Geometrical heterogeneities and permeability anisotropy of rough fractures

We develop a numerical model for describing a single phase viscous flow in a rough fracture and compare it successfully to previously-published experimental results. The aperture fluctuations are introduced as an isotropic self-affine fractal which includes geometrical heterogeneities, especially at the fracture scale. The model is based oil the lubrication approximation and solutions are obtained from two independent numerical schemes. The curves describing the evolution of the hydraulic aperture as a function of the mean fracture separation are shown to be well fitted by power law functions. A grid rotation technique is developed to explore the influence of the pressure drop orientation over a continuous range of orientations. A single fracture is shown to be either flow enhancing or flow inhibiting by comparison to a parallel plate model of identical mean separation, depending on the pressure drop orientation. This anisotropy of the fluid flow results from the geometrical heterogeneities at the fracture scale. Statistical analyses of the results when exploring different apertures distributions with the same measured scale invariance property show a large variability of the permeability, which is due to the same phenomenon. A prediction of the hydraulic transmittivity that takes account of the pressure drop orientation is proposed.