A variational phase-field model for hydraulic fracturing in porous media
A variational phase-field model for hydraulic fracturing in porous media
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DOI：
10.1016/j.cma.2018.12.037
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发表时间：
2019-04
影响因子：
7.2
通讯作者：
C. Chukwudozie;B. Bourdin;K. Yoshioka
中科院分区：
文献类型：
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作者：
C. Chukwudozie;B. Bourdin;K. Yoshioka
孔隙-多孔介质流体流动和复杂拓扑结构裂缝扩展的严格耦合在岩土工程和生物力学应用中具有重要的科学意义。在本文中，我们推导出一个统一的孔隙-多孔介质水力压裂模型，利用变分相场方法的固有能力来处理多个裂缝相互作用和发展沿着复杂的，但关键的，未指定的路径。驱动裂纹演化的基本原理是从Griffith理论导出的能量准则。这种方法的独创性在于裂纹路径本身是从能量最小化而不是额外的分支准则导出的。数值实现是基于一个正则化的方法，类似于相场模型，裂纹的位置是由一个光滑的函数定义在一个固定的网格。导出的模型显示了如何光滑的裂缝场可以用来模拟流体在裂缝多孔介质中的流动。我们验证了所提出的方法在一个简单的理想化的情况下，在文献中存在的封闭形式的解决方案。然后，我们展示了新方法的能力，在更现实的情况下，多个骨折转向，相互作用，并在某些情况下，与其他骨折合并。
Rigorous coupling of fracture–porous medium fluid flow and topologically complex fracture propagation is of great scientific interest in geotechnical and biomechanical applications. In this paper, we derive a unified fracture–porous medium hydraulic fracturing model, leveraging the inherent ability of the variational phase-field approach to fracture to handle multiple cracks interacting and evolving along complex yet, critically, unspecified paths. The fundamental principle driving the crack evolution is an energetic criterion derived from Griffith’s theory. The originality of this approach is that the crack path itself is derived from energy minimization instead of additional branching criterion. The numerical implementation is based on a regularization approach similar to a phase-field model, where the cracks location is represented by a smooth function defined on a fixed mesh. The derived model shows how the smooth fracture field can be used to model fluid flow in a fractured porous medium. We verify the proposed approach in a simple idealized scenario where closed form solutions exist in the literature. We then demonstrate the new method’s capabilities in more realistic situations where multiple fractures turn, interact, and in some cases, merge with other fractures.