An Introduction to Reservoir Simulation Using MATLAB/GNU Octave

Lie, Knut–Andreas

doi:10.1017/9781108591416

Cited by 287 publications

(132 citation statements)

References 242 publications

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“…In addition to open source code, we provide documented run scripts for the results shown in Section 3 at www.github.com/pmgbergen/porepy. The exception to the above is the implementation of the Star-Delta elimination procedure, which is used for comparison with the Schur complement procedure, and for which we rely on the Matlab Reservoir Simulation Toolbox (Lie, 2016).…”

Section: Introductionmentioning

confidence: 99%

Finite-Volume Discretisations for Flow in Fractured Porous Media

2018

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Over the last decade, finite volume discretizations for flow in porous media have been extended to handle situations where fractures dominate the flow. These discretizations have successfully been combined with the discrete fracture-matrix models to yield mass conservative methods capable of explicitly incorporating the impact of fractures and their geometry. When combined with a hybrid-dimensional formulation, two central concerns are the restrictions arising from small cell sizes at fracture intersections and the coupling between fractures and matrix. Focusing on these aspects, we demonstrate how finite volume methods effectively can be extended to handle fractures, providing generalizations of previous work. We address the finite volume methods applying a general hierarchical formulation, facilitating implementation with extensive code reuse and providing a natural framework for coupling of different subdomains. Furthermore, we demonstrate how a Schur complement technique may be used to obtain a robust and versatile method for fracture intersection cell elimination. We investigate the accuracy of the proposed elimination method through a series of numerical simulations in 3D and 2D. The simulations, performed on fractured domains containing permeability heterogeneity and anisotropy, also demonstrate the flexibility of the hierarchical framework.

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Section: Introductionmentioning

confidence: 99%

Finite-Volume Discretisations for Flow in Fractured Porous Media

2018

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“…The full simulation model will also require discretization of the flow within the fractures and, in most cases, in the matrix. We will comment on this when appropriate, but generally refer to Lie (2016) for an introduction to discretization of porous media flow. Quantitative comparisons between a number of different numerical approaches are presented for DFM models in Flemisch et al (2018), DFN models in and DFM and dual-continuum models in Moinfar et al (2013).…”

Section: Discretization Approachesmentioning

confidence: 99%

Flow in Fractured Porous Media: A Review of Conceptual Models and Discretization Approaches

2018

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The last decade has seen a strong increase of research into flows in fractured porous media, mainly related to subsurface processes, but also in materials science and biological applications. Connected fractures totally dominate flow-patterns, and their representation is therefore a critical part in model design. Due to the fracture's characteristics as approximately planar discontinuities with an extreme size to width ratio, they challenge standard macroscale mathematical and numerical modeling of flow based on averaging. Thus, over the last decades, various, and also fundamentally different, approaches have been developed. This paper reviews common conceptual models and discretization approaches for flow in fractured porous media, with an emphasis on the dominating effects the fractures have on flow processes. In this context, the paper discuss the tight connection between physical and mathematical modeling and simulation approaches. Extensions and research challenges related to transport, multi-phase flow and fluid-solid interaction are also commented on. arXiv:1805.05701v1 [physics.geo-ph]

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“…To conclude this section on heterogeneous fields, simulations has been performed on several of the 10th SPE heterogeneous slices comparing FV-MHMM with MsFv algorithm as it is implemented in MRST2016a [18]. MsFv is here considered as a stand-alone multiscale solver and no iterations are used in the reported results.…”

Section: Study Of Heterogeneous Samplementioning

confidence: 99%

FV-MHMM method for reservoir modeling

Franc

Jeannin²,

Debenest

et al. 2017

Comput Geosci

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International audienceThe present paper proposes a new family of multiscale finite volume methods. These methods usually deal with a dual mesh resolution, where the pressure field is solved on a coarse mesh, while the saturation fields, which may have discontinuities, are solved on a finer reservoir grid, on which petrophysical heterogeneities are defined. Unfortunately, the efficiency of dual mesh methods is strongly related to the definition of up-gridding and down-gridding steps, allowing defining accurately pressure and saturation fields on both fine and coarse meshes and the ability of the approach to be parallelized. In the new dual mesh formulation we developed, the pressure is solved on a coarse grid using a new hybrid formulation of the parabolic problem. This type of multiscale method for pressure equation called multiscale hybrid-mixed method (MHMM) has been recently proposed for finite elements and mixed-finite element approach (Harder et al. 2013). We extend here the MH-mixed method to a finite volume discretization, in order to deal with large multiphase reservoir models. The pressure solution is obtained by solving a hybrid form of the pressure problem on the coarse mesh, for which unknowns are fluxes defined on the coarse mesh faces. Basis flux functions are defined through the resolution of a local finite volume problem, which accounts for local heterogeneity, whereas pressure continuity between cells is weakly imposed through flux basis functions, regarded as Lagrange multipliers. Such an approach is conservative both on the coarse and local scales and can be easily parallelized, which is an advantage compared to other existing finite volume multiscale approaches. It has also a high flexibility to refine the coarse discretization just by refinement of the lagrange multiplier space defined on the coarse faces without changing nor the coarse nor the fine meshes. This refinement can also be done adaptively w.r.t. a posteriori error estimators. The method is applied to single phase (well-testing) and multiphase flow in heterogeneous porous medi

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An Introduction to Reservoir Simulation Using MATLAB/GNU Octave

Cited by 287 publications

References 242 publications

Finite-Volume Discretisations for Flow in Fractured Porous Media

Finite-Volume Discretisations for Flow in Fractured Porous Media

Flow in Fractured Porous Media: A Review of Conceptual Models and Discretization Approaches

FV-MHMM method for reservoir modeling

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