Coupled Hydro-Mechanical Upscaling for a Deformable Fractured Porous Medium: The Biot Coefficients Moduli Related to the Matrix-Cracks System

摘要

A methodology for upscaling 3D coupled Hydro-Mechanical (HM) properties of fractured porous rocks is developed theoretically and tested on synthetic fractured rock samples. We consider the case of water-saturated elastic rock modeled as a deformable porous matrix with deformable cracks filled with compressible water. The upscaling is a strain superposition method, in which the local strains in the matrix and in the cracks are superimposed under the effect of a frozen "effective" stress field. Given the geometric and coupled hydro-mechanical properties of the matrix and cracks, the superposition method yields a system of upscaled continuum laws with equivalent tensorial mechanical and HM coefficients. We obtain in the fluid production equation a "second" Biot coefficient, B_(ij(~(II) and two distinct Biot moduli, M~(I) and M~(II). The theoretical tensorial expressions are then specialized to the case of isotropic crack systems and are tested by running 3D upscaling "experiments" on synthetic, statistically homogeneous and isotropic, Poissonian crack systems.