Fractal Models of Porous Media

2014 ◽  
pp. 103-129 ◽  
Author(s):  
Allen Hunt ◽  
Robert Ewing ◽  
Behzad Ghanbarian
Keyword(s):  
Porous Media ◽  
Fractal Models

Advances and benefits of fractal models to predict streaming potentials in partially saturated porous media

2021 ◽  
Author(s):  
Damien Jougnot ◽  
Luong Duy Thanh ◽  
Mariangeles Soldi ◽  
Jan Vinogradov ◽  
Luis Guarracino
Keyword(s):  
Porous Media ◽  
Fractal Theory ◽  
Electrical Potential ◽  
Streaming Potential ◽  
Excess Charge ◽  
Distribution Law ◽  
Distribution Models ◽  
Streaming Potentials ◽  
Fractal Models ◽  
Partially Saturated Porous Media

<p>Understanding streaming potential generation in porous media is of high interest for hydrological and reservoir studies as it allows to relate water fluxes to measurable electrical potential distributions in subsurface geological settings. The evolution of streaming potential <span>stems</span> from electrokinetic coupling between water and electrical fluxes due to the presence of an electrical double layer at the interface between the mineral and the pore water. Two different approaches can be used to model and interpret the generation of the streaming potential in porous media: the classical coupling coefficient approach based on the Helmholtz-Smoluchowski equation, and the effective excess charge density. Recent studies based on both approaches use a mathematical up-scaling procedure that employs the so-called fractal theory. In these studies, the porous medium is represented by a bundle of tortuous capillaries characterized by a fractal capillary-size distribution law. The electrokinetic coupling between the fluid flow and electric current is obtained by averaging the processes that take place in a single capillary. In most cases, closed-form expressions for the electrokinetic parameters are obtained in terms of macroscopic hydraulic variables like permeability, saturation and porosity. In this presentation we propose a review of the existing fractal distribution models that predict the streaming potential in porous media and discuss their benefits compared against other published models.</p>

scholarly journals Seepage Characteristics Study on Power-Law Fluid in Fractal Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Meijuan Yun
Keyword(s):  
Porous Media ◽  
Power Law ◽  
Quantitative Description ◽  
Flow In Porous Media ◽  
Power Law Fluid ◽  
Related Data ◽  
Fractal Models ◽  
Fractal Properties ◽  
Seepage Characteristics ◽  
Analytical Expressions

We present fractal models for the flow rate, velocity, effective viscosity, apparent viscosity, and effective permeability for power-law fluid based on the fractal properties of porous media. The proposed expressions realize the quantitative description to the relation between the properties of the power-law fluid and the parameters of the microstructure of the porous media. The model predictions are compared with related data and good agreement between them is found. The analytical expressions will contribute to the revealing of physical principles for the power-law fluid flow in porous media.

A NUMERICAL STUDY ON FRACTAL DIMENSIONS OF CURRENT STREAMLINES IN TWO-DIMENSIONAL AND THREE-DIMENSIONAL PORE FRACTAL MODELS OF POROUS MEDIA

Fractals ◽  
2015 ◽  
Vol 23 (01) ◽  
pp. 1540012 ◽  
Author(s):  
WEI WEI ◽  
JIANCHAO CAI ◽  
XIANGYUN HU ◽  
PING FAN ◽  
QI HAN ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Numerical Study ◽  
Three Dimensional ◽  
Fractal Dimensions ◽  
Simple Relation ◽  
Two Dimensional ◽  
Random Walker ◽  
Fractal Models ◽  
Novel Method

The fractal dimension of random walker (FDRW) is an important parameter for description of electrical conductivity in porous media. However, it is somewhat empirical in nature to calculate FDRW. In this paper, a simple relation between FDRW and tortuosity fractal dimension (TFD) of current streamlines is derived, and a novel method of computing TFD for different generations of two-dimensional Sierpinski carpet and three-dimensional Sierpinski sponge models is presented through the finite element method, then the FDRW can be accordingly predicted; the proposed relation clearly shows that there exists a linear relation between pore fractal dimension (PFD) and TFD, which may have great potential in analysis of transport properties in fractal porous media.

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.

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