Modeling effective elastic properties of digital rocks using a new dynamic stress-strain simulation method

Abstract

We have developed a dynamic stress-strain simulation methodology to compute effective elasticity on digital rocks in a wide range of frequency based on the rotated staggered grid finite-difference method. The primary advantage of this simulator lies in characterizing the anisotropic behavior of complex porous rocks by setting specified boundary conditions along specified directions: The edges perpendicular to the propagating wave are applied with a strain boundary condition, and the edges parallel to the propagating wave are applied with a periodic boundary condition. The accuracy of the simulator is validated by comparing the simulating results in microinhomogeneous porous media containing randomly distributed inclusions and aligned oriented cracks, with that obtained by effective medium theories of self-consistent approximation in isotropic and anisotropic domains. This dynamic simulator can successfully capture anisotropic magnitude of rocks containing needle-like inclusions with different degrees of alignment. For real digital rock saturated with viscoelastic fluids, it is able to predict the dependence of velocities and attenuating factors on the frequency. We found that the magnitude of dispersion increases with the increase of pore fluid viscosity. Therefore, this method offers a robust and effective tool to compute effective elastic properties and anisotropy for real complex porous rocks.