Tag: effective medium

Effective Physical Properties of Sandstones

Post author By R Hilfer
Post date October 6, 1999

J. Widjajakusuma, R. Hilfer

in: IUTAM Symposium on Theoretical and Numerical Methods in Continuum Mechanics of Porous Materials
edited by: W. Ehlers
Solid Mechanics and Its Applications, vol. 87,Kluwer, Dordrecht, 113 (2001)
10.1007/0-306-46953-7
ISBN: 978-0-7923-6766-6

submitted on
Wednesday, October 6, 1999

In this paper we continue the investigation of the effective transport parameters of a digitized sample of Fontainebleau sandstone and three reconstruction models discussed previously in Biswal et. al., Physica A 273, 452 (1999). The effective transport parameters are computed directly by solving the disordered Laplace equation via a finite-volume method. We find that the transport properties of two stochastic models differ significantly from the real sandstone. Moreover, the effective transport parameters are predicted by employing local porosity theory and various traditional mixing-laws (such as effective medium approximation or Maxwell-Garnet theory). The prediction of local porosity theory is in good agreement with the exact result.

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Tags effective medium, sand stone

dielectric relaxation electrical conductivity Heterogeneous Materials

Macroscopic Dielectric Constant for Microstructures of Sedimentary Rocks

Post author By R Hilfer
Post date May 21, 1999

R. Hilfer, J. Widjajakusuma, B. Biswal

Granular Matter 2, 137 (1999)
https://doi.org/10.1007/s100359900035

submitted on
Friday, May 21, 1999

An approximate method to calculate dielectric response and relaxation functions for water saturated sedimentary rocks is tested for realistic three-dimensional pore space images. The test is performed by comparing the prediction from the approximate method against the exact solution. The approximate method is based on image analysis and local porosity theory. An empirical rule for the specification of the length scale in local porosity theory is advanced. The results from the exact solution are compared to those obtained using local porosity theory and various other approximate mixing laws. The calculation based on local porosity theory is found to yield improved quantitative agreement with the exact result.

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Tags effective medium, sand stone, sediments

dielectric relaxation electrical conductivity fluid flow Porous Media

Exact and Approximate Calculations for Conductivity of Sandstones

Post author By R Hilfer
Post date January 5, 1999

J. Widjajakusuma, C. Manwart, B. Biswal, R. Hilfer

Physica A 270, 325 (1999)
https://doi.org/10.1016/S0378-4371(99)00141-7

submitted on
Tuesday, January 5, 1999

We analyze a three-dimensional pore space reconstruction of Fontainebleau sandstone and calculate from it the effective conductivity using local porosity theory. We compare this result with an exact calculation of the effective conductivity that solves directly the disordered Laplace equation. The prediction of local porosity theory is in good quantitative agreement with the exact result.

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Tags effective medium, sand stone, sediments

dielectric relaxation diffusion electrical conductivity fluid flow Heterogeneous Materials Porous Media

Quantitative Prediction of Effective Material Properties of Heterogeneous Media

Post author By R Hilfer
Post date October 8, 1998

J. Widjajakusuma, B. Biswal, R. Hilfer

Computational Materials Science 16, 70 (1999)
https://doi.org/10.1016/S0927-0256(99)00047-6

submitted on
Thursday, October 8, 1998

Effective electrical conductivity and electrical permittivity of water-saturated natural sandstones are evaluated on the basis of local porosity theory (LPT). In contrast to earlier methods, which characterize the underlying microstructure only through the volume fraction, LPT incorporates geometric information about the stochastic microstructure in terms of local porosity distribution and local percolation probabilities. We compare the prediction of LPT and of traditional effective medium theory with the exact results. The exact results for the conductivity and permittivity are obtained by solving the microscopic mixed boundary value problem for the Maxwell equations in the quasistatic approximation. Contrary to the predictions from effective medium theory, the predictions of LPT are in better quantitative agreement with the exact results.

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Tags effective medium, 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