A mixed-dimensional finite volume method for two-phase flow in fractured porous media

Reichenberger, Volker; Jakobs, H.; Bastian, Peter; Helmig, Rainer

doi:10.1016/j.advwatres.2005.09.001

Cited by 258 publications

(193 citation statements)

References 30 publications

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“…Cell-centered Finite Volume schemes can be extended to general meshes and anisotropic permeability fields using MultiPoint Flux Approximations (MPFA) following the ideas introduced in [30], [28], and [2] for discontinuous pressure models. In [3], a Mixed Finite Element (MFE) method is proposed, and Control Volume Finite Element Methods (CVFE) using nodal unknowns have been introduced for such models in [25] and [24]. A MFE discretization adapted to non-matching fracture and matrix grids is also studied in [10].…”

Section: Introductionmentioning

confidence: 99%

Gradient Discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media

Brenner

Groza

Guichard

et al. 2014

Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems

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Section: Introductionmentioning

confidence: 99%

Gradient Discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media

Brenner

Groza

Guichard

et al. 2014

Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems

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“…Benes et al (2005), Mikyska (2005), Reichenberger et al (2006), and Hoteit and Firoozabadi (2008a,b) show that saturation discontinuities caused by capillary effects can not be represented by the FEFVM unless a special treatment is employed. The tests described here show that DFEFVM can be employed to solve such a problem by adding capillary diffusion term in Eq.…”

Section: Discussionmentioning

confidence: 99%

Comparison of Three FE-FV Numerical Schemes for Single- and Two-Phase Flow Simulation of Fractured Porous Media

Nick

Matthäi

2011

Transp Porous Med

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We benchmark a family of hybrid finite element-node-centered finite volume discretization methods (FEFV) for single-and two-phase flow/transport through porous media with discrete fracture representations. Special emphasis is placed on a new method we call DFEFVM in which the mesh is split along fracture-matrix interfaces so that discontinuities in concentration or saturation can evolve rather than being suppressed by nodal averaging of these variables. The main objective is to illustrate differences among three discretization schemes suitable for discrete fracture modeling: (a) FEFVM with volumetric finite elements for both fractures and porous rock matrix, (b) FEFVM with lower dimensional finite elements for fractures and volumetric finite elements for the matrix, and (c) DFEFVM with a mesh that is split along material discontinuities. Fracture discontinuities strongly influence single-and multi-phase fluid flow. Continuum methods, when used to model transport across such interfaces, smear out concentration/saturation. We show that the new DFEFVM addresses this problem producing significantly more accurate results. Sealed and open single fractures as well as a realistic fracture geometry are used to conduct tracer and water-flooding numerical experiments. The benchmarking results also reveal the limitations/mesh refinement requirements of FE node-centered FV hybrid methods. We show that the DFEFVM method produces more accurate results even for much coarser meshes.

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“…Such interface models have been studied extensively in the engineering literature, e.g. 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.…”

Section: Introductionmentioning

confidence: 99%

“…This model has been extended so that one may use non-matching grids [20,33], or disconnect the fracture mesh from that of the domain [31,16]. It has also been extended to treat Forchheimer flow in the fracture [21,27], and multiphase flow [32], but these extensions are not considered in this paper.…”

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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A mixed-dimensional finite volume method for two-phase flow in fractured porous media

Cited by 258 publications

References 30 publications

Gradient Discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media

Gradient Discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media

Comparison of Three FE-FV Numerical Schemes for Single- and Two-Phase Flow Simulation of Fractured Porous Media

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

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