Solute concentration at a well in non-Gaussian aquifers under constant and time-varying pumping schedule

Abstract

Our study is keyed to the analysis of the interplay between engineering factors (i.e., transient pumping rates versus less realistic but commonly analyzed uniform extraction rates) and the heterogeneous structure of the aquifer (as expressed by the probability distribution characterizing transmissivity) on contaminant transport. We explore the joint influence of diverse (a) groundwater pumping schedules (constant and variable in time) and (b) representations of the stochastic heterogeneous transmissivity ( ) field on temporal histories of solute concentrations observed at an extraction well. The stochastic nature of is rendered by modeling its natural logarithm, = ln , through a typical Gaussian representation and the recently introduced Generalized sub-Gaussian (GSG) model. The latter has the unique property to embed scaledependent non-Gaussian features of the main statistics of and its (spatial) increments, which have been documented in a variety of studies. We rely on numerical Monte Carlo simulations and compute the temporal evolution at the well of low order moments of the solute concentration ( ), as well as statistics of the peak concentration ( ), identified as the environmental performance metric of interest in this study. We show that the pumping schedule strongly affects the pattern of the temporal evolution of the first two statistical moments of , regardless the nature (Gaussian or non-Gaussian) of the underlying field, whereas the latter quantitatively influences their magnitude. Our results show that uncertainty associated with and estimates is larger when operating under a transient extraction scheme than under the action of a uniform withdrawal schedule. The probability density function (PDF) of displays a long positive tail in the presence of time-varying pumping schedule. All these aspects are magnified in the presence of non-Gaussian fields. Additionally, the PDF of displays a bimodal shape for all types of pumping schemes analyzed, independent of the type of heterogeneity considered. 1 Abstract 1Our study is keyed to the analysis of the interplay between engineering factors (i.e., transient 2 pumping rates versus less realistic but commonly analyzed uniform extraction rates) and the 3 heterogeneous structure of the aquifer (as expressed by the probability distribution characterizing 4 transmissivity) on contaminant transport. We explore the joint influence of diverse (a) Gaussian fields. Additionally, the PDF of displays a bimodal shape for all types of pumping 22 schemes analyzed, independent of the type of heterogeneity considered.

Solute transport in bounded porous media characterized by generalized sub-Gaussian log-conductivity distributions

“…These results reinforce the conclusions drawn by Riva et al (2017) and Libera et al (2017), who found that manifestations of -field Sub-Gaussianity on moments/metrics associated with flow and transport tend to become virtually undetectable for ≥ 1.8.…”

“…Riva et al (2017) present lead-order analytical flow and transport solutions in unbounded GSG log-conductivity fields under mean-uniform flow. Libera et al (2017) rely on a numerical Monte Carlo framework to analyze the joint effects of a GSG heterogeneous log-conductivity field and a temporally variable pumping rate on solute breakthrough curves (BTCs) detected at a pumping well operating in a twodimensional domain. Besides spatial dimensionality, three major limitations can be identified for the analytical study by Riva et al (2017): ( ) macrodispersion is the only transport metric analyzed, ( ) the joint impact of local dispersivity combined with the heterogeneous advection driven by is not evaluated, and ( ) output uncertainty due to finite size of the medium is not considered.…”

Generalized Sub‐Gaussian Processes: Theory and Application to Hydrogeological and Geochemical Data

“…As mentioned in section 1, statistics of its spatial increments have also been documented to display a behavior consistent with what we have observed here for porosity. These concepts have already been employed in the context of preliminary analytical and numerical studies of flow and transport in porous media associated with such a statistical description by Riva et al (2017) and Libera et al (2017).…”

Features of transport in non-Gaussian random porous systems

“…As expected, the difference between statistics of c(x, t) obtained with diverse α values decreases as the travel time increases and as Pe decreases (see also Figure 3.b). We point out that the effect of α on the concentration breakthrough curve (BTC) in a single realization of the permeability field has been investigated in the past [46,57]. In general, the authors observed that decreasing the value of α yields (i) a delayed first time of arrival of the solute and (b) an increasing degree of asymmetry (and heavier tails) of the BTC.…”

“…To date, this modeling strategy has been successfully applied to the interpretation of main features displayed by key parameters of porous media, including log-permeability and porosity [41,27,43], whose spatial heterogeneity is typical of natural subsurface settings. It has also been employed in preliminary analytical and numerical studies of flow and transport in porous media whose log-conductivity is characterized through a GSG model [45,46].…”