Abstract

In the paper, two modeling strategies for the computation of the effective permeability of heterogeneous, fractured rocks utilizing homogenization over a representative elementary volume (REV) are proposed and compared. One method is based on a new continuum micromechanics model. Here, the REV represents distributed fractures idealized as penny shaped inclusions in a porous matrix. The effective properties computed by this model are anisotropic and depend on the intrinsic properties of the porous matrix and the topology and density of the fractures. We propose a novel Cascade Continuum Micromechanics model (CCM), which is able to predict a fracture percolation threshold for a particular fracture density as a function of the topology of the fractures. The second modeling strategy is based on an Extended/Generalized Finite Element model (XFEM-GFEM) recently developed for numerical simulations of hydraulic fracturing in deep geothermal reservoirs. The predictions for the effective permeability from both models are compared for a REV containing distributed fractures with different aspect ratios and crack densities.

1 Introduction

The effective transport property of heterogeneous rocks with diffusively distributed fractures at various scales (from microcracks in the sub-mm to macroscopic fractures in the m range) is strongly influenced by their distribution, orientation and their interactions with the porous matrix material. Reliable estimates for effective transport properties of fractured rocks are relevant in various projects in subsurface engineering, such as the construction of tunneling or caverns, the exploitation of oil and gas and geothermal energy reservoirs or the installation of underground storage systems (see, e.g. Tiab & Donaldson (2012), Economides & Nolte (2000) and references therein). In this paper, we propose two methods to determine the effective permeability of heterogeneous rocks. The first strategy is based on continuum micromechanics. Based on a representative elementary volume element (REV), representing distributed fractures idealized as penny shaped inclusions in a porous matrix, the effective anisotropic permeability is predicted. To investigate the percolation probability of the fracture network, we use a novel Cascade Continuum Micromechanics model (CCM) (Timothy & Meschke 2013). The model predicts a fracture percolation threshold for a particular fracture density as a function of the topology of the fractures. This provides initial estimates for the connectivity characteristics of the fracture system and allows to characterize the interrelations between diffusivity, permeability and the anisotropic stiffness. The second strategy uses computational homogenization based on a discrete representation of distributed cracks using a novel Extended/Generalized Finite Element model (Meschke & Leonhart 2015) recently proposed for numerical simulations of hydraulic fracturing in deep geothermal reservoirs. Both modeling strategies are investigated and compared by means of different configurations of fractured rocks.

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