Anomalous transport in advection‐dominated convergent flow tracer tests can occurs due to small‐scale heterogeneities in aquifer hydraulic properties. These result in fluctuations of the groundwater velocity field and complex connectivity patterns between injection and extraction wells. While detailed characterization of heterogeneity is often not possible in practice, a proper understanding of what fundamental physical mechanisms can give rise to macroscopic behaviors that are measurable is essential for proper upscaling of solute transport processes. We analyze here how heavy‐tailed breakthrough curves can arise in radially convergent flow to a well. The permeability fields are three‐dimensional multi‐Gaussian fields with varying statistical geometry and degrees of heterogeneity. We consider transport of conservative tracers from multiple injection locations by varying distance and angle from the extraction well. Anomalous power law tailing in breakthrough curves is attributed to a variety of features including the initial vertical stratification of the solute that arises due to a flux‐weighted injection, the injection distance to the well relative to the depth of the aquifer, and the statistics of the heterogeneity field as defined by the correlation length and variance of the permeability. When certain conditions cooccur for a given injection, such as strong connectivity contrasts between aquifer layers, injection distances comparable to the horizontal heterogeneity integral scales, and large global variances, breakthrough curves tend to scale as a PL with unit slope at late time. These findings offer new insights to understand what physical processes must be understood to develop and choose appropriate upscaling approaches that might reproduce such anomalous transport in heterogeneous advection‐dominated systems.

The recently introduced geological entropy concept evaluates spatial order/disorder in the structure of the hydraulic conductivity (K) field to explain and predict certain characteristics of transport behavior. This concept is expanded in this work by introducing a novel tool for spatial analysis called entrogram from which a metric called entropic scale (H_S) can be calculated to measure the overall persistency of patterns of spatial association in a distributed field and to allow robust comparisons between different spatial structures. The entrogram and the entropic scale concepts are applied here to investigate the link between solute transport behavior and the spatial structure of K fields modeled as the distribution of three hydrofacies in alluvial aquifers. Accurate empirical relationships are found between H_S and key transport quantities confirming the clear correlation between transport and the structure of the K field described in terms of its entropic scale. The entrogram analysis is also applied to continuous 2‐D and 3‐D fields having identical lognormal K distributions, but with different connectivity. Comparisons between the entrograms and the calculated H_S values for these fields, as well as for their corresponding flow velocity distributions, shed light on the key differences among these structures in 2‐D and in 3‐D, which in turn explain their dissimilar impact on solute transport. The entrogram‐based interpretation of the transport simulations seems to confirm that the geological entropy is a promising approach for predicting solute transport behavior simply from a description of the K field heterogeneity.

Aquifer hydraulic properties such as hydraulic conductivity (K) are ubiquitously heterogeneous and typically only a statistical characterization can be sought. Additionally, statistical anisotropy at typical characterization scales is the rule. Thus, regardless of the processes governing solute transport at the local (pore) scale, transport becomes non‐Fickian. Mass‐transfer models provide an efficient tool that reproduces observed anomalous transport; in some cases though, these models lack predictability as model parameters cannot readily be connected to the physical properties of aquifers. In this study, we focus on a multirate mass‐transfer model (MRMT), and in particular the apparent capacity coefficient (β), which is a strong indicator of the potential of immobile zones to capture moving solute. We aim to find if the choice of an apparent β can be phenomenologically related to measures of statistical anisotropy. We analyzed an ensemble of random simulations of three‐dimensional log‐transformed multi‐Gaussian permeability fields with stationary anisotropic correlation under convergent flow conditions. It was found that apparent β also displays an anisotropic behavior, physically controlled by the aquifer directional connectivity, which in turn is controlled by the anisotropic correlation model. A high hydraulic connectivity results in large β values. These results provide new insights into the practical use of mass‐transfer models for predictive purposes.

We analyzed the behavior of convergent flow tracer tests performed in a 3‐D heterogeneous sandbox in presence of connected gravel channels under laboratory‐controlled conditions. We focused on the evaluation of connectivity metrics based on characteristic times calculated from experimental breakthrough curves (BTCs), and the selection of upscaling model parameters related to connectivity. A conservative compound was injected from several piezometers in the box, and depth‐integrated BTCs were measured at the central pumping well. Results show that transport was largely affected by the presence of gravel channels, which generate anomalous transport behavior such as BTC tailing and double peaks. Connectivity indicators based on BTC peak times provided better information about the presence of connected gravel channels in the box. One of these indicators, β, was defined as the relative temporal separation of the BTCs peaks from the BTCs centers of mass. The mathematical equivalence between β and the capacity coefficient adopted in mass transfer‐based formulations suggests how connectivity metrics could be directly embedded in mass transfer formulations. This finding is in line with previous theoretical studies and was corroborated by reproducing a few representative experimental BTCs using a 1‐D semianalytical bimodal solution embedding a mass transfer term. Model results show a good agreement with experimental BTCs when the capacity coefficient was constrained by measured β. Models that do not embed adequate connectivity metrics or do not adequately reproduce connectivity showed poor matching with observed BTCs.