Flow Simulation in Three-Dimensional Discrete Fracture Networks

Erhel, Jocelyne; Dreuzy, Jean‐Raynald de; Poirriez, Baptiste

doi:10.1137/080729244

Cited by 134 publications

(107 citation statements)

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“…Within a discrete fracture modelling approach, three distinct finite element formulations can be identified: special interface or joint elements Nguyen, 1995, 1999;Ng and Small, 1997;Nguyen and Selvadurai, 1998;Guvanasen and Chan, 2000;Steffen et al, 2014), the embedded manifold approach (Guvanasen and Chan, 2000;Juanes et al, 2002;Graf and Therrien, 2008;Erhel et al, 2009), and the conventional or direct approach, in which the fractures are modelled with the finite elements of the same spatial order; e.g. 3-D fractures are modelled with 3-D finite elements (Stanislavsky and Garven, 2003;Sykes et al, 2011).…”

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confidence: 99%

Thermo-hydro-mechanical processes in fractured rock formations during a glacial advance

2015

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Abstract. The paper examines the coupled thermo-hydromechanical (THM) processes that develop in a fractured rock region within a fluid-saturated rock mass due to loads imposed by an advancing glacier. This scenario needs to be examined in order to assess the suitability of potential sites for the location of deep geologic repositories for the storage of high-level nuclear waste. The THM processes are examined using a computational multiphysics approach that takes into account thermo-poroelasticity of the intact geological formation and the presence of a system of sessile but hydraulically interacting fractures (fracture zones). The modelling considers coupled thermo-hydro-mechanical effects in both the intact rock and the fracture zones due to contact normal stresses and fluid pressure at the base of the advancing glacier. Computational modelling provides an assessment of the role of fractures in modifying the pore pressure generation within the entire rock mass.

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confidence: 99%

Thermo-hydro-mechanical processes in fractured rock formations during a glacial advance

2015

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“…Figure 5.1 shows the geometry of the network and of one fracture (the black one) with its boundary and intersections. Figure 5.2 (left) shows the result of the first step using the meshing procedure proposed in [1] and Figure 5.3 (left) the corresponding 2D mesh (step 3). Figure 5.2 (right) displays the result of the first step of the new discretization procedure: a grid step has been chosen and the mesh centers are used to discretize the boundaries and intersections.…”

Section: Mesh Generation and Notationmentioning

confidence: 99%

“…On one hand, this stage 1 modifies slightly the position of the borders and intersections. However, this approximation is motivated by the necessity of having a good-quality mesh for any generated stochastic network as, in most case, a classical mesh generator would fail to mesh the initial geometry [1]. Moreover this approximation can be lowered by a refinement of the 2D/3D grids, since the intersections and borders discretizations will stand closer to the original geometry.…”

Section: Mesh Generation and Notationmentioning

confidence: 99%

“…As we are doing stochastic simulations, we rather need an automatic mesh generation suitable for any DFN. With the method proposed in [1], any DFN can be meshed but it requires matching grids at the intersection between fractures. The mesh generation we propose is more flexible in the sense that the grids may not match at the intersections, which allows us to choose a different mesh step from one fracture to another.…”

Section: Mesh Generation and Notationmentioning

confidence: 99%

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A Generalized Mixed Hybrid Mortar Method for Solving Flow in Stochastic Discrete Fracture Networks

Pichot¹,

Erhel²,

Dreuzy³

2012

SIAM J. Sci. Comput.

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Abstract. The simulation of flow in fractured media requires handling both a large number of fractures and a complex interconnecting network of these fractures. Networks considered in this paper are three-dimensional domains made up of two-dimensional fractures intersecting each other and randomly generated. Due to the stochastic generation of fractures, intersections can be highly intricate. The numerical method must generate a mesh and define a discrete problem for any discrete fracture network (DFN). A first approach [Erhel, de Dreuzy, and Poirriez, SIAM J. Sci. Comput., 31 (2009), pp. 2688-2705 is to generate a conforming mesh and to apply a mixed hybrid finite element method. However, the resulting linear system becomes very large when the network contains many fractures. Hence a second approach [Pichot, Erhel, and de Dreuzy, Appl. Anal., 89 (2010), pp. 1629-1643 is to generate a nonconforming mesh, using an independent mesh generation for each fracture. Then a Mortar technique applied to the mixed hybrid finite element method deals with the nonmatching grids. When intersections do not cross or overlap, pairwise Mortar relations for each intersection are efficient [Pichot, Erhel, and de Dreuzy, 2010]. But for most random networks, discretized intersections involve more than two fractures. In this paper, we design a new method generalizing the previous one and that is applicable for stochastic networks. The main idea is to combine pairwise Mortar relations with additional relations for the overlapping part. This method still ensures the continuity of fluxes and heads and still yields a symmetric positive definite linear system. Numerical experiments show the efficiency of the method applied to complex stochastic fracture networks. We also study numerical convergence when reducing the mesh step. This method makes it easy to perform mesh optimization and appears to be a very promising tool to simulate flow in multiscale fracture networks.

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“…Let F l be the set of fractures which contains I l . On each segment, continuity conditions are imposed to ensure the continuity of hydraulic heads and the conservation of fluxes [20], [38]:…”

Section: Flow Modelmentioning

confidence: 99%