Power-averaging method to characterize and upscale permeability in DFNs

Jean-Raynald De Dreuzy (1) , Julien Maillot (1) , Caroline Darcel (2) , Philippe Davy (1) , Yves Méheust (1) , Géraldine Pichot (3)

1 GR - Géosciences Rennes
2 Itasca Consultants
3 SAGE - Simulations and Algorithms on Grids for Environment

In a lot of geological environments, permeability is dominated by the existence of fractures and by their degree of interconnections. Models have shown that flow properties depends mainly on the statistical 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 fracture planes. None of them can be a priori discarded as fracture networks are potentially close to some percolation threshold. Still, most of the details of the fracture and network structures 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 Discrete Fracture Networks (DFNs) as well as on reference connectivity structures, we investigate the relation between the local fracture structures and the effective permeability. On the one hand, poor connectivity, small intersections, and fracture closures act as bottlenecks and obstacles limit permeability. If these patterns controlled the flow, permeability would derive from an ensemble 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, locally higher fracture densities, and preferential orthogonal fracture orientations enhance permeability. If these patterns controlled the flow, all fractures would contribute to flow equally, 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 provids a compact way of comparing fracture network hydraulics. It may further lead to some comprehensive upscaling rules. To this end, we determine numerically the power-law averaging exponent for a wide range of 2D and 3D DFNs [de Dreuzy et al., 2012; de Dreuzy et al., 2001] and compare them to reference connectivity structures and permeability fields [de Dreuzy et al., 2010]. 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 importance of local vs. global effects should help optimizing characterization strategies.

Domaines: Géologie appliquée

Jean-Raynald De Dreuzy, Julien Maillot, Caroline Darcel, Philippe Davy, Yves Méheust, et al.. Power-averaging method to characterize and upscale permeability in DFNs. AGU Fall Meeting 2015, American Geophysical Union, Dec 2015, San Francisco, United States. pp.H53I-03. ⟨insu-01241866⟩