We detail the energy balance of a propagating hydraulic fracture. Using the linear hydraulic fracture model which combines lubrication flow and linear elastic fracture mechanics, we demonstrate how different propagation regimes are related to the dominance of a given term of the power balance of a growing hydraulic fracture. Taking an energy point of view allows us to offer a physical explanation of hydraulic fracture growth behaviours, such as, for example, the transition from viscosity to toughness dominated growth for a radial geometry, fracture propagation after the end of the injection or transition to self-buoyant elongated growth. We quantify the evolution of the different power terms for a series of numerical examples. We also discuss the order of magnitudes of the different terms for a industrial-like hydraulic fracturing treatment accounting for the additional dissipation in the injection line.

中文翻译：

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深部水力裂缝的能量平衡


我们详细介绍了扩展水力裂缝的能量平衡。使用结合了润滑流和线性弹性断裂力学的线性水力裂缝模型，我们展示了不同的传播机制如何与不断增长的水力裂缝的功率平衡的给定项的主导地位相关。从能量的角度来看，我们可以对水力裂缝的增长行为进行物理解释，例如，径向几何形状从粘度到韧性主导的增长、注入结束后的裂缝扩展或向自浮力拉长增长的过渡。我们通过一系列数值示例量化了不同幂项的演变。我们还讨论了类似工业的水力压裂处理的不同术语的数量级，这些处理考虑了注入管线中的额外耗散。