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

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 (T) field on temporal histories of solute concentrations observed at an extraction well. The stochastic nature of T is rendered by modeling its natural logarithm, Y=lnT, through a typical Gaussian representation and the recently introduced Generalized sub-Gaussian (GSG) model. The latter has the unique property to embed scale-dependent non-Gaussian features of the main statistics of Y 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 (C), as well as statistics of the peak concentration (C_p), 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 C, regardless the nature (Gaussian or non-Gaussian) of the underlying Y field, whereas the latter quantitatively influences their magnitude. Our results show that uncertainty associated with C and C_p 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 C_p displays a long positive tail in the presence of time-varying pumping schedule. All these aspects are magnified in the presence of non-Gaussian Y fields. Additionally, the PDF of C_p displays a bimodal shape for all types of pumping schemes analyzed, independent of the type of heterogeneity considered.