Open-source MATLAB implementation of consistent discretisations on complex grids

Lie, Knut–Andreas; Krogstad, Stein; Ligaarden, Ingeborg Skjelkvåle; Natvig, Jostein R.; Nilsen, Halvor Møll; Skaflestad, Bård

doi:10.1007/s10596-011-9244-4

Cited by 373 publications

(197 citation statements)

References 26 publications

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“…The initial control values were chosen as the average of the upper and lower bounds. The whole exercise was performed in the open-source reservoir simulator MRST Lie et al [15], by modifying the adjoint-based optimization module to allow for robust optimization and combining it with the EnKF …”

Section: D Five-spot Modelmentioning

confidence: 99%

Value of information in closed-loop reservoir management

Barros

Hof

2015

Comput Geosci

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This paper proposes a new methodology to perform value of information (VOI) analysis within a closedloop reservoir management (CLRM) framework. The workflow combines tools such as robust optimization and history matching in an environment of uncertainty characterization. The approach is illustrated with two simple examples: an analytical reservoir toy model based on decline curves and a water flooding problem in a two-dimensional fivespot reservoir. The results are compared with previous work on other measures of information valuation, and we show that our method is a more complete, although also more computationally intensive, approach to VOI analysis in a CLRM framework. We recommend it to be used as the reference for the development of more practical and less computationally demanding tools for VOI assessment in real fields.

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Section: D Five-spot Modelmentioning

confidence: 99%

Value of information in closed-loop reservoir management

Barros

Hof

2015

Comput Geosci

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“…Some such models have recently been implemented using the CO 2 module of the open-source MATLAB Reservoir Simulation Toolbox (Lie et al 2012;MRST 2014;SINTEF ICT 2014), as demonstrated in several recent publications (Andersen et al 2014;Nilsen et al 2014a, b, c).…”

Section: Other Simplifying Assumptionsmentioning

confidence: 99%

Vertically Averaged Equations with Variable Density for $$\hbox {CO}_2$$ CO 2 Flow in Porous Media

2014

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Carbon capture and storage has been proposed as a viable option to reduce CO 2 emissions. Geological storage of CO 2 where the gas is injected into geological formations for practically indefinite storage, is an integral part of this strategy. Mathematical models and numerical simulations are important tools to better understand the processes taking place underground during and after injection. Due to the very large spatial and temporal scales involved, commercial 3D-based simulators for the petroleum industry quickly become impractical for answering questions related to the long-term fate of injected CO 2 . There is an interest in developing simplified modeling tools that are effective for this type of problem. One approach investigated in recent years is the use of upscaled models based on the assumption of vertical equilibrium (VE). Under this assumption, the simulation problem is essentially reduced from 3D to 2D, allowing much larger models to be considered at the same computational cost. So far, most work on VE models for CO 2 storage has either assumed incompressible CO 2 or only permitted lateral variations in CO 2 density (semi-compressible). In the present work, we propose a way to fully include variable CO 2 density within the VE framework, making it possible to also model vertical density changes. We derive the fine-scale and upscaled equations involved and investigate the resulting effects. In addition, we compare incompressible, semi-compressible, and fully compressible CO 2 flow for some model scenarios, using an in-house, fully-implicit numerical code based on automatic differentiation, implemented using the MATLAB reservoir simulation toolkit.

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“…The implementation of the mixed MsFEM is based on the code of Aarnes. For further details we refer to [5,18].…”

Section: Acknowledgmentmentioning

confidence: 99%

Multilevel Monte Carlo methods using ensemble level mixed MsFEM for two-phase flow and transport simulations

2013

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In this paper, we propose multilevel Monte Carlo (MLMC) methods that use ensemble level mixed multiscale methods in the simulations of multiphase flow and transport. The contribution of this paper is twofold: (1) a design of ensemble level mixed multiscale finite element methods and (2) a novel use of mixed multiscale finite element methods within multilevel Monte Carlo techniques to speed up the computations. The main idea of ensemble level multiscale methods is to construct local multiscale basis functions that can be used for any member of the ensemble. In this paper, we consider two ensemble level mixed multiscale finite element methods: (1) the no-local-solve-online ensemble level method (NLSO); and (2) the local-solve-online ensemble level method (LSO). The first approach was proposed in Aarnes and Efendiev (SIAM J. Sci. Comput. 30(5):2319-2339, 2008) while the second approach is new. Both mixed multiscale methods use a number of snapshots of the permeability media in generating multiscale basis functions. As a result, in the off-line stage, we construct multiple basis functions for each coarse region where basis functions correspond to different realizations. In the no-local-solve-online ensemble level method, one uses the whole set of precomputed basis functions to approximate the solution for an arbitrary realization. In the local-solve-online ensemble level method, one uses the precomputed functions to construct a multiscale basis for a particular realization. With this basis, the solution corresponding to this particular realization is approximated in LSO mixed multiscale finite element method (MsFEM). In both approaches, the accuracy of the method is related to the number of snapshots computed based on different realizations that one uses to precompute a multiscale basis. In this paper, ensemble level multiscale methods are used in multilevel Monte Carlo methods (Giles 2008a, Oper.Res. 56(3):607-617, b). In multilevel Monte Carlo methods, more accurate (and expensive) forward simulations are run with fewer samples, while less accurate (and inexpensive) forward simulations are run with a larger number of samples. Selecting the number of expensive and inexpensive simulations based on the number of coarse degrees of freedom, one can show that MLMC methods can provide better accuracy at the same cost as Monte Carlo (MC) methods. The main objective of the paper is twofold. First, we would like to compare NLSO and LSO mixed MsFEMs. Further, we use both approaches in the context of MLMC to speedup MC calculations

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Open-source MATLAB implementation of consistent discretisations on complex grids

Cited by 373 publications

References 26 publications

Value of information in closed-loop reservoir management

Value of information in closed-loop reservoir management

Vertically Averaged Equations with Variable Density for $$\hbox {CO}_2$$ CO 2 Flow in Porous Media

Multilevel Monte Carlo methods using ensemble level mixed MsFEM for two-phase flow and transport simulations

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