Smoothed particle hydrodynamics simulation of fluid flow in rock fractures

The process of fluid flow in rock fractures involves complicated dynamical behavior of fluids, and its modeling is a challenge to numerical methods. In this paper, the Smoothed Particle Hydrodynamics (SPH), a particle method based on Lagrangian formulation, is employed to simulate the fluid flow in rock fractures by solving the Navier-Stokes equations directly. Firstly, the SPH method and the boundary treatment method used in this simulation were introduced and the computer code of SPH was developed and validated by a series of numerical benchmark tests with analytical solutions. Then simulations were carried out to investigate the fluid flow both in single fractures and intersected fractures, with and without considering effects of surface roughness. The results of the simulations are discussed and compared with the analytical solution by using the Cubic law derived from the Reynolds equation. The results show that in both of rough single fractures and fracture intersections, although the relationship between mean velocity and the Reynolds number is still linear, the solutions by using Cubic law overestimated the mean fluid velocity with increasing the Reynolds number, indicating possible underestimate of travel time of mass transport in the fracture network models.