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

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.

Graphical abstract

Keywords

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

References

[1] Ai T,, Zhang R,, Zhou H,, Pei J. ( 2014). Box-counting methods to directly estimate the fractal dimension of a rock surface. Appl Surf Sci, 314: 610– 621

[2] Bear J ( 1972). Dynamics of Fluids in Porous Media. New York: Elsevier

[3] Bertrand F,, Buzzi O,, Collin F. ( 2019). Cleat-scale modelling of the coal permeability evolution due to sorption-induced strain. Int J Coal Geol, 216: 103320

[4] Fan N,, Wang J,, Deng C,, Fan Y,, Wang T,, Guo X. ( 2020). Quantitative characterization of coal microstructure and visualization seepage of macropores using CT-based 3D reconstruction. J Nat Gas Sci Eng, 81: 103384

[5] Fang H,, Sang S,, Wang J,, Liu S,, Ju W. ( 2017). Simulation of paleotectonic stress fields and distribution prediction of tectonic fractures at the Hudi coal mine, Qinshui Basin. Acta Geol Sin-Eng, 91( 6): 2007– 2023

[6] Fang H,, Sang S,, Liu S,, Liu S. ( 2019). Experimental simulation of replacing and displacing CH₄ by injecting supercritical CO₂ and its geological significance. Int J Greenh Gas Control, 81: 115– 125

[7] Fang H,, Sang S,, Liu S. ( 2020). Three-dimensional spatial structure of the macro-pores and flow simulation in anthracite coal based on X-ray μ-CT scanning data. Petrol Sci, 17( 5): 1221– 1236

[8] Fang H,, Sang S,, Du Y,, Liu H,, Xu H. ( 2021). Visualization characterization of minerals touched by interconnected pores and fractures and its demineralization effect on coal permeability during CO₂-ECBM process based on X-ray CT data. J Nat Gas Sci Eng, 95: 104213

[9] He Q, Li F, Shi A, He B, Chen J, Xie L ( 2021). Fractal characterization of complex hydraulic fracture networks of oil shale via 3D CT reconstruction. Petrol Geo Recov Effi, 28( 5): 116− 123 (in Chinese)

[10] Huang S,, Liu D,, Cai Y,, Gan Q. ( 2019). In situ stress distribution and its impact on CBM reservoir properties in the Zhengzhuang area, southern Qinshui Basin, north China. J Nat Gas Sci Eng, 61: 83– 96

[11] Katz A J,, Thompson A H. ( 1985). Fractal sandstone pores: implications for conductivity and pore formation. Phys Rev Lett, 54( 12): 1325– 1328

[12] Klimczak C,, Schultz R,, Parashar R,, Reeves D. ( 2010). Cubic law with aperture length correlation: implications for network scale fluid flow. Hydrogeol J, 18( 4): 851– 862

[13] Li Y,, Zhao Y,, Jiang Y,, Zhang B,, Song H,, Liu B. ( 2020). Characteristics of pore and fracture of coal with bursting proneness based on DIC and fractal theory. Energies, 13( 20): 5404

[14] Li Q,, Liu D,, Cai Y,, Zhao B,, Lu Y,, Zhou Y. ( 2021). Effects of natural micro-fracture morphology, temperature and pressure on fluid flow in coals through fractal theory combined with lattice Boltzmann method. Fuel, 286( 2): 119468

[15] Liu S,, Sang S,, Wang G,, Ma J,, Wang T,, Wang W,, Du Y,, Wang T. ( 2017). FIB-SEM and X-ray CT characterization of interconnected pores in high-rank coal formed from regional metamorphism. J Petrol Sci Eng, 148: 21– 31

[16] Liu R,, Ren Z,, Yang P,, He H,, Smith T,, Guo W,, Wu L. ( 2021). Mesozoic tectono-thermal event of the Qinshui Basin, central north China craton: insights from illite crystallinity and vitrinite reflectance. Front Earth Sci, 9: 765497

[17] Miao T,, Yu B,, Duan Y,, Fang Q. ( 2015a). A fractal analysis of permeability for fractured rocks. Int J Heat Mass Transf, 81: 75– 80

[18] Miao T,, Yang S,, Long Z,, Yu B. ( 2015b). Fractal analysis of permeability of dual-porosity media embedded with random fractures. Int J Heat Mass Transf, 88: 814– 821

[19] Miao T,, Chen A,, Xu Y,, Cheng S,, Wang K. ( 2018). A Permeability model for water-gas phase flow in fractal fracture networks. Fractals, 26( 6): 1850087

[20] Miao Z,, Li S,, Xie J,, Huo R,, Ding F,, Zhu H,, Yang X,, Li X. ( 2021). Three-dimensional reconstruction and numerical simulation analysis of acid-corroded sandstone based on CT. Shock Vib, 2021: 5582781

[21] Nazridoust K,, Ahmadi G,, Smith D. ( 2006). A new friction factor correlation for laminar, single-phase flows through rock fractures. J Hydrol (Amst), 329( 1−2): 315– 328

[22] Ni X,, Miao J,, Lv R,, Lin X. ( 2017). Quantitative 3D spatial characterization and flow simulation of coal macropores based on μCT technology. Fuel, 200: 199– 207

[23] Ni X,, Zhao Z,, Wang Y,, Wang L. ( 2020). Optimisation and application of well types for ground development of coalbed methane from No. 3 coal seam in shizhuang south block in Qinshui Basin, Shanxi Province, China. J Petrol Sci Eng, 193: 107453

[24] Taud H,, Martinez-Angeles R,, Parrot J,, Hernandez-Escobedo L. ( 2005). Porosity estimation method by X-ray computed tomography. J Petrol Sci Eng, 47( 3−4): 209– 217

[25] Wang G,, Qin X,, Shen J,, Zhang Z,, Han D,, Jiang C. ( 2019a). Quantitative analysis of microscopic structure and gas seepage characteristics of low-rank coal based on CT three-dimensional reconstruction of CT images and fractal theory. Fuel, 256: 115900

[26] Wang X,, Wang X,, Pan Z,, Yin X,, Chai P,, Pan S,, Yang Q. ( 2019b). Abundance and distribution pattern of rare earth elements and yttrium in vitrain band of high-rank coal from the Qinshui Basin, northern China. Fuel, 248: 93– 103

[27] Wang Y,, Mao C. ( 2021). Nano/micro pore structure and fractal characteristics of Baliancheng coalfield in Hunchun Basin. J Nanosci Nanotechnol, 21( 1): 682– 692

[28] Wang G,, Qin X,, Han D,, Liu Z. ( 2021a). Study on seepage and deformation characteristics of coal microstructure by 3D reconstruction of CT images at high temperatures. Int J Min Sci Technol, 31( 2): 175– 185

[29] Wang H,, Yao Y,, Huang C,, Liu D,, Cai Y. ( 2021b). Fault development characteristics and their effects on current gas content and productivity of No.3 coal seam in the Zhengzhuang field, southern Qinshui Basin, north China. Energy Fuels, 35( 3): 2268– 2281

[30] Wei M,, Liu J,, Elsworth D,, Liu Y,, Zeng J,, He Z. ( 2021). Impact of equilibration time lag between matrix and fractures on the evolution of coal permeability. Fuel, 290: 120029

[31] Wu H,, Yao Y,, Zhou Y,, Qiu F. ( 2019a). Analyses of representative elementary volume for coal using X-ray μ-CT and FIB-SEM and its application in permeability predication model. Fuel, 254: 115563

[32] Wu H,, Zhou Y,, Yao Y,, Wu K. ( 2019b). Imaged based fractal characterization of microfracture structure in coal. Fuel, 239: 53– 62

[33] Yang Y, Yang H, Tao L, Yao J, Wang W, Zhang K, Luquot L ( 2019). Microscopic determination of remaining oil distribution in sandstones with different permeability scales using computed tomography scanning. J Energy Resour Technol, 141( 9): 092903, 092903− 092911

[34] Yu B,, Li J. ( 2001). Some fractal characters of porous media. Fractals, 9( 03): 365– 372

[35] Zhang G,, Guo J,, Xu B,, Xu L,, Dai Z,, Yin S,, Soltanian M. ( 2021a). Quantitative analysis and evaluation of coal mine geological structures based on fractal theory. Energies, 14( 7): 1925

[36] Zhang K,, Sang S,, Zhou X,, Liu C,, Ma M,, Niu Q. ( 2021b). Influence of supercritical CO₂-H₂O-caprock interactions on the sealing capability of deep coal seam caprocks related to CO₂ geological storage: a case study of the silty mudstone caprock of coal seam no. 3 in the Qinshui Basin, China. Int J Greenh Gas Control, 106: 103282

[37] Zhang P,, Zhang C,, Liu B,, Wu Y. ( 2022). Leveraging local and global descriptors in parallel to search correspondences for visual localization. Pattern Recognit, 122: 108344

[38] Zhao W,, Wang K,, Wang L,, Cheng Y,, Dong H,, Li B,, Dai L. ( 2021). Influence of matrix size and pore damage path on the size dependence of gas adsorption capacity of coal. Fuel, 283: 119289

[39] Zhao Y,, Wang C,, Ning L,, Zhao H,, Bi J. ( 2022). Pore and fracture development in coal under stress conditions based on nuclear magnetic resonance and fractal theory. Fuel, 309: 122112

[40] Zhou G,, Zhang Q,, Bai R,, Ni G. ( 2016). Characterization of coal micro-pore structure and simulation on the seepage rules of low-pressure water based on CT scanning data. Minerals (Basel), 6( 3): 78

[41] Zhou X,, Sang S,, Niu Q,, Zhang K,, Liu F,, Wang W,, Chang J. ( 2021). Changes of multiscale surface morphology and pore structure of mudstone associated with supercritical CO₂-water exposure at different times. Energ Fuel, 35( 5): 4212– 4223

RIGHTS & PERMISSIONS

Higher Education Press