Tag: sand stone

Stochastic Reconstruction of Sandstones

Post author By R Hilfer
Post date February 4, 2000

C. Manwart, S. Torquato, R. Hilfer

Physical Review E 62, 893 (2000)
https://doi.org/10.1103/PhysRevE.62.893

submitted on
Friday, February 4, 2000

A simulated annealing algorithm is employed to generate a stochastic model for a Berea sandstone and a Fontainebleau sandstone, with each a prescribed two-point probability function, lineal-path function, and “pore size” distribution function, respectively. We find that the temperature decrease of the annealing has to be rather quick to yield isotropic and percolating configurations. A comparison of simple morphological quantities indicates good agreement between the reconstructions and the original sandstones. Also, the mean survival time of a random walker in the pore space is reproduced with good accuracy. However, a more detailed investigation by means of local porosity theory shows that there may be significant differences of the geometrical connectivity between the reconstructed and the experimental samples.

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Tags reconstruction models, sand stone

dielectric relaxation diffusion electrical conductivity fluid flow Porous Media

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

Porous Media Simulations

Reconstruction of Random Media Using Monte Carlo Methods

Post author By R Hilfer
Post date September 8, 1998

C. Manwart, R. Hilfer

Physical Review E 59, 5596 (1999)
https://doi.org/10.1103/PhysRevE.59.5596

submitted on
Tuesday, September 8, 1998

A simulated annealing algorithm is applied to the reconstruction of two-dimensional porous media with prescribed correlation functions. The experimental correlation function of an isotropic sample of Fontainebleau sandstone and a synthetic correlation function with damped oscillations are used in the reconstructions. To reduce the numerical effort we follow a proposal suggesting the evaluation of the correlation functions only along certain directions. The results show that this simplification yields significantly different microstructures as compared to a full evaluation of the correlation function. In particular, we find that the simplified reconstruction method introduces an artificial anisotropy that is originally not present.

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Tags reconstruction models, sand stone, sediments

Percolation 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