Simulations of solute transport in fractured porous media using 2D percolation networks with uncorrelated hydraulic conductivity fields

Two-dimensional percolation networks have been used to model a disordered and fractured porous medium. The advantage of percolation networks is that they allow the flow and transport properties of the system to be systematically studied as a function of the connectivity of the fractures and/or the permeable regions. The aim of this research is to study hydrodynamic dispersion in such networks, and to investigate the behavior of the longitudinal dispersion coefficient D-L with binary and log-normally distributed hydraulic conductivity fields. In particular, the study focuses on the behavior of D-L at the percolation threshold p, where the insufficiency of flow field homogenization and the limited number of tortuous paths for flow and transport force D-L to behave anomalously, i.e., to be scale- and time-dependent. The simulations indicate that the D-L population taken over a large number of the network realizations resembles a log-normal distribution, hence indicating that, unlike the hydraulic conductivity, D-L is not a self-averaged property whose variance should tend to zero when the size of the system tends to infinity. In addition, it was found that the power law that characterizes the scale dependence of D-L is contingent upon its computation method. Moreover, D-L is found to have a completely different behavior in networks with low and high connectivities.