Tag: local percolation probability

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Heterogeneous Materials Mathematical Physics Percolation Porous Media

Multiscale local porosity theory, weak limits, and dielectric response in composite and porous media

R. Hilfer

Journal of Mathematical Physics 59, 103511 (2018)
https://doi.org/10.1063/1.5063466

submitted on
Thursday, December 22, 2016

A mathematical scaling approach to macroscopic heterogeneity of composite and porous media is introduced. It is based on weak limits of uniformly bounded measurable functions. The limiting local porosity distributions, that were introduced in Advances in Chemical Physics, vol XCII, p. 299-424 (1996), are found to be related to Young measures of a weakly convergent sequence of local volume fractions. The Young measures determine frequency dependent complex dielectric functions of multiscale media within a generalized selfconsistent effective medium approximation. The approach separates scales by scale factor functions of regular variation. It renders upscaled results independent of the shape of averaging windows upon reaching the scaling limit.



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Percolation Porous Media

Local Percolation Probabilities for a Natural Sandstone

R. Hilfer, T. Rage, B. Virgin

Physica A 241, 105 (1997)
https://doi.org/10.1016/S0378-4371(97)00067-8

submitted on
Thursday, July 25, 1996

Local percolation probabilities are used to characterize the connectivity in porous and heterogeneous media. Together with local porosity distributions they allow to predict transport properties. While local porosity distributions are readily obtained, measurements of the local percolation probabilities are more difficult and have not been attempted previously. First measurements of three-dimensional local porosity distributions and percolation probabilities from the pore space reconstruction of a natural sandstone show that theoretical expectations and experimental results are consistent.



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Disordered Systems fluid flow Porous Media Transport Processes

Local Porosity Theory for Flow in Porous Media

R. Hilfer

Physical Review B 45, 7115 (1992)
https://doi.org/10.1103/PhysRevB.45.7115

submitted on
Thursday, March 28, 1991

A recently introduced geometric characterization of porous media based on local-porosity distributions and local-percolation probabilities is used to calculate dc permeabilities for porous media. The disorder in porous media is found to be intimately related to the percolation concept. The geometric characterization is shown to open a possibility for understanding experimentally observed scaling relations between permeability, formation factor, specific internal surface, and porosity. In particular, Kozeny’s equation relating effective permeability and bulk porosity and the power lawrelation between permeability and formation factor are analyzed. A simple and general consolidation model is introduced. It is based on the reduction of local porosities and emphasizes the general applicability and flexibility of the local-porosity concept. The theoretical predictions are compared with the experimentally observed range for the exponents, and are found to be in excellent agreement.



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