Power-averaging method to characterize and upscale permeability in DFNs

International audienceIn a lot of geological environments, permeability is dominated by the existence of fractures and bytheir degree of interconnections. Models have shown that flow properties depends mainly on thestatistical properties of the fracture population (length, apertures, orientation) and of intersections,on the topological properties of the network, as well as on some detailed properties within fractureplanes. None of them can be a priori discarded as fracture networks are potentially close to somepercolation threshold. Still, most of the details of the fracture and network structures are stronglyhomogenized by the inherent diffusive nature of flows. It should thus be possible to upscalepermeability on the basis of a limited number of descriptors.Based on an extensive analysis of 2D and 3D Discrete Fracture Networks (DFNs) as well as onreference connectivity structures, we investigate the relation between the local fracture structuresand the effective permeability. On the one hand, poor connectivity, small intersections, andfracture closures act as bottlenecks and obstacles limit permeability. If these patterns controlledthe flow, permeability would derive from an ensemble of fracture in series dominated by itsweakest element. Effective permeability could then be approached by the harmonic mean of thelocal permeabilities. On the other hand, extended fractures, locally higher fracture densities, andpreferential orthogonal fracture orientations enhance permeability. If these patterns controlled theflow, all fractures would contribute to flow equally, and effective permeability would tend to thearithmetic mean of the local permeabilities.Defined as the relative weight between the two extreme harmonic and arithmetic means, thepower-law averaging exponent provids a compact way of comparing fracture network hydraulics.It may further lead to some comprehensive upscaling rules. To this end, we determinenumerically the power-law averaging exponent for a wide range of 2D and 3D DFNs [de Dreuzyet al., 2012; de Dreuzy et al., 2001] and compare them to reference connectivity structures andpermeability fields [de Dreuzy et al., 2010]. Permeability is not only determined by globalconnectivity but also by more local effects. We measure them by defining a local connectivityindex equal to the number of fracture connections at some reference local scale. Knowledge ofthe relative importance of local vs. global effects should help optimizing characterizationstrategies