Department of Mathematical Modelling
Technical University of Denmark
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Porous media: Analysis, reconstruction and percolation
SummarySpatial 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
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