Adaptive multiscale finite-volume method for nonlinear multiphase transport in heterogeneous formations

Lee, S. H.; Zhou, Hui; Tchelepi, Hamdi A.

doi:10.1016/j.jcp.2009.09.009

Cited by 65 publications

(36 citation statements)

References 22 publications

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“…However, in cases where the dynamics of the problem is dictated by strong (saturation or component) fronts, it may not be possible to create a good static grid. Inspired by the adaptive multiscale method of Lee et al [16] and Zhou et al [21], we therefore also demonstrate how one can develop nonuniform grids with both static and dynamic flow adaption.…”

Section: Introductionmentioning

confidence: 73%

“…Finally, the basis functions are used to construct a global flow solution tational speed. The adaptive multiscale finite-volume method of Lee et al [16] and Zhou et al [21] is one approach in this direction, in which three prolongation operators with different computational complexity were used to construct a multiscale transport solver. Alternatively, to optimize the accuracy of a transport calculation, the coarsened grid should generally adapt to the flow patterns predicted by the flow solver.…”

Section: Introductionmentioning

confidence: 99%

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Flow-based coarsening for multiscale simulation of transport in porous media

2011

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Geological models are becoming increasingly large and detailed to account for heterogeneous structures on different spatial scales. To obtain simulation models that are computationally tractable, it is common to remove spatial detail from the geological description by upscaling. Pressure and transport equations are different in nature and generally require different strategies for optimal upgridding. To optimize the accuracy of a transport calculation, the coarsened grid should generally be constructed based on a posteriori error estimates and adapt to the flow patterns predicted by the pressure equation. However, sharp and rigorous estimates are generally hard to obtain, and herein we therefore consider various ad hoc methods for generating flow-adapted grids. Common for all is that they start by solving a single-phase flow problem once and then continue to form a coarsened grid by amalgamating cells from an underlying fine-scale grid. We present several variations of the original method. First, we discuss how to include a priori information in the coarsening process, e.g. to adapt to special geological features or to obtain less irregular grids in regions where flowadaption is not crucial. Second, we discuss the use of bi-directional versus net fluxes over the coarse blocks and show how the latter gives systems that better represent the causality in the flow equations, which can be exploited to develop very efficient nonlinear solvers. Finally, we demonstrate how to improve simulation accuracy by dynamically adding local resolution near strong saturation fronts.

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Section: Introductionmentioning

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Flow-based coarsening for multiscale simulation of transport in porous media

2011

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“…Once the coarse-scale system is solved, its solution is interpolated into the original fine-scale resolution using the sub-resolution of the basis functions. Among the proposed multiscale methods, multiscale finite-volume (MSFV) methods not only provide mass-conservative solutions at fine-scale, which is a crucial property for convergent solution of transport equations, but also enable relatively simple inclusion of the type of multiphase flow equations seen in contemporary reservoir models [6,[17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

The multiscale restriction smoothed basis method for fractured porous media (F-MsRSB)

Shah

Møyner

Ţene

et al. 2016

Journal of Computational Physics

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“…MSFV has been applied to a wide range of applications (see, e.g., [10,11,12,13,14,15,16,17,18,19,20,21]), thus recommending multiscale as a very promising framework for the next-generation reservoir simulators. However, most of these developments, including the state-of-the-art algebraic multiscale formulation (AMS) [19], have focused on the incompressible (linear) flow equations.…”

Section: Introductionmentioning

confidence: 99%

Adaptive algebraic multiscale solver for compressible flow in heterogeneous porous media

Ţene

Wang

Hajibeygi

2015

Journal of Computational Physics

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This paper presents the development of an Adaptive Algebraic Multiscale Solver for Compressible flow (C-AMS) in heterogeneous porous media. Similar to the recently developed AMS for incompressible (linear) flows [Wang et al., JCP, 2014], C-AMS operates by defining primal and dual-coarse blocks on top of the fine-scale grid. These coarse grids facilitate the construction of a conservative (finite volume) coarsescale system and the computation of local basis functions, respectively. However, unlike the incompressible (elliptic) case, the choice of equations to solve for basis functions in compressible problems is not trivial. Therefore, several basis function formulations (incompressible and compressible, with and without accumulation) are considered in order to construct an efficient multiscale prolongation operator. As for the restriction operator, C-AMS allows for both multiscale finite volume (MSFV) and finite element (MSFE) methods. Finally, in order to resolve highfrequency errors, fine-scale (pre-and post-) smoother stages are employed. In order to reduce computational expense, the C-AMS operators (prolongation, restriction, and smoothers) are updated adaptively. In addition to this, the linear system in the Newton-Raphson loop is infrequently updated. Systematic numerical experiments are performed to determine the effect of the various options, outlined above, on the C-AMS convergence behaviour. An efficient C-AMS strategy for heterogeneous 3D compressible problems is developed based on overall CPU times. Finally, C-AMS is compared against an industrial-grade Algebraic MultiGrid (AMG) solver. Results of this comparison illustrate that the C-AMS is quite efficient as a nonlinear solver, even when iterated to machine accuracy.Key words: multiscale methods, compressible flows, heterogeneous porous media, scalable linear solvers, multiscale finite volume method, multiscale finite element method, iterative multiscale methods, algebraic multiscale methods.

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Adaptive multiscale finite-volume method for nonlinear multiphase transport in heterogeneous formations

Cited by 65 publications

References 22 publications

Flow-based coarsening for multiscale simulation of transport in porous media

Flow-based coarsening for multiscale simulation of transport in porous media

The multiscale restriction smoothed basis method for fractured porous media (F-MsRSB)

Adaptive algebraic multiscale solver for compressible flow in heterogeneous porous media

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