Fractal and Multifractal Models Applied to Porous Media

Perfect, Edmund; Pachepsky, Yakov; Martı́n, Miguel Ángel

doi:10.2136/vzj2008.0127

Cited by 18 publications

(10 citation statements)

References 19 publications

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“…Approaches for extending our data to lower Q include backscattered electron imaging with the scanning electron microscope (BSE-SEM), spin-echo small angle neutron scattering (SE-SANS) and small angle light scattering (SALS). Radlinski et al (2004) have shown that some of these data can be provided by analysis of BSE-SEM images, which may also yield multifractal descriptions of the pore structure (see, for instance, Muller and McCauley, 1992;Muller, 1994;Muller, 1996;VandenBygaart and Protz, 1999;Posadas et al, 2003;Dathe et al, 2006;Kravchenko et al, 2009;Perfect et al, 2009 for references and examples of image processing approaches to multifractal analysis), and SALS has been successfully applied to coal aggregates and polymers (e.g. Chou and Hong, 2004;Liao et al, 2005).…”

Section: Concluding Remarks and Future Directionsmentioning

confidence: 99%

A new approach to quantification of metamorphism using ultra-small and small angle neutron scattering

Anovitz

Lynn

Cole

et al. 2009

Geochimica et Cosmochimica Acta

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Section: Concluding Remarks and Future Directionsmentioning

confidence: 99%

A new approach to quantification of metamorphism using ultra-small and small angle neutron scattering

Anovitz

Lynn

Cole

et al. 2009

Geochimica et Cosmochimica Acta

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“…Due to the complex geometric microstructure and multiscale pore structure [1][2][3], it is difficult to use conventional geometric methods to accurately describe the conductivity and permeability of porous media. Since fractal theory was introduced by Mandelbrot [4], it has contributed significantly to the research on the rock-electric and seepage characteristics in complex reservoirs [5][6][7][8][9][10][11][12][13]. Direct experimental measurements have been applied to the study of fractal characterizations [14], and fractal analysis has become a powerful tool for quantifying the irregularity and complexity of porous media [15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

The Percolation Properties of Electrical Conductivity and Permeability for Fractal Porous Media

et al. 2019

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Many cases have indicated that the conductivity and permeability of porous media may decrease to zero at a nonzero percolation porosity instead of zero porosity. However, there is still a lack of a theoretical basis for the percolation mechanisms of the conductivity and permeability. In this paper, the analytical percolation expressions of both conductivity and permeability are derived based on fractal theory by introducing the critical porosity. The percolation models of the conductivity and permeability were found to be closely related to the critical porosity and microstructural parameters. The simulation results demonstrated that the existence of the critical could lead to the non-Archie phenomenon. Meanwhile, the increasing critical porosity could significantly decrease the permeability and the conductivity at low porosity. Besides, the complex microstructure could result in more stagnant pores and a higher critical porosity. This study proves the importance of the critical porosity in accurately evaluating the conductivity and permeability, and reveals the percolation mechanisms of the conductivity and permeability in complex reservoirs. By comparing the predicted conductivity and permeability with the available experimental data, the validity of the proposed percolation models is verified.

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“…The fractal theory is developed in the 1980's [60] and is widely applied to many fields [61][62][63][64][65][66][67]. The mass of a fractal object (M) is related to measured scale ε through fractal dimension ( D ):…”

Section: Introduction Of Nanoparticle and Fractal Geometrymentioning

confidence: 99%

Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation

Cai

Xiao

et al. 2017

International Journal of Heat and Mass Transfer

160

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The properties of nanoparticles and its aggregation as well as convective heat transfer of nanofluids have received great attentions over the last few decades. It is well certified that nanoparticles and its aggregation can be successfully described by fractal geometry theory and technology. In this review, the fractal properties of nanoparticle and its aggregation are firstly introduced, and then the recent investigations on the fractal models and fractal-based approaches that applied for effective thermal conductivity, convective heat transfer, critical heat flux and subcooled pool boiling of nanofluids, fractal clusters and yield stress property of nanoparticle aggregation are summarized.

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Fractal and Multifractal Models Applied to Porous Media

Cited by 18 publications

References 19 publications

A new approach to quantification of metamorphism using ultra-small and small angle neutron scattering

A new approach to quantification of metamorphism using ultra-small and small angle neutron scattering

The Percolation Properties of Electrical Conductivity and Permeability for Fractal Porous Media

Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation

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