No-Flow Fraction (NFF) Permeability Model for Rough Fractures Under Normal Stress

Abstract

Flow through rock fractures is frequently represented using models that correct the cubic law to account for the effects of roughness and contact area. However, the scope of such models is often restricted to relatively smooth aperture fields under small confining stresses. This work studies the link between fracture permeability and fracture geometry under normal loads. Numerical experiments are performed to deform synthesized aperture fields of various correlation lengths and roughness values under normal stress. The results demonstrate that aperture roughness can more than triple for applied stresses up to 50 MPa – exceeding the valid range for roughness in most previously published models. Investigating the relationship between permeability and contact area indicates that the increase in flow obstructions due to the development of new contact points strongly depends on the correlation length of the unloaded aperture field. This study eliminates these dependencies by employing a parameter known as the No-Flow Fraction (NFF) to capture the effect of flow stagnation zones. With this concept, a new Cubic-law-based permeability model is proposed that significantly improves the accuracy of permeability estimations, compared to previous models. For cases, where the NFF is difficult to obtain, we introduce an empirical relationship to estimate the parameter from the aperture roughness. The new models yield permeability estimates accurate to within a factor of 2 of the simulated permeability in over three-quarters of the 3,000 deformed fractures studied. This compares with typical deviations of at least one order of magnitude for previously published permeability models.