Effects of uncertainty of lithofacies, conductivity and porosity distributions on stochastic interpretations of a field scale tracer test

TLDR: In this article, the authors investigate the importance of selecting two different methodologies for the determination of hydraulic conductivity from available grain-size distributions on the stochastic modeling of the depth-averaged breakthrough curve observed during a forced-gradient tracer test experiment.

Abstract: We investigate the importance of selecting two different methodologies for the determination of hydraulic conductivity from available grain-size distributions on the stochastic modeling of the depth-averaged breakthrough curve observed during a forced-gradient tracer test experiment. The latter was performed in the Lauswiesen alluvial aquifer, located near the city of Tubingen, Germany, by injecting NaBr into a well at a distance of about 50 m from a pumping well. We also examine the joint effect of the choice of the transport model adopted to describe solute transport at the site and the way the spatial distribution of porosity is assessed. In the absence of direct measurements of porosity, we consider: (a) the model used by Riva et al. (J Contam Hydrol 88:92–118, 2006; J Contam Hydrol 101:1–13, 2008), which relates the natural logarithms of effective porosity and conductivity through an empirical, experimentally-based, linear relationship derived for a nearby experimental site; and (b) a model based on a commonly used relationship linking the total porosity to the coefficient of uniformity of grain size distributions. Transport is described in terms of a purely advective process and/or by including mass exchange processes between mobile and immobile regions. Modeling of flow and transport is performed within a Monte Carlo framework, upon conceptualizing the aquifer as a random composite medium. Our results indicate that the model adopted to describe the correlation between conductivity and porosity and the way grain-sieve information are incorporated to depict the heterogeneous distribution of hydraulic conductivity can have relevant effects in the interpretation of the data at the site. All the conceptual models employed to describe the structural heterogeneity of the system and transport features can reasonably reproduce the global characteristics of the experimental depth-averaged breakthrough curve. Specific details, such as the peak concentration and the time of first arrival, can be better reproduced by a double porosity transport model when a correlation between conductivity and porosity based on grain size information at the site is considered. The best prediction of the late-time behavior of the measured breakthrough curves, in terms of the observed heavy tailing, is offered by directly linking porosity distribution to the spatial variability of particle size information.