Lubrication theory analysis of the permeability of rough-walled fractures

The flow of a fluid between the rough surfaces of a rock fracture is very complex, due to the tortuous paths followed by the fluid particles. Exact analytical modeling of these flows is made difficult by the irregular geometry of rock fracture surfaces, while full three-dimensional numerical simulations of these flows are as yet still impractical. To overcome the difficulties of working with the three-dimensional Navier-Stokes equations, the simpler Reynolds lubrication equation has sometimes been used to model flow in fractures. This paper focuses on two aspects of lubrication theory. First, lubrication theory is applied to two simplified aperture profiles, sinusoidal and sawtooth, and analytical expressions are found for the permeabilities. These results are then compared with numerical results obtained by solving the lubrication equation for fractures with random surfaces. Secondly, the validity of the lubrication equations for modeling flow in rough fractures is studied by examining higher-order perturbation solutions, as well as numerical solutions, to the Navier-Stokes equations for flow in fractures with sinusoidally-varying apertures. 22 refs., 6 figs