Percolation of Fracture Networks and Stereology

The overall properties of fractured porous media such as permeability and transport depend on the percolative character of the fracture network.

A very wide range of regular, irregular and random fracture shapes is considered, in monodisperse or polydisperse networks containing fractures with different shapes and/or sizes. A simple and new model involving a dimensionless density and a new shape factor is proposed for the percolation threshold rho_c, which accounts very efficiently for the influence of the fracture shape. It applies with very good accuracy to monodisperse or moderately polydisperse networks, and provides a good first estimation in other situations. A polydispersity index is shown to control the need for a correction, and the corrective term is modelled for the investigated size distributions.

Moreover, and this is practically crucial, the relevant quantities in rho_c can all be determined from trace maps. An exact and complete set of relations can be derived when the fractures are assumed to be Identical, Isotropically Oriented and Uniformly Distributed (I²OUD). Therefore, the dimensionless density of such networks can be derived directly from the trace maps and its percolating character can be a priori predicted.

Since these relations involve the first five moments of the trace lengths, truncation effect due to the boundaries of the sampling domain can be important. However, it can be shown that this effect can be exactly corrected, for any fracture shape, size and orientation distributions, if the fractures are UD.

Systematic applications are made to real fracture networks and to numerically simulated networks. Possible extension to networks which are not I²OUD are examined.