scholarly journals FRACTAL DIMENSIONS FOR UNSATURATED POROUS MEDIA

Fractals ◽  
2004 ◽  
Vol 12 (01) ◽  
pp. 17-22 ◽  
Author(s):  
BOMING YU ◽  
JIANHUA LI
Keyword(s):  
Porous Media ◽  
Transport Properties ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Thermal Dispersion ◽  
Unsaturated Porous Media ◽  
Empirical Constant ◽  
Pore Sizes ◽  
Analytical Expressions

The analytical expressions of the fractal dimensions for wetting and non-wetting phases for unsaturated porous media are derived and are found to be a function of porosity, maximum and minimum pore sizes as well as saturation. There is no empirical constant in the proposed fractal dimensions. It is also found that the fractal dimensions increase with porosity of a medium and are meaningful only in a certain range of saturation Sw, i.e. Sw>S min for wetting phase and Sw<S max for non-wetting phase at a given porosity, based on real porous media for requirements from both fractal theory and experimental observations. The present analysis of the fractal dimensions is verified to be consistent with the existing experimental observations and it makes possible to analyze the transport properties such as permeability, thermal dispersion in unsaturated porous media by fractal theory and technique.

FRACTAL DIMENSIONS FOR MULTIPHASE FRACTAL MEDIA

Fractals ◽  
2006 ◽  
Vol 14 (02) ◽  
pp. 111-118 ◽  
Author(s):  
BOMING YU
Keyword(s):  
Porous Medium ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Thermal Dispersion ◽  
Phase Content ◽  
Empirical Constant ◽  
Fractal Media ◽  
Content Ratio ◽  
Proposed Model ◽  
Three Phase

The simple expressions for the fractal dimensions of multiphase fractal media are derived and are found to be a function of porosity, phase content, ratio of the maximum to minimum pore sizes. There is no any empirical constant in the proposed fractal dimensions. For the three-phase fractal porous medium or unsaturated porous medium, the fractal dimensions are found to be meaningful only in certain ranges of saturation Sw, i.e. Sw > S min for wetting phase and Sw < S max for non-wetting phase for a given porosity, based on real porous media for requirements from both fractal theory and experimental observations. The present analysis of the fractal dimensions is verified by a comparison with the existing experimental measurements. It allows for the analysis of transport properties such as permeability, thermal dispersion, and conductivities (both thermal and electrical) in multiphase fractal media by the proposed model.

AN INVESTIGATION ON EFFECTIVE THERMAL CONDUCTIVITY OF UNSATURATED FRACTAL POROUS MEDIA WITH ROUGHENED SURFACES

Fractals ◽  
2020 ◽  
Vol 28 (05) ◽  
pp. 2050080
Author(s):  
BOQI XIAO ◽  
YIDAN ZHANG ◽  
YAN WANG ◽  
WEI WANG ◽  
HANXIN CHEN ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Porous Media ◽  
Effective Thermal Conductivity ◽  
Fractal Dimensions ◽  
Fractal Model ◽  
Unsaturated Porous Media ◽  
Empirical Constant ◽  
Microstructural Parameters ◽  
Physical Mechanisms ◽  
Relative Roughness

The effective thermal conductivity of unsaturated porous media is of interest in a number of applications of heat transfer. In this paper, a novel fractal solution for effective thermal conductivity is derived based on the fractal distribution of surface roughness and pore size in unsaturated porous media with roughened surfaces. The proposed fractal model explicitly relates the effective thermal conductivity to the microstructural parameters (relative roughness, porosity and fractal dimensions). The proposed fractal model is verified by a satisfying agreement of the effective thermal conductivity predicted by our model and that reported as existing experimental data in the literature. A parametric study is also elaborated to investigate the influences of the microstructural parameters on the effective thermal conductivity. The results demonstrate that our proposed fractal model improves our understanding of the physical mechanisms of heat transport through unsaturated porous media with roughened surfaces. One advantage of our fractal analytical model is that it contains no empirical constant, while it is usually required in previous models.

Research On The Fractal and Percolation Characteristics of Coal-Based Porous Media For Filtration and Impregnation

2021 ◽  
Author(s):  
Qili Wang ◽  
Jiarui Sun ◽  
Yuehu Chen ◽  
Yuyan Qian ◽  
Shengcheng Fei ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractal Structure ◽  
Mercury Intrusion Porosimetry ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Infinite Cluster ◽  
Porous Graphite ◽  
Local Aggregation ◽  
Gradual Expansion ◽  
The Difference

Abstract In order to distinguish the difference in the heterogeneous fractal structure of porous graphite used for filtration and impregnation, the fractal dimensions obtained through the mercury intrusion porosimetry (MIP) along with the fractal theory were used to calculate the volumetric FD of the graphite samples. The FD expression of the tortuosity along with all parameters from MIP test was optimized to simplify the calculation. In addition, the percolation evolution process of mercury in the porous media was analyzed in combination with the experimental data. As indicated in the analysis, the FDs in the backbone formation regions of sample vary from 2.695 to 2.984, with 2.923 to 2.991 in the percolation regions and 1.224 to 1.544 in the tortuosity. According to the MIP test, the mercury distribution in porous graphite manifested a transitional process from local aggregation, gradual expansion, and infinite cluster connection to global connection.

Fractal analysis of permeability near the wall in porous media

2014 ◽  
Vol 25 (07) ◽  
pp. 1450021 ◽  
Author(s):  
Mingchao Liang ◽  
Boming Yu ◽  
Li Li ◽  
Shanshan Yang ◽  
Mingqing Zou
Keyword(s):  
Porous Media ◽  
Pore Size ◽  
Pore Space ◽  
Fractal Theory ◽  
Particle Diameter ◽  
Fractal Dimensions ◽  
Fractal Model ◽  
Proposed Model ◽  
Medium Porosity ◽  
The Relationship

In this paper, a fractal model for permeability of porous media is proposed based on Tamayol and Bahrami's method and the fractal theory for porous media. The proposed model is expressed as a function of the mean particle diameter, the length along the macroscopic pressure drop in the medium, porosity, fractal dimensions for pore space and tortuous capillaries, and the ratio of the minimum pore size to the maximum pore size. The relationship between the permeability near the wall and the dimensionless distance from the wall under different conditions is discussed in detail. The predictions by the present fractal model are in good agreement with available experimental data. The present results indicate that the present model may have the potential in comprehensively understanding the mechanisms of flow near the wall in porous media.

A NEW METHOD FOR CALCULATING FRACTAL DIMENSIONS OF POROUS MEDIA BASED ON PORE SIZE DISTRIBUTION

Fractals ◽  
2018 ◽  
Vol 26 (01) ◽  
pp. 1850006 ◽  
Author(s):  
YUXUAN XIA ◽  
JIANCHAO CAI ◽  
WEI WEI ◽  
XIANGYUN HU ◽  
XIN WANG ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Pore Space ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
New Method ◽  
Distribution Data

Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.

PREDICTION OF MAXIMUM PORE SIZE OF POROUS MEDIA BASED ON FRACTAL GEOMETRY

Fractals ◽  
2010 ◽  
Vol 18 (04) ◽  
pp. 417-423 ◽  
Author(s):  
JIANCHAO CAI ◽  
BOMING YU
Keyword(s):  
Porous Media ◽  
Pore Size ◽  
Transport Properties ◽  
Fractal Geometry ◽  
Science And Engineering ◽  
Porosity And Permeability ◽  
Maximum Pore Size ◽  
Analytical Expressions ◽  
Good Agreement

The macroscopic transport properties of porous media have received steadily attention in science and engineering areas in the past decades. It has been shown that the maximum pore size in a porous medium plays the crucial role in determination of transport properties such as flow resistance, permeability, thermal conductivity and electrical conductivity, etc. In this study, two models for predicting the maximum pore size in porous media based on fractal geometry are presented. The present analytical expressions may be used to calculate the maximum pore size from porosity and permeability data, as well as from liquid properties, structure parameters of media and imbibition coefficient data, respectively. Predicted maximum pore sizes by the proposed models show good agreement with the available experimental results.

FRACTAL ANALYSIS OF HYDRAULICS IN POROUS MEDIA WITH WALL EFFECTS

Fractals ◽  
2014 ◽  
Vol 22 (03) ◽  
pp. 1440001 ◽  
Author(s):  
MINGCHAO LIANG ◽  
BOMING YU ◽  
SHANSHAN YANG ◽  
MINGQING ZOU ◽  
LONG YAO
Keyword(s):  
Porous Media ◽  
Power Law ◽  
Fractal Theory ◽  
Analytical Models ◽  
Wall Effects ◽  
Average Mass ◽  
Fractal Models ◽  
Power Law Fluids ◽  
Power Law Index ◽  
Analytical Expressions

The analytical expressions for the normalized average mass flux and pressure drop for power law fluids for wall effects in porous media are presented by using the fractal theory and technique for porous media. The proposed models are expressed as functions of power law index and structure parameters. These model predictions show that the proposed models can provide a good agreement with the experimental and other analytical results. This indicates that the fractal models may be helpful to much better understand the mechanisms of flow than other analytical models for porous media.

MODELING FOR HYDRAULIC PERMEABILITY AND KOZENY–CARMAN CONSTANT OF POROUS NANOFIBERS USING A FRACTAL APPROACH

Fractals ◽  
2015 ◽  
Vol 23 (03) ◽  
pp. 1550029 ◽  
Author(s):  
BOQI XIAO ◽  
XING TU ◽  
WEN REN ◽  
ZONGCHI WANG
Keyword(s):  
Experimental Data ◽  
Present Model ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Hydraulic Permeability ◽  
Fractal Approach ◽  
Microstructural Parameters ◽  
Fractal Models ◽  
Model Predictions ◽  
Analytical Expressions

In this study, the analytical expressions for the hydraulic permeability and Kozeny–Carman (KC) constant of porous nanofibers are derived based on fractal theory. In the present approach, the permeability is explicitly related to the porosity and the area fractal dimensions of porous nanofibers. The proposed fractal models for KC constant is also found to be a function of the microstructural parameters (porosity, area fractal dimensions). Besides, the present model clearly indicates that KC constant is not a constant and increases with porosity. However, KC constant is close to a constant value which is 18 for ϕ > 0.8. Every parameter of the proposed formulas of calculating permeability and KC constant has clear physical meaning. The model predictions are compared with the existing experimental data, and fair agreement between the model predictions and experimental data is found for different porosities.

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