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Numerical simulation of proppant transport in propagating fractures with the multi-phase particle-in-cell method

机译：多相单元格法数值模拟裂隙中支撑剂运移的数值模拟

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In this work, the proppant transport process in large-scale propagating fractures is simulated using an Eulerian-Lagrangian method. Fracture propagation is solved using the Perkins-Kern-Nordgren (PKN) model, while the fluid-particle system is solved with the multi-phase particle-in-cell (MP-PIC) method. The fluid motion is governed by volume-averaged Navier-Stokes equations, and solved using the finite volume method, and the particle motion is solved by applying Newton's second law in a Lagrangian manner. Based on the original MPPIC method, an extended 2D system of governing equations for fluid-particle flow is derived to solve the moving boundary problems associated with fracture propagation. By means of this method, the fluid-particle interaction is fully coupled, and the propagating fracture is considered as a prior-known boundary for the fluid and particle phases. Several numerical experiments are performed to validate the method for simulating fluid motion and proppant settling behaviors in a fracture through comparison with results in the literature. The simulation results of the 2D framework are also compared with those of 3D framework and show a good agreement. Large-scale problems of proppant transport in propagating fractures for different proppant and fracturing fluid properties, including the leak-off effect, are then simulated using this method. The Lagrangian feature of the MP-PIC method allows for flexible design of proppant injection, such as injection of proppant with multi-densities and/or multisizes.
机译：在这项工作中，使用欧拉-拉格朗日方法模拟了大规模传播裂缝中的支撑剂运移过程。使用Perkins-Kern-Nordgren（PKN）模型解决了裂纹扩展问题，而使用多相单元格内颗粒（MP-PIC）方法解决了流体-颗粒系统问题。流体运动由体积平均的Navier-Stokes方程控制，并使用有限体积法求解，而粒子运动则通过以拉格朗日方式应用牛顿第二定律来求解。基于原始的MPPIC方法，导出了扩展的二维控制流体-颗粒流方程的系统，以解决与裂缝扩展相关的运动边界问题。通过这种方法，流体-颗粒之间的相互作用被完全耦合，并且正在传播的裂缝被认为是流体和颗粒相的已知边界。通过与文献中的结果进行比较，进行了一些数值实验以验证模拟裂缝中的流体运动和支撑剂沉降行为的方法。还将2D框架的仿真结果与3D框架的仿真结果进行比较，并显示出良好的一致性。然后，使用该方法模拟了针对不同支撑剂和压裂液特性的扩展裂缝中支撑剂运输的大规模问题，包括泄漏效应。 MP-PIC方法的拉格朗日特征允许对支撑剂注入进行灵活的设计，例如以多种密度和/或多种尺寸注入支撑剂。

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