A fractal model for capillary flow through a single tortuous capillary with roughened surfaces in fibrous porous media

Hydraulic tortuosity is one of the key parameters for evaluating effective transport properties of natural and artificial porous media. A pore-scale model is developed for fluid flow through porous media based on fractal geometry, and a novel analytical tortuosity–porosity correlation is presented. Numerical simulations are also performed on two-dimensional Sierpinski carpet model. The proposed fractal model is validated by comparison with numerical results and available experimental data. Results show that hydraulic tortuosity depends on both statistical and morphological characteristics of porous media. The exponents for the scaling law between tortuosity and porosity depend on pore size distribution and tortuous fractal dimension. It has been found that hydraulic tortuosity indicates evident anisotropy for asymmetrical particle arrangements under the same statistical characteristics of porous media. The present work may be helpful to understand the transport mechanisms of porous materials and provide guidelines for the development of oil and gas reservoir, water resource and chemical engineering, etc.

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New Approach for Determining Tortuosity in Fibrous Porous Media

Journal of Engineered Fibers and Fabrics ◽

10.1177/155892501000500302 ◽

2010 ◽

Vol 5 (3) ◽

pp. 155892501000500 ◽

Cited By ~ 10

Author(s):

Rahul Vallabh ◽

Pamela Banks-Lee ◽

Abdel-Fattah Seyam

Keyword(s):

Porous Medium ◽

Porous Media ◽

Fiber Diameter ◽

Empirical Relationship ◽

Air Permeability ◽

New Approach ◽

Upper Limits ◽

Fibrous Porous Media ◽

Flow Through

A method to determine tortuosity in a fibrous porous medium is proposed. A new approach for sample preparation and testing has been followed to establish a relationship between air permeability and fiberweb thickness which formed the basis for the determination of tortuosity in fibrous porous media. An empirical relationship between tortuosity and fiberweb structural properties including porosity, fiber diameter and fiberweb thickness has been proposed unlike the models in the literature which have expressed tortuosity as a function of porosity only. Transverse air flow through a fibrous porous media increasingly becomes less tortuous with increasing porosity, with the value of tortuosity approaching 1 at upper limits of porosity. Tortuosity also decreased with increase in fiber diameter whereas increase in fiberweb thickness resulted in the increase in tortuosity within the range of fiberweb thickness tested.

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Fractal Model for Thermal Conductivity of Wetting, Fibrous Porous Media

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.496.12 ◽

2012 ◽

Vol 496 ◽

pp. 12-16

Author(s):

Fang Long Zhu ◽

De Hong Xia ◽

Yu Zhou

Keyword(s):

Thermal Conductivity ◽

Porous Media ◽

Fractal Dimension ◽

Effective Thermal Conductivity ◽

Fractal Model ◽

Self Similarity ◽

Conductivity Model ◽

Electrical Analogy ◽

Fibrous Porous Media ◽

Thermal Conductivity Model

The current paper deals with the fractal effective thermal conductivity model for fibrous porous media containing unsaturated water moisture. The model is based on the thermal-electrical analogy and statistical self-similarity of porous media. The fractal effective thermal conductivity model can be expressed as a function of the pore structure (fractal dimension) and architectural parameters of porous media. It is expected that the model will be helpful in the evaluation of thermal comfort for textiles in the whole range of porosity.

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A NEW RELATIVE PERMEABILITY MODEL OF UNSATURATED POROUS MEDIA BASED ON FRACTAL THEORY

Fractals ◽

10.1142/s0218348x20500024 ◽

2020 ◽

Vol 28 (01) ◽

pp. 2050002

Author(s):

KE CHEN ◽

HE CHEN ◽

PENG XU

Keyword(s):

Experimental Data ◽

Porous Media ◽

Fractal Dimension ◽

Multiphase Flow ◽

Relative Permeability ◽

Volume Fraction ◽

Fractal Model ◽

Accurate Estimation ◽

Unsaturated Porous Media ◽

Flow Through

The multiphase flow through unsaturated porous media and accurate estimation of relative permeability are significant for oil and gas reservoir, grounder water resource and chemical engineering, etc. A new fractal model is developed for the multiphase flow through unsaturated porous media, where multiscale pore structure is characterized by fractal scaling law and the trapped water in the pores is taken into account. And the analytical expression for relative permeability is derived accordingly. The relationships between the relative permeability and capillary head as well as saturation are determined. The proposed model is validated by comparison with 14 sets of experimental data, which indicates that the fractal model agrees well with experimental data. It has been found that the proposed fractal model shows evident advantages compared with BC-B model and VG-M model, especially for the porous media with fine content and texture. Further calculations show that water permeability decreases as the fractal dimension increases under fixed saturation because the cumulative volume fraction of small pores increases with the increment of the fractal dimension. The present fractal model for the relative permeability may be helpful to understand the multiphase flow through unsaturated porous media.

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RECENT ADVANCES ON FRACTAL MODELING OF PERMEABILITY FOR FIBROUS POROUS MEDIA

Fractals ◽

10.1142/s0218348x1540006x ◽

2015 ◽

Vol 23 (01) ◽

pp. 1540006 ◽

Cited By ~ 77

Author(s):

JIANCHAO CAI ◽

LIANG LUO ◽

RAN YE ◽

XIANGFENG ZENG ◽

XIANGYUN HU

Keyword(s):

Porous Media ◽

Pore Structure ◽

Fractal Geometry ◽

Influence Factor ◽

Fractal Model ◽

Fibrous Materials ◽

Permeability Model ◽

Fractal Modeling ◽

Fibrous Porous Media ◽

Future Work

Permeability is an important hydraulic parameter for characterizing heat and mass transfer properties of fibrous porous media. However, it is difficult to be quantitatively predicted due to the complex and irregular pore structure of fibrous porous media. Fractal geometry has been verified to be an effective method for determining the permeability of fibrous porous media. In this study, recent works on the permeability of fibrous porous media by means of fractal geometry are reviewed, the advances for each presented fractal model are analyzed and summarized, parameter equations used in available fractal permeability models are also briefly compared and reviewed. Future work for more generalized permeability model of fibrous porous media need to conducted by considering the special characters of fibrous materials, uniform pore structure parameter model and the influence factor of capillary pressure, electrokinetic phenomena, etc.

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A FRACTAL MODEL FOR KOZENY–CARMAN CONSTANT AND DIMENSIONLESS PERMEABILITY OF FIBROUS POROUS MEDIA WITH ROUGHENED SURFACES

Fractals ◽

10.1142/s0218348x19501160 ◽

2019 ◽

Vol 27 (07) ◽

pp. 1950116 ◽

Cited By ~ 2

Author(s):

BOQI XIAO ◽

YIDAN ZHANG ◽

YAN WANG ◽

GUOPING JIANG ◽

MINGCHAO LIANG ◽

...

Keyword(s):

Porous Media ◽

Fractal Dimension ◽

Fluid Transport ◽

Fractal Theory ◽

Fractal Model ◽

Physical Mechanisms ◽

Relative Roughness ◽

Fibrous Porous Media ◽

Effect Of Surface ◽

Good Agreement

In this paper, fluid transport through fibrous porous media is studied by the fractal theory with a focus on the effect of surface roughness of capillaries. A fractal model for Kozeny–Carman (KC) constant and dimensionless permeability of fibrous porous media with roughened surfaces is derived. The determined KC constant and dimensionless permeability of fibrous porous media with roughened surfaces are in good agreement with available experimental data and existing models reported in the literature. It is found that the KC constant of fibrous porous media with roughened surfaces increases with the increase of relative roughness, porosity, area fractal dimension of pore and tortuosity fractal dimension, respectively. Besides, it is seen that the dimensionless permeability of fibrous porous media with roughened surfaces decreases with increasing relative roughness and tortuosity fractal dimension. However, it is observed that the dimensionless permeability of fibrous porous media with roughened surfaces increases with porosity. With the proposed fractal model, the physical mechanisms of fluids transport through fibrous porous media are better elucidated.

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