Conforming, non-conforming and non-matching discretization couplings in discrete fracture network simulations

Abstract

Simulations of fluid flow in naturally fractured rocks have implications for several subsurface applications, including energy storage and extraction, and waste storage. We are interested in flow in discrete fracture networks, which explicitly represent flow in fracture surfaces, but ignore the impact of the surrounding host rock. Fracture networks, generated from observations or stochastic simulations, will contain intersections of arbitrary length, and intersection lines can further cross, forming a highly complex geometry. As the flow exchange between fractures, thus in the network, takes place in these intersections, an adequate representation of the geometry is critical for simulation accuracy. In practice, the intersection dynamics must be handled by a combination of the simulation grid, which may or may not resolve the intersection lines, and the numerical methods applied on the grid. In this work, we review different classes of numerical approaches proposed in recent years, covering both methods that conform to the grid, and non-matching cases. Specific methods considered herein include finite element, mixed and virtual finite elements and control volume methods. We expose our methods to an extensive set of test cases, ranging from artificial geometries designed to test difficult configurations, to a network extruded from a real fracture outcrop. The main outcome is guidances for choice of simulation models and numerical discretization with a trade off on the computational cost and solution accuracy.

An unfitted finite element method for the Darcy problem in a fracture network

“…Here we used (20) (which remains true with Ω i h and O(∂Γ i ) instead of Ω i h and Γ i ) and (21). For the rest of p − q h * we use interpolation properties of bilinear polynomials, (25) and (20) to obtain…”

“…Estimates (27)- (29) lead to the desired bound on p − q h * . Similar to (28)-(29), we use interpolation properties of bilinear polynomials, (25) and (20), to obtain…”

“…Although a triangulation of each fracture surface were build, these triangulations do not match the fracture intersection points, and the authors applied XFEM methodology to handle discontinuities in the solution over the junctions. The recent paper [20] reviews this and other numerical approaches, where a different degree of the conformity of fracture meshes at junction interfaces is assumed. However, triangulating each fracture branch can be itself a demanding task for large networks or complex geometry.…”

Discontinuous Boundary Elements for Fluid Flow Problems in Discrete Fracture Networks

“…DFN is alternative to EPM for multi-scale fracture networks where all the fractures must be explicitly represented. [30,26].…”

“…

generated over the entire fracture system and the flow field is then obtained by resorting to the Finite Element Method (FEM) or the Finite Volume Method (FVM). These methods offer considerable precision but, given the geometrical complexity of a DFN (see Fig.1a) the use implies high computational demand and memory usage [28], also originating from high-quality mesh generation and Local Grid Refinement (LGR), both required to accurately resolve the sharp pressure gradients around the intersections (traces) among fractures and in the near-field of a well [26]. In Fig.

…”