flow process is simulated with wave propagation equations in the double-porosity medium, two porous skeletons are usually assumed, namely, host and inclusions. Of them, the volume ratio of inclusion skeletons is low. All previous studies have ignored the consideration of local fluid flow velocity field in inclusions, and therefore they can not completely describe the physical process of local flow oscillation and should not be applied to the situation where the fluid kinetic energy in inclusions cannot be neglected. In this paper, we analyze the local fluid flow velocity fields inside and outside the inclusion, rewrite the kinetic energy function and dissipation function based on the double-porosity medium model containing spherical inclusions, and derive the reformulated Biot-Rayleigh (BR) equations of elastic wave propagation based on Hamilton’s principle. We present simulation examples with different rock and fluid types. Comparisons between BR equations and reformulated BR equations show that there are significant differences in wave response characteristics. Finally, we compare the reformulated BR equations with the previous theories and experimental data, and the results show that the theoretical results of this paper are correct and effective.