Reservoir Simulator Runtime Enhancement Based on<i>a Posteriori</i>Error Estimation Techniques

Gratien, Jean-Marc; Ricois, O.; Yousef, Soleiman

doi:10.2516/ogst/2016009

Cited by 7 publications

(4 citation statements)

References 16 publications

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“…Les contributions proposées présentent différentes techniques pour réduire cette empreinte. L'article proposé par J.-M. Gratien, O. Ricois et S. Yousef [5] illustre comment, dans une simulation de réservoir pour une application de récupération assistée des hydrocarbures (EOR), le recours à l'adaptation de maillage, couplée avec une estimation a posteriori de l'erreur, améliore la performance du calcul. L'utilisation du raffinement de maillage permet de réduire significativement le nombre de degrés de liberté du problème, ainsi que la consommation mémoire du calcul.…”

Section: Solveurs Linéaires Et Leur Passage à L'échelleunclassified

“…The contributions present different techniques used to reduce this problem. The paper written by J.-M. Gratien, O. Ricois and S. Yousef [5] presents the use of mesh refinement and coarsening techniques along with original a posteriori error estimates to improve the performance of a compositional reservoir simulation dedicated to enhanced oil recovery. The mesh refinement allows a significant reduction in the load of data to solve.…”

Section: Scalable Linear Solversmentioning

confidence: 99%

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IFP Energies Nouvelles Conference: SimRace 2015: Numerical Methods and High Performance Computing for Industrial Fluid Flows

Chaisemartin

Allaire

2017

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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Numerical simulation faces several challenges today. The different topics it relies on (scientific modelling, applied mathematics, High Performance Computing (HPC) and computer science) are continuously evolving, and not necessarily in compatible ways. The novelties emerging in the different fields involved in scientific computing, for instance graphics accelerators or manycore processors, programming languages, Domain Specific Languages (DSL; high level languages dedicated to an application domain), HPC libraries, mesh refinement, error estimates, high order numerical methods, ever finer models, . . . are often not so easy to combine.One part of the challenge of building the 21st century's ultimate numerical platform will be to create connections and joint works between these spheres so that they can feed each other and develop benefiting synergies.Following this trend, IFP Energies nouvelles organized, at the end of 2015, an international conference entitled SimRace, devoted to numerical methods and high performance computing. The aim of SimRace (Simulation Race) was to cover multi-disciplinary topics relating to scientific computing applied to the simulation of industrial fluid flows. Our objective was to bring together people from the spheres of computer science, applied mathematics and applications. Over these three days we tackled issues ranging from the upcoming OpenMp 5.0 norm to various industrial applications in chemical engineering, geosciences and automotive engines, including topics such as a multiscale discontinuous Galerkin method, virtual element or volume formulations, directivebased automatic code generation and many others.Among the topics raised by the conference, we have identified four main themes developed in the articles selected in this special issue of OGST. HIGH-PERFORMANCE COMPUTATIONAL AND PROGRAMMING MODELS FOR EMERGING ARCHITECTURESWe are currently facing on-going architectural changes in HPC systems. The number of nodes continues to grow, intra-node concurrency is greatly increasing and we are moving towards heterogeneous systems.

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Section: Solveurs Linéaires Et Leur Passage à L'échelleunclassified

Section: Scalable Linear Solversmentioning

confidence: 99%

IFP Energies Nouvelles Conference: SimRace 2015: Numerical Methods and High Performance Computing for Industrial Fluid Flows

Chaisemartin

Allaire

2017

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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“…(a) Water saturation (b) Cartesian estimate of[45,70] (c) Polygonal simplified estimate (6.23a) Two-phase flow: results on the fine mesh at 500 days…”

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confidence: 99%

A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows

Vohralı́k

Yousef

2018

Computer Methods in Applied Mechanics and Engineering

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This paper develops an a posteriori error estimate for lowest-order locally conservative methods on meshes consisting of general polytopal elements. We focus on the ease of implementation of the methodology based on H 1-conforming potential reconstructions and H(div, Ω)-conforming flux reconstructions. In particular, the evaluation of our estimates for steady linear diffusion equations merely consists in some local matrix-vector multiplications, where, on each mesh element, the matrices are either directly inherited from the given numerical method, or easily constructed from the element geometry, while the vectors are the flux and potential values on the given element. We next extend our approach to steady nonlinear problems. We obtain a guaranteed upper bound on the total error in the fluxes that is still obtained by local matrix-vector multiplications, with the same element matrices as above. Moreover, the estimate holds true on any linearization and algebraic solver step and allows to distinguish the different error components. Finally, we apply this methodology to unsteady nonlinear coupled degenerate problems describing complex multiphase flows in porous media. Also here, on each step of the time-marching scheme, linearization procedure, and linear algebraic solver, the estimate takes the simple matrix-vector multiplication form and distinguishes the different error components. It leads to an easy-to-implement and fast-to-run adaptive algorithm with guaranteed overall precision, adaptive stopping criteria, and adaptive space and time mesh refinements. Numerous numerical experiments on practical problems in two and three space dimensions illustrate the performance of our methodology.

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“…The largest numerical errors may occur in the transition zone with grid block sizes that may be compared to the size of the heterogeneities. Preux (2016), Gratien, Jean-Marc et al (2016) and references therein offer some indicators to check the quality of the coarse reservoir model. These indicators permit to define the zones where the grid should be refined.…”

Section: Gridding Issuesmentioning

confidence: 99%

Direct simulation of non-additive variables on unstructured grids : the case of permeability

Mourlanette¹

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Uncertainties related to permeability heterogeneity can be estimated using geostatistical simulation methods. Usually, these methods are applied on regular grids with cells of constant size, whereas unstructured grids are more flexible to honor geological structures and offer local refinements for fluid-flow simulations. However, cells of different sizes require to account for the support dependency of permeability statistics (support effect). This work presents a novel workflow based on the power averaging technique. The averaging exponent ω is estimated using a response surface calibrated from numerical upscaling experiments. Using spectral turning bands, permeability is simulated on points in each unstructured cell, and later averaged with a local value of ω that depends on the cell size and shape, but also on the proportion of each facies inside the cell. The method is first illustrated on a synthetic case, with a single facies. The simulation of a tracer experiment is used to compare this novel geostatistical simulation method with a conventional approach based on a fine scale Cartesian grid. The results show the consistency of both the simulated permeability fields and the tracer breakthrough curves. The application to an industrial case with two facies is then presented and shows both consistent permeability fields and computational costs acceptable for the industry. Indeed, the computational cost for several realizations is much lower than the conventional approach based on a pressure-solver upscaling. The method works for the presented cases, but its theoretical ro-bustness can still be improved. A discussion on pressure solver upscal-ing parameters selection and power averaging limits is available in the conclusion, as well as a few research perspectives on multiple facies and non stationary proportions inclusion, the management of anisotropy and the extension to multiphase flow.

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Reservoir Simulator Runtime Enhancement Based ona PosterioriError Estimation Techniques

Cited by 7 publications

References 16 publications

IFP Energies Nouvelles Conference: SimRace 2015: Numerical Methods and High Performance Computing for Industrial Fluid Flows

IFP Energies Nouvelles Conference: SimRace 2015: Numerical Methods and High Performance Computing for Industrial Fluid Flows

A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows

Direct simulation of non-additive variables on unstructured grids : the case of permeability

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