Numerical Simulation of Proppant Migration in Fractal Fractures during Fracturing Fluid Flowback

A particle-tracing method is proposed to investigate proppant reflux phenomena in hydraulically induced fractures at the mesoscale during fracturing fluid flowback. The fractures with fractal features were generated based on the Weierstrasse–Mandelbrot function. The process of fracturing fluid flowback was simulated by the steady Navier–Stokes equation and solved using the finite element method. In contrast, proppant migration is described by the Lagrangian method called particle tracing, in which particles are treated as discrete entities that can interact with fluid flow fields and boundaries in the surrounding geometry. A set of equations from Newton’s second law of motion are solved in the time domain to obtained particle trajectories. The approach was then employed to investigate the fluid flow characteristic within the rough fractures and the effects of rough fracture surfaces on proppant particles migration. The results indicate that the presented model can be employed to investigate the interaction between fracturing fluid and proppant particles. Fracture roughness can remarkably alter the trajectories of proppant particles, thus affecting proppant reflux.