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[1] We examine three stochastic transport models of the Macrodispersion Experiment (MADE) site using high-resolution conductivity fields derived from a new geostatistical interpretation of the flowmeter data. Evaluation of the spatial continuity of the hydraulic conductivity data revealed a hole effect structure indicating the occurrence of periodic structures, i.e., clustered lenses or facies. Alternatively, we examine geostatistical models based on indicator variables and found a similarity to bivariate Gaussian properties. Tritium transport was simulated in kriged fields and in random fields generated using different geostatistical models, at a grid spacing equal to the vertical support scale of the flowmeter measurements to explicitly represent small-scale heterogeneity. Only those simulations obtained using the hole effect model resulted in a subset of realizations which reproduced the strong anomalous tracer spreading. Neglecting the hole effect structure of the spatial model in the Gaussian simulations resulted in a reduced tailing of the tracer, illustrating the importance of preferential flow on anomalous solute transport at the Columbus aquifer. Furthermore, we found that a multivariate Gaussian random function is adequate to model the spatial distribution of hydraulic conductivity at the MADE site, based on the results of the indicator transport simulations and the univariate and bivariate normality detected in the analysis of the flowmeter data. We conclude that, when small-scale variability of hydraulic conductivity is correctly modeled at the flowmeter measurement support scale, the ADE is capable of reproducing the tracer spreading. Results suggest that the main contributor to the operational ''memory function'' used in previous successful mass transfer models is mostly a reflection of the suppressed spatial variation of hydraulic conductivity at the model scale.

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 (phi), 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.

[1] We provide a quantitative interpretation of the column experiment reported by Gramling et al. (2002). The experiment involves advection-dominated transport in porous media of three dissolved species, i.e., two reactants undergoing a fast irreversible reaction and the resulting product. The authors found that their observations could not be properly fitted with a model based on an advection-dispersion-reaction equation (ADRE) assuming the reaction was instantaneous, the actual measured total reaction product being lower than predictions for all times. The data have been recently well reproduced by Edery et al. (2009Edery et al. ( , 2010) by means of a particle tracking approach in a continuous time random walk framework. These and other authors have questioned the use of partial differential equation (PDE)-based approaches to quantify reactive transport because of the difficulty in capturing local-scale mixing and reaction. We take precisely this approach and interpret the experiments mentioned by means of a continuum-scale model based on the ADRE. Our approach differs from previous modeling attempts in that we imbue effects of incomplete mixing at the pore scale in a time-dependent kinetic reaction term and show that this model allows quantitative interpretation of the experiments in terms of both reaction product profiles and time-dependent global production rate. The time dependence of the kinetic term presented accounts for the progressive effects of incomplete mixing due to pore-scale rate-limited mass transfer, and follows a power law, which is consistent with the compilation of existing experiments reported by Haggerty et al. (2004). Our interpretation can form the basis for further research to assess the potential use of PDE approaches for the interpretation of reactive transport problems in moderately heterogeneous media.Citation: Sanchez-Vila, X., D. Fernàndez-Garcia, and A. Guadagnini (2010), Interpretation of column experiments of transport of solutes undergoing an irreversible bimolecular reaction using a continuum approximation, Water Resour.

[1] The complexity of mass transfer processes often complicates solute transport simulations. We present a new approach for the implementation of the multirate mass transfer model into random walk particle tracking. This novel method allows for a spatially heterogeneous distribution of mass transfer coefficients as well as hydrodynamic parameters in three dimensions, and it is well suited for avoiding numerical dispersion and solving computationally demanding transport simulations. For this purpose the normalized zeroth spatial moments of the multirate transport equations are derived and used as phase transition probabilities. Performing a simple Bernoulli trial on the appropriate phase transition probabilities the particle distribution between the mobile domain and any immobile domain can be determined. The approach is compared satisfactorily to analytical and semianalytical solutions for one-dimensional, advectivedispersive transport with different types of mass transfer. Aspects of the numerical implementation of this approach are presented, and it is demonstrated that two restrictive criteria for the time step size have to be considered. By adjusting the time step size for each grid cell on the basis of the cell specific velocity field and mass transfer rate a correct simulation of solute transport is assured, while at the same time computational efficiency is preserved. Finally, an example is presented evaluating the effect of a heterogeneous intraparticle pore diffusion in a synthetic aquifer. The results demonstrate that for this specific case the heterogeneous distribution of mass transfer rates does not have a significant influence on mean solute transport behavior but that at low concentration ranges, differences between the different mass transfer models become visible.