Attenuation of elastic waves due to wave-induced vorticity diffusion in porous media

Abstract

A theory for attenuation of elastic waves due to wave-induced vorticity diffusion in the presence of randomly correlated pore-scale heterogeneities in porous media is developed. It is shown that the vorticity field is associated with a viscous wave in the pore space, the so-called slow shear wave. The latter is linked to the porous medium acoustics through incorporation of the fluid strain rate tensor of a Newtonian fluid in the poroelastic constitutive relations. The method of statistical smoothing in random media is used to derive dynamic-equivalent elastic wave numbers accounting for the conversion scattering process into the slow shear wave. The result is a model for wave attenuation and dispersion associated with the transition from viscosity- to inertia-dominated flow regime in porous media. It is also shown that the momentum flux transfer from the slow compressional into the slow shear wave is a proxy for the dynamic permeability in porous media. A dynamic permeability model is constructed that consists of an integral over the covariance function of the random pore-scale heterogeneities modulated by the slow shear wave. In a smooth pore-throat limit, the results reproduce the dynamic permeability model proposed by Johnson etal. [J. Fluid Mech. 176, 379 (1987).]