Renormalization group theory outperforms other approaches in statistical comparison between upscaling techniques for porous media

S. Hanasoge, U. Agarwal, K. Tandon, J.M.V.A. Koelman

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)

Abstract

Determining the pressure differential required to achieve a desired flow rate in a porous medium requires solving Darcy's law, a Laplace-like equation, with a spatially varying tensor permeability. In various scenarios, the permeability coefficient is sampled at high spatial resolution, which makes solving Darcy's equation numerically prohibitively expensive. As a consequence, much effort has gone into creating upscaled or low-resolution effective models of the coefficient while ensuring that the estimated flow rate is well reproduced, bringing to the fore the classic tradeoff between computational cost and numerical accuracy. Here we perform a statistical study to characterize the relative success of upscaling methods on a large sample of permeability coefficients that are above the percolation threshold. We introduce a technique based on mode-elimination renormalization group theory (MG) to build coarse-scale permeability coefficients. Comparing the results with coefficients upscaled using other methods, we find that MG is consistently more accurate, particularly due to its ability to address the tensorial nature of the coefficients. MG places a low computational demand, in the manner in which we have implemented it, and accurate flow-rate estimates are obtained when using MG-upscaled permeabilities that approach or are beyond the percolation threshold.

LanguageEnglish
Article number033313
Pages1-10
JournalPhysical Review E
Volume96
Issue number3
DOIs
StatePublished - 25 Sep 2017

Fingerprint

Upscaling
group theory
Group Theory
Renormalization Group
Porous Media
Permeability
permeability
Coefficient
coefficients
Flow Rate
flow velocity
Percolation Threshold
Darcy Equation
differential pressure
Darcy's Law
Numerical Accuracy
thresholds
Laplace equation
tradeoffs
Laplace

Cite this

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title = "Renormalization group theory outperforms other approaches in statistical comparison between upscaling techniques for porous media",
abstract = "Determining the pressure differential required to achieve a desired flow rate in a porous medium requires solving Darcy's law, a Laplace-like equation, with a spatially varying tensor permeability. In various scenarios, the permeability coefficient is sampled at high spatial resolution, which makes solving Darcy's equation numerically prohibitively expensive. As a consequence, much effort has gone into creating upscaled or low-resolution effective models of the coefficient while ensuring that the estimated flow rate is well reproduced, bringing to the fore the classic tradeoff between computational cost and numerical accuracy. Here we perform a statistical study to characterize the relative success of upscaling methods on a large sample of permeability coefficients that are above the percolation threshold. We introduce a technique based on mode-elimination renormalization group theory (MG) to build coarse-scale permeability coefficients. Comparing the results with coefficients upscaled using other methods, we find that MG is consistently more accurate, particularly due to its ability to address the tensorial nature of the coefficients. MG places a low computational demand, in the manner in which we have implemented it, and accurate flow-rate estimates are obtained when using MG-upscaled permeabilities that approach or are beyond the percolation threshold.",
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Renormalization group theory outperforms other approaches in statistical comparison between upscaling techniques for porous media. / Hanasoge, S.; Agarwal, U.; Tandon, K.; Koelman, J.M.V.A.

In: Physical Review E, Vol. 96, No. 3, 033313, 25.09.2017, p. 1-10.

Research output: Contribution to journalArticleAcademicpeer-review

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