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Modeling the effect of turbulence on the simultaneous propagation of multiple parallel hydraulic fractures

机译：湍流效果对多平行液压裂缝同时传播的影响

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The injection of slick-water at the high rates used to fracture unconventional shale-gas reservoirs results in flows that are turbulent - particularly near the wellbore. In this paper we consider the effect of turbulence on the simultaneous propagation of multiple hydraulic fractures that are constrained to evolve in parallel planes. The effect of turbulence is captured using a modification of the Darcy-Weisbach fluid-flow model with an adaptation of Churchill's friction factor approximation to fracture flow geometries that is able to capture the transition from laminar to fully turbulent flow. Since the Reynlods number is proportional to the fracture width, the flow transitions to laminar close to the tip where the fracture width approaches zero. The model used in this paper is therefore able to exploit the multi-scale laminar tip asymptotic behaviour in order to use the Implicit Level Set Scheme (ILSA) to locate the fracture free boundary and to identify the propagation regime. We provide a numerical example for an array of five uniformly distributed planar fractures in which the laminar model exhibits significant stress shadowing while the turbulent model predicts substantially less. This reduction in stress shadowing in the turbulent flow model is due to the significantly larger pressure drop near the well-bore compared to the laminar case that dominates the mutual stress interactions between the fractures in the array.
机译：在用于破裂的高速率下的光滑水注入非传统的页岩气藏产生湍流的流动 - 特别是在井筒附近。在本文中，我们考虑了湍流对多个液压裂缝同时传播的影响，该液压裂缝被限制为在平行平面上发展。利用达西 - Weisbach流体流模型的修改，捕获湍流的效果，该流体流动模型的改变具有丘吉尔的摩擦因子近似，以便能够捕获从层流过渡到完全湍流的过渡。由于Reynlods数与裂缝宽度成比例，因此流动过渡到靠近尖端的层流，其中裂缝宽度接近零。因此，本文中使用的模型能够利用多尺度层尖渐近行为，以便使用隐式水平设定方案（ILSA）来定位裂缝自由边界并识别传播状态。我们提供了五个均匀分布的平面裂缝的阵列的数值示例，其中层流模型表现出显着的应力阴影，而湍流模型预测得显着较低。这种湍流模型中的应力阴影的减小是由于与层状壳体相比，孔孔附近的压力下降显着较大，该层孔在阵列中的裂缝之间的裂缝之间的相互应力相互作用相比。

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