Lattice Boltzmann simulation of fluid flow in fracture networks with rough, self-affine surfaces

Using the lattice Boltzmann method, we study fluid flow in a two-dimensional (2D) model of fracture network of rock. Each fracture in a square network is represented by a 2D channel with rough, self-affine internal surfaces. Various parameters of the model, such as the connectivity and the apertures of the fractures, the roughness profile of their surface, as well as the Reynolds number for flow of the fluid, are systematically varied in order to assess their effect on the effective permeability of the fracture network. The distribution of the fractures' apertures is approximated well by a log-normal distribution, which is consistent with experimental data. Due to the roughness of the fractures' surfaces, and the finite size of the networks that can be used in the simulations, the fracture network is anisotropic. The anisotropy increases as the connectivity of the network decreases and approaches the percolation threshold. The effective permeability K of the network follows the power law K approximately (beta), where is the average aperture of the fractures in the network and the exponent beta may depend on the roughness exponent. A crossover from linear to nonlinear flow regime is obtained at a Reynolds number Re approximately O(1), but the precise numerical value of the crossover Re depends on the roughness of the fractures' surfaces.