Enhanced multiscale mixed methods for two-phase flows in high-contrast porous media

Rocha, Franciane Fracalossi

doi:10.11606/t.55.2020.tde-14092020-180529

Cited by 3 publications

(9 citation statements)

References 68 publications

(106 reference statements)

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“…Therefore the use of physics-based interface spaces is advantageous in comparison with polynomial spaces also for problems with gravity. This observation increases the importance of the aMRCM-PBS, which has shown accurate results, presenting error reductions up to one order of magnitude in cases with strong channelized structures [17,40]. We remark that typical values of saturation error attained by multiscale methods are in the order of 10%.…”

Section: An Example With Gravitysupporting

confidence: 52%

“…It is well known that the classical polynomials are not optimal for high-contrast channelized permeability fields [16]. Here we recall novel interface spaces based on physics to deal with permeability fields containing highly-permeable channels and barriers, that has been introduced recently [17,40]. These interface spaces are particularly relevant when the channels and barriers are relatively large as happens in karst reservoirs [41,42].…”

Section: Interface Spacesmentioning

confidence: 99%

“…From the saturation maps we can conclude that the SFI solver is more accurate, and captures well the fingering instabilities when compared to the SI scheme. In terms of computational efficiency, the SFI is clearly more expensive than the SI (see [50,51,40] that would significantly decrease the cost of the SFI procedure). However, larger time steps can be chosen when using the SFI solver.…”

Section: Sequential Fully-implicit Approximationmentioning

confidence: 99%

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A multiscale Robin-coupled implicit method for two-phase flows in high-contrast formations

Rocha¹,

Sousa²,

Ausas³

et al. 2021

Preprint

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In the presence of strong heterogeneities, it is well known that the use of explicit schemes for the transport of species in a porous medium suffers from severe restrictions on the time step. This has led to the development of implicit schemes that are increasingly favoured by practitioners for their computational efficiency. The transport equation requires knowledge of the velocity field, which results from an elliptic problem (Darcy problem) that is the most expensive part of the computation. When considering large reservoirs, a cost-effective way of approximating the Darcy problems is using multiscale domain decomposition (MDD) methods. They allow for the pressure and velocity fields to be computed on coarse meshes (large scale), while detailed basis functions are defined locally, usually in parallel, in a much finer grid (small scale). In this work we adopt the Multiscale Robin Coupled Method (MRCM, [Guiraldello, et al., J. Comput. Phys., 355 (2018) pp. 1-21], [Rocha, et al., J. Comput. Phys., (2020) 109316]), which is a generalization of previous MDD methods that allows for great flexibility in the choice of interface spaces. In this article we investigate the combination of the MRCM with implicit transport schemes. A sequentially implicit strategy is proposed, with different trust-region algorithms ensuring the convergence of the transport solver. The method is assessed on several very stringent 2D two-phase problems, demonstrating its stability even for large time steps. It is also shown that the best accuracy is achieved by considering recently introduced non-polynomial interface spaces, since polynomial spaces are not optimal for high-contrast channelized permeability fields.

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Section: An Example With Gravitysupporting

confidence: 52%

Section: Interface Spacesmentioning

confidence: 99%

Section: Sequential Fully-implicit Approximationmentioning

confidence: 99%

See 1 more Smart Citation

A multiscale Robin-coupled implicit method for two-phase flows in high-contrast formations

Rocha¹,

Sousa²,

Ausas³

et al. 2021

Preprint

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“…Although the MRCM allows for the use different spaces for P H and U H [5], in this work, for simplicity, we restrict ourselves to the case where both spaces are the same. Several choices of interface spaces have been proposed in [5,17,18].…”

Section: A Domain Decomposition Multiscale Mixed Methodsmentioning

confidence: 99%

“…Also, Rocha et al [12] have proposed an adaptive strategy to improve accuracy by setting this algorithmic parameter as a function of the permeability contrast. Concerning the interface spaces for the flux and pressure coupling unknowns on the skeleton of the domain decomposition, Guiraldello et al [17] and Rocha et al [18,19] have introduced, respectively, informed and physically based basis functions that can yield more accurate results than polynomial spaces. Finally, the coupling to a transport solver in the linear passive case [20] and in the non-linear (two phase flow) case [12] have also been carefully investigated.…”

Section: Introductionmentioning

confidence: 99%

Towards HPC simulations of Billion-cell Reservoirs by Multiscale Mixed Methods

Jaramillo¹,

Guiraldello²,

Paz³

et al. 2021

Preprint

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A three dimensional parallel implementation of Multiscale Mixed Methods based on non-overlapping domain decomposition techniques is proposed for multi-core computers and its computational performance is assessed by means of numerical experimentation. As a prototypical method, from which many others can be derived, the Multiscale Robin Coupled Method is chosen and its implementation explained in detail. Numerical results for problems ranging from millions up to more than 2 billion computational cells in highly heterogeneous anisotropic rock formations based on the SPE10 benchmark are shown. The proposed implementation relies on direct solvers for both local problems and the interface coupling system. We find good weak and strong scalalability as compared against a state-of-the-art global fine grid solver based on Algebric Multigrid preconditioning in single and two-phase flow problems.

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The Multiscale Perturbation Method for Two-Phase Reservoir Flow Problems

Rocha¹,

Mankad²,

Sousa³

et al. 2021

Preprint

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In this work we formulate and test a new procedure, the Multiscale Perturbation Method for Two-Phase Flows (MPM-2P), for the fast, accurate and naturally parallelizable numerical solution of two-phase, incompressible, immiscible displacement in porous media approximated by an operator splitting method. The proposed procedure is based on domain decomposition and combines the Multiscale Perturbation Method (MPM) [Ali, et al., Appl. Math. and Comput., 125023 (2020)] with the Multiscale Robin Coupled Method (MRCM)

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Enhanced multiscale mixed methods for two-phase flows in high-contrast porous media

Abstract: ROCHA, F. F. Enhanced multiscale mixed methods for two-phase flows in high-contrast porous media. 2020. 150 p. Tese (Doutorado em Ciências-Ciências de Computação e

Cited by 3 publications

References 68 publications

A multiscale Robin-coupled implicit method for two-phase flows in high-contrast formations

A multiscale Robin-coupled implicit method for two-phase flows in high-contrast formations

Towards HPC simulations of Billion-cell Reservoirs by Multiscale Mixed Methods

The Multiscale Perturbation Method for Two-Phase Reservoir Flow Problems

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