Open-source MATLAB implementation of consistent discretisations on complex grids
Knut-Andreas Lie,Knut-Andreas Lie,Stein Krogstad,Ingeborg Skjelkvåle Ligaarden,Jostein R. Natvig,Halvor Møll Nilsen,Bård Skaflestad +6 more
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An open-source Matlab® toolkit that can be used as an efficient test platform for (new) discretisation and solution methods in reservoir simulation is presented and examples of multiscale methods and adjoint methods for use in optimisation of rates and placement of wells are shown.Abstract:
Accurate geological modelling of features such as faults, fractures or erosion requires grids that are flexible with respect to geometry. Such grids generally contain polyhedral cells and complex grid-cell connectivities. The grid representation for polyhedral grids in turn affects the efficient implementation of numerical methods for subsurface flow simulations. It is well known that conventional two-point flux-approximation methods are only consistent for K-orthogonal grids and will, therefore, not converge in the general case. In recent years, there has been significant research into consistent and convergent methods, including mixed, multipoint and mimetic discretisation methods. Likewise, the so-called multiscale methods based upon hierarchically coarsened grids have received a lot of attention. The paper does not propose novel mathematical methods but instead presents an open-source Matlab® toolkit that can be used as an efficient test platform for (new) discretisation and solution methods in reservoir simulation. The aim of the toolkit is to support reproducible research and simplify the development, verification and validation and testing and comparison of new discretisation and solution methods on general unstructured grids, including in particular corner point and 2.5D PEBI grids. The toolkit consists of a set of data structures and routines for creating, manipulating and visualising petrophysical data, fluid models and (unstructured) grids, including support for industry standard input formats, as well as routines for computing single and multiphase (incompressible) flow. We review key features of the toolkit and discuss a generic mimetic formulation that includes many known discretisation methods, including both the standard two-point method as well as consistent and convergent multipoint and mimetic methods. Apart from the core routines and data structures, the toolkit contains add-on modules that implement more advanced solvers and functionality. Herein, we show examples of multiscale methods and adjoint methods for use in optimisation of rates and placement of wells.read more
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MonographDOI
An Introduction to Reservoir Simulation Using MATLAB/GNU Octave: User Guide for the MATLAB Reservoir Simulation Toolbox (MRST)
TL;DR: This book provides a self-contained introduction to the simulation of flow and transport in porous media, written by a developer of numerical methods, and will prove invaluable for researchers, professionals and advanced students using reservoir simulation methods.
Journal ArticleDOI
An efficient multi-point flux approximation method for Discrete Fracture-Matrix simulations
TL;DR: This work considers a control volume discretization with a multi-point flux approximation to model Discrete Fracture-Matrix systems for anisotropic and fractured porous media in two and three spatial dimensions and explicitly account for the fractures by representing them as hybrid cells between the matrix cells.
Journal ArticleDOI
Benchmarks for single-phase flow in fractured porous media
Bernd Flemisch,Inga Berre,Wietse M. Boon,Alessio Fumagalli,Nicolas Schwenck,Anna Scotti,Ivar Stefansson,Alexandru Tatomir +7 more
TL;DR: Several test cases intended to be benchmarks for numerical schemes for single-phase fluid flow in fractured porous media are presented, including a vertex and two cell-centred finite volume methods, a non-conforming embedded discrete fracture model, a primal and a dual extended finite element formulation, and a mortar discrete fractures model.
Proceedings ArticleDOI
MRST-AD - an Open-Source Framework for Rapid Prototyping and Evaluation of Reservoir Simulation Problems
Stein Krogstad,Knut-Andreas Lie,Olav Møyner,Halvor Møll Nilsen,Xavier Raynaud,Bård Skaflestad +5 more
TL;DR: MRST-AD is presented, a free, open-source framework written as part of the Matlab Reservoir Simulation Toolbox and designed to provide researchers with the means for rapid prototyping and experimentation for problems in reservoir simulation.
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