A Power-Law-Based Predictive Model for Proppant Settling Velocity in Non-Newtonian Fluid

Effective proppant transport is critical to the success of hydraulic fracturing, particularly when using a non-Newtonian fluid. However, accurately predicting the proppant settling behavior under complex rheological conditions is still a significant challenge. This study proposes a new method for estimating the velocity of proppant settling in the power-law non-Newtonian fluid by accounting for spatial variations in viscosity within the fracture domain. The local shear rate field is first obtained using an analytical expression derived from the velocity gradient, and then used to approximate spatially varying viscosity based on the power-law rheological model. This allows the modification of Stokes’ law, which was initially developed for Newtonian fluid, to be used for the power-law non-Newtonian fluid. The results indicate that the model achieved high accuracy in the fracture center region, with an average relative error of 8.2%. The proposed approach bridges the gap between traditional settling models and the non-Newtonian behavior of the fracturing fluid, offering a practical and physically grounded framework for predicting the velocity of proppant settling within a hydraulic fracture. By considering the distribution of the shear rate and viscosity of the fracturing fluid, this method enables an accurate prediction of proppant settling velocity, which further provides theoretical support to the optimization of pumping schedules and operation parameters for hydraulic fracturing.