Department of Mathematical Modelling

Technical University of Denmark Building 321/305 DK-2800 Lyngby Denmark

Telephone: +45 4588 1433 Telefax : +45 4588 2673 E-mail : imm@imm.dtu.dk

Porous media: Analysis, reconstruction and percolation

Thomas Rogon

Summary

Spatial structure of selected porous media has been analysed in terms of the two first spatial moments (i.e. porosity and autocorrelation). Having established directional isotropy in the three spatial planes, multiple geometrical features measured in 2-d are attempted generalized to 3-d using stereological methods. The measured sample autocorrelations are modeled by analytical correlation functions.

A method for simulating porous networks from their porosity and spatial correlation originally developed by Joshi (14) is presented. This method is based on a conversion between spatial autocorrelation functions of Gaussian fields and spatial autocorrelation functions of binary fields. An enhanced approach which embodies semi-analytical solutions for the conversions has been made. The scope and limitations of the method have been analysed in terms of realizability of different model correlation functions in binary fields.

Percolation threshold of reconstructed porous media has been determined for different discretizations of a selected model correlation function. Also critical exponents such as the correlation length exponent v, the strength of the infinite network and the mean size of finite clusters have been determined. We have obtained results which indicate that the effect of spatial correlation does affect not only the percolation threshold but also the exponents with respect to the values known for random media. We have attempted to predict key percolation values for a continuous medium (i.e. beyond discretization effects).

Key words: Porous media, Stereology, Autocorrelation, Filtering of Gaussian noise, Hermite transformations, Reconstruction, Percolation.

IMM Ph.D Thesis 17

Last modi fied April 18, 1997

For further information, please contact, Finn Kuno Christensen, IMM, Bldg. 321, DTU
Phone: (+45) 4588 1433. Fax: (+45) 4588 2673, E-mail: fkc@imm.dtu.dk

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