Numerical Simulation of Mechanical Properties and Damage Modes of Shales with Cross⁃Fractures under Triaxial Stress

doi:10.12422/j.issn.1672-6952.2024.02.007

Abstract

Abstract:

In order to study the influence of cross?fracture on the mechanical properties and damage modes of deep shale, and better understand the damage evolution law of shale containing cross?fracture under high temperature and high pressure coupling, 15 groups of shale models containing cross?fracture with different inclination angles were established, and simulation experiments were carried out to study the stress?strain relationship, damage evolution and acoustic emission characteristics of the shale specimens. The results show that the compressive strength and modulus of elasticity of shale are negatively correlated with the inclination angle of the main cracks, and show an upward concave trend with the increase of the inclination angle of the secondary cracks, and the compressive strength of shale decreases significantly when there are cracks perpendicular to or close to perpendicular to the loading direction; the damage modes of shale specimens under the influence of cross?cracks are mainly divided into "X"?shaped damage, diagonal "N"?shaped damage, diagonal "W"?shaped damage, inverted "V"?shaped damage, damage along the main crack, "V"?shaped damage and "λ"?shaped damage; the fractal dimension of shale specimens is negatively correlated with the inclination angle of the main crack, and as the inclination angle of the main crack decreases, the value of fractal dimension tends to increase, and the corresponding damage pattern of the specimens is more complicated and the internal damage is more intense.

Key words: Shale, Thermosolid coupling, Cross?fracture, Acoustic emission, Fractal dimension

摘要：

为研究交叉裂缝对深层页岩力学特性及破坏模式的影响，更好地了解在高温高压耦合作用下含交叉裂缝页岩的损伤演化规律，建立了15组含不同倾角交叉裂缝页岩模型，并对页岩试件的应力?应变关系、损伤演化及声发射特征进行了模拟实验。结果表明，页岩的抗压强度和弹性模量与主裂缝倾角整体呈负相关，并随次裂缝倾角的增大呈上凹的变化趋势；当页岩中存在垂直或接近垂直于加载方向的裂缝时，其抗压强度显著下降；页岩试件的破坏模式在交叉裂缝影响下主要分为“X”形破坏、斜“N”形破坏、斜“W”形破坏、倒“V”形破坏、沿主裂缝贯穿破坏、“V”形破坏与“λ”形破坏；页岩试件的分形维数与主裂缝倾角整体呈负相关，随着主裂缝倾角的减小，分形维数整体趋于增大，相应的试件破坏模式更复杂，内部损伤更剧烈。

关键词: 页岩, 热固耦合, 交叉裂缝, 声发射, 分形维数

CLC Number:

TE31

Heng QU, Zhonghu WU. Numerical Simulation of Mechanical Properties and Damage Modes of Shales with Cross⁃Fractures under Triaxial Stress[J]. Journal of Liaoning Petrochemical University, 2024, 44(2): 42-49.

瞿恒, 邬忠虎. 三轴应力下含交叉裂缝页岩的力学特性及破坏模式数值模拟[J]. 辽宁石油化工大学学报, 2024, 44(2): 42-49.

Figures/Tables 11

Fig.1 X?ray whole rock diffraction quantitative analysis diagram

Table1 Mechanical parameters of shale matrix and quartz minerals[16]

材料	弹性模量/GPa	均质度/m	抗压强度/MPa	泊松比	摩擦角/（°）	压拉比	热容量/(J $⋅$ kg^-1 $⋅$ ℃^-1)	热膨胀系数 $×$ 10⁶/℃^-1	密度/(g $⋅$ cm^-3)
页岩基质	51 600	4	145	0.22	35	14	1 250	1.36	2.56
石英矿物	96 000	8	375	0.08	60	15	700	1.10	2.60

Table1 Mechanical parameters of shale matrix and quartz minerals[16]

材料	弹性模量/GPa	均质度/m	抗压强度/MPa	泊松比	摩擦角/（°）	压拉比	热容量/(J $⋅$ kg^-1 $⋅$ ℃^-1)	热膨胀系数 $×$ 10⁶/℃^-1	密度/(g $⋅$ cm^-3)
页岩基质	51 600	4	145	0.22	35	14	1 250	1.36	2.56
石英矿物	96 000	8	375	0.08	60	15	700	1.10	2.60

Table 2 Shale samples conditions

试件	α/（°）	β/（°）	试件	α/（°）	β/（°）
S1	30	0	S9	45	60
S2	30	30	S10	45	90
S3	30	45	S11	60	0
S4	30	60	S12	60	30
S5	30	90	S13	60	45
S6	45	0	S14	60	60
S7	45	30	S15	60	90
S8	45	45

Fig.2 Loading diagram of shale with cross fractures

Fig.3 Stress?strain curve and peak stress diagram of shale samples

Fig.4 Elastic modulus diagram of shale samples

Table 3 Compressive strength and elastic modulus of shale samples

β/(°)	抗压强度/MPa			弹性模量/GPa
β/(°)	α=30°	α=45°	α=60°	α=30°	α=45°	α=60°
0	81.733	85.548	67.585	31.945	31.981	31.710
30	79.282	73.225	60.288	32.234	31.792	30.973
45	74.542	60.851	57.777	31.710	31.169	31.478
60	63.894	68.398	66.266	31.100	31.631	31.700
90	68.212	76.490	64.085	31.799	32.126	31.724

Fig.6 Damage variable?strain relationship curve of shale sample S15

Fig.5 Acoustic emission count and cumulative acoustic emission map of shale samples

Fig.7 Evolution diagram of cracks and acoustic emission of shale samples

Table 4 Dip angle and fractal dimension of cross fractures

β/(°)	分形维数
β/(°)	α=30°	α=45°	α=60°
0	1.355	1.227	1.330
30	1.277	1.341	1.315
45	1.368	1.277	1.262
60	1.388	1.339	1.333
90	1.346	1.249	1.214

References 21

1	申云生，马海燕，温博，等.页岩油加工工艺实验研究［J］.辽宁石油化工大学学报，2015，35（1）：20⁃23.
	SHEN Y S，MA H Y，WEN B，et al.Experimental research of shale oil processing technology［J］.Journal of Liaoning Shihua University，2015，35（1）：20⁃23.
2	江铭，李志强，段贵府，等.水力裂缝导流能力对深层页岩气产能的影响规律［J］. 新疆石油天然气，2023，19（1）：35⁃41.
	JIANG M，LI Z Q，DUAN G F，et al.Effect of hydraulic fracture conductivity on deep shale gas production［J］.Xinjiang Oil & Gas，2023，19（1）：35⁃41.
3	张金川，陶佳，李振，等.中国深层页岩气资源前景和勘探潜力［J］.天然气工业，2021，41（1）：15⁃28.
	ZHANG J C，TAO J，LI Z，et al.Prospect of deep shale gas resources in China［J］.Natural Gas Industry，2021，41（1）：15⁃28.
4	魏娟明，贾文峰，陈昊，等.深层页岩气压裂用高黏高降阻一体化稠化剂的制备与性能评价［J］.油田化学，2022，39（2）：234⁃238.
	WEI J M， JIAW F， CHEN H， et al. Preparation and performance evaluation of integrated thickener with high viscosity and high drag reduction used for fracturing deeper shale gas ［J］. Oilfield Chemistry，2022，39（2）：234⁃238.
5	赵海军，马凤山，刘港，等.不同尺度岩体结构面对页岩气储层水力压裂裂缝扩展的影响［J］.工程地质学报，2016，24（5）：992⁃1007.
	ZHAO H J，MA F S，LIU G，et al.Influence of different scales of structural planes on propagation mechanism of hydraulic fracturing［J］.Journal of Engineering Geology，2016，24（5）：992⁃1007.
6	汪道兵.水力压裂裂缝暂堵转向机理与转向规律研究［D］. 北京：中国石油大学（北京），2017.
7	赵彦昕，许文俊，王雷，等.陆相页岩储层水力裂缝穿层扩展规律［J］.石油钻采工艺，2023，45（1）：76⁃84.
	ZHAO Y X， XU W J， WANG L， et al. Through⁃layer propagation laws of hydraulic fractures in continental shale reservoirs［J］. Oil Drilling & Production Technology， 2023， 45（1）： 76⁃84.
8	潘林华，程礼军，张士诚，等.页岩储层体积压裂裂缝扩展机制研究［J］. 岩土力学， 2015， 36（1）： 205⁃211.
	PAN L H， CHENG L J， ZHANG S C， et al. Mechanism of fracture propagation via numerical stimulation of reservoir volume fracture in shale reservoirs［J］. Rock and Soil Mechanics， 2015， 36（1）： 205⁃211.
9	李亚龙，刘先贵，胡志明，等. 页岩储层压裂缝网模拟研究进展［J］. 石油地球物理勘探， 2019， 54（2）： 480⁃492.
	LI Y L， LIU X G， HU Z M， et al. Research progress on fracture network simulation in shale reservoirs［J］. Oil Geophysical Prospecting， 2019， 54（2）： 480⁃492.
10	尹丛彬，李彦超，王素兵，等. 页岩压裂裂缝网络预测方法及其应用［J］. 天然气工业， 2017， 37（4）： 60⁃68.
	YIN C B， LI Y C， WANG S B， et al. Methodology of hydraulic fracture network prediction in shale reservoirs and its application［J］. Natural Gas Industry， 2017， 37（4）： 60⁃68.
11	王瑜，王辉明，朱海波. 水力压裂物理实验模拟初探［J］. 地球物理学进展， 2021， 36（3）： 1130⁃1137.
	WANG Y， WANG H M， ZHU H B. Preliminary study on physical experimental simulation of hydraulic fracturing［J］. Progress in Geophysics， 2021， 36（3）： 1130⁃1137.
12	侯冰，木哈达斯.叶尔甫拉提，付卫能，等.页岩暂堵转向压裂水力裂缝扩展物模试验研究［J］.辽宁石油化工大学学报，2020，40（4）：98⁃104.
	HOU B，YEERFULATI M，FU W N，et al.Experimental study on the hydraulic fracture propagation for shale temporary plugging and diverting fracturing［J］.Journal of Liaoning Shihua University， 2020， 40（4）：98⁃104.
13	MARTIN C D， CHANDLER N A. The progressive fracture of lac du bonnet granite［J］. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts， 1994， 31（6）： 643⁃659.
14	崔恒涛，邬忠虎，娄义黎，等. 基于微观尺度的页岩损伤破裂数值试验［J］. 煤田地质与勘探， 2020， 48（5）： 137⁃143.
	CUI H T， WU Z H， LOU Y L， et al. Numerical experiment on damage and fracture of shale based on micro⁃scale［J］. Coal Geology & Exploration， 2020， 48（5）： 137⁃143.
15	邹才能，杨智，崔景伟，等. 页岩油形成机制、地质特征及发展对策［J］. 石油勘探与开发， 2013， 40（1）： 14⁃26.
	ZOU C N， YANG Z， CUI J W， et al. Formation mechanism， geological characteristics and development strategy of nonmarine shale oil in China［J］. Petroleum Exploration and Development， 2013， 40（1）： 14⁃26.
16	WANG W T， WU Z H， SONG H L， et al. Study on the failure mechanism of lower cambrian shale under different bedding dips with thermosolid coupling［J］. Geofluids， 2022， 2022： 1976294.
17	李术才，许新骥，刘征宇，等. 单轴压缩条件下砂岩破坏全过程电阻率与声发射响应特征及损伤演化［J］. 岩石力学与工程学报， 2014， 33（1）： 14⁃23.
	LI S C， XU X J， LIU Z Y， et al. Electrical resistivity and acoustic emission response characteristics and damage evolution of sandstone during whole process of uniaxial compression［J］. Chinese Journal of Rock Mechanics and Engineering， 2014， 33（1）： 14⁃23.
18	刘保县，黄敬林，王泽云，等.单轴压缩煤岩损伤演化及声发射特性研究［J］.岩石力学与工程学报，2009，28（Z1）：3234⁃3238.
	LIU B X，HUANG J L，WANG Z Y，et al.Study on damage evolution and acoustic emission character of coal⁃rock under uniaxial compression［J］. Chinese Journal of Rock Mechanics and Engineering， 2009， 28（S1）： 3234⁃3238.
19	MANDELBROT B. How long is the coast of Britain？ Statistical self⁃similarity and fractional dimension［J］. Science， 1967， 156（3775）： 636⁃638.
20	LIU H， ZHENG L L， ZUO Y J， et al. Study on mesoscopic damage evolution characteristics of single joint sandstone based on Micro⁃CT image and fractal theory［J］. Shock and Vibration， 2021， 2021： 6547028.
21	张波，李术才，杨学英，等.含交叉裂隙岩体相似材料试件力学性能单轴压缩试验［J］.岩土力学，2012，33（12）：3674⁃3679.
	ZHANG B， LI S C， YANG X Y， et al. Uniaxial compression tests on mechanical properties of rock mass similar material with cross⁃cracks［J］. Rock and Soil Mechanics， 2012，33（12）：3674⁃3679.

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