Random fracture networks: percolation, geometry and flow
Abstract:This paper reviews some of the basic properties of fracture networks. Most of the data can only be derived numerically, and to be useful they need to be rationalized, i.e., a large set of numbers should be replaced by a simple formula which is easy to apply for estimating orders of magnitude.
Three major tools are found useful in this rationalization effort. First, analytical results can usually be derived for infinite fractures, a limit which corresponds to large densities. Second, the excluded volume and the dimensionless density prove crucial to gather data obtained at intermediate densities. Finally, shape factors can be used to further reduce the influence of fracture shapes.
Percolation of fracture networks is of primary importance since this characteristic controls transport properties such as permeability. Recent numerical studies for various types of fracture networks (isotropic, anisotropic, heterogeneous in space, polydisperse, mixture of shapes) are summarized; the percolation threshold rho is made dimensionless by means of the excluded volume. A general correlation for rho is proposed as a function of the gyration radius.
The statistical characteristics of the blocks which are cut in the solid matrix by the network are presented, since they control transfers between the porous matrix and the fractures. Results on quantities such as the volume, surface and number of faces are given and semi empirical relations are proposed.
The possible intersection of a percolating network and of a cubic cavity is also summarized. This might be of importance for the underground storage of wastes. An approximate reasoning based on the excluded volume of the percolating cluster and of the cubic cavity is proposed.
Finally, consequences on the permeability of fracture networks are briefly addressed. An empirical formula which verifies some theoretical properties is proposed.