A New Approach to Simulating Flow in Discrete Fracture Networks with an Optimized Mesh

Abstract

Natural fractured media are highly unpredictable because of existing complex structures at the fracture and at the network levels. Fractures are by themselves heterogeneous objects of broadly distributed sizes, shapes, and orientations that are interconnected in large correlated networks. With little field data and evidence, numerical modeling can provide important information on the underground hydraulic phenomena. However, it must overcome several barriers. First, the complex network structure produces a structure difficult to mesh. Second, the absence of a priori homogenization scale, along with the double fracture and network heterogeneity levels, requires the calculation of large but finely resolved fracture networks resulting in very large simulation domains. To tackle these two related issues, we reduce the highly complex geometry of the fractures by applying a local transformation that suppresses the cumbersome meshing configurations while keeping the networks fundamental, geological, and geometrical characteristics. We show that the flow properties are marginally affected while the problem complexity (i.e., memory capacity and resolution time) can be divided by orders of magnitude. The goal of this article is to propose a method of resolution which takes into account the geometrical complexity met in the networks and which makes it possible to treat a few thousand fractures. The principal aim of this article is to present a tool to slowly modify the structures of the fracture networks to have a good quality mesh with a marginal loss in precision. Introduction.The underground waste repository projects and exploitation of hot, dry, rock geothermal energy have spurred studies in fracture networks transport properties. Many site-specific studies have flourished around various projects [7], which are generally based on a careful characterization of the structure of the fractured rock mass, with the classical difficulty of deducing three-dimensional information from one-or two-dimensional field data [3]. Then the hydraulic properties are computed by using reconstructed model networks, based on the experimental geometrical characteristics, and various flow models. The flow fluid modeling in underground media requires taking into account the very high geological heterogeneity. The complexity of the geological mediums comes from metamorphic and sedimentary processes, and mechanics which create structures having hydraulic properties varying on several orders of magnitude and correlated on a broad range of scales. A general overview of stochastic generation of fractured media problems is given in [11]. Numerically, the challenge is to integrate this range of heterogeneity in models of great extension and good resolution outcome, with linear systems from 10 6 to 10 8 unknown factors. In the fractured medium with a matrix of very low permeability, the fluid flow is focused in the highly heterogeneous fractures [21]. The objective of numerical modeling consists of simulating hydraulic phenomena in a large number of ne...

Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks

“…The results showed that the stress-permeability coupling may be one of the reasons for the usually less than expected inflow into larger diameter holes. Mustapha and Mustapha (2007) simulated fluid flow through 3-D DFNs composed of thousands of fractures, by applying a local transformation to simplify the highly complex geometry of fractures. Zhou et al (2008) established a 3-D fracture network model based on the field mapping data of the Laxiwa Hydraulic Power Station, China, and then calculated the equivalent permeability in different flow directions.…”

G23FM: a tool for meshing complex geological media

“…Moreover, the mesh cannot be refined at a given location because the transformation made is global and based on only one general structured grid. For more details, we refer to [14][15][16].…”

“…A simplification procedure using 2D/3D structured grid is used by [14,15]. A global projection over a 2D/3D unstructured grid is discussed in [9,16]; recently, a novel method based on a local transformation of the fractures is developed for 2D problems in [16], and extended to 3D problems in [17].…”

“…Stochastically generated fractures [1][2][3][4][14][15][16][17] lead to very complex geometrical structures. The complexity mainly arises from the large number of fractures contained in a fractured media, and the corresponding critical configurations generated.…”

Heterogeneity preserving upscaling for heat transport in fractured geothermal reservoirs

“…The explicit representation of fractures in DFM models necessitate large flexibility in terms of grid generation. Frameworks that slightly modifies the fracture network to align with a background grid have been developed to avoid excessive grid refinement close to, e.g., fracture intersections [20,24]. In addition to gridding and discretization challenges, numerical representation using DFM models typically leads to a high number of degrees of freedom compared to using continuum models.…”