Category: Porous Media

Local Percolation Probabilities for a Natural Sandstone

Post author By R Hilfer
Post date July 25, 1996

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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Tags local percolation probability, sand stone

Disordered Systems Fractals Porous Media

Probabilistic Methods, Upscaling and Fractal Statistics in Porous Media

Post author By R Hilfer
Post date April 24, 1996

R. Hilfer

Zentralblatt für Geologie und Paläontologie, Teil I 11/12, 1035 (1997)

submitted on
Friday, May 24, 1996

This contribution gives a brief introduction to local porosity theory. It is shown that fractal porosity fluctuations may arise for macroscopic media in a suitable upscaling limit.

Tags Scaling Limit, Upscaling

Percolation Porous Media

Rescaling Relations between Two- and Three Dimensional Local Porosity Distributions for Natural and Artificial Porous Media

Post author By R Hilfer
Post date March 29, 1996

B. Virgin, E. Haslund, R. Hilfer

Physica A 232, 1-10 (1996)
https://doi.org/10.1016/0378-4371(96)00131-8

submitted on
Friday, March 29, 1996

Local porosity distributions for a three-dimensional porous medium and local porosity distributions for a two-dimensional plane-section through the medium are generally different. However, for homogeneous and isotropic media having finite correlation lengths, a good degree of correspondence between the two sets of local porosity distributions can be obtained by rescaling lengths, and the mapping associating corresponding distributions can be found from two-dimensional observations alone. The agreement between associated distributions is good as long as the linear extent of the measurement cells involved is somewhat larger than the correlation length, and it improves as the linear extent increases. A simple application of the central limit theorem shows that there must be a correspondence in the limit of very large measurement cells, because the distributions from both sets approach normal distributions. A normal distribution has two independent parameters: the mean and the variance. If the sample is large enough, LPDs from both sets will have the same mean. Therefore corresponding distributions are found by matching variances of two and three dimensional local porosity distributions. The variance can be independently determined from correlation functions. Equating variances leads to a scaling relation for lengths in this limit. Three particular systems are examined in order to show that this scaling behavior persists at smaller length-scales.

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Tags local porosity theory

Percolation Porous Media

Local Porosity Theory for the Transition from Microscales to Macroscales in Porous Media

Post author By R Hilfer
Post date February 12, 1996

R. Hilfer, B. Virgin, T. Rage

ERCOFTAC Bull. 28, 6 (1996)

submitted on
Monday, February 12, 1996

A quantitative understanding of fluid flow and other transport processes in porous media remains a prerequisite for progress in many disciplines such as hydrology, petroleum technology, chemical engineering, environmental protection, nuclear waste storage, drug transport in biological tissues, catalysis, paleontology, filtration and separation technology to name but a few. While the microscopic equations governing flow and transport in porous media are often well known, the macroscopic laws are usually different and much less understood. Most approaches in computational fluid dynamics for porous media avoid to discuss or control the problems arising in the transition from a microscale (pores) to the macroscale (field or laboratory). As a consequence the upscaling of transport processes, particularly for immiscible fluid-fluid displacement, has remained difficult.

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Tags effective medium, local porosity theory

Porous Media Transport Processes

Transport and Relaxation Phenomena in Porous Media

Post author By R Hilfer
Post date May 9, 1995

R. Hilfer

Advances in Chemical Physics XCII, 299 (1996)
ISBN: 978-0-470-14204-2

submitted on
Tuesday, May 9, 1995

Almost all studies of transport and relaxation in porous media are motivated by one central question. How are the effektive macroscopic transport parameters influenced by the microscopic geometric structure of the medium?

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dielectric relaxation Disordered Systems Porous Media

Measurement of Local Porosities and Dielectric Dispersion for a Water Saturated Porous Medium

Post author By R Hilfer
Post date October 4, 1993

E. Haslund, B.D. Hansen, R. Hilfer, B. Nøst

Journal of Applied Physics 76, 5473 (1994)
https://doi.org/10.1063/1.357205

submitted on
Monday, October 4, 1993

The frequency‐dependent conductivity and dielectric constant of a salt‐water‐saturated porous glass specimen have been measured. The measurements cover the full frequency range of the Maxwell–Wagner dispersion. The experimental results have been compared with the recently introduced local porosity theory and with previous theories. For the purpose of comparing with the local porosity theory experimental measurements of local porosity distributions from digitized pore space images are presented. These experimental porosity distributions are then used for a first experimental test of local porosity theory. The comparison with previous theoretical expressions for the frequency‐dependent effective dielectric function shows that local porosity theory constitutes a significant improvement in the quantitative agreement.

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Tags local porosity theory

Disordered Systems fluid flow Porous Media Transport Processes

Local Porosity Theory for Flow in Porous Media

Post author By R Hilfer
Post date March 28, 1991

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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Tags local percolation probability, local porosity theory

dielectric relaxation Porous Media

Geometric and Dielectric Characterization of Porous Media

Post author By R Hilfer
Post date October 12, 1990

R. Hilfer

Physical Review B 44, 60 (1991)
https://doi.org/10.1103/PhysRevB.44.60

submitted on
Friday, October 12, 1990

This paper introduces local porosity distributions and local percolation probabilities as well-defined and experimentally observable geometric characteristics of general porous media. Based on these concepts the dielectric response is analyzed using the effective-medium approximation and percolation scaling theory. The theoretical origin of static and dynamic scaling laws for the dielectric response including Archie’s law in the low-porosity limit are elucidated. The zero-frequency real dielectric constant is found to diverge as as a power law in the high-porosity limit with an exponent analogous to the cementation exponent. Model calculations are presented for the interplay between geometric characteristics and the frequency-dependent dielectric response. Three purely geometric mechanisms are identified, each of which can give rise to a large dielectric enhancement.

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