PyFrac: A planar 3D hydraulic fracture simulator

Fluid driven fractures propagate in the upper earth crust either naturally or in response to engineered fluid injections. The quantitative prediction of their evolution is critical in order to better understand their dynamics as well as to optimize their creation. We present an open-source Python implementation of a hydraulic fracture growth simulator based on the implicit level set algorithm originally developed by Peirce & Detournay (2008). This algorithm couples a finite discretization of the fracture with the use of the near tip asymptotic solutions of a steadily propagating semi-infinite hydraulic fracture. This allows to resolve the multi-scale processes governing hydraulic fracture propagation accurately, even on relatively coarse meshes. We present an overview of the mathematical formulation, the numerical scheme and the details of our implementation. A series of problems including a radial hydraulic fracture verification test, the propagation of a height contained hydraulic fracture, the lateral spreading of a magmatic dyke and an example of fracture closure are presented to demonstrate the capabilities, accuracy and robustness of the implemented algorithm.流体驱动裂缝既会自然地在上地壳中扩展，也会因工程流体注入作用而萌生并扩展。对其演化过程进行定量预测，对于深入理解其动力学机制以及优化人工造缝效果均至关重要。本研究提出了一种基于Peirce与Detournay（2008）最初开发的隐式水平集算法（implicit level set algorithm）的开源Python版水力裂缝（hydraulic fracture）扩展模拟器实现方案。该算法将裂缝的有限离散化方法，与稳态扩展的半无限长水力裂缝的尖端渐近解相结合，即便采用相对粗糙的网格，也能够精准解析控制水力裂缝扩展的多尺度过程。本文对该模拟器的数学表述、数值求解格式以及具体实现细节进行了全面概述。本文呈现了一系列测试案例以展示所实现算法的性能、精度与鲁棒性，涵盖径向水力裂缝验证试验、受限高度水力裂缝扩展过程、岩浆岩脉的侧向扩展以及裂缝闭合过程示例。