Power-averaging method to characterize and upscale permeability in DFNs

Abstract:

In a lot of geological environments, permeability is dominated by the existence of fractures and by their degree of interconnections. Flow properties depend mainly on the statistical properties of the fracture population (length, apertures, orientation), on the network topology, as well as on some detailed properties within fracture planes. None of them can be a priori discarded as fracture networks are potentially close to some percolation threshold. Still, most details are strongly homogenized by the inherent diffusive nature of flows. It should thus be possible to upscale permeability on the basis of a limited number of descriptors.

Based on an extensive analysis of 2D and 3D DFNs as well as on reference connectivity structures, we investigate the relation between the local fracture structures and the effective permeability. On one hand poor connectivity, small intersections and fracture closures limit permeability. If these patterns control flow, permeability would derive from a suite of fracture in series dominated by its weakest element. Effective permeability could then be approached by the harmonic mean of the local permeabilities. On the other hand, extended fractures and locally higher fracture densities, enhance permeability. If these patterns control flow, all fractures would take equally part to flow and effective permeability would tend to the arithmetic mean of the local permeabilities.

Defined as the relative weight between the two extreme harmonic and arithmetic means, the power-law averaging exponent gives a compact way to compare fracture network hydraulics. It may further lead to some comprehensive upscaling rules. Permeability is not only determined by global connectivity but also by more local effects. We measure them by defining a local connectivity index equal to the number of fracture connections at some reference local scale. Knowledge of the relative local to global effects should help optimizing characterization strategies.