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.

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We study the applicability of a model order reduction technique to the solution of transport of passive scalars in homogeneous and heterogeneous porous media. Transport dynamics are modeled through the advection-dispersion equation (ADE) and we employ Proper Orthogonal Decomposition (POD) as a strategy to reduce the computational burden associated with the numerical solution of the ADE. Our application of POD relies on solving the governing ADE for selected times, termed snapshots. The latter are then employed to achieve the desired model order reduction. We introduce a new technique, termed Snapshot Splitting Technique (SST), which allows enriching the dimension of the POD subspace and damping the temporal increase of the modeling error. Coupling SST with a modeling strategy based on alternating over diverse time scales the solution of the full numerical transport model to its reduced counterpart allows extending the benefit of POD over a prolonged temporal window so that the salient features of the process can be captured at a reduced computational cost. The selection of the time scales across which the solution of the full and reduced model are alternated is linked to the Péclet number (P e), representing the interplay between advective and dispersive processes taking place in the system. Thus, the method is adaptive in space and time across the heterogenous structure of the domain through the combined use of POD and SST and by way of alternating the solution of the full and reduced models. We find that the width of the time scale within which the PODbased reduced model solution provides accurate results tends to increase with decreasing P e. This suggests that the effects of local scale dispersive processes facilitate the POD method to capture the salient features of the system dynamics embedded in the selected snapshots. Since the dimension of the reduced model is much lower than that of the full numerical model, the methodology we propose enables one to accurately simulate transport at a markedly reduced computational cost.

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