Abstract This article presents the first monolithic coupled numerical model for simulating proppant transport through a non-planar propagating hydraulic fracture. A fracture is propagated through a two-dimensional domain, driven by the flow of a proppant-laden slurry. Modeling of the slurry flow includes the effects of proppant bridging and the subsequent flow of fracturing fluid through the packed proppant. This allows for simulation of a tip screen-out, a phenomenon in which there is a high degree of physical interaction between the rock deformation, fluid flow, and proppant transport and leads to shock formation in the solution. The numerical implementation is verified and the model is used to simulate a tip screen-out in both planar and non-planar fractures. An analysis of the results is performed for three different coupling schemes: monolithic, sequential, and loose coupling. The monolithic scheme is shown to be optimal in terms of computational efficiency, robustness, and accuracy. In addition, a robust and more efficient algorithm for injection-rate controlled hydraulic fracturing simulation based on global mass conservation is presented in this article.

中文翻译：

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具有支撑剂输运的整体耦合水力压裂模型

摘要 本文提出了第一个整体耦合数值模型，用于模拟支撑剂通过非平面扩展水力压裂的传输。在载有支撑剂的泥浆流动的驱动下，裂缝通过二维域传播。泥浆流的建模包括支撑剂桥接的影响和压裂液随后通过填充支撑剂的流动。这允许模拟尖端筛分现象，在这种现象中，岩石变形、流体流动和支撑剂输送之间存在高度的物理相互作用，并导致溶液中形成冲击波。数值实现得到验证，该模型用于模拟平面和非平面裂缝中的尖端筛分。对三种不同的耦合方案进行了结果分析：单片、顺序和松散耦合。单片方案在计算效率、鲁棒性和准确性方面被证明是最佳的。此外，本文还提出了一种基于全局质量守恒的用于注入速率控制的水力压裂模拟的稳健且更有效的算法。