Combined effects of connectivity and heterogeneity on effective hydraulic conductivity of simulated fracture systems subjected to different types of flow

We use 2-D Monte Carlo simulations to explore how different flow types (radial and unidirectional) may lead to different characterisations of connectivity and heterogeneity in fracture networks based on the same fracture geometry and statistics. The percolation theory is applied to examine the behaviour of discrete fracture networks with fracture densities that range between the percolation threshold and the correlation density, where the geometric configuration of the fracture network may lead to scale-dependence of physical parameters, including the effective hydraulic conductivity. Fractures with a power law length distribution are generated randomly without spatial correlation. Steady-state flow simulations are then conducted based on the resultant percolating backbones. The results show interesting differences between systems based on the same fracture geometry but undergoing different types of flows, especially near the percolation threshold. A power law scaling behaviour exists near the critical density for the radial flow but not for the unidirectional flow. In other words, the results show that near the percolation threshold, fracture connectivity is also a function of the flow type. This brings into question the applicability of aquifer pump test parameters (derived from radial flow geometry) for modelling flow conditions that are not radial. The results also suggest that the seemingly contrasting scaling effects with respectively decreasing and increasing trends of effective hydraulic conductivity in the power law with scale reported in the literature could be a reflection of the fracture density status (i.e., networks near the percolation threshold experience the former effect and those significantly above the threshold experience the latter effect).