A Homogenization Framework for Inelastic Layered Porous Materials

Abstract:

Many applications involving geomaterials, such as reservoir engineering, geothermal energy, and waste storage, entail tight coupling between multiphase fluid flow, transport, as well as thermo-mechanical and poromechanical deformations. Natural rocks are often highly heterogeneous and consist of fractures, solid and fluid phases that form complex structures at multiple scales. Explicit incorporation of multiple scales of fractures and heterogeneities into large-scale tightly coupled models is impractical and would cause tremendous computational costs. Therefore, efficient multi-scale strategies are necessary for capturing the impacts of sub-grid-scale processes on macroscopic behavior.

In this work, we present a homogenization framework for inelastic multi-scale layered porous media. Subsequently, we demonstrate extension of the framework to coupled hydro-mechanical problems. We describe a homogenization strategy for computing both the mechanical and fluid flow constitutive behavior of fractured rock. Contrary to continuum-scale constitutive models, the present framework accounts for the coupling between planes of weakness and the matrix. In addition, the proposed approach allows for separate micro-constitutive laws and properties for each layer, explicit representation of layers with different properties and their distribution, as well as incorporation of imperfect bonding between the adjacent layers. Simulation results show that important features such as strength and permeability anisotropy are derived naturally from the small-scale description of the layered structure and fracture distribution. We show how the proposed material models can be readily incorporated into discrete-fracture-network or continuum simulations of reservoir systems, to provide an efficient way of capturing both small- and large-scale processes.