Estimating permeability and its scale dependence at pore scale using renormalization group theory
File(s)
Accepted version
Author(s)
Esmaeilpour, Misagh
Ghanbarian, Behzad
Sousa, Rita
King, Peter R
Type
Journal Article
Abstract
Investigating hydraulic and petrophysical properties of porous media has been an active area of research. Despite numerous progress in modeling flow and transport over the past decades, we are still far from accurately estimating the scale dependence of soil and rock properties. In this study, we propose applying renormalization group theory (RGT) at the pore scale. Using the RGT, we determine the scale dependence of effective pore-throat radius (rteff) and develop two theoretical models to estimate permeability (k) in pore networks of various sizes. The first theoretical model estimates k(L) from the rteff(L) and simulated formation factor F(L), while the second model uses information at the smallest scale (L = Lmin) in addition to rteff(L) and F(L). By comparing with 25 pore-network simulations, we show that the RGT estimates the scale-dependent k reasonably well. The first model estimates k(L) with average relative errors ranged between −53.1% and −3.0%, while the second model between −1.0% and 14.33%. We also conduct fluid flow simulations in 40 other pore networks above the representative elementary volume and compare the results of the RGT with those of the effective-medium approximation (EMA). Results showed that both RGT and EMA accurately estimate k from pore-throat radius distribution and formation factor with root mean square log-transformed error = 0.119 and 0.096, respectively.
Date Issued
2023-05
Date Acceptance
2023-04-20
Citation
Water Resources Research, 2023, 59 (5), pp.1-20
ISSN
0043-1397
Publisher
Wiley
Start Page
1
End Page
20
Journal / Book Title
Water Resources Research
Volume
59
Issue
5
Copyright Statement
© 2023. American Geophysical Union. All Rights Reserved.
An edited version of this paper was published by AGU. Published 2023 American Geophysical Union. Esmaeilpour, M., Ghanbarian, B., Sousa, R., & King, P. R. (2023). Estimating permeability and its scale dependence at pore scale using renormalization group theory. Water Resources Research, 59, e2022WR033462. https://doi.org/10.1029/2022WR033462. To view the published open abstract, go to http://dx.doi.org and enter the DOI.
An edited version of this paper was published by AGU. Published 2023 American Geophysical Union. Esmaeilpour, M., Ghanbarian, B., Sousa, R., & King, P. R. (2023). Estimating permeability and its scale dependence at pore scale using renormalization group theory. Water Resources Research, 59, e2022WR033462. https://doi.org/10.1029/2022WR033462. To view the published open abstract, go to http://dx.doi.org and enter the DOI.
Identifier
https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2022WR033462
Publication Status
Published
Article Number
e2022WR033462
Date Publish Online
2023-05-02