Permeability, porosity, and percolation properties of two-dimensional disordered fracture networks.

Using extensive Monte Carlo simulations, we study the effective permeability, porosity, and percolation properties of two-dimensional fracture networks in which the fractures are represented by rectangles of finite widths. The parameters of the study are the width of the fractures and their number density. For low and intermediate densities, the average porosity of the network follows a power-law relation with the density. The exponent of the power law itself depends on the fractures' width through a power law. For an intermediate range of the densities, the effective permeability scales with the fractures' width as a power law, with an exponent that depends on the density. For high densities the effective permeability also depends on the porosity through a power law, with an exponent that depends on the fractures' width. In agreement with the results, experimental data also indicate the existence of a power-law relationship between the effective permeability and porosity in consolidated sandstones and sedimentary rocks with a nonuniversal exponent. The percolation threshold or critical number density of the fractures depends on their width and is maximum if they are represented by squares, rather than rectangles.