Gradient Discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media

Brenner, Konstantin; Groza, Mayya; Guichard, Cindy; Lebeau, Gilles; Masson, Roland

doi:10.1007/978-3-319-05591-6_52

Cited by 31 publications

(70 citation statements)

References 20 publications

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“…We consider the fractures as (approximated by) planar objects, following e.g. [37,20,32,2,27]. The extension to curved fractures is possible, but the analysis and the presentation will increase in complexity, see [28,35].…”

Section: Mathematical Modelmentioning

confidence: 99%

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

Fumagalli

Keilegavlen

Scialò

2019

Journal of Computational Physics

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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.

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Section: Mathematical Modelmentioning

confidence: 99%

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

Fumagalli

Keilegavlen

Scialò

2019

Journal of Computational Physics

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“…For instance, in [4] the case of a single immersed fracture is analyzed, but eventually using a primal formulation only for the pressure. In [24] the authors consider the case of a partially immersed network, yet employing different (simpler) coupling conditions, and a gradient discretization method is proposed for the numerical solution. In this work we limit ourselves to describing the mathematical model and showing, by numerical experiments, that the corresponding discretization by a mimetic/finite volume scheme gives satisfactory results.…”

Section: The Case Of Immersed Fracture Networkmentioning

confidence: 99%

Mimetic finite difference approximation of flows in fractured porous media

et al. 2016

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Abstract.We present a possible framework for the numerical simulation of flow in fractured porous media that couples mimetic finite differences for the porous matrix with a finite volume scheme for the flow in the fractures. The resulting method is theoretically analyzed in the case of a single fracture. Moreover, several numerical experiments show the capability of the method to deal also with complicated networks of fractures. Thanks to the implementation of rather general coupling conditions, it encompasses both "conductive fractures", i.e., fractures with high permeability and "sealed fractures", i.e., fractures with low permeability which act as a flow barrier.Mathematics Subject Classification. 65N30, 35Q86, 76S05.

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“…see [4,25,24,32,26,22], as well as in the mathematical literature, e.g. see [30,3,29,16,20,34,27,12,11], to name just a few. We use here the model developed in [30], where flow in the fracture as well as in the rock is governed by Darcy's law.…”

Section: Introductionmentioning

confidence: 99%

First-order indicators for the estimation of discrete fractures in porous media

Ameur

Chavent

Fatma

et al. 2017

Inverse Problems in Science and Engineering

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Abstract:Faults and geological barriers can drastically affect the flow patterns in porous media. Such fractures can be modeled as interfaces that interact with the surrounding matrix. We propose a new technique for the estimation of the location and hydrogeological properties of a small number of large fractures in a porous medium from given distributed pressure or flow data. At each iteration, the algorithm builds a short list of candidates by comparing fracture indicators. These indicators quantify at the first order the decrease of a data misfit function; they are cheap to compute. Then, the best candidate is picked up by minimization of the objective function for each candidate. Optimally driven by the fit to the data, the approach has the great advantage of not requiring remeshing, nor shape derivation. The stability of the algorithm is shown on a series of numerical examples representative of typical situations.

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Gradient Discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media

Cited by 31 publications

References 20 publications

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

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

Mimetic finite difference approximation of flows in fractured porous media

First-order indicators for the estimation of discrete fractures in porous media

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