A Novel Fractal Model for the Invasion Depth of Fluid Through the Tortuous Capillary Bundle With Roughened Surfaces in Porous Media

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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Fractal model for permeability estimation in low-permeable porous media with variable pore sizes and unevenly adsorbed water lay

Marine and Petroleum Geology ◽

10.1016/j.marpetgeo.2021.105135 ◽

2021 ◽

pp. 105135

Author(s):

Quanqi Dai ◽

Guiwen Wang ◽

Xing Zhao ◽

Zongyan Han ◽

Kai Lu ◽

...

Keyword(s):

Porous Media ◽

Adsorbed Water ◽

Fractal Model ◽

Pore Sizes ◽

Permeability Estimation

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A FRACTAL MODEL FOR PREDICTING OXYGEN EFFECTIVE DIFFUSIVITY OF POROUS MEDIA WITH ROUGH SURFACES UNDER DRY AND WET CONDITIONS

Fractals ◽

10.1142/s0218348x21500766 ◽

2021 ◽

pp. 2150076

Author(s):

BOQI XIAO ◽

QIWEN HUANG ◽

BOMING YU ◽

GONGBO LONG ◽

HANXIN CHEN

Keyword(s):

Porous Media ◽

Fractal Dimension ◽

Oxygen Diffusion ◽

Water Saturation ◽

Rough Surfaces ◽

Effective Diffusivity ◽

Fractal Model ◽

Relative Roughness ◽

Oxygen Diffusivity ◽

Dry And Wet Conditions

Oxygen diffusion in porous media (ODPM) with rough surfaces (RS) under dry and wet conditions is of great interest. In this work, a novel fractal model for the oxygen effective diffusivity of porous media with RS under dry and wet conditions is proposed. The proposed fractal model is expressed in terms of relative roughness, the water saturation, fractal dimension for tortuosity of tortuous capillaries, fractal dimension for pores, and porosity. It is observed that the normalized oxygen diffusivity decreases with increasing relative roughness and fractal dimension for capillary tortuosity. It is found that the normalized oxygen diffusivity increases with porosity and fractal dimension for pore area. Besides, it is seen that that the normalized oxygen diffusivity under wet condition decreases with increasing water saturation. The determined normalized oxygen diffusivity is in good agreement with experimental data and existing models reported in the literature. With the proposed analytical fractal model, the physical mechanisms of oxygen diffusion through porous media with RS under dry and wet conditions are better elucidated. Every parameter in the proposed fractal model has clear physical meaning, with no empirical constant.

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Estimation of Two-Phase Relative Permeabilities Based on Treelike Fractal Model and Pressure Drop Around Gas Bubbles in Porous Media

Fractals ◽

10.1142/s0218348x21502169 ◽

2021 ◽

Author(s):

Keming Gu ◽

Zhengfu Ning ◽

Zhongqi Mu ◽

Fangtao Lv

Keyword(s):

Porous Media ◽

Pressure Drop ◽

Gas Bubbles ◽

Fractal Model ◽

Relative Permeabilities ◽

Two Phase

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Anisotropic fractal model for the effective thermal conductivity of random metal fiber porous media with high porosity

Physics Letters A ◽

10.1016/j.physleta.2017.08.003 ◽

2017 ◽

Vol 381 (37) ◽

pp. 3193-3196 ◽

Cited By ~ 1

Author(s):

Hangming Shen ◽

Qian Ye ◽

Guoxiang Meng

Keyword(s):

Thermal Conductivity ◽

Porous Media ◽

Effective Thermal Conductivity ◽

Fractal Model ◽

High Porosity ◽

Metal Fiber

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A FRACTAL SCALING LAW BETWEEN TORTUOSITY AND POROSITY IN POROUS MEDIA

Fractals ◽

10.1142/s0218348x20500255 ◽

2020 ◽

Vol 28 (02) ◽

pp. 2050025

Author(s):

PENG XU ◽

LIPEI ZHANG ◽

BINQI RAO ◽

SHUXIA QIU ◽

YUQING SHEN ◽

...

Keyword(s):

Porous Media ◽

Chemical Engineering ◽

Oil And Gas ◽

Scaling Law ◽

Morphological Characteristics ◽

Fractal Model ◽

Statistical Characteristics ◽

Scale Model ◽

Reservoir Water ◽

Flow Through

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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A Fractal Model for Predicting the Relative Permeability of Rough-Walled Fractures

Advances in Civil Engineering ◽

10.1155/2021/6623275 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Zuyang Ye ◽

Wang Luo ◽

Shibing Huang ◽

Yuting Chen ◽

Aiping Cheng

Keyword(s):

Porous Media ◽

Multiphase Flow ◽

Relative Permeability ◽

Fractal Model ◽

Numerical Results ◽

Flow Paths ◽

Capillary Model ◽

Lognormal Distributions ◽

Fractal Characteristics ◽

Aperture Distribution

The relative permeability and saturation relationships through fractures are fundamental for modeling multiphase flow in underground geological fractured formations. In contrast to the traditional straight capillary model from porous media, the realistic flow paths in rough-walled fractures are tortuous. In this study, a fractal relationship between relative permeability and saturation of rough-walled fractures is proposed associated with the fractal characteristics of tortuous parallel capillary plates, which can be generalized to several existing models. Based on the consideration that the aperture distribution of rough-walled fracture can be represented by Gaussian and lognormal distributions, aperture-based expressions between relative permeability and saturation are explicitly derived. The developed relationships are validated by the experimental observations on Gaussian distributed fractures and numerical results on lognormal distributed fractures, respectively.

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A stress sensitivity model for the permeability of porous media based on bi-dispersed fractal theory

International Journal of Modern Physics C ◽

10.1142/s0129183118500195 ◽

2018 ◽

Vol 29 (02) ◽

pp. 1850019 ◽

Cited By ~ 9

Author(s):

X.-H. Tan ◽

C.-Y. Liu ◽

X.-P. Li ◽

H.-Q. Wang ◽

H. Deng

Keyword(s):

Porous Media ◽

Fractal Dimension ◽

Fractal Theory ◽

Stress Sensitivity ◽

Maximum Diameter ◽

Proposed Model ◽

Fractal Parameters ◽

Stress Changes ◽

Capillary Bundle ◽

Definition Of

A stress sensitivity model for the permeability of porous media based on bidispersed fractal theory is established, considering the change of the flow path, the fractal geometry approach and the mechanics of porous media. It is noted that the two fractal parameters of the porous media construction perform differently when the stress changes. The tortuosity fractal dimension of solid cluster [Formula: see text] become bigger with an increase of stress. However, the pore fractal dimension of solid cluster [Formula: see text] and capillary bundle [Formula: see text] remains the same with an increase of stress. The definition of normalized permeability is introduced for the analyzation of the impacts of stress sensitivity on permeability. The normalized permeability is related to solid cluster tortuosity dimension, pore fractal dimension, solid cluster maximum diameter, Young’s modulus and Poisson’s ratio. Every parameter has clear physical meaning without the use of empirical constants. Predictions of permeability of the model is accordant with the obtained experimental data. Thus, the proposed model can precisely depict the flow of fluid in porous media under stress.

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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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