Minimum Hydraulic Resistance and Least Resistance Path in Heterogeneous Porous Media

The transport dynamics of a solute plume in porous media are strictly related to the hydrogeological properties. Despite progress in simulation techniques, quantifying transport in strongly heterogeneous geological formations is still a challenge. It is well established that the heterogeneity of the hydraulic conductivity (K) field is one of the main factors controlling solute transport phenomena. Increasing the heterogeneity level of the K-field will enhance the probability of having preferential paths, that are fundamental in predicting the first time arrivals. In this work, we focus on the relationship between the connectivity structure of the K-field to transport quantities. We compute connectivity based on the concept of hydraulic resistance and the corresponding least resistance paths. We present a new efficient algorithm based on graph theory that enables us to extract useful information from the K-field without resorting to the solution of the governing equations for flow and transport. For this reason, an exhaustive and fast analysis can be carried out using a Monte Carlo framework for randomly generated K-fields which allows the computation of the least resistance path and its uncertainty. We examine the minimum hydraulic resistance for both multi-Gaussian (MG) and non-MG log K-fields. The analysis carried out indicates that the expected value of the minimum hydraulic resistance between two points scales exponentially with the standard deviation of the log K-field. Given the strong correlation with plume's first time arrival, our results illustrate how hydraulic resistance and least resistance path can be used as a computationally efficient risk metric.