New Renormalization Schemes for Conductivity Upscaling in Heterogeneous Media

Karim, Md. Rezaul; Krabbenhøft, K.

doi:10.1007/s11242-010-9585-9

Cited by 41 publications

(47 citation statements)

References 24 publications

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“…Somewhat surprisingly, the approximations differ significantly from this approximation, even for relatively small standard deviations. Although a similar behavior has been described in [81] for a finite element based method, our findings should be covarianceκ considered an experimental result. In fact, in contrast to the two-dimensional case, we did not simulate the underlying random fields exactly but by the turning bands method whose error is somewhat difficult to assess.…”

Section: Log-normal Mediasupporting

confidence: 87%

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Anomaly Detection in Random Heterogeneous Media

Simón¹

2015

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Section: Log-normal Mediasupporting

confidence: 87%

“…This idea is clearly inspired by the work [159], where a stochastic method based on simulation of the Brownian motion is introduced which is indeed considered to be rather accurate, cf. Karim and Krabbenhoft [81].…”

Section: A Continuum Micro-scale Monte Carlo Methodsmentioning

confidence: 99%

Anomaly Detection in Random Heterogeneous Media

Simón¹

2015

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“…[9] and references therein). Coarsening a highly resolved coefficient first requires a target resolution, e.g., we might wish to upscale a 512 × 512 model to 32 × 32.…”

Section: Upscaling Methods and Costmentioning

confidence: 99%

“…(iii) KK method: this is an algorithm designed to replace (2 × 2)-sized blocks of xx and yy components by combinations of their arithmetic and geometric means (see [9] and Appendix A). By construction, KK can only handle a block size of N block = 2, i.e., KK is designed specifically to decimate (2 × 2)-sized blocks (a xx ,a yy ), at adjacent x-and y-grid points, to corresponding effective values.…”

Section: Upscaling Methods and Costmentioning

confidence: 99%

“…More sophisticated techniques such as renormalization group theory and the technique of [9], termed KK hereafter, explicitly address the tensorial nature of the coefficient (although KK only handles diagonal components of the coefficient tensor). The renormalization group, which has a celebrated history in particle physics, made possible the construction of effective (low-wave-number) theories in multiscale, multicomponent systems.…”

Section: Introductionmentioning

confidence: 99%

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

Hanasoge¹,

Agarwal²,

Tandon³

et al. 2017

Phys. Rev. E

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Hanasoge, S.; Agarwal, U.; Tandon, K.; Koelman, J.M.V.A. Published in:Physical Review E DOI:10.1103/PhysRevE.96.033313Published: 25/09/2017 Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. 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 percola...

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Scale‐up of pore‐level relative permeability from micro‐ to macro‐scale

Bashtani

Kantzas

2020

Can J Chem Eng

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Scaling up relative permeability curves of wetting and nonwetting phase of drainage and imbibition processes from pore scale to macro scale is a challenge. A new method for scaling up relative permeability from micro‐ to macro‐scale is proposed based on electrical analogy of multiphase fluid flow at pore scale. The method is validated against four synthetic porous media generated using homogeneous and heterogeneous grain size distributions, each of which were cut into eight sub‐segments. Single‐phase and two‐phase flow properties were calculated for the main blocks and the subsequent sub‐segments using random network modelling technique. Then, the subsegments were randomly distributed in space to reconstruct the main blocks and the proposed scale‐up method was employed to calculate the relative permeability curves of the reconstructed blocks. Results were compared to the ones obtained directly from the network model of the original blocks and show good agreement between the calculated and scaled‐up relative permeability curves of primary drainage and secondary imbibition. Furthermore, the model was tested on real media. Eight network models were extracted from pore size distribution of core samples obtained from the Green River basin located in the Mesaverde Formation. Flow properties obtained from the network models were validated against experimental data and good agreement was observed. These network models show a higher level of heterogeneity at micro‐scale. Then, the scale‐up methods were employed in order to reconstruct the macro‐scale sample and predict its properties. Scale‐up methods successfully predict the single‐phase and two‐phase flow properties of the sample.

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New Renormalization Schemes for Conductivity Upscaling in Heterogeneous Media

Cited by 41 publications

References 24 publications

Anomaly Detection in Random Heterogeneous Media

Anomaly Detection in Random Heterogeneous Media

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

Scale‐up of pore‐level relative permeability from micro‐ to macro‐scale

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