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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A variational phase-field model for hydraulic fracturing in porous media
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A variational phase-field model for hydraulic fracturing in porous media

机译：多孔介质水力压裂的变分相场模型

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摘要

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.(C) 2019 Elsevier B.Y. All rights reserved.
机译：裂缝-多孔介质流体流与拓扑复杂的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大的科学意义。在本文中，我们利用变分相场方法对裂缝的固有能力，来处理沿着复杂但关键的，未指定路径相互作用和演化的多个裂缝，从而得出统一的裂缝-多孔介质水力压裂模型。推动裂纹发展的基本原理是从格里菲思的理论中得出的一个有力的判据。这种方法的独创性是裂纹路径本身是从能量最小化而不是附加的分支准则中得出的。数值实现基于类似于相场模型的正则化方法，其中裂缝位置由在固定网格上定义的平滑函数表示。导出的模型显示了如何使用平滑的裂缝场来模拟裂缝多孔介质中的流体流动。我们在一个简单的理想情况下（在文献中存在封闭形式的解决方案）验证了该方法。然后，我们在更现实的情况下证明新方法的功能，这些情况是多个裂缝发生旋转，相互作用以及在某些情况下与其他裂缝合并。（C）2019 Elsevier B.Y.版权所有。

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