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 experi mental results. The aperture fluctuations are introduced as an isotropic se lf-affine fractal which includes geometrical heterogeneities, especially at the fracture scale. The model is based oil the lubrication approximation a nd solutions are obtained from two independent numerical schemes. The curve s describing the evolution of the hydraulic aperture as a function of the m ean fracture separation are shown to be well fitted by power law functions. A grid rotation technique is developed to explore the influence of the pre ssure drop orientation over a continuous range of orientations. A single fr acture is shown to be either flow enhancing or flow inhibiting by compariso n to a parallel plate model of identical mean separation, depending on the pressure drop orientation. This anisotropy of the fluid flow results from t he geometrical heterogeneities at the fracture scale. Statistical analyses of the results when exploring different apertures distributions with the sa me measured scale invariance property show a large variability of the perme ability, which is due to the same phenomenon. A prediction of the hydraulic transmittivity that takes account of the pressure drop orientation is prop osed.