Experimental study on the wall factor for spherical particles settling in parallel plates filled with power-law fluids

Hydraulic fracturing is a widespread stimulation technology in the petroleum industry. The retardation due to the fracture wall existence impacts the efficient placement of the proppant in fractures. Accurate prediction of the wall factor for proppant settling in fractures filled with Power-law fluids is important in predicting the transport distance and bed height of proppant in hydraulic fractures. However, few studies were conducted to analyze the wall factor of fracture on the settling proppant. In this study, a set of transparent parallel plates and a high-speed camera were used to record the settling behaviors of the proppant in the fracture. A total of 756 tests were carried out to analyze the effects of fluid properties, the dimensionless diameter, particle size, particle density, and the particle Reynolds number on the wall factor, involving the ranges of the dimensionless diameter and the particle Reynolds number are 0.04-0.9 and 0.0001-144.25, respectively. Results indicate that the wall factor is a function of both the dimensionless diameter and the particle Reynolds number. And a new model with 1.23% relative error was developed to predict the wall factor of the parallel plates on the spherical particles settling in the Power-law fluid. Finally, it was found that the wall effect vanishes when the dimensionless diameter is smaller than 0.057. The results of this study could help field engineers optimize proppant size and fracturing parameters.