Constrained energy minimization based upscaling for coupled flow and mechanics

TL;DR

This paper introduces an embedded fracture model and an energy minimization-based upscaling method for coupled flow and mechanics in fractured porous media, enabling efficient and accurate coarse-scale simulations.

Contribution

It develops a novel nonlocal multicontinuum upscaling approach using energy minimization for coupled flow and mechanics in fractured media.

Findings

Effective coarse-scale model with physical meaning

Fast and accurate solver for poroelasticity problems

Numerical validation on 2D model problem

Abstract

In this paper, our aim is to present (1) an embedded fracture model (EFM) for coupled flow and mechanics problem based on the dual continuum approach on the fine grid and (2) an upscaled model for the resulting fine grid equations. The mathematical model is described by the coupled system of equation for displacement, fracture and matrix pressures. For a fine grid approximation, we use the finite volume method for flow problem and finite element method for mechanics. Due to the complexity of fractures, solutions have a variety of scales, and fine grid approximation results in a large discrete system. Our second focus in on constructing the upscaled coarse grid poroelasticity model for fractured media. Our upscaled approach is based on the nonlocal multicontinuum (NLMC) upscaling for coupled flow and mechanics problem, which involves computations of local basis functions via an energy minimization principle. This concept allows a systematic upscaling for processes in the fractured porous media, and provides an effective coarse scale model whose degrees of freedoms have physical meaning. We obtain a fast and accurate solver for the poroelasticity problem on a coarse grid and, at the same time, derive a novel upscaled model. We present numerical results for the two dimensional model problem.