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Three-dimensional local porosity analysis of porous media

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  • Biswal, B.
  • Manwart, C.
  • Hilfer, R.

Abstract

A quantitative comparison of the pore space geometry for three natural sandstones is presented. The comparison is based on local porosity theory which provides a geometric characterization of stochastic microstructures. The characterization focusses on porosity and connectivity fluctuations. Porosity fluctuations are measured using local porosity distributions while connectivity fluctuations are measured using local percolation probabilities. We report the first measurement of local percolation probability functions for experimentally obtained three-dimensional pore space reconstructions. Our results suggest the use of local porosity distributions and percolation probabilities as a quantitative method to compare microstructures of models and experiment.

Suggested Citation

  • Biswal, B. & Manwart, C. & Hilfer, R., 1998. "Three-dimensional local porosity analysis of porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 255(3), pages 221-241.
    • Handle: RePEc:eee:phsmap:v:255:y:1998:i:3:p:221-241
    DOI: 10.1016/S0378-4371(98)00111-3
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    References listed on IDEAS

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    1. Hilfer, R., 1993. "Local porosity theory for electrical and hydrodynamical transport through porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 194(1), pages 406-414.
    2. Boger, F. & Feder, J. & Jøssang, T. & Hilfer, R., 1992. "Microstructural sensitivity of local porosity distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 187(1), pages 55-70.
    3. Hilfer, R. & Nøst, B. & Haslund, E. & Kautzsch, Th. & Virgin, B. & Hansen, B.D., 1994. "Local porosity theory for the frequency dependent dielectric function of porous rocks and polymer blends," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 207(1), pages 19-27.
    4. Virgin, B. & Haslund, E. & Hilfer, R., 1996. "Rescaling relations between two-and three-dimensional local porosity distributions for natural and artificial porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 232(1), pages 1-20.
    5. Andraud, C. & Beghdadi, A. & Haslund, E. & Hilfer, R. & Lafait, J. & Virgin, B., 1997. "Local entropy characterization of correlated random microstructures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 235(3), pages 307-318.
    6. Andraud, C. & Beghdadi, A. & Lafait, J., 1994. "Entropic analysis of random morphologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 207(1), pages 208-212.
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    Cited by:

    1. Marina V Karsanina & Kirill M Gerke & Elena B Skvortsova & Dirk Mallants, 2015. "Universal Spatial Correlation Functions for Describing and Reconstructing Soil Microstructure," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-26, May.
    2. Biswal, B. & Hilfer, R., 1999. "Microstructure analysis of reconstructed porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 307-311.
    3. Chen, DongDong & Liu, Yang & Wang, XiaoRui & Wang, Mei, 2022. "Reconstruction of the microstructure based on hierarchical simulated annealing with erosion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    4. Kurochkina, E.P. & Soboleva, O.N., 2011. "Effective coefficients of quasi-steady Maxwell’s equations with multiscale isotropic random conductivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 231-244.
    5. Chen, Dongdong & He, Xiaohai & Teng, Qizhi & Xu, Zhi & Li, Zhengji, 2014. "Reconstruction of multiphase microstructure based on statistical descriptors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 240-250.
    6. Manwart, C. & Hilfer, R., 2002. "Numerical simulation of creeping fluid flow in reconstruction models of porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 706-713.
    7. Chen, DongDong & Wang, XiaoRui & Nan, JiaoFen, 2023. "A new framework for the reconstruction of porous media based on statistical characteristics: Multiscale erosion simulated annealing method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    8. Latief, F.D.E. & Biswal, B. & Fauzi, U. & Hilfer, R., 2010. "Continuum reconstruction of the pore scale microstructure for Fontainebleau sandstone," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1607-1618.
    9. Biswal, B. & Manwart, C. & Hilfer, R. & Bakke, S. & Øren, P.E., 1999. "Quantitative analysis of experimental and synthetic microstructures for sedimentary rock," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 273(3), pages 452-475.
    10. Widjajakusuma, J & Manwart, C & Biswal, B & Hilfer, R, 1999. "Exact and approximate calculations for the conductivity of sandstones," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(1), pages 325-331.

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