Thus far, hydraulic fracturing has played a crucial role in improving the production of unconventional gas resources. During hydraulic fracturing, the proppant is pumped into an artificial fracture with a low-viscosity fracturing fluid. Then, the proppant settles and makes the artificial fracture open. Therefore, the investigation of proppant settling in the hydraulic fracture is important for the development of unconventional gas reservoirs. This paper proposes a comprehensive mathematical model for quantitatively evaluating the proppant settling rate in the hydraulic fracture of unconventional gas reservoirs. In particular, the model considers the effects of fracture width, proppant size, proppant concentration, fluid viscosity, and flow regime. The model is verified by the experimental data and models found in literatures, and the effects of key parameters (e.g., fluid viscosity, concentration, fracture wall, proppant size, and flow regime) on the settling rate are analyzed. The results show that, with increasing fracture width or decreasing proppant diameter, the dimensionless settling rate increases. By contrast, fluid viscosity has a small effect on the dimensionless settling rate. In addition, the increase of proppant concentration results in a decrease in the dimensionless settling rate. The proppant concentration is the main factor affecting the settling rate, followed by the flow regime, the ratio of proppant diameter to fracture width, and the fluid viscosity. This work can provide a theoretical basis for the study of proppant placement in fractures of unconventional gas reservoirs. Additionally, the developed model can be easily incorporated into fracture simulators to simulate proppant transport.

中文翻译：

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考虑多因素影响的非常规气藏水力裂缝综合支撑剂沉降模型

迄今为止，水力压裂在改善非常规天然气资源的生产中起着至关重要的作用。在水力压裂过程中，将支撑剂与低粘度压裂液一起泵入人工裂缝中。然后，支撑剂沉降并使人造裂缝打开。因此，对水力压裂中支撑剂沉降的研究对于非常规气藏的开发具有重要意义。本文提出了一个综合数学模型，用于定量评价非常规气藏水力裂缝中支撑剂的沉降速率。特别地，该模型考虑了裂缝宽度，支撑剂尺寸，支撑剂浓度，流体粘度和流动状态的影响。该模型已通过文献中的实验数据和模型进行了验证，并分析了关键参数（例如，流体粘度，浓度，裂缝壁，支撑剂尺寸和流动状态）对沉降速率的影响。结果表明，随着裂缝宽度的增加或支撑剂直径的减小，无因次沉降速率增加。相反，流体粘度对无因次沉降速率的影响很小。另外，支撑剂浓度的增加导致无因次沉降速率的降低。支撑剂浓度是影响沉降速率的主要因素，其次是流动方式，支撑剂直径与裂缝宽度之比以及流体粘度。这项工作可为研究非常规气藏裂缝中支撑剂的位置提供理论依据。另外，