Numerical upscaling of frequency-dependent P- and S-wave moduli in fractured porous media

ABSTRACT Relating seismic attributes to the characteristics of mesoscopic fractures is inherently challenging, yet these heterogeneities tend to dominate the mechanical and hydraulic properties of the medium. Analytical approaches linking the effects of material properties on seismic attributes, such as attenuation and velocity dispersion, tend to be limited to simple geometries, low fracture densities, and/or non‐interacting fractures. Furthermore, the influence of fluid flow within interconnected fractures on P‐wave and S‐wave attenuation is difficult to accommodate in analytical models. One way to overcome these limitations is through numerical upscaling. In this paper, we apply a numerical upscaling approach based on the theory of quasi‐static poroelasticity to fluid‐saturated porous media containing randomly distributed horizontal and vertical fractures. The inferred frequency‐dependent elastic moduli represent the effective behaviour of the underlying fractured medium if the considered sub‐volume has at least the size of a representative elementary volume. We adapt a combined statistical and numerical approach originally proposed for elastic composites to explore wether the overall statistical properties of simple fracture networks can be captured by computationally feasible representative‐elementary‐volume sizes. Our results indicate that, for the considered scenarios, this is indeed possible and thus represent an important first step towards the estimation of frequency‐dependent effective moduli of realistic fracture networks.