Determination of representative elementary volume of digital coal based on fractal theory with X-ray CT data and its application in fractal permeability predication model

doi:10.1007/s11707-021-0963-0

Front. Earth Sci.

2022, Vol. 16

Issue (3) : 657-670 https://doi.org/10.1007/s11707-021-0963-0

RESEARCH ARTICLE

Determination of representative elementary volume of digital coal based on fractal theory with X-ray CT data and its application in fractal permeability predication model

Huihuang FANG^1,^2,³(

), Shuxun SANG^4,^5,⁶, Shiqi LIU^4,^5,⁶, Huihu LIU^1,^2,³, Hongjie XU^1,^2,³, Yanhui HUANG^7,^1,²

¹. State Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mines, Anhui University of Science and Technology, Huainan 232001, China
². School of Earth and Environment, Anhui University of Science and Technology, Huainan 232001, China
³. Institute of Energy, Hefei Comprehensive National Science Center, Hefei 230000, China
⁴. Low Carbon Energy Institute, China University of Mining and Technology, Xuzhou 221008, China
⁵. School of Resources and Geosciences, China University of Mining and Technology, Xuzhou 221116, China
⁶. Jiangsu Key Laboratory of Coal-based Greenhouse Gas Control and Utilization, China University of Mining and Technology, Xuzhou 221008, China
⁷. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China

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Abstract

Representative elementary volume (REV) is the key to study the heterogeneity of digital coal and characterize its macroscopic and microscopic properties. The permeability evolution law of digital coal based on REV analysis can provide theoretical support for the application of permeability prediction model in multi-scale reservoirs. This study takes typical coal samples from Bofang and Sihe coal mines in Qinshui basin as research object. First, the nondestructive information of two samples is scanned and visualized. Secondly, the calculation methods of two-dimensional (2D) and three-dimensional (3D) fractal dimensions of pores and fractures are illustrated. Then, the determination methods of REV based on porosity and fractal dimension are compared. Finally, the distribution pattern of fractal dimension and porosity curves is studied, the relationship between 2D and 3D fractal dimension is characterized, and the application of fractal permeability model in permeability analysis of multi-scale reservoir is further discussed. The REV size varies greatly in different vertex directions of the same sample and between samples, so REV analysis can only be performed in specific directions. When the REV based on fractal dimension is determined, the porosity curve continues to maintain a downward trend and then tends to be stable. The 2D fractal dimension has a positive linear correlation with the 3D fractal dimension, and the porosity can be expressed as a linear function of the fractal dimension. The permeability through REV analysis domain is mainly affected by fractal dimension, dip angle, azimuth angle and maximum fracture length, which is of great significance for exploring permeability evolution law of coal reservoir at different scales. This study is of great significance for enriching the determination methods of REV in digital coal and exploring the permeability evolution law of multi-scale reservoirs.

Keywords representative elementary volume fractal dimension permeability digital coal X-ray CT Qinshui Basin

Corresponding Author(s): Huihuang FANG

Online First Date: 03 August 2022 Issue Date: 29 December 2022

Cite this article:

Huihuang FANG,Shuxun SANG,Shiqi LIU, et al. Determination of representative elementary volume of digital coal based on fractal theory with X-ray CT data and its application in fractal permeability predication model[J]. Front. Earth Sci., 2022, 16(3): 657-670.

URL:

https://academic.hep.com.cn/fesci/EN/10.1007/s11707-021-0963-0
https://academic.hep.com.cn/fesci/EN/Y2022/V16/I3/657

Fig.1 Change in attribute value as a function of sample size to define REV.

Fig.2 Geological setting of the Qinshui basin (Modified from Fang et al., 2017). (a) Four uplift belts in the Qinshui basin, and (b) vertical sequences of the sedimentary system of the Shanxi formation.

Fig.3 Sampling point distribution. (a) Location of the Qinshui basin in China and the distribution of sampling point, and (b) Anti-oxidation treatment of coal sample.

Tab.1 Key properties of coal sample used in this study.

Fig.4 X-ray CT scanning system using the BF sample as an example. (a) Preparation of sample; (b) imaging system components; (c) typical 2D CT slices of BF sample.

Fig.5 Image processing flow diagram using the BF sample as an example. (a) Original section; (b) median filtering processing; (c) binarization processing.

Fig.6 Schematic diagram of fractal dimension calculation based on the digital coal images.

Fig.7 Schematic diagram of sub-analysis domain selection. (a) Eight vertex directions of A, B, C, D, E, F, G and H in analysis area; and (b) An example of 3 different 3D images that initialized from position B are highlighted with different color.

Fig.8 Results of porosity-based REV and fractal dimension-based REV of BF sample.

Fig.9 Results of porosity-based REV and fractal dimension-based REV of SH sample.

Tab.2 Porosity-based REV and fractal dimension-based REV with different vertexes of BF and SH samples

Fig.10 Pore and fracture structures of digital coal based on the selected REV. (a)?(c) are BF sample; and (d)?(f) are SH sample.

Fig.11 Distribution pattern of curve between porosity and fractal dimension after REV determined. (a) Vertex direction A of BF sample; (b) vertex direction C of SH sample; (c) vertex direction D of BF sample; (d) vertex direction H of BF sample.

Tab.3 Statistical results of curve distribution patterns of fractal dimension and porosity in BF and SH samples

Fig.12 Relationship between 2D and 3D fractal dimension. A, B, C, D, E, F, G and H are the data of 8 vertex directions, and I is all the data from A to H.

Tab.4 Data statistics of parameters M_i and N_i between 2D and 3D fractal dimension of BF and SH samples

Fig.13 Relationship between 2D/3D fractal dimension and porosity of BF sample.

Fig.14 Relationship between 2D/3D fractal dimension and porosity of SH sample.

Fig.15 Schematic diagram of inclination angle (α) and azimuth angle (β) of fracture (Modified from Miao et al., 2015). (a) Diagram of fracture distribution and fluid migration direction; (b) fracture distribution within REV, wherer_i is the length of REV, r is the fracture trace length,h is the fracture aperture, α is the fracture plane dip angle with respect to the fluid flow direction at β = 0.

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