Depth-averaged Lattice Boltzmann and Finite Element methods for single-phase flows in fractures with obstacles. (15th May 2018)

• Record Type: Journal Article
• Authors: Dzikowski, Michal; Jasinski, Lukasz; Dabrowski, Marcin
• Is Part Of: Computers & mathematics with applications. Volume 75:issue 10(2018)
• Page Start: 3453
• Page End: 3470
• Publication Date: 2018-05-15
• Subjects: FEM -- LBM -- Fracture flow -- Brinkman approximation; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.02.010
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: 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.