Numerical Simulation of Proppant Transport and Placement in Hydraulic Fractures with the Hybrid Perkins-Kern-Nordgren-Carter (PKN-C) Model and Particle Tracking Algorithm

Abstract

Summary Although non-Newtonian fracturing fluids have been widely used, numerical simulation of field-scale proppant transport considering non-Newtonian fracturing fluids is far from satisfactory. In this study, a novel numerical scheme based on the Eulerian-Lagrangian (E-L) method has been developed and validated to simulate such a proppant transport and placement behavior. More specifically, hydraulic fracture propagation is characterized by the Perkins-Kern-Nordgren-Carter (PKN-C) model, and the injected proppants are described using the classic particle tracking algorithm. Proppants are vertically dragged by the gravitational force and horizontally driven by the velocity field conditioned to the fracture propagation and proppant dune packing. The settling velocity of proppants is quantified considering the in-situ shear rate and concentration, while their transport at each dune surface is quantified by performing drag/lift force analysis. The numerical model is first validated by reproducing experimental measurements inside a visual parallel plate. Subsequently, field-scale simulations are performed to identify the factors dominating proppant transport and placement under various conditions. As indicated by simulated results, the accumulated concentration at the lower region of a fracture usually results in a growing proppant dune with a “heel-biased” distribution. The non-Newtonian fluid yields a higher slurry coverage together with a longer proppant dune than the Newtonian fluid when their average viscosities are consistent. In addition to the dependence of the premature tip screenout configuration on the power-law fluid parameter n, both parameters of K and n impose a generally consistent effect (on proppant transport) with that of Newtonian viscosity (i.e., an increase of either K or n effectively improves the average viscosity and mitigates the proppant settling). A mild increase in proppant density and size significantly enhances the proppant dune formation; however, a further increase of these two factors aggravates the “heel-biased” distribution of proppants. Also, an increased leakoff coefficient improves the overall proppant concentration as well as the dune and slurry coverage. The used particle tracking algorithm enables proppant transport to be individually and accurately evaluated and analyzed with an acceptable computational cost, while such a numerical model can deal with both the Newtonian and non-Newtonian fluids at the field scale. This numerical study allows us to optimize the growth, propagation, and coverage of proppant dunes for maximizing fracture conductivity during hydraulic fracturing operations.