AN INTRODUCTION TO FLOW AND TRANSPORT IN FRACTAL MODELS OF POROUS MEDIA: PART I

Fractals ◽  
2014 ◽  
Vol 22 (03) ◽  
pp. 1402001 ◽  
Author(s):  
JIANCHAO CAI ◽  
FERNANDO SAN JOSÉ MARTÍNEZ ◽  
MIGUEL ANGEL MARTÍN ◽  
EDMUND PERFECT
Keyword(s):  
Porous Media ◽  
Surface Erosion ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Fractal Structures ◽  
Flow And Transport ◽  
Fractal Models ◽  
Statics And Dynamics ◽  
Self Similar ◽  
Erosion Properties

This special issue gathers together a number of recent papers on fractal geometry and its applications to the modeling of flow and transport in porous media. The aim is to provide a systematic approach for analyzing the statics and dynamics of fluids in fractal porous media by means of theory, modeling and experimentation. The topics covered include lacunarity analyses of multifractal and natural grayscale patterns, random packing's of self-similar pore/particle size distributions, Darcian and non-Darcian hydraulic flows, diffusion within fractals, models for the permeability and thermal conductivity of fractal porous media and hydrophobicity and surface erosion properties of fractal structures.

scholarly journals COMPUTER SIMULATION OF RANDOM PACKINGS FOR SELF-SIMILAR PARTICLE SIZE DISTRIBUTIONS IN SOIL AND GRANULAR MATERIALS: POROSITY AND PORE SIZE DISTRIBUTION

Fractals ◽  
2014 ◽  
Vol 22 (03) ◽  
pp. 1440009 ◽  
Author(s):  
MIGUEL ANGEL MARTÍN ◽  
FRANCISCO J. MUÑOZ ◽  
MIGUEL REYES ◽  
F. JAVIER TAGUAS
Keyword(s):  
Computer Simulation ◽  
Particle Size ◽  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Total Porosity ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Self Similar ◽  
Random Packings

A 2D computer simulation method of random packings is applied to sets of particles generated by a self-similar uniparametric model for particle size distributions (PSDs) in granular media. The parameter p which controls the model is the proportion of mass of particles corresponding to the left half of the normalized size interval [0,1]. First the influence on the total porosity of the parameter p is analyzed and interpreted. It is shown that such parameter, and the fractal exponent of the associated power scaling, are efficient packing parameters, but this last one is not in the way predicted in a former published work addressing an analogous research in artificial granular materials. The total porosity reaches the minimum value for p = 0.6. Limited information on the pore size distribution is obtained from the packing simulations and by means of morphological analysis methods. Results show that the range of pore sizes increases for decreasing values of p showing also different shape in the volume pore size distribution. Further research including simulations with a greater number of particles and image resolution are required to obtain finer results on the hierarchical structure of pore space.

scholarly journals AN INTRODUCTION TO FLOW AND TRANSPORT IN FRACTAL MODELS OF POROUS MEDIA: PART II

Fractals ◽  
2015 ◽  
Vol 23 (01) ◽  
pp. 1502001 ◽  
Author(s):  
JIANCHAO CAI ◽  
FERNANDO SAN JOSÉ MARTÍNEZ ◽  
MIGUEL ANGEL MARTÍN ◽  
XIANGYUN HU
Keyword(s):  
Porous Media ◽  
Fractal Geometry ◽  
70Th Birthday ◽  
Review Article ◽  
Research Articles ◽  
Original Research ◽  
Special Issue ◽  
Flow And Transport ◽  
Transport In Porous Media ◽  
Fractal Models

This is the second part of the special issue on fractal geometry and its applications to the modeling of flow and transport in porous media, in which 10 original research articles and one review article are included. Combining to the first part of 11 original research articles, these two issues summarized current research on fractal models applied to porous media that will help to further advance this multidisciplinary development. This whole special issue is published also to celebrate the 70th birthday of Professor Boming Yu for his distinguished researches on fractal geometry and its application to transport physics of porous media.

A DISCUSSION ON FRACTAL MODELS FOR TRANSPORT PHYSICS OF POROUS MEDIA

Fractals ◽  
2015 ◽  
Vol 23 (03) ◽  
pp. 1530001 ◽  
Author(s):  
PENG XU
Keyword(s):  
Porous Media ◽  
Network Model ◽  
Scaling Laws ◽  
Fractal Model ◽  
Size Distributions ◽  
Capillary Bundle Model ◽  
Fractal Models ◽  
Fracture Size ◽  
Capillary Bundle ◽  
Multi Scales

Fractal model provides an alternative and useful means for studying the transport phenomenon in porous media and analyzing the macroscopic transport properties of porous media, as fractal geometry can successfully characterize disordered and heterogeneous geometrical microstructures of porous media on multi scales. Recently, fractal models on porous media have attracted increasing interests from many different disciplines. In this mini-review paper, a review on fractal models for number-size distribution in porous media is made, and a unified fractal model to characterize pore and particle size distributions is proposed according to the statistical fractal property of the complex microstructure in porous media. Using the fractal scaling laws for pore and fracture size distributions, a fractal capillary bundle model and a fractal tree-like network model are presented and summarized for homogenous and fractured porous media, respectively. And the applications of the fractal capillary bundle model and fractal tree-like network model for analysis of transport physics in porous media are also reviewed.

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