颗粒填充型分形孔隙结构复杂组构表征

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摘要颗粒填充型多孔介质广泛发育于自然储层中，且常常表现出复杂的颗粒形貌、随机的空间分布以及分形的尺度结构等特征，它们的空间组配严重影响着油气资源的赋存运移。因此阐明孔隙结构细观控制机制是实现资源高效开发利用的基础，而其定量表征是根本。为此，依托于新近出现的分形拓扑理论标定了颗粒填充型分形多孔介质中孔隙结构的两类复杂类型，即描述颗粒几何形貌的原始复杂性，以及主宰尺度不变属性的行为复杂性。依据尺度不变属性的基本要求，判识出原始复杂性与行为复杂性相互独立的关系，明确了复杂类型组构模式。在此基础上，借助四参数随机生长算法实现了原始复杂性要素的等效表征，利用分形拓扑理论实现了自相似、自仿射属性的尺度不变定义，进而构建了任意颗粒填充型分形多孔介质模型定量表征的数学框架。最后，系统分析了原始复杂性以及行为复杂性对孔隙结构特征的控制，即颗粒团簇破碎程度、随机分布特征、边界粗糙度隶属于原始复杂性，自相似、自仿射等尺度结构特征则受控于行为复杂性，而孔隙结构的各向异性特征是原始复杂性及行为复杂性耦合作用结果。

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	金毅1
	2
	王俏俏1
	董佳斌1
	刘顺喜1
	郑军领1
	李延祥3

关键词 ：岩石力学, 四参数随机生长算法, 分形拓扑, 复杂组构模式, 多孔介质, 各向异性

Abstract：Bed-packing porous media widely exists in natural geological reservoirs，and always features complex geometrical morphology，random spatial distribution and fractal structure，etc. Pore space derived from such a complex assembly would significantly affect the storage and transport of oil and gas resources. Therefore，clarifying the meso-control mechanism of the complex pore structure on microscale is the basis of efficient exploitation and utilization of these resources. Apparently，quantitative characterization of the microstructure of the pore space is fundamental. In this work，two types of complexity in fractal bed-packing porous media were identified as per the newly emerged fractal topology theory，namely，the original complexity describing the particle geometry and the behavioral complexity dominating the invariant scale property. According to the basic requirements of scale invariance，the relationship between these two types of complexity were clarified to be independent of each other and the complex assembly patterns were confirmed. Based on these patterns，the quartet structure generation set(QSGS) algorithm was employed to characterize the original complexity，while the fractal topography theory was used to define self-similar and self-affine properties of the pore structure. A mathematical framework was then constructed to quantitatively characterize arbitrary fractal bed-packing porous media. Afterwards，the effects of the original and behavioral complexities on the pore structure were analyzed. The results indicate that the fragmentation degree of particle clusters，random distribution characteristics and boundary roughness of particle are determined by the original complexity，and the scale-invariant characteristics of self-similarity and self-affinity are controlled by the behavioral complexity. The anisotropy of pore structure is the coupling result of the original complexity and the behavior complexity.

Key words： rock mechanics quartet structure generation set(QSGS) fractal topology complexity assembly pattern porous media anisotropic property

引用本文:

金毅1，2，王俏俏1，董佳斌1，刘顺喜1，郑军领1，李延祥3. 颗粒填充型分形孔隙结构复杂组构表征[J]. 岩石力学与工程学报, 2022, 41(6): 1160-1171.
JIN Yi1，2，WANG Qiaoqiao1，DONG Jiabin1，LIU Shunxi1，ZHENG Junling1，LI Yanxiang3. Characterization of the complexity assembly of fractal bed-packing porous media#br#. , 2022, 41(6): 1160-1171.

链接本文:

http://rockmech.whrsm.ac.cn/CN/Y2022/V41/I6/1160

[2]	YAO Y B，SUN X X，ZHENG S J，et al. Methods for petrological and petrophysical characterization of gas shales[J]. Energy and Fuels，2021，35：11 061-11 088.
[32]	EDITH P，NIGEL B，MICHEL R. Generalizing the fractal model of soil structure: the pore-solid fractal approach[J]. Developments in Soil Science，2000，27：47-74.
[49]	ZHENG J L，LIU X K，JIN Y，et al. Effects of surface geometry on advection-diffusion process in rough fractures[J]. Chemical Engineering Journal，2021，414：128745.
[3]	傅雪海，秦勇，薛秀谦，等. 煤储层孔、裂隙系统分形研究[J]. 中国矿业大学学报，2001，30(3)：225-228.(FU Xuehai，QIN Yong，XUE Xiuqian，et al. Research on fractals of pore and fracture of coal reservoirs[J]. International Journal of Mining Science and Technology，2001，30(3)：225-228.(in Chinese))
[5]	NIU Q H，PAN J N，JIN Y，et al. Fractal study of adsorption-pores in pulverized coals with various metamorphism degrees using N2 adsorption，X-ray scattering and image analysis methods[J]. Journal of Petroleum Science and Engineering，2019，176：584-493.
[8]	姚艳斌，刘大锰. 煤储层孔隙系统发育特征与煤层气可采性研究[J]. 煤炭科学技术，2006，34(3)：64-68.(YAO Yanbin，LIU Dameng. Developing features of fissure system in Henan coal reserves seams and research on mining of coal bed methane[J]. Coal Science and Technology，2006，34(3)：64-68.(in Chinese))
[10]	WANG B，LI B B，LI J H，et al. Measurement and modeling of coal adsorption-permeability based on the fractal method[J]. Journal of Natural Gas Science and Engineering，2021，88：103824.
[13]	YAO Y B，LIU D M，CAI Y D，et al. Advanced characterization of pores and fractures in coals by nuclear magnetic resonance and X-ray computed tomography[J]. Science China Earth Science，2010，53：854-862.
[15]	JIN Y，ZHU Y B，LIU S X，et al. Scaling invariant effects on the permeability of fractal porous media[J]. Transport in Porous Media，2015，109(2)：433-453.
[18]	HAGHVERDI A，BANIASSADI M，BAGHANI M，et al. A modified simulated annealing algorithm for hybrid statistical reconstruction of heterogeneous microstructures[J]. Computational Materials Science，2021，197：110636.
[20]	罗良. 非对称分叉网络及分形多孔介质流动特性研究[博士学位论文][D]. 武汉：华中科技大学，2011.(LUO Liang. Study of the properties for flow in fractal porous media and asymmetrical branching networks[Ph. D. Thesis][D]. Wuhan：Huazhong University of Science and Technology，2011.(in Chinese))
[23]	XIAO B Q，HUANG Q W，CHEN H X，et al. A fractal model for capillary flow through a single tortuous capillary with roughened surfaces in fibrous porous media[J]. Fractals，2021，29(1)：2150017.
[25]	袁越锦，杨彬彬，焦阳，等. 多孔介质干燥过程分形孔道网络模型与模拟：I. 模型建立[J]. 中国农业大学学报，2007，12(3)：65-69. (YUAN Yuejin，YANG Binbin，JIAO Yang，et al. Fractal pore network simulation on drying of porous media：I．model building[J]. Journal of China Agricultural University，2007，12(3)：65-69.(in Chinese))
[28]	WANG Z，JIN X，WANG X，et al. Pore-scale geometry effects on gas permeability in shale[J]. Journal of Natural Gas Science and Engineering，2016，34：948-957.
[30]	冯月丽，刘月田，毛小龙，等. 裂缝各向异性介质方向渗透率半解析计算方法[J]. 能源与环保，2020，42(11)：82-87.(FENG Yueli，LIU Yuetian，MAO Xiaolong，et al. Semi-analytical calculation method for directional permeability of fractured anisotropic media[J]. China Energy and Environmental Protection，2020，42(11)：82-87.(in Chinese))
[33]	WANG M R，WANG J K，PAN N，et al. Mesoscopic predictions of the effective thermal conductivity for microscale random porous media[J]. Physical Review E Statistical Nonlinear and Soft Matter Physics，2007，75(3)：036702.
[35]	费锁柱，谭晓慧，孙志豪，等. 基于微结构模拟的土体自相关距离分析[J]. 岩土力学，2019，40(12)：4 751-4 758.(FEI Suozhu，TAN Xiaohui，SUN Zhihao，et al. Analysis of autocorrelation distance of soil based on microstructure simulation[J]. Rock and Soil Mechanics，2019，40(12)：4 751-4 758.(in Chinese))
[38]	YAO Y B，LIU D M，TANG D Z，et al. Fractal characterization of seepage-pores of coals from China：An investigation on permeability of coals[J]. Computers and Geosciences，2008，35(6)：1 159-1 166.
[40]	JIN Y，WANG C，LIU S X，et al. Systematic definition of complexity assembly in fractal porous media[J]. Fractals，2020，28(5)：16.
[43]	MANDELBROT B. How long is the coast of Britain statistical self-similarity and fractional dimension[J]. Science，1967，156(3775)：636-638.
[45]	XIE H P，WANG J A，M.A K. Multifractal characterization of rock fracture surfaces[J]. International Journal of Rock Mechanics and Mining Sciences，1999，36(1)：19-27.
[48]	孙盛玥，李迎春，唐春安，等. 天然岩石节理双阶粗糙度分形特征研究[J]. 岩石力学与工程学报，2019，38(12)：2 502-2 511.(SUN Shengyue，LI Yingchun，TANG Chun?an，et al. Dual fractal features of the surface roughness of natural rock joints[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(12)：2 502-2 511.(in Chinese))
[50]	JIN Y，ZHENG J L，DONG J B，et al. Fractal topography and complexity assembly in multifractals[J]. Fractals，2022，30(3)：2250052.
[4]	张慧. 煤孔隙的成因类型及其研究[J]. 煤炭学报，2001，26(1)：40-44.(ZHANG Hui. Genetical type of pores in coal reservoir and its research significance[J]. Journal of China Coal Society，2001，26(1)：40-44.(in Chinese))
[6]	KROHN C E，THOMPSON A H. Fractal sandstone pores: Automated measurements using scanning-electron-microscope images[J]. Physical Review B，1986，33(9)：6 366-6 374.
[14]	金毅，宋慧波，潘结南，等. 煤微观结构三维表征及其孔-渗时空演化模式数值分析[J]. 岩石力学与工程学报，2013，32(增1)：2 632-2 641.(JIN Yi，SONG Huibo，PAN Jienan，et al. Three-dimensional representation of coal?s microstructure and numerical analysis of its pore-permeability spatial-temporal evolution mode[J]. Chinese Journal of Rock Mechanics and Engineering，2013，32(Supp.1)：2 632-2 641.(in Chinese))
[16]	JIANG Z，CHEN W，BURKHART C. Efficient 3D porous microstructure reconstruction via Gaussian random field and hybrid optimization[J]. Journal of Microscopy，2013，252(2)：135-148.
[24]	金毅，权伟哲，秦建辉，等. 孔隙-孔喉分形多孔介质复杂类型组构模式表征[J]. 煤炭学报，2020，45(5)：1 845-1 854.(JIN Yi，QUAN Weizhe，QIN Jianhui，et al. Quantitative characterization of complex assembly in fractal pore-throat porous media[J]. Journal of China Coal Society，2020，45(5)：1 845-1 854.(in Chinese))
[26]	CAI J，HUAI X L. A lattice Boltzmann model for fluid-solid coupling heat transfer in fractal porous media[J]. Chinese Physics Letters，2009，26(6)：064401.
[34]	GRACZYK K，MATYKA M. Predicting porosity，permeability，and tortuosity of porous media from images by deep learning[J]. Scientific Reports，2020，10(1)：21488.
[36]	ZHAO Y X，SUN Y F，YUAN L，et al. Impact of nanopore structure on coal strength: A study based on synchrotron radiation nano-CT[J]. Results in Physics，2020，17：103029.
[44]	JIN Y，DONG J B，ZHANG X Y，et al. Scale and size effects on fluid flow through self-affine rough fractures[J]. International Journal of Heat and Mass Transfer，2017，105：443-451.
[46]	JIN Y，LI X，ZHAO M Y，et al. A mathematical model of fluid flow in tight porous media based on fractal assumptions[J]. International Journal of Heat and Mass Transfer，2017，108：1 078-1 088.
[1]	伏海蛟，汤达祯，许浩，等. 致密砂岩储层特征及气藏成藏过程[J]. 断块油气田，2012，19(1)：47-50.(FU Haijiao，TANG Dazhen，XU Hao，et al. Characteristics of tight sandstone reservoir and accumulation process of gas pool[J]. Faut-Block Oil and Gas Field，2012，19(1)：47-50.(in Chinese))
[7]	DONG J B，JU Y，GAO F，et al. Estimation of the fractal dimension of weierstrass-mandelbrot function based on cuckoo search methods[J]. Fractals，2017，25(6)：1750065.
[9]	李波波，高政，杨康，等. 温度与孔隙压力耦合作用下煤岩吸附-渗透率模型研究[J]. 岩石力学与工程学报，2020，39(4)：668-681.(LI Bobo，GAO Zheng，YANG Kang，et al. Study on coal adsorption-permeability model under the coupling of temperature and pore pressure[J]. Chinese Journal of Rock Mechanics and Engineering，2020，39(4)：668-681.(in Chinese))
[11]	赵海燕，宫伟力. 基于图像分割的煤岩割理CT图像各向异性特征[J]. 煤田地质与勘探，2009，37(6)：14-18.(ZHAO Haiyan，GONG Weili. Characterization on anisotropic fractures of coal and rocks by computed X-ray tomography based on image segmentation[J]. Coal Geology and Exploration，2009，37(6)：14-18.(in Chinese))
[12]	YANG Y，WANG D，YANG J Y，et al. Fractal analysis of CT images of tight sandstone with anisotropy and permeability prediction[J]. Journal of Petroleum Science and Engineering，2021，205：108919.
[17]	JU Y，ZHENG J T，MARCELO E，et al. 3D numerical reconstruction of well-connected porous structure of rock using fractal algorithms[J]. Computer Methods in Applied Mechanics and Engineering，2014，279：212-226.
[19]	NATARAJAN C，KAREL M，PHILIPPE H. Reconstruction of periodic unit cells of multimodal random particulate composites using genetic algorithms[J]. Computational Materials Science，2007，42(2)：352-367.
[21]	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)：1 787-1 796. (DING Ziwei，LI Xiaofei，TANG Qingbao，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)：1 787-1 796.(in Chinese))
[22]	蔡建超，夏宇轩，徐赛，等. 含水合物沉积物多相渗流特性研究进展[J]. 力学学报，2020，52(1)：208-223.(CAI Jianchao，XIA Yuxuan，XU Sai，et al. Advances in multiphase seepage characteristics of natural gas hydrate sediments[J]. Chinese Journal of Theoretical and Applied Mechanics，2020，52(1)：208-223.(in Chinese))
[27]	LIANG M C，FU C G，XIAO B Q，et al. A fractal study for the effective electrolyte diffusion through charged porous media[J]. International Journal of Heat and Mass Transfer，2019，137：365-371.
[29]	李滔，李闽，荆雪琪，等. 孔隙尺度各向异性与孔隙分布非均质性对多孔介质渗透率的影响机制[J]. 石油勘探与开发，2019，46(3)：569-579.(LI Tao，LI Min，JING Xueqi，et al. Influence mechanism of pore-scale anisotropy and pore distribution heterogeneity on permeability of porous media[J]. Petroleum Exploration and Development，2019，46(3)：569-579.(in Chinese))
[31]	XIAO B Q，WANG W，ZHANG X，et al. A novel fractal solution for permeability and Kozeny-Carman constant of fibrous porous media made up of solid particles and porous fibers[J]. Powder Technology，2019，349：92-98.
[39]	JIN Y，WU Y，LI H，et al. Definition of fractal topography to essential understanding of scale-invariance[J]. Scientific Reports，2017，7(1)：636.
[41]	林澜，李飒，孙立强，等. 基于分形理论的钙质土颗粒破碎状态演化研究[J]. 岩石力学与工程学报，2021，40(3)：640-648.(LIN Lan，LI Sa，SUN Liqiang，et al. Study on evolution of particle breakage of carbonate soils based on fractal theory[J]. Chinese Journal of Rock Mechanics and Engineering，2021，40(3)：640-648.(in Chinese))
[42]	JIN Y，LIU X H，SONG H B，et al. General fractal topography: an open mathematical framework to characterize and model mono- scale-invariances[J]. Nonlinear Dynamics，2019，96(4)：2 413-2 436.
[37]	YU B M，LI J H，LI Z H，et al. Permeabilities of unsaturated fractal porous media[J]. International Journal of Multiphase Flow，2003，29(10)：1 625-1 642.
[47]	汪轶群，洪义，国振，等. 南海钙质砂宏细观破碎力学特性[J]. 岩土力学，2018，39(1)：199-206.(WANG Yiqun，HONG Yi，GUO Zhen，et al. Micro-and macro-mechanical behavior of crushable calcareous sand in South China Sea[J]. Rock and Soil Mechanics，2018，39(1)：199-206.(in Chinese)