Verification benchmarks for single-phase flow in three-dimensional fractured porous media

Berre, Inga; Boon, Wietse M.; Flemisch, Bernd; Fumagalli, Alessio; Gläser, Dennis; Keilegavlen, Eirik; Scotti, Anna; Stefansson, Ivar; Tatomir, Alexandru; Brenner, Konstantin; Burbulla, Samuel; Devloo, Philippe R.B.; Durán, Omar; Favino, Marco; Hennicker, Julian; Lee, Ivan; Lipnikov, Konstantin; Masson, Roland; Mosthaf, Klaus; Nestola, Maria Giuseppina Chiara; Ni, Chuen-Fa; Nikitin, Kirill D.; Schädle, Philipp; Svyatsky, Daniil; Yanbarisov, Ruslan M.; Zulian, Patrick

doi:10.1016/j.advwatres.2020.103759

Cited by 90 publications

(112 citation statements)

References 29 publications

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“…This last example considers the simulations of a 3D problem taken from another benchmark study [6], a threedimensional analogue to the test case in Section 5.1. The geometry is extended to the unit cube and the fracture network now consists of 9 fracture planes, 69 intersection lines and 27 intersection points (see Fig.…”

Section: Example: Three-dimensional Regular Fracture Networkmentioning

confidence: 99%

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Block preconditioners for mixed-dimensional discretization of flow in fractured porous media

Budiša

2020

Comput Geosci

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In this paper, we are interested in an efficient numerical method for the mixed-dimensional approach to modeling single-phase flow in fractured porous media. The model introduces fractures and their intersections as lower-dimensional structures, and the mortar variable is used for flow coupling between the matrix and fractures. We consider a stable mixed finite element discretization of the problem, which results in a parameter-dependent linear system. For this, we develop block preconditioners based on the well-posedness of the discretization choice. The preconditioned iterative method demonstrates robustness with regard to discretization and physical parameters. The analytical results are verified on several examples of fracture network configurations, and notable results in reduction of number of iterations and computational time are obtained.

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Section: Example: Three-dimensional Regular Fracture Networkmentioning

confidence: 99%

“…These methods mostly differ in two aspects: whether the fractures conform to the discrete grid of the porous medium [9] or are placed arbitrarily within the grid [13,17,32], or whether pressure or flux continuity is preserved. Comparison studies of different discretization methods and their properties can be found in [6,16,29].…”

Section: Introductionmentioning

confidence: 99%

Block preconditioners for mixed-dimensional discretization of flow in fractured porous media

Budiša

2020

Comput Geosci

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“…Moreover, hybriddimensional models rely on the assumption of negligible aperture. However, fracture apertures which are two-orders-of-magnitude less than the background size are often encountered [10,5,2]. In these cases, the assumption of negligible aperture is not applicable and the error coming from the lower-dimensional representation of the fractures may dominate the discretization error.…”

Section: Introductionmentioning

confidence: 99%

An Equi-Dimensional Finite Element Approach for Flow Problems in Fractured Porous Media

Favino¹,

Nestola²

2021

14th WCCM-ECCOMAS Congress

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We propose a novel approach for flow simulations in fractured porous media based on an equi-dimensional representation of the fractures and a standard continuous finite element (FE) method. We employ an adaptive mesh refinement strategy to automatically adjust an initial regular mesh to any fracture distribution with a desired accuracy. The proposed approach is easily implementable in any FE software, does not involve the coupling of different discretizations, and provides symmetric and positive definite stiffness matrices. We provide a systematic validation of our method and we show that it can be used to simulate fluid flow for fracture networks of realistic complexity.

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“…benchmark case 1 fromBerre et al (2020), who compare 17 different methods of simulating single-phase flow in fractured porous media. The initial setup (displayed in a) in figure A2) consists of an inclined fracture with an hydraulic aperture of 10 −2 m embedded in a cube of 100 m length with a matrix hydraulic conductivity of 10 −6 m 2 , whereas the hydraulic conductivity of a small band of 10 m width at the bottom is increased to 10 −5 m 2 .…”

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confidence: 99%

“…CC BY 4.0 License. Benchmark case fromBerre et al (2020). a) shows the benchmark geometry of an embedded fracture (aperture of 10 −2 m)…”

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Equivalent continuum-based upscaling of flow in discrete fracture networks: The fracture-and-pipe model

Kottwitz¹,

Popov²,

Abe³

et al. 2021

Preprint

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Abstract. Predicting effective permeabilities of fractured rock masses is a key component of reservoir modelling. This is often realized with the discrete fracture network (DFN) method, where single-phase incompressible fluid flow is modelled in discrete representations of individual fractures in a network. Depending on the overall number of fractures, this can result in significant computational costs. Equivalent continuum models (ECM) provide an alternative approach by subdividing the fracture network into a grid of continuous medium cells, over which hydraulic properties are averaged for fluid flow simulations. While this has the advantage of lower computational costs and the possibility to include matrix properties, choosing the right cell size for discretizing the fracture network into an ECM is crucial to provide accurate flow results and conserve anisotropic flow properties. Whereas several techniques exist to map a fracture network onto a grid of continuum cells, the complexity related to flow in fracture intersections is often ignored. Here, numerical simulations of Stokes-flow in simple fracture intersections are utilized to analyze their effect on permeability. It is demonstrated that intersection lineaments oriented parallel to the principal direction of flow increase permeability in a process termed intersection flow localization (IFL). We propose a new method to generate ECM's that includes this effect with a directional pipe flow parametrization: the fracture-and-pipe model. Our approach is tested by conducting resolution tests with a massively parallelized Darcy-flow solver, capable of representing the full permeability anisotropy for individual grid cells. The results suggest that as long as the cell size is smaller than the minimal fracture length and larger than the maximal hydraulic aperture of the considered fracture network, the resulting effective permeabilities and anisotropies are resolution-independent. Within that range, ECM's are applicable to upscale flow in fracture networks, which reduces computational expenses for numerical permeability predictions of fractured rock masses. Furthermore, incorporating the off-diagonal terms of the individual permeability tensors into numerical simulations results in an improved representation of anisotropy in ECM's that was previously reserved for the DFN method.

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Verification benchmarks for single-phase flow in three-dimensional fractured porous media

Cited by 90 publications

References 29 publications

Block preconditioners for mixed-dimensional discretization of flow in fractured porous media

Block preconditioners for mixed-dimensional discretization of flow in fractured porous media

An Equi-Dimensional Finite Element Approach for Flow Problems in Fractured Porous Media

Equivalent continuum-based upscaling of flow in discrete fracture networks: The fracture-and-pipe model

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