Lagrangian Numerical Simulation of Proppant Transport in Channel Fracturing

Abstract

This paper focuses on the numerical simulation of particle (“proppant”) transport in channel fracturing, in which fiber-proppant fluid is pumped intermittently into hydraulic fractures, alternated with clean fluid pulses. The pulsed pumping protocol leads to heterogeneous/channelized proppant distribution in fractures, generating open flow channels with high conductivity. To understand the evolution of the channelized proppant distribution, we develop an efficient pseudo-3D multiphase particle-in-cell (P3D MP-PIC) method to simulate the proppant transport during the pumping process. Compared with the Eulerian-Eulerian (EE) models, the MP-PIC approach has higher accuracy in modeling particle-fluid and particle-particle interactions by tracing the particles in a Lagrangian fashion. Compared with the computational fluid dynamics-discrete element method (CFD-DEM), the MP-PIC method is more computationally efficient due to a parcel feature and the fast calculation of particle forces. Reduced from the 3D MP-PIC method, the P3D MP-PIC method has better computational efficiency and flexibility to couple with other subsurface processes (e.g., fracture propagation and fluid leakoff) while also achieving sufficient accuracy for engineering purposes. Due to the Eulerian-Lagrangian (EL) nature, the P3D MP-PIC method can track the trajectories of the fiber-proppant clusters whose effective viscosity and the settling velocity are determined based on the laboratory results. With an accurate description of fluid and particle dynamics, this work reveals the critical physical mechanisms of the proppant transport in channel fracturing: stable displacement and Saffman-Taylor (ST) instability. The alternate occurrence of these two mechanisms gives rise to the channelized proppant distribution. To investigate the influential factors of the channel patterns, we conduct parametric studies on the operational parameters, including injection rate, fiber concentration, and pulsing mode. The effect of fracture propagation and gravitational settling is also discussed in detail.