Pore scale numerical modeling of elastic wave dispersion and attenuation in periodic systems of alternating solid and viscous fluid layers

Numerical pore-scale simulation of elastic wave propagation is an emerging tool in the analysis of static and dynamic elastic properties of porous materials. Rotated staggered-grid (RSG) finite difference method has proved to be particularly effective in modeling porous media saturated with ideal fluids. Recently this method has been extended to viscoelastic (Maxwell) media, which allows simulation of wave propagation in porous solids saturated with Newtonian fluids. To evaluate the capability of the viscoelastic RSG algorithm in modeling wave dispersion and attenuation we perform numerical simulations for an idealized porous medium, namely a periodic system of alternating solid and viscous fluid layers. Simulations are performed for a single frequency of 50kHz (for shear waves) and 500kHz (for compressional waves) and a large range of fluid viscosities. The simulation results show excellent agreement with the theoretical predictions. Specifically the simulations agree with the prediction of Biot’s theory of poroelasticity at lower viscosities and with the viscoelastic dissipation at higher viscosities. The finite-difference discretization is required to be sufficiently fine for the appropriate sampling of the viscous boundary layer to achieve accurate simulations at the low values of viscosity. This is an additional accuracy condition for finite-difference simulations in viscoelastic media.