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

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 Tübingen, 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.

A kriging approach based on Aitchison geometry for the characterization of particle-size curves in heterogeneous aquifers

“…Barahona-Palomo et al (2011) compared hydraulic conductivity estimates obtained through PSCs and impeller flowmeter measurements. Riva et al (2006Riva et al ( , 2008Riva et al ( , 2010 performed numerical Monte Carlo analyses of a tracer test and well-related capture zones at the site upon relying on the information provided by the available PSCs. The latter were measured on core samples associated with characteristic length ranging from 5 to 26.5 cm and indicating the occurrence of heterogeneous and highly conducive alluvial deposits.…”

“…4 might indicate some degree of non-stationarity, even though it can be noted that the number of data pairs decreases with increasing lag. Since the stationarity assumption along the vertical direction is supported by prior knowledge of the field site (Riva et al 2006(Riva et al , 2010, non-stationarity has not been considered in the present study. The structure of spatial dependence among the particle-size densities has been explored being the kriging prediction at s i obtained upon removing the i-th datum (i.e., PSC) from the dataset.…”

“…With reference to hydraulic conductivity estimates which can be inferred from particle-based formulations, we compare the results which can be obtained through our FCK approach against those associated with a classical kriging technique applied directly to quantiles of a PSC. These quantiles can be either directly measured or, as in (Riva et al 2010), estimated through interpolation on the available measured particle sizes.…”

“…The functional approach allows modeling a global variogram for the functional process and the solution of the ensuing kriging system of equations is performed only once yielding the prediction (and associated prediction variance) of the complete particle-size curve at unsampled locations. On the other hand, typical geostatistical analyses [e.g., Riva et al (2006Riva et al ( , 2008Riva et al ( , 2010; Bianchi et al (2011) and references therein] treat each quantile separately (possibly introducing estimated crosscorrelations in terms of cross-variograms) and project their predictions through kriging on a computational grid. Such an approach, besides being methodologically different from the one we propose, can produce inconsistent results (Tolosana-Delgado et al 2008).…”

“…These types of data are typically based on standard grain sieve analysis of soil samples, yielding a discrete representation of the curves by measuring selected particle diameters which, in turn, correspond to quantiles of the particle-size curve. The information can then be employed to classify soil types [e.g., Riva et al (2006) and references therein], to infer hydraulic parameters such as porosity and hydraulic conductivity [e.g., amongst others, Lemke and Abriola (2003); Riva et al (2006Riva et al ( , 2008Riva et al ( , 2010; Bianchi et al (2011);Tong et al (2010); Barahona-Palomo et al (2011) and references therein], or, in the presence of inorganic compounds, to provide estimates of the porous medium sorption capacity [e.g., Hu et al (2004) and references therein].…”