Alraune Zech

Is unique scaling of aquifer macrodispersivity supported by field data

Spreading of conservative solutes in groundwater due to aquifer heterogeneity is quantified by the macrodispersivity, which was found to be scale dependent. It increases with travel distance, stabilizing eventually at a constant value. However, the question of its asymptotic behavior at very large scale is still a matter of debate. It was surmised in the literature that macrodispersivity scales up following a unique scaling law. Attempts to define such a law were made by fitting a regression line in the log-log representation of an ensemble of macrodispersivities from multiple experiments. The functional relationships differ among the authors, based on the choice of data. Our study revisits the data basis, used for inferring unique scaling, through a detailed analysis of literature marcodispersivities. In addition, values were collected from the most recent tracer tests reported in the literature. We specified a system of criteria for reliability and reevaluated the reliability of the reported values. The final collection of reliable estimates of macrodispersivity does not support a unique scaling law relationship. On the contrary, our results indicate, that the field data can be explained as a collection of macrodispersivities of aquifers with varying degree of heterogeneity where each exhibits its own constant asymptotic value. Our investigation concludes that transport, and particularly the macrodispersivity, is formation-specific, and that modeling of transport cannot be relegated to a unique scaling law. Instead, transport requires characterization of aquifer properties, e.g., spatial distribution of hydraulic conductivity, and the use of adequate models.

Debates—Stochastic subsurface hydrology from theory to practice: The relevance of stochastic subsurface hydrology to practical problems of contaminant transport and remediation. What is characterization and stochastic theory good for?

The emergence of stochastic subsurface hydrology stemmed from the realization that the random spatial variability of aquifer properties has a profound impact on solute transport. The last four decades witnessed a tremendous expansion of the discipline, many fundamental processes and principal mechanisms being identified. However, the research findings have not impacted significantly the application in practice, for several reasons which are discussed. The paper discusses the current status of stochastic subsurface hydrology, the relevance of the scientific results for applications and it also provides a perspective to a few possible future directions. In particular, we discuss how the transfer of knowledge can be facilitated by identifying clear goals for characterization and modeling application, relying on recent recent advances in research in these areas.

Transition state theory with Tsallis statistics

We discuss the rate of an elementary chemical reaction. We use the reaction path and especially its saddle point on the potential energy surface. The reaction path connects reactant and product of a reaction over the transition state (TS). Usually, the TS is assumed near or at the single saddle point of the reaction path. By means of comparison of the statistics of states at the reactant and at the TS, one can estimate the reaction rate by the Eyring theory. We propose to use the Tsallis statistics at the TS, a statistics of seldom accidents. Thus, we propose to generalize the well‐known Boltzmann–Gibbs statistics, which is the limiting case of the Tsallis statistics. We use features of this nonextensive thermostatistics. The basic properties of the statistics are used to derive (approximated) partition functions, and they are applied on reaction rates. The approximation includes a factorization of the partition functions. The theory is applied to HCN isomerization to HNC, and to the reaction H2 + CN → H + HCN. It allows an accordance with experimental estimations of the reaction rates.

Extending theis' solution: Using transient pumping tests to estimate parameters of aquifer heterogeneity

A framework for interpreting transient pumping tests in heterogeneous transmissivity fields is developed to infer the overall geostatistical parameters of the medium without reconstructing the specific heterogeneous structure point wise. The methodology of Radial Coarse Graining is applied to deduce an effective radial description of multi-Gaussian transmissivity. It was used to derive an Effective Well Flow Solution for transient flow conditions including not only the storativity, but also the geometric mean, the variance, and the correlation length of log-transmissivity. This solution is shown to be appropriate to characterize the pumping test drawdown behavior in heterogeneous transmissivity fields making use of ensembles of simulated pumping tests with multiple combinations of statistical parameters. Based on the Effective Well Flow Solution, a method is developed for inferring heterogeneity parameters from transient pumping test drawdown data by inverse estimation. Thereby, the impact of statistical parameters on the drawdown is analyzed, allowing to determine the dependence of reliability of parameter estimates on location and number of measurements. It is shown, that the number of measurements can be reduced compared to steady state pumping tests. Finally, a sampling strategy for single aquifer analysis is developed, which allows to estimate the statistical parameters, in particular variance and correlation length for individual heterogeneous transmissivity fields making use of transient pumping test measurements at multiple locations. This article is protected by copyright. All rights reserved.