Rheology of polyacrylamide-based fluids and its impact on proppant transport in hydraulic fractures

Rheological experiments and measurements of particle settling velocity under static conditions were conducted for two types of polyacrylamide (PAA-based) fluids. The flow behavior of the viscoelastic fluids is described by a simplified, three-parameter model that integrates a constant viscosity at low shear rates with a power-law viscosity dependency at higher shear rates. The estimated dependencies of the rheological parameters and particle settling velocity on PAA concentration align with the classical power-law scaling for semi-dilute polymer solutions. The identified scaling offers valuable insight for optimizing the chemical composition of fracturing fluids, thereby improving the efficiency of hydraulic fracturing technology. By applying the lubrication approximation to the Navier–Stokes equations, a set of equations for the suspension flow in a vertical plane channel, characterized by the three-parameter rheology model, was derived. In typical fracturing conditions, the conventional power-law viscosity model used in current fracturing simulators significantly overestimates the gap-averaged apparent fluid viscosity compared to the proposed model. The novel model of the suspension flow aims to enhance the accuracy of proppant transport models applied in hydraulic fracturing simulators. Based on the three-parameter rheology model, a new model of particle settling in the studied PAA-based fluids is developed. It is based on smart Stokes' law, where viscosity is calculated according to either the plateau or power-law region, depending on the self-induced shear rate. The new model more accurately approximates experimentally determined settling velocity of proppant under static conditions across a broad range of PAA concentrations than existing models.