Imaged based fractal characterization of micro-fracture structure in coal

Hao Wu; Yingfang Zhou; Yanbin Yao; Kejian Wu

doi:10.1016/j.fuel.2018.10.117

Imaged based fractal characterization of micro-fracture structure in coal

Hao Wu, Yingfang Zhou^* (Corresponding Author), Yanbin Yao, Kejian Wu

^*Corresponding author for this work

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Abstract

To better understand the fractal characteristics of coal fracture network and find the relation between 2D and 3D fractal dimensions, we utilized the improved box counting method to calculate 2D and 3D fractal dimensions based on high resolution CT images of 4 coal samples (Ro from 2.915% to 4.69%). Based on the calculated 2D and 3D fractal dimension and porosity, the size of representative element volume (REV), the relationship between Df2 and Df3 and the relationship between porosity and fractal dimension are investigated extensively. It is noticed that the fractal dimension-based REV of coal is smaller than the porosity-based REV. As the complement of previous theoretical studies, it is proved that porosity has an exponential relationship with fractal dimension. By deducing formulas based on fractal theory, a new way to get the lower self-similar region size from relation between porosity and fractal dimension is provided. Evidently, the relation between 2D and 3D fractal dimension of coal could be expressed as
Df3=CDf2+ φ, and the slope of the line, C, depends on the average 2D fractal dimension of the sample. Finally, the reference of the relation between Df2 and C of high rank coal is provided as C= -0.75Df2 +2.75.

Original language	English
Pages (from-to)	53-62
Number of pages	10
Journal	Fuel
Volume	239
Early online date	8 Nov 2018
DOIs	https://doi.org/10.1016/j.fuel.2018.10.117
Publication status	Published - Mar 2019

Bibliographical note

We acknowledge financial support from the National Natural Science Foundation of China (41830427; 41472137), the Petro China Innovation Foundation (2018D-5007-0101), the Key research and development project of Xinjiang Uygur Autonomous Region (2017B03019-1), the Royal Society Edinburgh and National Natural Science Foundation China (NSFC 41711530129), and the Foreign Experts’ Recruiting Program from the State Administration of Foreign Experts Affairs P.R. China.

Keywords

fractal dimension
coal
micro-CT images
box-counting method
REV
porosity
Micro-CT images
Fractal dimension
Box-counting method, REV
Coal

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Cite this

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title = "Imaged based fractal characterization of micro-fracture structure in coal",

abstract = " To better understand the fractal characteristics of coal fracture network and find the relation between 2D and 3D fractal dimensions, we utilized the improved box counting method to calculate 2D and 3D fractal dimensions based on high resolution CT images of 4 coal samples (Ro from 2.915% to 4.69%). Based on the calculated 2D and 3D fractal dimension and porosity, the size of representative element volume (REV), the relationship between Df2 and Df3 and the relationship between porosity and fractal dimension are investigated extensively. It is noticed that the fractal dimension-based REV of coal is smaller than the porosity-based REV. As the complement of previous theoretical studies, it is proved that porosity has an exponential relationship with fractal dimension. By deducing formulas based on fractal theory, a new way to get the lower self-similar region size from relation between porosity and fractal dimension is provided. Evidently, the relation between 2D and 3D fractal dimension of coal could be expressed asDf3=CDf2+ φ, and the slope of the line, C, depends on the average 2D fractal dimension of the sample. Finally, the reference of the relation between Df2 and C of high rank coal is provided as C= -0.75Df2 +2.75.",

keywords = "fractal dimension, coal, micro-CT images, box-counting method, REV, porosity, Micro-CT images, Fractal dimension, Box-counting method, REV, Coal",

author = "Hao Wu and Yingfang Zhou and Yanbin Yao and Kejian Wu",

note = "We acknowledge financial support from the National Natural Science Foundation of China (41830427; 41472137), the Petro China Innovation Foundation (2018D-5007-0101), the Key research and development project of Xinjiang Uygur Autonomous Region (2017B03019-1), the Royal Society Edinburgh and National Natural Science Foundation China (NSFC 41711530129), and the Foreign Experts{\textquoteright} Recruiting Program from the State Administration of Foreign Experts Affairs P.R. China.",

year = "2019",

month = mar,

doi = "10.1016/j.fuel.2018.10.117",

language = "English",

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journal = "Fuel",

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T1 - Imaged based fractal characterization of micro-fracture structure in coal

AU - Wu, Hao

AU - Zhou, Yingfang

AU - Yao, Yanbin

AU - Wu, Kejian

N1 - We acknowledge financial support from the National Natural Science Foundation of China (41830427; 41472137), the Petro China Innovation Foundation (2018D-5007-0101), the Key research and development project of Xinjiang Uygur Autonomous Region (2017B03019-1), the Royal Society Edinburgh and National Natural Science Foundation China (NSFC 41711530129), and the Foreign Experts’ Recruiting Program from the State Administration of Foreign Experts Affairs P.R. China.

PY - 2019/3

Y1 - 2019/3

N2 - To better understand the fractal characteristics of coal fracture network and find the relation between 2D and 3D fractal dimensions, we utilized the improved box counting method to calculate 2D and 3D fractal dimensions based on high resolution CT images of 4 coal samples (Ro from 2.915% to 4.69%). Based on the calculated 2D and 3D fractal dimension and porosity, the size of representative element volume (REV), the relationship between Df2 and Df3 and the relationship between porosity and fractal dimension are investigated extensively. It is noticed that the fractal dimension-based REV of coal is smaller than the porosity-based REV. As the complement of previous theoretical studies, it is proved that porosity has an exponential relationship with fractal dimension. By deducing formulas based on fractal theory, a new way to get the lower self-similar region size from relation between porosity and fractal dimension is provided. Evidently, the relation between 2D and 3D fractal dimension of coal could be expressed asDf3=CDf2+ φ, and the slope of the line, C, depends on the average 2D fractal dimension of the sample. Finally, the reference of the relation between Df2 and C of high rank coal is provided as C= -0.75Df2 +2.75.

AB - To better understand the fractal characteristics of coal fracture network and find the relation between 2D and 3D fractal dimensions, we utilized the improved box counting method to calculate 2D and 3D fractal dimensions based on high resolution CT images of 4 coal samples (Ro from 2.915% to 4.69%). Based on the calculated 2D and 3D fractal dimension and porosity, the size of representative element volume (REV), the relationship between Df2 and Df3 and the relationship between porosity and fractal dimension are investigated extensively. It is noticed that the fractal dimension-based REV of coal is smaller than the porosity-based REV. As the complement of previous theoretical studies, it is proved that porosity has an exponential relationship with fractal dimension. By deducing formulas based on fractal theory, a new way to get the lower self-similar region size from relation between porosity and fractal dimension is provided. Evidently, the relation between 2D and 3D fractal dimension of coal could be expressed asDf3=CDf2+ φ, and the slope of the line, C, depends on the average 2D fractal dimension of the sample. Finally, the reference of the relation between Df2 and C of high rank coal is provided as C= -0.75Df2 +2.75.

KW - fractal dimension

KW - coal

KW - micro-CT images

KW - box-counting method

KW - REV

KW - porosity

KW - Micro-CT images

KW - Fractal dimension

KW - Box-counting method, REV

KW - Coal

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U2 - 10.1016/j.fuel.2018.10.117

DO - 10.1016/j.fuel.2018.10.117

M3 - Article

SN - 0016-2361

VL - 239

SP - 53

EP - 62

JO - Fuel

JF - Fuel

ER -

Imaged based fractal characterization of micro-fracture structure in coal

Abstract

Bibliographical note

Keywords

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