Field-Scale Simulation on Multi-Slug Proppant Transport in a Propagating Fracture via Modified Perkins-Kern-Nordgren-Carter (PKN-C) Model and Particle Tracking Algorithm

During hydraulic fracturing operations in unconventional low-permeability reservoirs, non-Newtonian fracturing fluids are commonly injected with multi-slug proppants of varying particle sizes; however, efficiently representing the coupled evolution of such proppant transport at field-scale remains challenging. In this work, a computationally efficient framework is developed to simulate and evaluate proppant transport dynamics within a propagating fracture by modifying the Perkins-Kern-Nordgren-Carter (PKN-C) model and coupling it with a parcel-based Lagrangian particle-tracking algorithm. The framework incorporates not only empirical correlations derived from laboratory measurements to represent concentration-dependent fluid rheology, hindered settling, and bed-load transport, but also a modified width solution accounting for stress anisotropy and wellbore radius to represent realistic fracture morphology and quantify geometric fracture permeability/conductivity distributions conditioned to multi-slug proppant dynamics. Following its validation against experimental measurements and field-scale observations, a sensitivity analysis of 14 scenarios is performed. Proppant transport is found to be highly path-dependent, and dynamic fluid property scheduling produces more spatially uniform conductivity architectures than constant scheduling within the studied cases. A sequential injection of larger particles followed by smaller ones generates a foundational dune that facilitates transport of subsequent particles, yielding more favourable conductivity architectures than the reverse sequence within the studied parameter ranges. Overall, the proposed framework enables field-scale evaluation of multi-slug proppant transport dynamics and spatially variable conductivity in a propagating fracture by addressing several limitations (e.g., a single particle size, constant fluid viscosity, isotropic formation stress and fixed fracture dimensions) that were normally assumed with conventional models.