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The scope of this work is to discuss the proper choice of macrodispersion coefficients in modeling contaminant transport through the advection dispersion equation (ADE). It is common to model solute concentrations in transport by groundwater with the aid of the ADE. Spreading is quantified by macrodispersivity coefficients, which are much larger than the laboratory observed pore‐scale dispersivities. In the frame of stochastic theory, longitudinal macrodispersivity is related to the hydraulic conductivity spatial variability via its statistical moments (mean, variance, integral scales), which are generally determined by geostatistical analysis of field measurements. In many cases, especially for preliminary assessment of contaminant spreading, these data are not available and ad hoc values are adopted by practitioners. The present study aims at recommending dispersivity values based on a thorough analysis of tens of field experiments. Aquifers are classified as of weak, medium, and high heterogeneity and for each class a range of macrodispersivity values is recommended. Much less data are available for the transverse macrodispersivities, which are significantly smaller than the longitudinal one. Nevertheless, a few realistic values based on field data, are recommended for applications. Transport models using macrodispersivities can predict mean concentrations, different from the local ones. They can be used for estimation of robust measures, like plumes spatial moments, longitudinal mass distribution and breakthrough curves at control planes. Article impact statement: Practitioner's guideline on how to identify macrodispersivity for subsurface transport models from reliable field tracer tests. [ABSTRACT FROM AUTHOR]

Aquifer heterogeneity in combination with data scarcity is a major challenge for reliable solute transport prediction. Velocity fluctuations cause non-regular plume shapes with potentially long-tailing and/or fast-travelling mass fractions. High monitoring cost and a shortage of simple concepts have limited the incorporation of heterogeneity into many field transport models up to now. We present an easily applicable hierarchical conceptualization strategy for hydraulic conductivity to integrate aquifer heterogeneity into quantitative flow and transport modelling. The modular approach combines large-scale deterministic structures with random substructures. Depending on the modelling aim, the required structural complexity can be adapted. The same holds for the amount of monitoring data. The conductivity model is constructed step-wise following field evidence from observations, seeking a balance between model complexity and available field data. The starting point is a structure of deterministic blocks, derived from head profiles and pumping tests. Then, subscale heterogeneity in the form of random binary inclusions is introduced to each block. Structural parameters can be determined, for example, from flowmeter measurements or hydraulic profiling. As proof of concept, we implemented a predictive transport model for the heterogeneous MADE site. The proposed hierarchical aquifer structure reproduces the plume development of the MADE-1 transport experiment without calibration. Thus, classical advection–dispersion equation (ADE) models are able to describe highly skewed tracer plumes by incorporating deterministic contrasts and effects of connectivity in a stochastic way without using uni-modal heterogeneity models with high variances. The reliance of the conceptual model on few observations makes it appealing for a goal-oriented site-specific transport analysis of less well investigated heterogeneous sites. [ABSTRACT FROM AUTHOR]

A new method is presented which allows interpreting steady-state pumping tests in heterogeneous isotropic transmissivity fields. In contrast to mean uniform flow, pumping test drawdowns in heterogeneous media cannot be described by a single effective or equivalent value of hydraulic transmissivity. An effective description of transmissivity is required, being a function of the radial distance to the well and including the parameters of log-transmissivity: mean, variance, and correlation length. Such a model is provided by the upscaling procedure radial coarse graining, which describes the transition of near-well to far-field transmissivity effectively. Based on this approach, an analytical solution for a steady-state pumping test drawdown is deduced. The so-called effective well flow solution is derived for two cases: the ensemble mean of pumping tests and the drawdown within an individual heterogeneous transmissivity field. The analytical form of the solution allows inversely estimating the parameters of aquifer heterogeneity. For comparison with the effective well flow solution, virtual pumping tests are performed and analysed for both cases, the ensemble mean drawdown and pumping tests at individual transmissivity fields. Interpretation of ensemble mean drawdowns showed proof of the upscaling method. The effective well flow solution reproduces the drawdown for two-dimensional pumping tests in heterogeneous media in contrast to Thiem's solution for homogeneous media. Multiple pumping tests conducted at different locations within an individual transmissivity field are analysed, making use of the effective well flow solution to show that all statistical parameters of aquifer heterogeneity can be inferred under field conditions. Thus, the presented method is a promising tool with which to estimate parameters of aquifer heterogeneity, in particular variance and horizontal correlation length of log-transmissivity fields from steady-state pumping test measurements. [ABSTRACT FROM AUTHOR]

The knowledge of subsurface heterogeneity is a prerequisite to describe flow and transport in porous media. Of particular interest are the variance and the correlation scale of hydraulic conductivity. In this study, we present how these aquifer parameters can be inferred using empirical steady state pumping test data. We refer to a previously developed analytical solution of “effective well flow” and examine its applicability to pumping test data as under field conditions. It is examined how the accuracy and confidence of parameter estimates of variance and correlation length depend on the number and location of head measurements. Simulations of steady state pumping tests in a confined virtual aquifer are used to systematically reduce sampling size while determining the rating of the estimates at each level of data density. The method was then applied to estimate the statistical parameters of a fluvial heterogeneous aquifer at the test site Horkheimer Insel, Germany. We conclude that the “effective well flow” solution is a simple alternative to laboratory investigations to estimate the statistical heterogeneity parameter using steady state pumping tests. However, the accuracy and uncertainty of the estimates depend on the design of the field study. In this regard, our results can help to improve the conceptual design of pumping tests with regard to the parameter of interest. [ABSTRACT FROM AUTHOR]

Subsurface transport models are valuable tools to predict the behavior of solutes in groundwater, e.g. after a spill event or of controlled tracer experiments. Solute movement does not only depend on the mean flow velocity, but its spreading is strongly influenced by the spatially variable distribution of hydraulic conductivity i.e. on heterogeneity. The prevailing lack of transport data at the given site usually prevents model calibration. Thus, there is a need for predictive models based on knowledge of the subsurface structure. A multitude of aquifer heterogeneity conceptualizations exist, from deterministic hydraulic conductivity structures to stochastic and geostatistical approaches such as Multi-Gaussian or multi-indicator models. These concepts have been applied to model tracer distribution patterns of controlled field-scale transport experiments at a few sites. One of the critical questions is "How should transport models be compared to observed data?". There are multiple influencing factors and thus the method of comparing impinges on the outcome. We discuss significant aspects like: • What are meaningful indicators for a quantitative comparison? • What are pros and cons of a qualitative/visual comparison? • What is the impact of data preparation with regard to the scale (linear/log) and mass recovery? • What is the area of interest? Is the emphasis on predicting the mean, the peak concentration, the tail or the leading front? • Is the evaluation in time (BTC) or in space (mass distribution) the preferred mode? Given the different aspects of relevance, we emphasize that there is no straight forward way of comparing and the evaluation of models depends on the goal-orientation.To illustrate the issue we present examples from the MADE site. The aquifer is known to display a complex transport behavior which was monitored in detailed experiments. Multiple predictive transport models are available for the site with conductivity conceptualization ranging from deterministic to stochastic and geostatistical. The different concepts make use of the multitude of available data obtained by distinct methods like DPIL, litho-logs, pumping tests, or flowmeter logs. The comparison of predictive transport models for the MADE site provides valuable insights to merits and drawbacks of several hydraulic conductivity models given a specific goal-orientation. [ABSTRACT FROM AUTHOR]

• Random forest model is trained on hydrogeological dataset for aquitards. • Dominant factors are clay fraction, depth, geology, sedimentology and location. • Detailed grain size fractions and grain size percentiles do not improve the model. Aquitards are common hydrogeological features and their hydraulic conductivity is an important property for various groundwater management issues. Predicting their hydraulic conductivity proves challenging, given its dependence on numerous variables. In this study, the dominant factors for predicting aquitard hydraulic conductivity are identified. To this end, a random forest model is trained on a dataset consisting of more than 1000 hydraulic conductivity measurements of core-scale sediment samples from a wide range of stratigraphic units and depths in the Netherlands. The dataset contains textural properties, such as the grain size distribution and porosity, as well as structural data, such as location, sampling depth, stratigraphical unit, lithofacies, organic carbon content, carbonate content and groundwater chloride concentration. Results show that clay fraction, stratigraphic unit, depth, lithofacies and x-coordinate are the most important features for predicting the hydraulic conductivity. Here, x-coordinate is presumably a proxy for distance from marine influence. Using a more detailed grain size distribution or using derived parameters such as the grain size percentiles does not improve the model any further. Our findings indicate that structural properties play a significant role in predicting aquitard conductivity, as they serve as indicators of processes such as compaction and soft-sediment deformation. The model is furthermore an effective method to estimate hydraulic conductivity for sediment samples without conducting costly and time-consuming hydraulic conductivity measurements. [ABSTRACT FROM AUTHOR]