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Abstract The Fracture Cut (FraC) approach to mesh three-dimensional (3D) Discrete Fracture Networks (DFN) is presented. The considered DFNs consist of a network of planar two-dimensional (2D) fractures sharing intersections that can in turn intersect themselves, resulting in highly complex meshing issues. The key idea of FraC is to decompose each fracture into a set of connected closed contours, with the original intersection traces located at the boundaries of the contours. Thus, intersection segments can be more easily accounted for when building a conforming mesh. Three distinct strategies for intersection points management are also proposed to enhance the quality of resulting meshes. Steady-state single-phase flow simulations are performed to validate the conform meshes obtained using FraC. The results from flow simulations as well as from a mesh quality analysis on a benchmark case show that a flexible AoM strategy (Adding or Moving intersection points) appears to be the best choice to generate ready-to-run meshes for complex DFN. This approach also allows accounting for tiny features within the fracture networks while keeping a good mesh quality and respecting DFN connectivity. Finally, a scalability of the mesh generator is conducted to assess the performance of the approach. Highlights • An original and innovative conforming mesh approach is presented for DFN mesh generation. • Three distinct strategies for intersection points management are proposed. • This approach allows to account for tiny features within the fracture network. • High-accuracy flow simulations are obtained using Cast3M and DuMux open source code. [ABSTRACT FROM AUTHOR]

Most industrial and field studies of transport processes in Discrete Fracture Networks (DFNs) involve strong simplifying assumptions, especially at the meshing stage. High-accuracy simulations are therefore required for validating these simplified models and their domain of validity. The present paper proposes an efficient workflow based on open-source software to obtain transport simulations. High-quality computational meshes for DFNs are first generated using the conforming meshing approach FraC. Then, a tracer transport model implemented in the open-source code DuMux is used for simulating tracer transport driven by the advection-dispersion equation. We adopt the box method, a vertex-centered finite volume scheme for spatial discretization, which ensures concentration continuity and mass conservation at intersections between fractures. Numerical results on simple networks for validation purposes and on complex realistic DFNs are presented. An a-posteriori convergence study of the discretization method shows an order of convergence O ( h ) for tracer concentration with h the mesh size. [ABSTRACT FROM AUTHOR]

Single and multiphase flows in fractured porous media at the scale of natural reservoirs are often handled by resorting to homogenized models that avoid the heavy computations associated with a complete discretization of both fractures and matrix blocks. For example, the two overlapping continua (fractures and matrix) of a dual porosity system are coupled by way of fluid flux exchanges that deeply condition flow at the large scale. This characteristic is a key to realistic flow simulations, especially for multiphase flow as capillary forces and contrasts of fluid mobility compete in the extraction of a fluid from a capacitive matrix then conveyed through the fractures. The exchange rate between fractures and matrix is conditioned by the so-called mean matrix block size which can be viewed as the size of a single matrix block neighboring a single fracture within a mesh of a dual porosity model. We propose a new evaluation of this matrix block size based on the analysis of discrete fracture networks. The fundaments rely upon establishing at the scale of a fractured block the equivalence between the actual fracture network and a Warren and Root network only made of three regularly spaced fracture families parallel to the facets of the fractured block. The resulting matrix block sizes are then compared via geometrical considerations and two-phase flow simulations to the few other available methods. It is shown that the new method is stable in the sense it provides accurate sizes irrespective of the type of fracture network investigated. The method also results in two-phase flow simulations from dual porosity models very close to that from references calculated in finely discretized networks. Finally, calculations of matrix block sizes by this new technique reveal very rapid, which opens the way to cumbersome applications such as preconditioning a dual porosity approach applied to regional fractured reservoirs. [ABSTRACT FROM AUTHOR]

We present in this Note a stochastic approach to the matrix-fracture exchange in a heterogeneous fractured porous medium. We introduce an intermediate scale, called the unit-scale, between the local-scale (fracture-scale) and the large-scale characteristic of the reservoir mesh (reservoir block). This paper focuses on the problem of upscaling fluid exchange phenomena from the unit scale to the reservoir mesh or block scale. Simplifying the Darcian flow terms enables us to obtain a probabilistic solution of the dual continuum problem, in continuous time, in the case of a purely random exchange coefficient. This is then used to develop several upscaling approaches to the fluid exchange problem, and to analyze the so-called ‘effective’ exchange coefficient. The results are a first contribution to the more general problem of upscaling multidimensional flow-exchange processes in space and time, in randomly heterogeneous dual continua. To cite this article: M. Kfoury et al., C. R. Mecanique 332 (2004). [Copyright &y& Elsevier]