Direct numerical simulation of proppant transport in hydraulic fractures with the immersed boundary method and multi-sphere modeling

In this paper, a resolved CFD-DEM method based on the immersed boundary method is proposed to simulate the proppant transport process, which is a multi-phase problem with strong fluid-particle coupling mechanisms in the oil and gas industry. A multi-sphere model is integrated into this method to describe complex particle shapes, in which Lagrangian points uniformly distributed on the particle surface are efficiently utilized for solving particle-particle interactions. This approach is validated by several benchmarks, including single-sphere and two-sphere settling tests. A modified driving pressure gradient is also adopted to satisfy bulk velocity constraints for simulating particle settling problems in periodic channels. Transport and settling behaviors of hundreds of sphere and cylinder proppant particles in periodic narrow channels with different widths are investigated, and settling laws and apparent viscosity models for proppant clouds with different shapes are then extracted from the simulation results. Benefiting from the features of multi-sphere modeling, this approach is demonstrated to be both robust and efficient for simulating fluid-particle coupling flow with complex particle shapes.