A review on numerical simulation of proppant transport: Eulerian–Lagrangian views

Proppant transport is a very important topic in hydraulic fracturing, having a direct influence on the production performance of hydraulically fractured wells. An accurate and in-depth understanding of transport behavior and placement characteristics of proppants is crucial. Owing to great advances in computer science and technology, numerical simulation has become a practical and powerful tool for proppant transport study. Eulerian–Lagrangian and Eulerian–Eulerian methods are two commonly used numerical methods. Between them, Eulerian–Lagrangian methods have received more attention because they retain the discreteness of particles and can achieve higher resolution at the level of the particle phase. Eulerian–Lagrangian methods that have been commonly used in the numerical study of proppant transport include the dense discrete phase model, coupled computational fluid dynamics and discrete element method, and multiphase particle-in-cell method. In this study, a review on numerical simulations of proppant transport based on the Eulerian–Lagrangian methods is presented. First, some important mechanisms (e.g., hydrodynamic drag, particle–particle and particle–wall interactions, and gravitational settling) dominating the proppant transport process are introduced and discussed. Then, the basic ideas and research progress of the above Eulerian–Lagrangian methods are presented. Lastly, the current challenges facing Eulerian–Lagrangian methods in proppant transport simulation are summarized.