Abstract

A usual method to obtain aquifer parameters is to analyze the moments of the breakthrough curves (BTCs) in tracer tests. The parameters to be estimated in this analysis would depend on the conceptual model adopted. Intuitively, if different processes were considered, the shape of the BTCs should be quite different, and one would tend to think that the time and space evolution of the temporal moments should also be quite different. Contrarily, in this paper, we show that two very different conceptual models of solute transport lead to virtually identical moments of the BTC. The two models selected for this study are the classical advection–dispersion equation with a Fickian macrodispersive term and a homogeneous medium advection model with mass-transfer between mobile and immobile matrix phases, for three different models of matrix shape. In both models, the first three moments are linear with travel distance, while the fourth moment is a second order polynomial. This agreement allows us to choose parameters yielding the same moments in the two models. As we consider two fitting parameters, we select them to match the second and third moment. Match in the first moment is obtained from physical arguments. It turns out that the resulting leading term of the fourth moment is identical for both models. As a direct consequence of this work, it follows that for large travel distances it would not be possible to discriminate between conceptual models using data from a single BTC.

Abstract

We analyze the relative importance of the selection of (1) the geostatistical model depicting the structural heterogeneity of an aquifer, and (2) the basic processes to be included in the conceptual model, to describe the main aspects of solute transport at an experimental site. We focus on the results of a forced-gradient tracer test performed at the “Lauswiesen” experimental site, near Tübingen, Germany. In the experiment, NaBr is injected into a well located 52 m from a pumping well. Multilevel breakthrough curves (BTCs) are measured in the latter. We conceptualize the aquifer as a three-dimensional, doubly stochastic composite medium, where distributions of geomaterials and attributes, e.g., hydraulic conductivity (K) and porosity (ϕ), can be uncertain. Several alternative transport processes are considered: advection, advection–dispersion and/or mass-transfer between mobile and immobile regions. Flow and transport are tackled within a stochastic Monte Carlo framework to describe key features of the experimental BTCs, such as temporal moments, peak time, and pronounced tailing. We find that, regardless the complexity of the conceptual transport model adopted, an adequate description of heterogeneity is crucial for generating alternative equally likely realizations of the system that are consistent with (a) the statistical description of the heterogeneous system, as inferred from the data, and (b) salient features of the depth-averaged breakthrough curve, including preferential paths, slow release of mass particles, and anomalous spreading. While the available geostatistical characterization of heterogeneity can explain most of the integrated behavior of transport (depth-averaged breakthrough curve), not all multilevel BTCs are described with equal success. This suggests that transport models simply based on integrated measurements may not ensure an accurate representation of many of the important features required in three-dimensional transport models.

Abstract

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.