﻿ 水平井多裂纹同步扩展的偏折分析<sup>*</sup>
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1. 北京航空航天大学 航空科学与工程学院, 北京 100083;
2. 中国科学院力学研究所 流固耦合系统力学重点实验室, 北京 100190

Deflection of multi-crack synchronous propagation in horizontal well
CHEN Minwei1, LI Min1, CHEN Weimin2
1. School of Aeronautic Science and Engineering, Beihang University, Beijing 100083, China;
2. Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
Received: 2018-05-04; Accepted: 2018-07-27; Published online: 2018-08-22 08:57
Foundation item: National Natural Science Foundation of China (11232012, 11372320)
Corresponding author. CHEN Weimin, E-mail: wmchen@imech.ac.cn
Abstract: Horizontal well fracturing, a popular new technology developed in oil and gas industry, is utilized to enhance the production of wells. However, crack tips determine the crack initiation and propagation direction in the process of fracture growth and have a significant effect on the fracturing results. In this sense, in-depth understanding is required for this technology. In this paper, weight function at the crack tip is built according to the characteristics of stress field at the tip. The function can accurately describe the stress state at the crack tip and determine the growth direction. Based on the analysis of multi-crack propagation in the horizontal well, which is simulated by mesh regeneration method together with maximum principal stress principle, weight function at the crack tip is used to explain the reason of crack deflection under the conditions of stress contrast, crack number and distance among cracks. The final results indicate that the equivalent stresses in x and y direction at the crack tip have no distinct change and the deflections are mainly related to the equivalent stresses in xy direction.
Keywords: horizontal well fracturing     weight function     finite element method     crack propagation     crack deflection

1 裂尖权函数 1.1 权函数的建立

 (1)
 图 1 裂尖附近单元及高斯点分布图 Fig. 1 Distribution diagram of element and Gauss point near crack tip

 (2)

 图 2 Ⅰ型裂尖附近的应力误差云图 Fig. 2 Error contour of stresses near model-Ⅰ crack tip
 图 3 Ⅱ型裂尖附近的应力误差云图 Fig. 3 Error contour of stresses near model-Ⅱ crack tip

 (3)
 图 4 角度与距离函数曲线 Fig. 4 Curves of angle and distance function

1.2 权函数的验证

 (4)

 图 5 裂纹路径误差示意图 Fig. 5 Schematic of crack path error

1.2.1 算例1

 图 6 带孔板边缘多裂纹扩展的模型示意图 Fig. 6 Schematic of model of multiple edge cracks propagation of hole plate

 图 7 不同方法的开裂路径对比(算例1) Fig. 7 Comparison of crack path among different methods (Example 1)

1.2.2 算例2

 图 8 四点弯曲梁试件模型 Fig. 8 Model of 4-point bending beam specimen

 图 9 不同方法的开裂路径对比(算例2) Fig. 9 Comparison of crack path among different methods (Example 2)

2 水平井多裂纹有限元模型的建立 2.1 模型描述

 图 10 有限元模型示意图 Fig. 10 Schematic of finite element model
 图 11 有限元网格模型 Fig. 11 Mesh of finite element model
2.2 模型假设

3 水平井多裂纹扩展结果

3.1 间长比的变化

 图 12 不同间长比条件下裂纹扩展路径 Fig. 12 Crack propagation path under different RSL

 图 13 不同间长比条件下裂尖等效应力随裂纹数目的变化情况 Fig. 13 Variation of equivalent stress at crack tip with crack number under different RSL
 图 14 不同裂纹数目条件下裂尖等效应力随间长比的变化情况 Fig. 14 Variation of equivalent stress at crack tip with RSL under different crack numbers
 图 15 不同裂纹数目条件下裂纹偏折角度与水压随间长比的变化情况 Fig. 15 Variation of deflection angle and hydraulic pressure with RSL under different crack numbers
3.2 应力差的变化

 图 16 不同应力差条件下的裂纹扩展路径 Fig. 16 Crack propagation path under different stress contrast
 图 17 不同裂纹数目条件下裂尖等效应力随应力差的变化情况 Fig. 17 Variation of equivalent stress at crack tip with stress contrast under different crack numbers

 图 18 不同裂纹数目条件下裂尖偏折角度与水压随应力差的变化情况 Fig. 18 Variation of deflection angle and hydraulic pressure at crack tip with stress contrast under different crack numbers
4 结论

1) 相比一条裂纹而言，裂纹数目增加后，裂纹的开裂方向会向外产生偏折，这是因为裂纹尖端的xy方向的等效应力突然增大，而其他方向的等效应力基本不发生变化而导致的。

2) 当裂纹的间长比逐渐增加时，裂尖的xy方向等效应力会明显减小，而主应力与y方向的等效应力差值并没变化，因此裂纹的偏折角度会相应地变小。

3) 在应力差变大的过程中，相比同裂纹数目应力差为0的条件下，xy方向的等效应力与主应力并没有什么太大变化，但是y方向的等效应力明显地增加，因此偏折角度逐渐减小。

 图 A1 不同系数n下带孔板边缘的裂纹扩展对比 Fig. A1 Comparison of edge crack propagation of hole plate under different coefficient n

 图 A2 不同系数n下四点弯曲梁试件模型的裂纹扩展对比 Fig. A2 Crack propagation comparison of 4-point bending beam specimen under different coefficient n

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#### 文章信息

CHEN Minwei, LI Min, CHEN Weimin

Deflection of multi-crack synchronous propagation in horizontal well

Journal of Beijing University of Aeronautics and Astronsutics, 2019, 45(1): 99-108
http://dx.doi.org/10.13700/j.bh.1001-5965.2018.0255