Abstract Unconventional reservoir hydraulic fracturing is often characterized with diverting and branching. A fundamental understanding of the fracture branching mechanism remains elusive due to the complicated fusion of geo stress, formation heterogeneity and pre-existed complex natural fracture topologies. Existing sharp fracture models such as, finite-element method (FEM) and its modified versions, often suffer in complex fracture topologies owing to the computationally expensive remeshing when fracture diverts and/or branches. In this paper, phase-field modeling (PFM) is proposed to quantitatively investigate the hydraulic fracture branching condition in heterogeneous formation under anisotropic in-situ stress. The PFM is featured with the diffusive interface, enabling it to automatically capture the fracture branching and diverting without the need of tracking the fracture interface. The model is first verified in predicting the fracture width, stress distribution and fracture propagation via benchmark examples, followed by the comprehensive investigation on hydraulic fracture branching in a heterogeneous formation where a rock strip is laid across the shale main formation with anisotropic in-situ stress. Parametric study shows no branching occurs when the hydraulic fracture propagates towards soft strip (e.g. soft shale), while fracture branches when it propagates towards stiff strip (e.g. hard shale or sandstone) as long as the Young's modulus ratio (ER = Estrip/Emain) exceeds a critical value. Such a critical value increases as the principal in-situ stress difference (Sd) goes up. Finally, the hydraulic fracture branching is quantified in terms of the deviation distance and reentry angle, both of which are found to rise as the ER increases, and as Sd decreases, which indicates relatively low Sd and high ER are in favor of increasing the fracture complexity and drainage area. These results could provide valuable insights in predicating and creating complex reservoir hydraulic fracturing patterns.

中文翻译：

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各向异性地应力作用下非均质地层水力压裂分支的定量相场模拟

摘要 非常规油藏水力压裂往往具有分流和分流的特点。由于地应力、地层非均质性和预先存在的复杂天然裂缝拓扑的复杂融合，对裂缝分支机制的基本理解仍然难以捉摸。现有的尖锐裂缝模型，例如有限元法 (FEM) 及其修改版本，由于裂缝转向和/或分支时计算成本高昂的重新划分网格，通常会遇到复杂的裂缝拓扑结构。在本文中，提出了相场模型（PFM）来定量研究各向异性地应力下非均质地层中的水力压裂分支条件。PFM 具有扩散界面，使其能够自动捕获裂缝分支和转向，而无需跟踪裂缝界面。该模型首先通过基准实例对裂缝宽度、应力分布和裂缝扩展的预测进行了验证，然后对非均质地层中的水力裂缝分支进行了全面调查，该地层中的岩石条带穿过具有各向异性地应力的页岩主地层. 参数研究表明，只要杨氏模量比（ER = Estrip/Emain），当水力裂缝向软条带（例如软页岩）扩展时不会发生分支，而当向硬条带（例如硬页岩或砂岩）扩展时裂缝会发生分支超过临界值。这种临界值随着主要原位应力差 (Sd) 的增加而增加。最后，水力压裂分支是根据偏差距离和折返角量化的，发现两者都随着 ER 的增加而增加，随着 Sd 的减小，这表明相对较低的 Sd 和较高的 ER 有利于增加裂缝复杂性和流域。这些结果可以为预测和创建复​​杂的油藏水力压裂模式提供有价值的见解。