Abstract
This paper deals with the computational homogenization and numerical model reduction of deformation driven pressure diffusion in fractured porous rock. Exposed to seismic waves, the heterogeneity of the material leads to local fluid pressure gradients which are equilibrated via pressure diffusion. However, a macroscopic observer is not able to measure the diffusion process directly but senses the intrinsic attenuation of an apparently monophasic viscoelastic solid. The aim of this paper is to establish a reliable, yet numerically efficient, computational homogenization method to identify the viscoelastic properties of the macroscopic substitute model. Inspired by the Nonuniform Transformation Field Analysis, we incorporate a Numerical Model Reduction procedure. The proposed method is validated for several scenarios ranging from pressure diffusion in an unfractured poroelastic matrix, via localized pressure diffusion in interconnected fractures embedded in an impermeable matrix, to the fully coupled pressure diffusion both in fractures and the embedding poroelastic matrix.
Highlights
Fractures that are present in subsurface formations dominate their mechanical properties and their hydraulic properties [2,31]
A few numerical upscaling approaches have been used in the recent years to compute, at the level of a Representative Volume Element (RVE), frequency-dependent attenuation and the corresponding dispersion of the elastic moduli caused by squirt-type flow in interconnected fractures [22,23,26,30]
In this paper we develop a Numerical Model Reduction (NMR) technique based on the concepts of computational homogenization
Summary
Fractures that are present in subsurface formations dominate their mechanical properties and their hydraulic properties [2,31]. When interconnected, they can increase the hydraulic conductivity of a rock by several orders of magnitude [20,28]. They can increase the hydraulic conductivity of a rock by several orders of magnitude [20,28] This makes the detection and characterization of fracture networks of enormous interest for applications such as the geological sequestration of CO2, production of deep geothermal energy, nuclear waste storage, and the explo-
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