致密砂岩裂缝网络复杂性及其影响因素研究

刘圣鑫; 付汇琪; 冯兴强; 韩晓祥; 王炳乾

doi:10.12090/j.issn.1006-6616.2023128

致密砂岩裂缝网络复杂性及其影响因素研究

doi: 10.12090/j.issn.1006-6616.2023128

刘圣鑫^{1, 2,},
付汇琪^3, ,,
冯兴强^{1, 2},
韩晓祥^{2, 4},
王炳乾⁴

1.
中国地质科学院地质力学研究所，北京 100081
2.
中国地质调查局油气地质力学重点实验室，北京 100081
3.
吉林省地质矿产局二所，吉林吉林 132001
4.
中国矿业大学（北京）力学与土木工程学院，北京 100083

基金项目: 中国地质调查局地质调查项目（DD20243449）；国家自然科学基金项目（42277167）

详细信息

作者简介:
刘圣鑫（1978—），男，助理研究员，主要从事岩石力学研究。Email：807228351@qq.com

通讯作者:
付汇琪（1983—），女，高级工程师，主要从事大地构造研究。Email：253458813@qq.com

中图分类号: TD315
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- HTML全文浏览量: 55
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- 被引次数: 0
出版历程
- 收稿日期: 2023-08-03
- 修回日期: 2023-12-18
- 录用日期: 2024-01-04
- 预出版日期: 2024-01-04
- 刊出日期: 2024-08-28

Fracture network complexity of tight sandstone and its influencing factors

LIU Shengxin^{1, 2
,},
FU Huiqi^{3
, ,},
FENG Xingqiang^{1, 2},
HAN Xiaoxiang^{2, 4},
WANG Bingqian⁴

1.
Institue of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China
2.
Key Laboratory of Petroleum Geomechanics, China Geological Survey, Beijing 100081, China
3.
The Second Survey of Jilin Geological mineral, Jilin 132001, Jilin, China
4.
School of Mechanics and Civil Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China

Funds: This research is financially supported by the Geological Survey Projects of the China Geological Survey (Grant No. DD20221660) and National Natural Science Foundation of China (Grant No. 42277167).

摘要

摘要: 裂缝网络分析在油气藏勘探开发过程中发挥着着重要作用，致密砂岩裂缝网络复杂性分析对水力压裂优化、裂缝网络预测、裂缝建模等具有重要意义。文章结合致密砂岩复杂的裂缝网络动态演化的实验研究，明确了裂缝网络的分形和多重分形谱特征，深入分析了裂缝网络的复杂性及其主控因素。通过岩石力学和X射线CT扫描实验确定了岩石力学和裂缝网络特征；通过扫描电镜实验、裂缝网络的分形分析定量化表征了致密砂岩微观组构和裂缝网络的分形特征。研究结果表明：致密砂岩的石英含量为 28.08～52.88%，黏土含量为11.54～25.45%，粒度为61.18～184.55 μm，孔隙度为8.125%～10.296%；单轴抗压强度介于69.09～188.33 MPa，弹性模量介于31.69～92.76 GPa；分形维数（D_B）为1.28～2.35，谱宽（Δα）平均值为1.0851～1.3638。裂缝的萌生、扩展贯穿于应力–应变的全过程，裂缝网络的复杂性主要受控于致密砂岩的微观组构特征，并且具有明显的围压和尺度效应。三维裂缝网络的分形维数、多重分形谱的谱宽平均值可分别表征裂缝空间分布的复杂性和非均质性，两者之间具有相对的独立性。砂岩中石英、长石等脆性矿物含量越高、储层孔隙度越大、砂岩组成粒度越小裂缝网络分形维数越大，谱宽平均值越小；无围压情况下，样品裂缝网络的复杂性主要受控于微观组构特征，且随着轴向压力的增加而增加；存在围压的情况下，围压起主导作用，围压越大分形维数越小，谱宽平均值越大。而黏土矿物不利于复杂裂缝的形成；小尺度样品的分形维数和谱宽平均值大于尺度大样品的分形维数和谱宽平均值。砂岩的弹性模量和抗压强度与分形维数和谱宽平均值具有一定的正相关性。
- 致密砂岩 /
- 裂缝网络 /
- 分形维数 /
- 多重分形谱 /
- 岩石力学
Abstract: Objective Fracture network analysis plays an important role in oil and gas exploration and development. However, complexity analysis of tight sandstone fracture networks and their control factors is relatively lagging. Based on an experimental study of the dynamic evolution of the complex fracture network in tight sandstone, the fractal and multifractal spectral characteristics of the fracture network were defined, and the complexity and main controlling factors of the fracture network were analyzed. Fracture network complexity analysis of tight sandstone plays an important role in hydraulic fracturing optimization, fracture network prediction, and fracture modeling. Methods Rock mechanics and X-ray computed tomography scan experiments determined the characteristics of rock mechanics and fracture networks . The microstructure and fracture network fractal characteristics of tight sandstone were quantitatively characterized by SEM and fracture network fractal analysis. Results The results showed that the quartz content of tight sandstone ranges from 28.08 to 52.88%, clay content ranges from 11.54 to 25.45%, particle size ranges from 61.18 to 184.55 μm, and porosity ranges from 8.125 to 10.296%. Uniaxial compressive strength ranges from 69.09 to 188.33 MPa, and the elastic modulus ranges from 31.69 to 92.76 GPa. The fractal dimension (D_B) ranges from 1.28 to 2.35 and average spectral width (Δα) ranges from 1.0851 to 1.3638. Conclusion The initiation and propagation of fractures extend through the entire stress–strain process. The complexity of the fracture network of tight sandstone is mainly controlled by microscopic fabric characteristics, and has obvious confining pressure as well as scale effects. The D_B of the three-dimensional fracture network and average Δα of the multifractal spectrum represents the complexity and heterogeneity of the fracture spatial distribution, respectively, and are relatively independent. As the content of quartz, feldspar, and other brittle minerals in sandstone increases, the porosity of the reservoir increases, particle size of the sandstone decreases, D_B of the fracture network increases, and average Δα decreases. In the absence of confining pressure, the complexity of the sample fracture network is mainly controlled by the microscopic fabric characteristics, and the complexity increases with increase of axial pressure. When present confining pressure plays a leading role; the higher it is, the lower the D_B value, and the higher the mean Δα value. Clay minerals are unconducive to complex fractures formation. The mean values of D_B and Δα of small-scale samples are greater than those of large-scale samples. The elastic modulus and compressive strength of sandstone are positively correlated with D_B and mean Δα.
- tight sandstone /
- fracture network /
- fractal dimension /
- multifractal spectrum /
- rock mechanics

HTML全文

图 1 微米CT内置压缩装置及数据处理过程

a—实验装置；b—处理流程

Figure 1. Micron CT built-in compression device and data processing process diagram

(a) Experimental equipment; (b) Processing processes

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图 2 多重分形谱示意图

Figure 2. Schematic diagram of multifractal spectrum

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图 3 砂岩样品的扫描电镜图像和矿物分析（2个样品的粒度有显著的差异）

a—样品1-1背散射图像；b—样品1-2背散射图像；c—样品1-1AMICS矿物分析图；d—样品1-2AMICS矿物分析图

Figure 3. Backscattering image and mineral analysis diagram of sandstone sample.

(a) Sample 1-1 backscatter image; (b) Sample 1-2 backscatter images; (c) Sample 1-1AMICS mineral analysis diagram; (d) Sample 1-2AMICS mineral analysis diagram (there is a significant difference in particle size between the two samples)

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图 4 致密砂岩单轴压缩应力与轴向位移曲线

Figure 4. Uniaxial compression stress and axial displacement curve of sandstone

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图 5 1-1样品的应力–轴向位移曲线和不同载荷下的三维裂缝网络（不同颜色代表不同的CT扫描次数）

Figure 5. Stress-axial displacement curves of 1-1 samples and three-dimensional fracture networks under different loads (colors represent different CT scans)

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图 6 QXY组样品不同载荷下的三维裂缝网络（CT扫描后经过数据处理得到三维裂缝网络，用颜色区分不同的扫描次数。次数1—4为破裂前扫描，次数5为破裂后扫描）

Figure 6. Three-dimensional crack network of QXY group samples under different loads(3D fracture network is obtained through data processing after CT scan, and the colors represent different scan times. digits 1-4 were scanned before rupture and digits 5 is scanned after rupture).

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图 7 QDY组砂岩样品破裂后的二维CT切片和三维裂缝网络（图中x、y、z为坐标，数字代表切片位置）

a—xy方向的CT切片；b—xz方向的CT切片；c—yz方向的CT切片；d—三维裂缝网络

Figure 7. Two-dimensional CT slices and three-dimensional fracture network of sandstone samples of QDY formation after fracture

(a) xy direction CT section; (b) xz direction CT section; (c) yz direction CT section; (d) 3D crack network (x, y and z are coordinates, and the numbers represent slice positions)

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图 8 砂岩样品的二维裂缝网络和对应的多重分形谱

a—最大分形维数为1.51的二维裂缝网络； b—最大分形维数为1.45的二维裂缝网络；c—最大分形维数为1.31的二维裂缝网络；d—多重分形谱

Figure 8. Two-dimensional fracture network and corresponding multifractal spectrum of sandstone samples.

(a) Two-dimensional fracture network with a maximum fractal dimension of 1.51; (b) Two-dimensional fracture network with a maximum fractal dimension of 1.45; (c) Two-dimensional fracture network with a maximum fractal dimension of 1.31; (d) Multifractal spectrum

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图 9 二维裂缝网络多重分形谱的最大分形维数与谱宽之间的关系（图中数字为样品编号）

Figure 9. Relationship between the maximum fractal dimension and the spectral width of the multifractal spectrum of a two-dimensional fracture network (the number in the figure is the sample number)

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图 10 矿物含量与三维分形维数（$ {D_B} $）、谱宽（$ \Delta \alpha $）平均值之间的关系(单轴压缩样品的数据)

a—三维分形维数与矿物含量； b—谱宽平均值与矿物含量

Figure 10. Relationship between mineral content and three-dimensional fractal dimension as well as mean spectral width (uniaxial compression sample data)

(a) Three-dimensional fractal dimension and mineral content; (b) Average spectral width and mineral content;

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图 11 QXY组砂岩孔隙度与谱宽平均值和三维裂缝网络分形维数之间的关系

Figure 11. Relationship between the porosity of QXY formation sandstone and the mean value of and the fractal dimension of three-dimensional fracture network

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图 12 砂岩试样颗粒粒度分布图

Figure 12. Grain size distribution of sandstone samples

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图 13 砂岩平均粒径与三维裂缝网络分形维数（$ {D_B} $）、谱宽（$ \Delta \alpha $）平均值之间的关系（单轴压缩样品的数据）

a—三维裂缝网络分形维数与粒度； b—谱宽平均值与粒度

Figure 13. Relation shaps between average particle size of sandstone and fractal dimension as well as average spectral width of three-dimensional fracture network (data of uniaxial compression sample)

(a) Fractal dimension of three-dimensional fracture network and particle size; (b) Average spectral width and particle size

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图 14 砂岩三维裂缝网络的分形维数随应力的增加的变化趋势

Figure 14. Effect of stress level on fractal dimension of sandstone 3D fracture network changes with the increase of stress

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图 15 围压与分形维数和谱宽平均值之间的关系

Figure 15. Relationship between confining pressure and fractal dimension and mean spectral width

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表 1 致密砂岩试样矿物含量及粒度特征

Table 1. Mineral content and particle size characteristics of tight sandstone samples

样品组	样品编号	石英/%	长石/%	黏土/%	其他/%	粒度平均值/μm
QXY	1-1	52.88	15.19	11.54	20.39	184.55
	1-2	28.08	6.65	22.38	32.89	61.18
	1-3	45.37	15.05	14.90	20.68	71.42
QDY	2-1	39.99	21.09	25.45	13.47	65.12
	2-2	36.90	34.93	18.15	10.02	130.59
	2-3	37.77	28.12	14.85	19.26	79.08
	2-4	46.18	26.61	24.98	2.23	110.23

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表 2 致密砂岩的裂缝网络体积和孔隙度

Table 2. Volume and porosity of 3D fracture network

样品组	样品编号	孔隙度/%	孔隙体积/‰
QXY	1-1	10.296	3.54E+09
	1-2	8.516	3.26E+09
	1-3	8.917	3.43E+09
QDY	2-1	8.125	1.96E+12
	2-2	8.288	1.84E+12
	2-3	8.654	1.97E+12
	2-4	8.123	1.68E+12

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表 3 致密砂岩试样基本物理力学参数

Table 3. Basic physical and mechanical parameters of tight sandstone samples

样品组	样品编号	直径/mm	高度/mm	围压/MPa	抗压强度/MPa	弹性模量/GPa	泊松比
QXY	1-1	4.00	8.12	0	69.09	31.69	/
	1-2	4.00	7.92	0	125.79	67.47	/
	1-3	4.00	8.06	0	188.33	92.76	/
QDY	2-1	25.00	49.97	0	110.77	22.03	0.279
	2-2	25.00	50.01	0	80.97	14.29	0.260
	2-3	25.00	50.11	15	187.95	25.81	0.259
	2-4	25.00	50.07	30	234.27	27.98	0.288

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表 4 裂缝网络分形特征参数

Table 4. Fractal characteristic parameters of fracture network

样品组	样品编号	二维$ \Delta \alpha $平均值	三维分形维数$ {D_B} $
QXY	1-1	1.2173	2.35
	1-2	1.3638	2.12
	1-3	1.1924	2.20
QDY	2-1	1.3133	1.59
	2-2	1.2267	1.92
	2-3	1.0066	1.48
	2-4	1.0851	1.28

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参考文献(104)

[1]	BARTON C C, 1995. Fractal analysis of scaling and spatial clustering of fractures[M]. In: Fractals in the Earth Sciences. Springer, 141–178.
[2]	BERKOWITZ B. , HADAD A, 1997. Fractal and multifractal measures of natural and synthetic fracture networks[J]. Journal Of Geophysical Research-solid Earth 102: 12205–12218
[3]	BIENIAWSKI Z T, 1967. Mechanism of brittle fracture of rock: Part II-experimental studies[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 4(4): 407-423.
[4]	CAI M, KAISER P K, TASAKA Y, et al., 2004. Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations[J]. International Journal of Rock Mechanics and Mining Sciences, 41(5): 833-847. doi: 10.1016/j.ijrmms.2004.02.001
[5]	CAI M, MORIOKA H, KAISER P K, et al., 2007. Back-analysis of rock mass strength parameters using AE monitoring data[J]. International Journal of Rock Mechanics and Mining Sciences, 44(4): 538-549. doi: 10.1016/j.ijrmms.2006.09.012
[6]	CHEN X, MA L T, SHI C L, et al., 2022. Water occurrence and identification method of the water-bearing degree of tight sandstone reservoirs in the Linxing block[J]. Geology and Exploration, 58(6): 1331-1340. (in Chinese with English abstract
[7]	DERSHOWITZ W S, HERDA H H, et al. , 1992. Interpretation of fracture spacing and intensity[C]. In: The 33th Us Symposium on Rock Mechanics. USRMS, American Rock. Mechanics Association.
[8]	DING C D, ZHANG Y, YANG X T, et al., 2019. Permeability evolution of tight sandstone under high confining pressure and high pore pressure and its microscopic mechanism[J]. Rock and Soil Mechanics, 40(9): 3300-3308. (in Chinese with English abstract
[9]	DUAN M K, JIANG C B, GAN Q, et al., 2020. Experimental investigation on the permeability, acoustic emission and energy dissipation of coal under tiered cyclic unloading[J]. Journal of Natural Gas Science and Engineering, 73: 103054. doi: 10.1016/j.jngse.2019.103054
[10]	DUNCAN P M, EISNER L, 2010. Reservoir characterization using surface microseismic monitoring[J]. Geophysics, 75(5): 75A139-75A146. doi: 10.1190/1.3467760
[11]	EBERHARDT E, STIMPSON B, STEAD D, 1999. Effects of grain size on the initiation and propagation thresholds of stress-induced brittle fractures[J]. Rock Mechanics and Rock Engineering, 32(2): 81-99. doi: 10.1007/s006030050026
[12]	FAN J M, CHEN X D, LEI Z D, et al., 2019. Characteristics of natural and hydraulic fractures in tight oil reservoir in Ordos Basin and its implication to field development[J]. Journal of China University of Petroleum, 43(3): 98-106. (in Chinese with English abstract
[13]	GAO C Y, ZHAO F H, GAO L F, et al., 2023. The methods of fracture prediction based on structural strain analysis and its application[J]. Journal of Geomechanics, 29(1): 21-33. (in Chinese with English abstract
[14]	GHASEMI S, KHAMEHCHIYAN M, TAHERI A, et al., 2020. Crack evolution in damage stress thresholds in different minerals of granite rock[J]. Rock Mechanics and Rock Engineering, 53(3): 1163-1178. doi: 10.1007/s00603-019-01964-9
[15]	GRIFFITH A A, 1924. The theory of rupture[C]. In: Proceedings of the First International Congress for Applied Mechanics, 55-63.
[16]	GRIFFITH A. A., 1920. The Phenomena of Rupture and Flow in Solids[J]. Phil Trans Roy Soc(London), A221: 162-198.
[17]	GUO Y H, 2018. Experimental study on the effect of particle size on the mechanical properties of sandstone[D]. Qingdao: Shandong University of Science and Technology. (in Chinese with English abstract
[18]	HOU B, ZHANG R X, ZENG Y J, et al., 2018. Analysis of hydraulic fracture initiation and propagation in deep shale formation with high horizontal stress difference[J]. Journal of Petroleum Science and Engineering, 170: 231-243. doi: 10.1016/j.petrol.2018.06.060
[19]	JARVIE D M, HILL R J, RUBLE T E, et al., 2007. Unconventional shale-gas systems: the Mississippian Barnett Shale of north-central Texas as one model for thermogenic shale-gas assessment[J]. AAPG Bulletin, 91(4): 475-499. doi: 10.1306/12190606068
[20]	LI B, LI J L, WANG P, et al., 2023. Confining pressure effect and quantitative characterization of rock shear strength parameters[J]. China Mining Magazine, 32(2): 157-164. (in Chinese with English abstract
[21]	LI M, GUO Y H, WANG H C, et al., 2020. Effects of mineral composition on the fracture propagation of tight sandstones in the Zizhou area, east Ordos Basin, China[J]. Journal of Natural Gas Science and Engineering, 78: 103334. doi: 10.1016/j.jngse.2020.103334
[22]	LI S Y, HE T M, YIN X C, 2010. Introduction of rock fracture mechanics[M]. Hefei: University of Science and Technology of China Press. (in Chinese)
[23]	LI Y W, YANG S, ZHAO W C, et al., 2018. Experimental of hydraulic fracture propagation using fixed-point multistage fracturing in a vertical well in tight sandstone reservoir[J]. Journal of Petroleum Science and Engineering, 171: 704-713. doi: 10.1016/j.petrol.2018.07.080
[24]	LING J M, 1993. Study on the mesoscopical characteristics of rock damage under compressive loading[J]. Journal of Tongji University, 21(2): 219-226. (in Chinese with English abstract
[25]	LIU F Y, YANG T H, ZHANG P H, et al., 2018. Dynamic inversion of rock fracturing stress field based on acoustic emission[J]. Rock and Soil Mechanics, 39(4): 1517-1524. (in Chinese with English abstract
[26]	LIU J S, DING W L, XIAO Z K, et al., 2019. Advances in comprehensive characterization and prediction of reservoir fractures[J]. Progress in Geophysics, 34(6): 2283-2300. (in Chinese with English abstract
[27]	LIU S X, WANG Z X, ZHANG L Y, 2018. Experimental study on the cracking process of layered shale using X-ray microCT[J]. Energy Exploration & Exploitation, 36(2): 297-313.
[28]	LIU S X, WANG Z X, ZHANG L Y, et al., 2018. Micromechanics properties analysis of shale based on nano-indentation[J]. Journal of Experimental Mechanics, 33(6): 957-968. (in Chinese with English abstract
[29]	LIU S X, WANG Z X, ZHANG L Y, et al., 2019. Effects of microstructure characteristics of shale on development of complex fracture network[J]. Journal of Mining and Safety Engineering, 36(2): 420-428. (in Chinese with English abstract
[30]	MA S W, WEI L, WANG Y J, et al., 2022. Characterization and evaluation of microscopic pore structures of tight sandstone reservoir in the 8th member of Shihezi Formation in southern Ordos Basin[J]. Geology and Exploration, 58(6): 1321-1330. (in Chinese with English abstract
[31]	MANDELBROT B B, 1982. The Fractal Geometry of Nature, vol. 1. WH freeman, New York. Matsumoto, N., Yomogida, K., Honda, S., 1992. Fractal analysis of fault systems in Japan and the Philippines[J]. Geophys. Res. Lett, 19: 357-360. doi: 10.1029/92GL00202
[32]	MIAO S Y, ZHANG H J, CHEN Y K, et al. , 2019. Surface microseismic monitoring of shale gas hydraulic fracturing based on microseismic location and tomography[J]. Geophysical Prospecting for Petroleum, 58(2): 262-271, 284. (in Chinese with English abstract
[33]	NASSERI M H, RAO K S, RAMAMURTHY T, 1997. Failure mechanism in schistose rocks[J]. International Journal of Rock Mechanics and Mining Sciences, 34(3-4): 219. e1-219. e15.
[34]	PAN L Y, HAO L H, LIU K X, et al., 2023. Fracture Propagation Law of Hydraulic Fracturing in High-Salinity Reservoir of Fengcheng Formation in Mahu[J]. Xinjiang Oil & Gas, 19(4): 20-28
[35]	PESTMAN B J, VAN MUNSTER J G, 1996. An acoustic emission study of damage development and stress-memory effects in sandstone[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 33(6): 585-593.
[36]	RENARD F, MCBECK J, CORDONNIER B, et al., 2019. Dynamic in situ three-dimensional imaging and digital volume correlation analysis to quantify strain localization and fracture coalescence in sandstone[J]. Pure and Applied Geophysics, 176(3): 1083-1115. doi: 10.1007/s00024-018-2003-x
[37]	SHANG C J, KANG Y S, DENG Z, et al., 2019. The influence mechanism of filled natural fractures on the variation law of shale permeability in loading process[J]. Journal of Geomechanics, 25(3): 382-391. (in Chinese with English abstract
[38]	SHI X, PAN J, HOU Q, et al. , 2018. Micrometer-scale fractures in coal related to coal rank based on micro-ct scanning and fractal theory[J]. Fuel 212: 162–172.
[39]	TAN Y L, WANG Z X, FENG X Q, et al., 2021. Structural preservation conditions analysis of oil and gas in complex structural area: A case study of structural analysis in the Well Wanjingdi-1, Anhui, China[J]. Journal of Geomechanics, 27(3): 441-452. (in Chinese with English abstract
[40]	THIELE S T, GROSE L, SAMSU A, MICKLETHWAITE S, et al. , 2017. Rapid, semi-automatic fracture and contact mapping for point clouds, images and geophysical data[J]. Solid Earth 8: 1241–1253.
[41]	WANG D K, ZENG F C, WEI J P, et al., 2021. Quantitative analysis of fracture dynamic evolution in coal subjected to uniaxial and triaxial compression loads based on industrial CT and fractal theory[J]. Journal of Petroleum Science and Engineering, 196: 108051. doi: 10.1016/j.petrol.2020.108051
[42]	WANG L S, SUN D S, ZHENG X H, et al., 2017. Size effect experiment of uniaxial compressive strength of three typical rocks[J]. Journal of Geomechanics, 23(2): 327-333. (in Chinese with English abstract
[43]	WANG S, XU Y, ZHANG Y B, et al., 2023. Effects of sandstone mineral composition heterogeneity on crack initiation and propagation through a microscopic analysis technique[J]. International Journal of Rock Mechanics and Mining Sciences, 162: 105307. doi: 10.1016/j.ijrmms.2022.105307
[44]	WANG Y, WANG H M, ZHU H B, 2021. Preliminary study on physical experimental simulation of hydraulic fracturing[J]. Progress in Geophysics, 36(3): 1130-1137. (in Chinese with English abstract
[45]	WEIBULL W, 1939. A statistical theory of the strength of materials[M]. Stockholm: Generalstabens Litografiska Anstalts Förlag: 1-29.
[46]	WEN X L, KONG M W, LUO Y, et al., 2021. Study and Application of Fracturing Technology for Tight Reservoir With HPHT Closure Stress in the Southern Margin of Junggar Basin[J]. Xinjiang oil & Gas, 17(4): 15-20.
[47]	WEN S S, YIN C, SHI X W, et al., 2023. Multi-scale rupture characteristics dominated by pre-existing fractures of Longmaxi shale during hydraulic fracturing in Luzhou block[J]. Progress in Geophysics, 38(5): 2172-2181. (in Chinese with English abstract
[48]	WU F Q, QIAO L, GUAN S G, et al., 2021. Uniaxial compression test study on size effect of small size rock samples[J]. Chinese Journal of Rock Mechanics and Engineering, 40(5): 865-873. (in Chinese with English abstract
[49]	WU H, ZHOU Y, YAO Y, et al., 2019. Imaged based fractal characterization of microfracture structure in coal[J]. Fuel, 239: 53-62. doi: 10.1016/j.fuel.2018.10.117
[50]	WU N, SHI S, ZHENG S Q, et al., 2022. Formation pressure calculation of tight sandstone gas reservoir based on material balance inversion method[J]. Coal Geology & Exploration, 50(9): 115-121. (in Chinese with English abstract
[51]	WU S T, YANG Z, PAN S Q, et al., 2020. Three-dimensional imaging of fracture propagation in tight sandstones of the Upper Triassic Chang 7 member, Ordos Basin, Northern China[J]. Marine and Petroleum Geology, 120: 104501. doi: 10.1016/j.marpetgeo.2020.104501
[52]	XIE H P, CHEN Z D, 1989. Analysis of rock fracture micro-mechanism[J]. Journal of China Coal Society(2): 57-66. (in Chinese with English abstract
[53]	XING H T, ZHANG X L, HE J X, et al., 2022. Mineral composition characteristics and petroleum geological significance of tight sandstone of Longtan Formation in Weixin area, eastern Yunnan[J]. Coal Geology & Exploration, 50(4): 52-60. (in Chinese with English abstract
[54]	XIONG L F, 2021. Mechanisms and factors of the localized deformation in porous rocks[D]. Beijing: University of Science and Technology Beijing. (in Chinese with English abstract
[55]	XIONG L F, 2022. Study on deformation and failure mechanism of porous rock and its influencing factors [ D ]. Beijing University of Science and Technology.
[56]	YANG F, MEI W B, LI L, et al., 2023. Propagation of hydraulic fractures in thin interbedded tight sandstones[J]. Coal Geology & Exploration, 51(7): 61-71. (in Chinese with English abstract
[57]	YANG S Q, SU C D, XU W Y, 2005. Experimental and theoretical study of size effect of rock material[J]. Engineering Mechanics, 22(4): 112-118. (in Chinese with English abstract
[58]	YU X, LI G, CHEN Z, et al., 2021. Experimental study on physical and mechanical characteristics of tight sandstones in the Xujiahe Formation in western Sichuan after high-temperature exposure[J]. Journal of Geomechanics, 27(1): 1-9. (in Chinese with English abstract
[59]	ZENG L B, LYU W Y, LI J, et al., 2016. Natural fractures and their influence on shale gas enrichment in Sichuan Basin, China[J]. Journal of Natural Gas Science and Engineering, 30: 1-9. doi: 10.1016/j.jngse.2015.11.048
[60]	ZHANG D M, WANG P, ZANG D G, et al., 2023. Pre-stack reservoir prediction of tight sandstone of the fifth member of Xujiahe Formation in the Wubaochang area of northeastern Sichuan[J]. Geology and Exploration, 59(6): 1356-1365. (in Chinese with English abstract
[61]	ZHANG H, KANG Y L, CHEN J S, et al., 2007. Experimental study on mechanical properties of dense sandstone under different confining pressures[J]. Chinese Journal of Rock Mechanics and Engineering, 26(S2): 4227-4231. (in Chinese with English abstract
[62]	ZHANG Y F, NIU S Y, DU Z M, et al., 2020. Dynamic fracture evolution of tight sandstone under uniaxial compression in high resolution 3D X-ray microscopy[J]. Journal of Petroleum Science and Engineering, 195: 107585. doi: 10.1016/j.petrol.2020.107585
[63]	ZHAO C, LIU F M, TIAN J Y, et al., 2016. Study on single crack propagation and damage evolution mechanism of rock-like materials under uniaxial compression[J]. Chinese Journal of Rock Mechanics and Engineering, 35(S2): 3626-3632. (in Chinese with English abstract
[64]	ZHAO N, WANG L, ZHANG L, et al. , 2022. Mechanical properties and fracturing characteristics of tight sandstones based on granularity classification: a case study of Permian Lower Shihezi Formation, Ordos Basin[J]. Petroleum Geology & Experiment, 44(4): 720-729, 738. (in Chinese with English abstract
[65]	ZHONG J H, LIU S X, MA Y S, et al., 2015. Macro-fracture mode and micro-fracture mechanism of shale[J]. Petroleum Exploration and Development, 42(2): 242-250. (in Chinese with English abstract
[66]	ZHOU J, SHEN Z Z, 2021. The effect of grain size on the mechanical properties of sandstone[J]. China Petroleum and Chemical Standard and Quality, 41(18): 81-82. (in Chinese with English abstract
[67]	ZHU H Y, SONG Y J, LEI Z D, et al., 2022a. 4D-stress evolution of tight sandstone reservoir during horizontal wells injection and production: A case study of Yuan 284 block, Ordos Basin, NW China[J]. Petroleum Exploration and Development, 49(1): 156-169. doi: 10.1016/S1876-3804(22)60012-0
[68]	ZHU W W, HE X P, LI Y T, et al., 2022b. Impacts of fracture properties on the formation and development of stimulated reservoir volume: a global sensitivity analysis[J]. Journal of Petroleum Science and Engineering, 217: 110852. doi: 10.1016/j.petrol.2022.110852
[69]	ZHU W W, LEI G, HE X P, et al., 2022c. Fractal and multifractal characterization of stochastic fracture networks and real outcrops[J]. Journal of Structural Geology, 155: 104508. doi: 10.1016/j.jsg.2021.104508
[70]	ZHU W W, LEI G, HE X P, et al., 2022d. Can we infer the percolation status of 3D fractured media from 2D outcrops?[J]. Engineering Geology, 302: 106648. doi: 10.1016/j.enggeo.2022.106648
[71]	陈鑫,马立涛,史长林,等,2022. 临兴区块致密砂岩储层水赋存状态及气层含水程度识别方法[J]. 地质与勘探,58(6):1331-1340.
[72]	丁长栋,张杨,杨向同,等,2019. 致密砂岩高围压和高孔隙水压下渗透率演化规律及微观机制[J]. 岩土力学,40(9):3300-3308.
[73]	樊建明,陈小东,雷征东,等,2019. 鄂尔多斯盆地致密油藏天然裂缝与人工裂缝特征及开发意义[J]. 中国石油大学学报(自然科学版),43(3):98-106. doi: 10.3969/j.issn.1673-5005.2019.03.011
[74]	高晨阳,赵福海,高莲凤,等,2023. 基于构造应变分析的裂缝预测方法及其应用[J]. 地质力学学报,29(1):21-33. doi: 10.12090/j.issn.1006-6616.2022089
[75]	郭宇航,2018. 粒度对红砂岩力学性质的影响规律试验研究[D]. 青岛:山东科技大学.
[76]	李斌,李佳伦,王鹏,等,2023. 岩石抗剪强度参数的围压效应与定量表征[J]. 中国矿业,32(2):157-164.
[77]	李世愚,和泰名,尹祥础,2010. 岩石断裂力学导论[M]. 合肥:中国科学技术大学出版社.
[78]	凌建明,1993. 压缩荷载条件下岩石细观损伤特征的研究[J]. 同济大学学报,21(2):219-226.
[79]	刘飞跃,杨天鸿,张鹏海,等,2018. 基于声发射的岩石破裂应力场动态反演[J]. 岩土力学,39(4):1517-1524.
[80]	刘敬寿,丁文龙,肖子亢,等,2019. 储层裂缝综合表征与预测研究进展[J]. 地球物理学进展,34(6):2283-2300. doi: 10.6038/pg2019CC0290
[81]	刘圣鑫,王宗秀,张林炎,等,2019. 页岩微观组构特征对复杂裂缝网络形成的影响[J]. 采矿与安全工程学报,36(2):420-428.
[82]	马尚伟,魏丽,王一军,等,2022. 鄂尔多斯盆地南部盒8段致密砂岩储层微观孔隙结构表征与评价[J]. 地质与勘探,58(6):1321-1330. doi: 10.12134/j.dzykt.2022.06.016
[83]	缪思钰,张海江,陈余宽,等,2019. 基于微地震定位和速度成像的页岩气水力压裂地面微地震监测[J]. 石油物探,58(2):262-271,284. doi: 10.3969/j.issn.1000-1441.2019.02.012
[84]	潘丽燕,郝丽华,刘凯新,等,2023. 玛湖风城组高含盐储层水力压裂裂缝扩展规律[J]. 新疆石油天然气,19(4):20-28 doi: 10.12388/j.issn.1673-2677.2023.04.003
[85]	尚春江,康永尚,邓泽,等,2019. 充填天然裂缝对页岩受载过程中渗透率变化规律影响机理分析[J]. 地质力学学报,25(3):382-391.
[86]	谭元隆,王宗秀,冯兴强,等,2021. 复杂构造区油气构造保存条件分析:来自皖泾地1井的构造解析[J]. 地质力学学报,27(3):441-452. doi: 10.12090/j.issn.1006-6616.2021.27.03.040
[87]	王连山,孙东生,郑秀华,等,2017. 三种典型岩石单轴抗压强度的尺寸效应试验研究[J]. 地质力学学报,23(2):327-333.
[88]	王瑜,王辉明,朱海波,2021. 水力压裂物理实验模拟初探[J]. 地球物理学进展,36(3):1130-1137. doi: 10.6038/pg2021EE0258
[89]	文贤利,孔明炜,罗垚,等,2021,准噶尔盆地南缘高温高压高闭合应力致密储层改造技术研究及应用[J]. 新疆石油天然气,17(4):15-20
[90]	文山师,尹陈,石学文,等,2023. 天然裂缝主导模式下泸州龙马溪组页岩水力压裂多尺度破裂特征[J]. 地球物理学进展,38(5):2172-2181.
[91]	伍法权,乔磊,管圣功,等,2021. 小尺寸岩样单轴压缩试验尺寸效应研究[J]. 岩石力学与工程学报,40(5):865-873.
[92]	武男,石石,郑世琪,等,2022. 基于物质平衡反演法的致密砂岩气藏地层压力计算[J]. 煤田地质与勘探,50(9):115-121. doi: 10.12363/issn.1001-1986.21.12.0801
[93]	谢和平,陈至达,1989. 岩石断裂的微观机理分析[J]. 煤炭学报(2):57-66.
[94]	邢慧通,张晓丽,何金先,等,2022. 滇东威信地区龙潭组致密砂岩矿物组成特征及其油气地质意义[J]. 煤田地质与勘探,50(4):52-60. doi: 10.12363/issn.1001-1986.21.07.0403
[95]	熊良锋,2021. 孔隙岩石变形破坏机制及其影响因素研究[D]. 北京:北京科技大学.
[96]	熊良锋,2022. 孔隙岩石变形破坏机制及其影响因素研究[D]. 北京科技大学.
[97]	杨帆,梅文博,李亮,等,2023. 薄互层致密砂岩水力压裂裂缝扩展特征研究[J]. 煤田地质与勘探,51(7):61-71. doi: 10.12363/issn.1001-1986.22.10.0788
[98]	杨圣奇,苏承东,徐卫亚,2005. 岩石材料尺寸效应的试验和理论研究[J]. 工程力学,22(4):112-118. doi: 10.3969/j.issn.1000-4750.2005.04.022
[99]	于鑫,李皋,陈泽,等,2021. 川西须家河组致密砂岩高温后的物理力学特征参数试验研究[J]. 地质力学学报,27(1):1-9.
[100]	张德明,王鹏,臧殿光,等,2023. 川东北五宝场地区须五段致密砂岩叠前储层预测[J]. 地质与勘探,59(6):1356-1365. doi: 10.12134/j.dzykt.2023.06.020
[101]	张浩,康毅力,陈景山,等,2007. 变围压条件下致密砂岩力学性质实验研究[J]. 岩石力学与工程学报,26(S2):4227-4231.
[102]	赵程,刘丰铭,田加深,等,2016. 基于单轴压缩试验的岩石单裂纹扩展及损伤演化规律研究[J]. 岩石力学与工程学报,35(S2):3626-3632.
[103]	钟建华,刘圣鑫,马寅生,等,2015. 页岩宏观破裂模式与微观破裂机理[J]. 石油勘探与开发,42(2):242-250.
[104]	周婧,沈振振,2021. 粒度对砂岩力学性质的作用[J]. 中国石油和化工标准与质量,41(18):81-82.