Dependence of percolation and flow properties of fracture networks on the morphology

Extensive experimental data have provided evidence that rock fractures have finite widths, and that their length is typically distributed according to some probability distribution function (PDF). Almost all the past modeling and computer simulation of fluid flow through fracture networks assumed that the fractures’ width is vanishingly small, and their length is constant. Using extensive Monte Carlo simulation and a model in which the fractures have a finite width and their length follows a PDF, we study the effect of the PDF on the effective permeability, the mean porosity, the excluded volume (area), and the percolation threshold of the network. Five PDFs of the fractures’ lengths, namely, uniform, Gaussian, log-normal, exponential, and power law, are considered, and their effect on the aforementioned properties of the fracture networks is studied. If the distributions are narrow, their effect on the properties of the fracture network is not strong. The effect is, however, quite strong when the PDFs are broad, which is also what experimental data indicate. Both the mean porosity and effective permeability depend on the fracture density as power laws, with exponents that are nonuniversal and depend on the width of the PDF, in agreement with many sets of experimental data reported in the literature.