Algebraic Multigrid Methods (AMG) for the Efficient Solution of Fully Implicit Formulations in Reservoir Simulation

Stueben, Klaus; Clees, Tanja; Klíe, Héctor; Lu, Bo; Wheeler, Mary F.

doi:10.2118/105832-ms

Cited by 68 publications

(54 citation statements)

References 34 publications

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“…Traditionally finite difference methods dominate but finite elements and streamlined numerical models are also used. Recently even more advanced computational techniques, such as neural networks and fuzzy logic [26] or algebraic multigrids [27], have been used to model reservoir flows.…”

Section: Depletion-driven Production Declinementioning

confidence: 99%

Depletion rate analysis of fields and regions: A methodological foundation

Höök

2014

Fuel

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PostprintThis is the accepted version of a paper published in Fuel. This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination.Citation for the original published paper (version of record):Depletion rate analysis of fields and regions: a methodological foundation. Fuel Abstract:This paper presents a comprehensive mathematical framework for depletion rate analysis and ties it to the physics of depletion. Theory was compared with empirical data from 1036 fields and a number of regions. Strong agreement between theory and practice was found, indicating that the framework is plausible. Both single fields and entire regions exhibit similar depletion rate patterns, showing the generality of the approach. The maximum depletion rates for fields were found to be well described by a Weibull distribution.Depletion rates were also found to strongly correlate with decline rates. In particular, the depletion rate at peak was shown to be useful for predicting the future decline rate. Studies of regions indicate that a depletion rate of remaining recoverable resources in the range of 2-3% is consistent with historical experience. This agrees well with earlier "peak oil" forecasts and indicates that they rest on a solid scientific ground.

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Section: Depletion-driven Production Declinementioning

confidence: 99%

Depletion rate analysis of fields and regions: A methodological foundation

Höök

2014

Fuel

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“…• For the first stage, one VAMG cycle for an IMPES-style "pressure" matrix [quasi-IMPES, see Stüben et al (2007), Cao et al (2005), and Fung and Dogru (2008)], realized by using an appropriately restricted UAMG-style coarsening based on a "pressure" matrix, additionally created and stored in memory…”

Section: Cpr-vamg Methods Used For the Numerical Testsmentioning

confidence: 99%

“…As analyzed by Klie (1996), Stüben et al (2007), and Klie et al (2007), the pressure block is basically elliptic. Saturations add hyperbolic behavior to the system.…”

Section: Aimsmentioning

confidence: 96%

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An Efficient Algebraic Multigrid Solver Strategy for Adaptive Implicit Methods in Oil-Reservoir Simulation

Clees

Ganzer

2010

SPE Journal

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We propose a new, efficient, adaptive algebraic multigrid (AMG) solver strategy for the discrete systems of partial-differential equations (PDEs) arising from structured or unstructured grid models in reservoir simulation. The proposed strategy has been particularly tailored to linear systems of equations arising in adaptive implicit methods (AIMs). The coarsening process of the AMG method designed automatically employs information on the physical structure of the models; as a smoother, an adaptive incomplete LU factorization with thresholding (ILUT) method is employed, taking care of an efficient solution of the hyperbolic parts while providing adequately smooth errors for the elliptic parts. To achieve a good compromise of high efficiency and robustness for a variety of problem classes-ranging from simple, small black-oil to challenging, large compositional models-an automatic, adaptive ILUT parameter and AMG solver switching strategy, ␣-SAMG, has been developed. Its efficiency is demonstrated for eight industrial benchmark cases by comparison against standard one-level and AMG solvers, including constraint pressure residual (CPR), as well as the pure one-level variant of the proposed new strategy. In addition, very promising results of first parallel runs are shown.

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“…The nonlinear system of equations is resolved by some variant of Newton's method, whereafter a preconditioning technique is applied to the resulting linear system, and the preconditioned linear system is solved by a Krylov iterative method. Within this framework, the focus has largely been on the development of better preconditioners for the linearized system, such as multiscale methods (Juanes and Tchelepi 2008;Nordbotten 2009), two-stage preconditioners (Cao et al 2005;Stüben et al 2007;Wallis et al 1985), sequential splitting strategies (Watts 1986), and domain decomposition (DD) methods (Quarteroni and Valli 1999;Smith et al 1996;Toselli and Widlund 2005). It should, however, be noted that some multiscale methods also take the full nonlinear problem into account, to a varying degree (Jenny et al 2006;Juanes and Tchelepi 2008).…”

Section: Introductionmentioning

confidence: 99%

Two-Scale Preconditioning for Two-Phase Nonlinear Flows in Porous Media

2015

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Solving realistic problems related to flow in porous media to desired accuracy may be prohibitively expensive with available computing resources. Multiscale effects and nonlinearities in the governing equations are among the most important contributors to this situation. Hence, developing methods that handle these features better is essential in order to be able to solve the problems more efficiently. Focus has until recently largely been on preconditioners for linearized problems. This article proposes a two-scale nonlinear preconditioning technique for flow problems in porous media that allows for incorporating physical intuition directly in the preconditioner. By assuming a certain dominant physical process, this technique will resemble upscaling in the equilibrium limit, with the computational benefits that follow. In this study, the method is established as a preconditioner with good scalability properties for challenging problems regardless of dominant physics, thus laying the foundation for further studies with physical information in the preconditioner.

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Algebraic Multigrid Methods (AMG) for the Efficient Solution of Fully Implicit Formulations in Reservoir Simulation

Cited by 68 publications

References 34 publications

Depletion rate analysis of fields and regions: A methodological foundation

Depletion rate analysis of fields and regions: A methodological foundation

An Efficient Algebraic Multigrid Solver Strategy for Adaptive Implicit Methods in Oil-Reservoir Simulation

Two-Scale Preconditioning for Two-Phase Nonlinear Flows in Porous Media

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