An Extended Finite Element Model for Fluid Flow in Fractured Porous Media

Fei Liu,Li-Qiang Zhao,Nian-Yin Li,Pei-Shan Wang,Zhi-Feng Luo,Ping-Li Liu

doi:10.1155/2015/604212

Abstract

This paper proposes a numerical model for the fluid flow in fractured porous media with the extended finite element method. The governing equations account for the fluid flow in the porous medium and the discrete natural fractures, as well as the fluid exchange between the fracture and the porous medium surrounding the fracture. The pore fluid pressure is continuous, while its derivatives are discontinuous on both sides of these high conductivity fractures. The pressure field is enriched by the absolute signed distance and appropriate asymptotic functions to capture the discontinuities in derivatives. The most important advantage of this method is that the domain can be partitioned as nonmatching grid without considering the presence of fractures. Arbitrarily multiple, kinking, branching, and intersecting fractures can be treated with the new approach. In particular, for propagating fractures, such as hydraulic fracturing or network volume fracturing in fissured reservoirs, this method can process the complex fluid leak-off behavior without remeshing. Numerical examples are presented to demonstrate the capability of the proposed method in saturated fractured porous media.

Highlights

This paper proposes a numerical model for the fluid flow in fractured porous media with the extended finite element method
Flow models estimating the flow in fractured porous media mainly include the equivalent continuum model [1], dual continuum model [2], discrete fracture model [3], and discrete fracture network model [4, 5]
In the equivalent continuum model, a representative elementary volume (REV) is required, the fractures are assumed to distribute regularly, and the equivalent permeability is hard to determine [6], which make it unavailable while several large fractures existed such as hydraulic fractures, complex fractures network, and big faults

Summary

Introduction

Flow models estimating the flow in fractured porous media mainly include the equivalent continuum model [1], dual continuum model [2], discrete fracture model [3], and discrete fracture network model [4, 5]. Discrete fracture network model is more real and gains worldwide concern recently because the fractures are treated explicitly and the effect of one crack on the whole flow could be considered [9]. Yao Jun et al [10] presented a two-dimensional two-phase finite element flow model based on explicit treating of discrete fracture network. Lamb [17] and Lamb et al [18] combined XFEM with the dual-porosity and dual-permeability model to describe the fluid flow, deformation, and fracture propagation in fractured porous medium. The results demonstrate that the XFEM is an efficient method for simulating fluid flow in fractured porous medium with nonmatching grids, especially when the fissure is propagating, such as hydraulically driven fractures

Governing Equation

Pressure Enrichment with XFEM

Discretization Equation of XFEM

Numerical Examples