标题： 传播的长条形流体驱动裂缝：岩石韧性与流体粘度 显示英文标题

标题： Propagation of Elongated Fluid-Driven Fractures: Rock Toughness vs. Fluid Viscosity

摘要： 本文研究了岩石裂缝韧性对拉伸流体驱动裂缝传播的影响。 我们使用了 Sarvaramini 和 Garagash (2015) 的 `tough PKN' 模型，这是经典 PKN 模型(Perkins 和 Kern, 1961; Nordgren, 1972)的扩展，该模型允许在推进的裂缝前端有非零的能量释放率。 我们在忽略流体漏失的假设下，对由任意流体注入定律驱动的 `tough' 拉伸裂缝进行了自洽分析。 我们利用量纲分析来确定控制传播区及其随时间演变的无量纲参数，提供了任意幂律注入在极限区域中的若干解析解，并提出了一个简化的运动方程方法，以解决注入和关井期间一般拉伸裂缝传播问题。 最后，我们利用为 tough 拉伸裂缝开发的解决方案，推测粘性和韧性相关耗散在裂缝动力学中的相对重要性，并探讨可能的韧性尺度依赖性的含义。 显示英文摘要

摘要： This paper studies the effect of the rock fracture toughness on the propagation of elongated fluid-driven fractures. We use the `tough PKN' model of Sarvaramini and Garagash (2015), an extension of the classical PKN model(Perkins and Kern, 1961; Nordgren, 1972), which allows for a non-zero energy release rate into the advancing fracture front(s). We provide a self-consistent analysis of a `tough' elongated fracture driven by arbitrary fluid injection law under the assumption of negligible fluid leak-off. We use scaling considerations to identify the non-dimensional parameters governing the propagation regimes and their succession in time, provide a number of analytical solutions in the limiting regimes for an arbitrary power-law injection, and also posit a simplified, equation-of-motion, approach to solve a general elongated fracture propagation problem during the injection and shut-in periods. Finally, we use the developed solutions for a tough elongated fracture to surmise the relative importance of the viscous and toughness-related dissipation on the fracture dynamics and broach the implications of the possible toughness scale-dependence.