Depth-averaged Lattice Boltzmann and Finite Element methods for single-phase flows in fractures with obstacles

We use Lattice Boltzmann Method (LBM) MRT and Cumulant schemes to study the performance and accuracy of single-phase flow modeling for propped fractures. The simulations are run using both the two- and three-dimensional Stokes equations, and a 2.5D Stokes-Brinkman approximate model. The LBM results are validated against Finite Element Method (FEM) simulations and an analytical solution to the Stokes-Brinkman flow around an isolated circular obstacle. Both LBM and FEM 2.5D Stokes-Brinkman models are able to reproduce the analytical solution for an isolated circular obstacle. In the case of 2D Stokes and 2.5D Stokes-Brinkman models, the differences between the extrapolated fracture permeabilities obtained with LBM and FEM simulations for fractures with multiple obstacles are below 1%. The differences between the fracture permeabilities computed using 3D Stokes LBM and FEM simulations are below 8% . The differences between the 3D Stokes and 2.5 Stokes-Brinkman results are less than 7% for FEM study, and 8% for the LBM case. The velocity perturbations that are introduced around the obstacles are not fully captured by the parabolic velocity profile inherent to the 2.5D Stokes-Brinkman model.