Abstract Perforation is the key to the successful implementation of hydraulic fracturing. The research on perforation mechanism is of great significance to perforation planning, completion design, hydraulic fracturing design, and proppant migration analysis. In this paper, a finite element model for simulating crack initiation and propagation in the presence of multiple perforations is established based on the global embedded cohesive zone model (CZM). The reservoir is considered as a dense, low-permeability porous elastic medium, and the coupling between fluid flow and geomechanics, as well as the back-stress effect, are considered. The Blanton's (1982) criteria were used to verify the accuracy of the global embedded CZM. Then five cases are used to discuss the effects of perforation density, horizontal stress difference (HSD) on fracture initiation, propagation, and fracture complexity. The results show: There are four competitive fracture initiation modes for multiple perforations: First, fracture initiation at an early stage and keeping on; Second, hole deformed but not cracked; Third, fracture initiation first and then close; Fourth, at the beginning, there is no fracture initiation, initiation later. With the increase of perforation density, affected by the decrease of flow distribution, increase of friction and stress interference, the initiation rate of perforations gradually decreases, and the fracture pressure shows a tendency of decreasing first and then increasing. When multiple perforations exist, the crack propagation changes from complex to simple, and the number of cracks changes from more to less. Finally, the expansion mode is formed with 2–3 main cracks as the main and micro cracks as the auxiliary. The increase of perforation density can increase the complexity of fractures around the wellbore, and is beneficial to the diversion of fractures and the expansion of the impact range of fractures. However, it can also cause distortion and deformation of the fracture wall and decrease of fracture opening near the wellbore, which can lead to difficulty in proppant migration. Under low HSD, under the influence of stress inversion, connected horizontal cracks are easy to form between holes, and the fractures are easier to turn and more complicated. Under high HSD, disconnected horizontal micro-cracks can be formed between holes, and the main fractures tend to develop into simple straight fractures. The results of our research have important practical guiding significance for the development of perforation plan, hydraulic fracturing design and proppant migration analysis.

中文翻译：

---

存在多孔眼时裂缝起裂、扩展和裂缝复杂性的数值模拟

摘要 射孔是水力压裂成功实施的关键。射孔机理研究对射孔规划、完井设计、水力压裂设计、支撑剂运移分析等具有重要意义。在本文中，基于全局嵌入粘性带模型（CZM）建立了用于模拟存在多个穿孔时裂纹萌生和扩展的有限元模型。储层被认为是一种致密、低渗透的多孔弹性介质，考虑了流体流动与地质力学的耦合以及背应力效应。Blanton's (1982) 标准被用来验证全局嵌入式 CZM 的准确性。然后用五个案例来讨论穿孔密度的影响，水平应力差 (HSD) 对裂缝起裂、扩展和裂缝复杂性的影响。结果表明：多穿孔有四种竞争起裂模式：一是早期起裂并持续；二、孔变形不开裂；三、先起裂后闭合；第四，开始时没有起裂，起裂较晚。随着射孔密度的增加，受流量分布减小、摩擦力增大和应力干扰的影响，射孔起裂速率逐渐降低，破裂压力呈先减小后增大的趋势。当存在多个穿孔时，裂纹扩展由复杂变简单，裂纹数量由多变少。最后，膨胀模式以2~3条主裂纹为主，微裂纹为辅。射孔密度的增加会增加井筒周围裂缝的复杂性，有利于裂缝的导流和裂缝影响范围的扩大。但也会引起裂缝壁的扭曲变形和井筒附近裂缝开口的减小，从而导致支撑剂运移困难。在低HSD下，在应力反转的影响下，孔间容易形成连接的水平裂缝，裂缝更容易转向且更复杂。在高HSD下，孔间可形成不连续的水平微裂缝，主裂缝倾向于发展为简单的直缝。