Volume 41 Issue 3
May  2022
Turn off MathJax
Article Contents
Zhang Zihan, Wei Wen, Zhang Jie, Jia Hongbiao. Determining method of multiscale fractal dimension of red bed sandstone pores based on CT scanning[J]. Bulletin of Geological Science and Technology, 2022, 41(3): 254-263. doi: 10.19509/j.cnki.dzkq.2021.0066
Citation: Zhang Zihan, Wei Wen, Zhang Jie, Jia Hongbiao. Determining method of multiscale fractal dimension of red bed sandstone pores based on CT scanning[J]. Bulletin of Geological Science and Technology, 2022, 41(3): 254-263. doi: 10.19509/j.cnki.dzkq.2021.0066

Determining method of multiscale fractal dimension of red bed sandstone pores based on CT scanning

doi: 10.19509/j.cnki.dzkq.2021.0066
  • Received Date: 02 Dec 2021
  • The distribution of pore structure inside rock has fractal characteristics in statistical sense, the determination of itsfractal dimension is of great significance to characterize the distribution law of pore structure quantitatively and reveal various mechanical behaviors and physical and mechanical indexes of rock.By combining image processing, fractal theory and mathematical statistics, the spatial distribution model of three-dimensional pore structure was reconstructed based on CT scan slice images, and the distribution box dimension and cluster dimension of pore structure in Hausdorff measure space were calculated. In order to quantitatively characterize the spatial complexity of pore structure distribution, the hypothesis of voxel box dimension and cylinder space bundle dimension was put forward, and the hypothesis was tested by various mathematical statistical methods. Finally, it is pointed out that the pore structure distribution is a multi-scale fractal model, and a single dimension cannot describe all its characteristics.The analysis results show that the voxel box dimension constructed for gray CT images can replace the traditional box dimension, and can quantitatively characterize the pore volume distribution law more reliably, accurately and comprehensively at the meso-scale. In essence, cluster dimension is used to quantitatively characterize the distribution law of pore position. If it is equal to Euclidean dimension, it indicates that pore position distribution has randomness.


  • loading
  • [1]
    Zhang C, Tu S H, Bai Q S. Evaluation of pore size and distribution impacts on uniaxial compressive strength of lithophysal rock[J]. Arabian Journal for Science and Engineering, 2018, 43(3): 1235-1246. doi: 10.1007/s13369-017-2810-x
    Yan C Z, Zheng H. FDEM-flow 3D: A 3D hydro-mechanical coupled model considering the pore seepage of rock matrix for simulating three-dimensional hydraulic fracturing[J]. Computers and Geotechnics, 2017, 81: 212-228. doi: 10.1016/j.compgeo.2016.08.014
    Yang X L. Effect ofpore-water pressure on 3D stability of rock slope[J]. International Journal of Geomechanics, 2017, 17(9): 06017015. doi: 10.1061/(ASCE)GM.1943-5622.0000969
    Matthew A. A quantified study of segmentation techniques on synthetic geological XRM and FIB-SEM images[J]. Computational Geosciences, 2018, 22(6): 1503-1512. doi: 10.1007/s10596-018-9768-y
    Wu J, Zhou W, Sun S S, et al. Graptolite-derived organic matter and pore characteristics in the Wufeng-Longmaxi black shale of the Sichuan Basin and its periphery[J]. Acta Geologica Sinica: English Edition, 2019, 93(4): 982-995. doi: 10.1111/1755-6724.13860
    Cyprien S, Patrice C, Hamdi A T. Micro-continuum framework for pore-scale multiphase fluid transport in shale formations[J]. Transport in Porous Media, 2019, 127(1): 85-112. doi: 10.1007/s11242-018-1181-4
    Zhang L, Chen S, Zhang C, et al. The characterization of bituminous coal microstructure and permeability by liquid nitrogen fracturing based on μCT technology[J]. Fuel, 2020, 262: 116635. doi: 10.1016/j.fuel.2019.116635
    Tang C S, Zhu C, Leng T, et al. Three-dimensional characterization of desiccation cracking behavior of compacted clayey soil using X-ray computed tomography[J]. Engineering Geology, 2019, 255: 1-10. doi: 10.1016/j.enggeo.2019.04.014
    Khishvand M, Alizadeh A H, Piri M. In-situ characterization of wettability and pore-scale displacements during two- and three-phase flow in natural porous media[J]. Advances in Water Resources, 2016, 97: 279-298. doi: 10.1016/j.advwatres.2016.10.009
    Raynaud S, Fabre D, Mazerolle F, et al. Analysis of the internal structure of rocks and characterisation of mechanical deformation by a non-destructive method: X-ray tomodensitometry[J]. Tectonophysics, 1989, 159(1/2): 149-159.
    鞠杨, 杨永明, 宋振铎, 等. 岩石孔隙结构的统计模型[J]. 中国科学: 技术科学, 2008, 38(7): 1026-1041. doi: 10.3321/j.issn:1006-9275.2008.07.005

    Ju Y, Yang Y M, Song Z D, et al. Statistical models of rock pore structure[J]. Scientia Sinica: Technologica, 2008, 38(7): 1026-1041(in Chinese with English abstract). doi: 10.3321/j.issn:1006-9275.2008.07.005
    王家禄, 高建, 刘莉. 应用CT技术研究岩石孔隙变化特征[J]. 石油学报, 2009, 30(6): 887-893. doi: 10.3321/j.issn:0253-2697.2009.06.015

    Wang J L, Gao J, Liu L. Porosity characteristics of sandstone by X-ray CT scanning system[J]. Acta Petrolei Sinica, 2009, 30(6): 887-893(in Chinese with English abstract). doi: 10.3321/j.issn:0253-2697.2009.06.015
    赵建鹏, 孙建孟, 黎明, 等. 岩石颗粒胶结方式对储层岩石弹性及渗流性质的影响[J]. 地球科学: 中国地质大学学报, 2014, 39(6): 769-774. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX201406012.htm

    Zhao J P, Sun J M, Li M, et al. Effects of cementation on elastic property and permeability of reservoir rocks[J]. Earth Science: Journal of China University of Geosciences, 2014, 39(6): 769-774(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX201406012.htm
    张天付, 谢淑云, 鲍征宇, 等. 基于高分辨率CT的孔隙型白云岩储层孔隙系统分形与多重分形研究[J]. 地质科技情报, 2016, 35(6): 55-62. https://www.cnki.com.cn/Article/CJFDTOTAL-DZKQ201606009.htm

    Zhang T F, Xie S Y, Bao Z Y, et al. Fractal and multifractal research on pore system for porous dolomite reservoirs based on high-resolution CT[J]. Geological Science and Technology Information, 2016, 35(6): 55-62 (in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-DZKQ201606009.htm
    彭瑞东, 杨彦从, 鞠杨, 等. 基于灰度CT图像的岩石孔隙分形维数计算[J]. 科学通报, 2011, 56(26): 2256-2266. https://www.cnki.com.cn/Article/CJFDTOTAL-KXTB201126019.htm

    Peng R D, Yang Y C, Ju Y, et al. Computation of fractal dimension of rock pores based on gray CT images[J]. Chinese Science Bulletin, 2011, 56(26): 2256-2266(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-KXTB201126019.htm
    Wang G, Qin X J, Shen J N, et al. 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[J]. Fuel, 2019, 256: 115900. doi: 10.1016/j.fuel.2019.115900
    谢和平. 分形几何及其在岩土力学中的应用[J]. 岩土工程学报, 1992, 14(1): 14-24. doi: 10.3321/j.issn:1000-4548.1992.01.002

    Xie H P. Fractal geometry and its application to rock and soil materials[J]. Chinese Journal of Geotechnical Engineering, 1992, 14(1): 14-24(in Chinese with English abstract). doi: 10.3321/j.issn:1000-4548.1992.01.002
    谢和平. 分形-岩石力学导论[M]. 北京: 科学出版社, 1996.

    Xie H P. An introduction to the fractal-rock mechanics[M]. Beijing: Science Press, 1996(in Chinese).
    张季如, 陶高梁, 黄丽, 等. 表征孔隙孔径分布的岩土体孔隙率模型及其应用[J]. 科学通报, 2010, 55(增刊2): 2661-2670. https://www.cnki.com.cn/Article/CJFDTOTAL-KXTB2010Z2015.htm

    Zhang J R, Tao G L, Huang L, et al. Porosity models for determining the pore-size distribution of rocks and soils and their applications[J]. Chinese Science Bulletin, 2010, 55(S2): 2661-2670(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-KXTB2010Z2015.htm
    刘凯, 石万忠, 王任, 等. 鄂尔多斯盆地杭锦旗地区盒1段致密砂岩孔隙结构分形特征及其与储层物性的关系[J]. 地质科技通报, 2021, 40(1): 57-68. doi: 10.19509/j.cnki.dzkq.2021.0102

    Liu K, Shi W Z, Wang R, et al. Pore structure fractal characteristics and its relationship with reservoir properties of the first Member of lower Shihezi Formation tight sandstone in Hangjinqi area, Ordos Basin[J]. Bulletin of Geological Science and Technology, 2021, 40(1): 57-68(in Chinese with English abstract). doi: 10.19509/j.cnki.dzkq.2021.0102
    方海平, 谢淑云, 张天付, 等. 五大连池玄武岩三维孔隙组构的多重分形特征[J]. 地质科技情报, 2015, 34(3): 24-29. https://www.cnki.com.cn/Article/CJFDTOTAL-DZKQ201503004.htm

    Fang H P, Xie S Y, Zhang T F, et al. Multifractality of basalt micropores based on high-resolution digital CT image[J]. Geological Science and Technology Information, 2015, 34(3): 24-29(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-DZKQ201503004.htm
    张宝鑫, 傅雪海, 张苗, 等. 山西省域煤系泥页岩孔隙分形特征[J]. 地质科技情报, 2019, 38(4): 82-92. https://www.cnki.com.cn/Article/CJFDTOTAL-DZKQ201904010.htm

    Zhang B X, Fu X H, Zhang M, et al. Fractal features of coal measures shale in Shanxi Province[J]. Geological Science and Technology Information, 2019, 38(4): 82-92(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-DZKQ201904010.htm
    程志林, 隋微波, 宁正福, 等. 数字岩心微观结构特征及其对岩石力学性能的影响研究[J]. 岩石力学与工程学报, 2018, 37(2): 449-460.

    Cheng Z L, Sui W B, Ning Z F, et al. Microstructure characteristics and its effects on mechanical properties of digital core[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(2): 449-460(in Chinese with English abstract).
    Feldkamp L A, Davis L C, Kress J W. Practical cone-beam algorithm[J]. Journal of the Optical Society of America A: Optics Image Science and Vision, 1984, 1(6): 612-619. doi: 10.1364/JOSAA.1.000612
    丁自伟, 李小菲, 唐青豹, 等. 砂岩颗粒孔隙分布分形特征与强度相关性研究[J]. 岩石力学与工程学报, 2020, 39(9): 1787-1796. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX202009006.htm

    Ding Z W, Li X F, Tang Q B, et al. Study on correlation between fractal characteristics of pore distribution and strength of sandstone particles[J]. Chinese Journal of Rock Mechanics and Engineering, 2020, 39(9): 1787-1796(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX202009006.htm
    周盛涛, 方文, 蒋楠, 等. 冻融循环作用下砂岩单轴压缩破坏断口特征分形研究[J]. 地质科技通报, 2020, 39(5): 61-68. doi: 10.19509/j.cnki.dzkq.2020.0518

    Zhou S T, Fang W, Jiang N, et al. Fractal geometry study on uniaxial compression fracture characteristics of sandstone subjected to freeze-thaw cycles[J]. Bulletin of Geological Science and Technology, 2020, 39(5): 61-68(in Chinese with English abstract). doi: 10.19509/j.cnki.dzkq.2020.0518
  • 加载中


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article Views(55) PDF Downloads(16) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint