The Multiscale Perturbation Method for Two-Phase Reservoir Flow Problems

Rocha, Franciane Fracalossi; Mankad, Het; Sousa, Fabrício S.; Pereira, Felipe

doi:10.48550/arxiv.2103.11050

Cited by 2 publications

(2 citation statements)

References 31 publications

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“…The authors and their collaborators are currently applying the Multiscale Perturbation Method [3,39] to further speed up MCMC studies.…”

Section: Discussionmentioning

confidence: 99%

Conditioning by Projection for the Sampling from Prior Gaussian Distributions

Ali¹,

Mamun²,

Pereira³

et al. 2021

Preprint

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In this work we are interested in the (ill-posed) inverse problem for absolute permeability characterization that arises in predictive modeling of porous media flows. We consider a Bayesian statistical framework with a preconditioned Markov Chain Monte Carlo (MCMC) algorithm for the solution of the inverse problem. Reduction of uncertainty can be accomplished by incorporating measurements at sparse locations (static data) in the prior distribution. We present a new method to condition Gaussian fields (the log of permeability fields) to available sparse measurements. A truncated Karhunen-Loève expansion (KLE) is used for dimension reduction. In the proposed method the imposition of static data is made through the projection of a sample (expressed as a vector of independent, identically distributed normal random variables) onto the nullspace of a data matrix, that is defined in terms of the KLE. The numerical implementation of the proposed method is straightforward. Through numerical experiments for a model of second-order elliptic equation, we show that the proposed method in multi-chain studies converges much faster than the MCMC method without conditioning. These studies indicate the importance of conditioning in accelerating the MCMC convergence.

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“…The authors and their collaborators are currently applying the Multiscale Perturbation Method [3,39] to further speed up MCMC studies.…”

Section: Discussionmentioning

confidence: 99%

Conditioning by Projection for the Sampling from Prior Gaussian Distributions

Ali¹,

Mamun²,

Pereira³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

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“…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%

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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The Multiscale Perturbation Method for Two-Phase Reservoir Flow Problems

Cited by 2 publications

References 31 publications

Conditioning by Projection for the Sampling from Prior Gaussian Distributions

Conditioning by Projection for the Sampling from Prior Gaussian Distributions

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

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