A Numerical Procedure To Estimate The Effective Moduli In Highly Heterogeneous Fluid-Saturated Porous Media

Abstract

An important upscaling effect in heterogeneous poroelastic Biot media is the dissipation
mechanism due to wave-induced fluid flow caused by mesoscopic scale heterogeneities, which are larger
than the pore size but much smaller than the average wavelengths of the fast waves in the seismic range of
frequencies. To perform numerical simulations using Biot’s equations of motion, it would be necessary
to employ extremely fine meshes to properly represent these mesoscopic heterogeneities. An alternative
approach to model this type of Biot medium is to determine effective complex moduli defining locally
a viscoelastic medium having in the average the same properties than the original medium. This work
presents a finite element procedure combined with a Montecarlo approach to estimate the effective phase
velocity and mesoscopic attenuation in highly heterogeneous porous rocks. The method involves the use
of stochastic fractals to generate different stochastic parameter patterns within the porous sample. For
each realization of the stochastic parameters, a local boundary value problem is solved on a representative
volume of bulk material. Numerical experiments showing the implementation of the procedure are
presented.