Minimum Hydraulic Resistance Uncertainty and the Development of a Connectivity-Based Iterative Sampling Strategy

The presence of well-connected paths is commonly observed in spatially heterogeneous porous formations. Channels consisting of high hydraulic conductivity (K) values strongly affect fate and transport of dissolved species in the subsurface environment. Several studies have established a correlation between connectivity properties of the spatially variable K-field and solute first arrival times. However, due to limited knowledge of the spatial structure of the K-field, connectivity metrics are subject to uncertainty. In this work, we utilize the concept of the minimum hydraulic resistance and least resistance path to evaluate the connectivity of a K-field in a stochastic framework. We employ a fast graph theory-based algorithm to alleviate the computational burden associated with stochastic computations in order to investigate both the impact of the hydrogeological structural conceptualization and domain dimensionality (2-D vs. 3-D) on the uncertainty of the minimum hydraulic resistance. Finally, we propose an iterative data acquisition strategy that can be utilized to identify the least resistance path (which is linked to preferential flow channels) in real sites. A synthetic benchmark test is presented, showing the advantages of the proposed sampling strategy when compared to a regular sampling strategy. By using the iterative data sampling strategy, we were able to reduce first arrival time uncertainty by 47% (when compared to the regular sampling strategy), while maintaining site characterization efforts constant.