An efficient multi-point flux approximation method for Discrete Fracture–Matrix simulations

Sandve, Tor Harald; Berre, Inga; Nordbotten, Jan Martin

doi:10.1016/j.jcp.2012.01.023

Cited by 266 publications

(167 citation statements)

References 101 publications

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“…Its consistency is obtained using (28), (29) (Ω, Γ) in H Σ (Ω, Γ) given by Proposition 2.3. Its compactness results from Lemma 5.6 of [13] and Lemma 1.57 of [11].…”

Section: Proposition 44 (Main Results On Hfv)mentioning

confidence: 99%

“…In [19] a cell-centered Finite Volume scheme using a Two Point Flux Approximation (TPFA) is proposed assuming the orthogonality of the mesh and isotropic permeability fields. 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].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…Its consistency is obtained using (28), (29) (Ω, Γ) in H Σ (Ω, Γ) given by Proposition 2.3. Its compactness results from Lemma 5.6 of [13] and Lemma 1.57 of [11].…”

Section: Proposition 44 (Main Results On Hfv)mentioning

confidence: 99%

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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“…These are a special class of unstructured grid simulations, the so-called Discrete Fracture Matrix (DFM) models, which represent both the fracture network and the rock matrix, in a reservoir simulation using fully unstructured grids (e.g. Karimi-Fard et al 2004;Reichenberger et al 2006;Matthäi et al 2007;Hoteit & Firoozabadi 2008a, b;Sandve et al 2012;Geiger & Matthäi 2014). Results from such DFM simulations (Ahmed Elfeel et al 2013c;Geiger et al 2013), in combination with theoretical and mathematical analysis of fracture-matrix transfer processes (Schmid et al 2011, 2013, have recently led to a new transfer function for dual-continua models in which the transfer processes are computed using exact analytical solutions of the underlying physical processes.…”

Section: ; Moog 2013)mentioning

confidence: 99%

Fundamental controls on fluid flow in carbonates: current workflows to emerging technologies

Agar

Geiger

2014

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The introduction reviews topics relevant to the fundamental controls on fluid flow in carbonate reservoirs and to the prediction of reservoir performance. The review provides research and industry contexts for papers in this volume only. A discussion of global context and frameworks emphasizes the value yet to be captured from compare and contrast studies. Multidisciplinary efforts highlight the importance of greater integration of sedimentology, diagenesis and structural geology. Developments in analytical and experimental methods, stimulated by advances in the materials sciences, support new insights into fundamental (pore-scale) processes in carbonate rocks. Subsurface imaging methods relevant to the delineation of heterogeneities in carbonates highlight techniques that serve to decrease the gap between seismically resolvable features and well-scale measurements. Methods to fuse geological information across scales are advancing through multiscale integration and proxies. A surge in computational power over the last two decades has been accompanied by developments in computational methods and algorithms. Developments related to visualization and data interaction support stronger geoscience-engineering collaborations. High-resolution and real-time monitoring of the subsurface are driving novel sensing capabilities and growing interest in data mining and analytics. Together, these offer an exciting opportunity to learn more about the fundamental fluid-flow processes in carbonate reservoirs at the interwell scale.

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“…This approach is usually denoted by reduced Darcy model and is followed for example in [5,2,6,7,8,9,10,11]. Another possible approach is based, e.g., on hybridgrid models, where fractures are n−1-dimensional only in the geometric grid, whereas an n-dimensional grid taking into account fracture aperture is then used for computations, as done, among others, in [12,13].…”

Section: Introductionmentioning

confidence: 99%

Flow simulations in porous media with immersed intersecting fractures

Berrone

Pieraccini

Scialò

2017

Journal of Computational Physics

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A novel approach for fully 3D flow simulations in porous media with immersed networks of fractures is presented. The method is based on the discrete fracture model, in which fractures are represented as n − 1-dimensional objects in an n-dimensional porous matrix. The problem, written in primal formulation on both the fractures and the porous matrix, is solved resorting to the constrained minimization of a properly designed cost functional that expresses the matching conditions at fracture-fracture and fracture-matrix interfaces. The method, originally conceived for intricate fracture networks in impervious rock matrices, is here extended to fractures in a porous permeable rock matrix. The purpose of the optimization approach is to allow for an easy meshing process, independent of the geometrical complexity of the domain, and for a robust and efficient resolution tool, relying on a strong parallelism. The present work is devoted to the presentation of the new method and of its applicability to flow simulations in poro-fractured domains.

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An efficient multi-point flux approximation method for Discrete Fracture–Matrix simulations

Cited by 266 publications

References 101 publications

Gradient Discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media

Gradient Discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media

Fundamental controls on fluid flow in carbonates: current workflows to emerging technologies

Flow simulations in porous media with immersed intersecting fractures

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