How Connected Is Connected? Structural Measures to Estimate Effective Conductivity

Abstract

Connectivity has been a target of investigation for subsurface hydrology for decades. We apply seven new and existing connectivity measures to 2-D, binary hydraulic conductivity (K) grids that include a range of percent high K mixtures. Effective conductivity (Keff) for 1-D flow through the domain is calculated from the results of flow simulation (MODFLOW) and compared with connectivity measures. In addition, characteristics of the percolating network (connected high K bodies that span entire domain) are investigated. Results indicate that most of the range of Keff (80%-90%) for approximately 1 million randomly generated grids over a range of percent high K mixtures only exists among percolating grids. We demonstrate that the number of unique percolating paths (NPP) is the most important structural feature for predicting Keff. We show that NPP can explain to a large degree the mean behavior of Keff as a function of percent high K material. It may also explain the variance of Keff as a function of percent high K, however this has not been shown conclusively. Most connectivity measures were not found to correlate with Keff. In general, it seems connectivity is only important for Keff when high and low K values are similar (one order of magnitude different). Therefore, the overall impact of connectivity is relatively small. The dependence of Keff on the continuity of high K paths suggests that methods that return volume-averaged properties (e.g. electrical resistivity tomography) may have limited ability to predict Keff. High resolution imagery or water isotopic tracer tests to infer structure may be necessary for accurate estimation of Keff.