Comprehensive proppant settling model in hydraulic fractures of unconventional gas reservoir considering multifactorial influence

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.