A general gridding, discretization, and coarsening methodology for modeling flow in porous formations with discrete geological features

Karimi-Fard, Mohammad; Durlofsky, Louis J.

doi:10.1016/j.advwatres.2016.07.019

Cited by 129 publications

(59 citation statements)

References 75 publications

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“…One important component of our approach is a local fine grid simulation, which is typical in many multiscale and numerical upscaling techniques. In general, a fine grid simulation involving flow and transport in heterogenous fracture media can be decomposed into two parts (we refer [24] for an overview). First of all, an unstructured fine mesh is needed to model the geometries of the fractures and background heterogeneities.…”

Section: Introductionmentioning

confidence: 99%

Constraint Energy Minimizing Generalized Multiscale Finite Element Method

Chung

Efendiev

Leung

2018

Computer Methods in Applied Mechanics and Engineering

149

129

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The dual continuum model serves as a powerful tool in the modeling of subsurface applications. It allows a systematic coupling of various components of the solutions. The system is of multiscale nature as it involves high heterogeneous and high contrast coefficients. To numerically compute the solutions, some types of reduced order methods are necessary. We will develop and analyze a novel multiscale method based on the recent advances in multiscale finite element methods. Our method will compute multiple local multiscale basis functions per coarse region. The idea is based on some local spectral problems, which are important to identify high contrast channels, and an energy minimization principle. Using these concepts, we show that the basis functions are localized, even in the presence of high contrast long channels and fractures. In addition, we show that the convergence of the method depends only on the coarse mesh size. Finally, we present several numerical tests to show the performance.

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Section: Introductionmentioning

confidence: 99%

Constraint Energy Minimizing Generalized Multiscale Finite Element Method

Chung

Efendiev

Leung

2018

Computer Methods in Applied Mechanics and Engineering

149

129

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“…with | f | the face area, and x f a collocation point on f that allows for enforcing point-wise pressure continuity across the face in case of incompressible single-phase flow. In our implementation x f is selected as the intersection of the face and the line connecting the cell centroids x K and x L [94] as shown in Fig. A.1.…”

Section: Appendix a Tpfa Transmissibility Computationmentioning

confidence: 99%

A two-stage preconditioner for multiphase poromechanics in reservoir simulation

White

Castelletto

Klevtsov

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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Many applications involving porous media-notably reservoir engineering and geologic applications-involve tight coupling between multiphase fluid flow, transport, and poromechanical deformation. While numerical models for these processes have become commonplace in research and industry, the poor scalability of existing solution algorithms has limited the size and resolution of models that may be practically solved. In this work, we propose a two-stage Newton-Krylov solution algorithm to address this shortfall. The proposed solver exhibits rapid convergence, good parallel scalability, and is robust in the presence of highly heterogeneous material properties. The key to success of the solver is a block-preconditioning strategy that breaks the fully-coupled system of mass and momentum balance equations into simpler sub-problems that may be readily addressed using targeted algebraic methods. Numerical results are presented to illustrate the performance of the solver on challenging benchmark problems.

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“…We consider a case of two-continua at the (7)) c ∂ξ ∂t − div(κ∇ξ) = 0 in the RVE and impose ξ = 1 at the fracture nodes. One can also use a source term in the fracture or the local eigenvalue problems see [21]. It is assumed that zero Neumann boundary conditions are imposed on the rest of the boundaries.…”

Section: Rve-based Multi-continuum Computationsmentioning

confidence: 99%

Coupling of multiscale and multi-continuum approaches

et al. 2017

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Simulating complex processes in fractured media requires some type of model reduction. Well-known approaches include multi-continuum techniques, which have been commonly used in approximating subgrid effects for flow and transport in fractured media. Our goal in this paper is to (1) show a relation between multi-continuum approaches and Generalized Multiscale Finite Element Method (GMsFEM) and (2) to discuss coupling these approaches for solving problems in complex multiscale fractured media. The GMsFEM, a systematic approach, constructs multiscale basis functions via local spectral decomposition in pre-computed snapshot spaces. We show that GMsFEM can automatically identify separate fracture networks via local spectral problems. We discuss the relation between these basis functions and continuums in multi-continuum methods. The GMsFEM can automatically detect each continuum and represent the interaction between the continuum and its surrounding (matrix). For problems with simplified fracture networks, we propose a simplified basis construction with the GMs-FEM. This simplified approach is effective when the fracture networks are known and have simplified geometries. We show that this approach can achieve a similar result compared to the results using the GMsFEM with spectral basis functions. Further, we discuss the coupling between the GMsFEM and multi-continuum approaches. In this case, many fractures are resolved while for unresolved fractures, we use a multicontinuum approach with local Representative Volume Element (RVE) information. As a result, the method deals with a system of equations on a coarse grid, where each equation represents one of the continua on the fine grid. We present various basis construction mechanisms and numerical results. The GMsFEM framework, in addition, can provide adaptive and online basis functions to improve the accuracy of coarse-grid

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A general gridding, discretization, and coarsening methodology for modeling flow in porous formations with discrete geological features

Cited by 129 publications

References 75 publications

Constraint Energy Minimizing Generalized Multiscale Finite Element Method

Constraint Energy Minimizing Generalized Multiscale Finite Element Method

A two-stage preconditioner for multiphase poromechanics in reservoir simulation

Coupling of multiscale and multi-continuum approaches

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