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With advances in instrumentation and the tremendous increase in computational power, vast amounts of data are becoming available for many complex phenomena in macroscopically heterogeneous media, particularly those that involve flow and transport processes, which are problems of fundamental interest that occur in a wide variety of physical systems. The absence of a length scale beyond which such systems can be considered as homogeneous implies that the traditional volume or ensemble averaging of the equations of continuum mechanics over the heterogeneity is no longer valid and, therefore, the issue of discovering the governing equations for flow and transport processes is an open question. We propose a data-driven approach that uses stochastic optimization and symbolic regression to discover the governing equations for flow and transport processes in heterogeneous media. The data could be experimental or obtained by microscopic simulation. As an example, we discover the governing equation for anomalous diffusion on the critical percolation cluster at the percolation threshold, which is in the form of a fractional partial differential equation, and agrees with what has been proposed previously.

The interactions between surface water and groundwater in river corridors lead to temporal fluctuations in subsurface water fluxes which have a critical role on solute transport dynamics. In this work, we develop a framework to analyze the relative impacts of different temporal frequencies of the flow field in a spatially heterogeneous aquifer on solute transport. Our analysis indicates that the advection-dispersion equation behaves as a low-pass filter by wiping out the effect of high-frequency velocity fluctuations on the first two spatial moments of the solute plume, namely its center of mass and spreading. The concepts discussed in the theoretical analysis are then applied to understand solute transport dynamics at the 300 Area of the Hanford site (USA) adjacent to the Columbia River. We examine the temporal behavior of the solute plume's spatial moments for different temporal frequencies utilizing geostatistical parameters estimated in the 300 Area. Due to the proximity to the Columbia river, groundwater fluxes at the Hanford site are highly dynamic resulting in a large range of characteristic temporal frequencies. Nonetheless, similar to the theoretical analysis, our results show that the effect of high-frequency fluctuations is filtered, with most of the solute transport dynamics being controlled by fluctuations characterized by a large characteristic period., (Copyright © 2020 Elsevier B.V. All rights reserved.)

Assessing the health risks associated with emerging contaminants in groundwater systems is a complex issue that has been receiving increased attention in indirect potable reuse applications. Among several emerging contaminants, our study focuses on developing a numerical model that aims to compute the transport characteristics of Bisphenol A (BPA) in a 3D spatially heterogeneous aquifer under uncertainty. Traditional approaches that characterize the health risk of BPA to humans rely on the monotonic dose-response (MDR) relationship with a regulatory dose limit. Recent public health studies indicate that BPA can cause endocrine-related health effects in specific low dose ranges, which requires the consideration of the non-monotonic dose-response (NMDR) model. This work investigates the impact of different BPA DR models (i.e., monotonic vs. non-monotonic) on the resilience of the aquifer against BPA contamination in the presence of hydrogeological heterogeneity. For the resilience estimation, a systematic stochastic methodology linking risk characterization to aquifer resilience is established. Our results show the importance of the interplay between the DR models and aquifer heterogeneity on controlling the uncertainty of the resilience loss R L (d) at a specified environmentally sensitive target. In the increased level of aquifer heterogeneity, the uncertainty bounds are higher for R L estimated through the NMDR model as opposed to the MDR model. Moreover, R L is controlled by η (-), the ratio of the volumetric flow rate at the source zone to the average flow rate at the background aquifer. In a risk management perspective, the consideration of the NMDR model needs to be emphasized due to its impact on the uncertainty of R L . A critical case is when the land use of a contamination site indicates a large number of the vulnerable population to endocrine-related health effects. In this case, η as an indicator of aquifer resilience can reduce the uncertainty of R L ., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 Elsevier B.V. All rights reserved.)

This study investigates the potential impact of climate change on residual contaminants in vadose zones and groundwater. We assume that the effect of climate changes can be represented by perturbations in the natural recharge through the aquifer system. We perform numerical modeling of unsaturated/saturated flow and transport and consider different performance metrics: contaminant concentrations at observation wells and contaminant export at the site's boundary. We evaluate the effect of increasing and decreasing recharge as well as the impact of potential failure of surface capping structures employed to immobilize vadose zone contaminants. Our approach is demonstrated in a real case study by simulating transport of non-reactive radioactive tritium at the U.S. Department of Energy's Savannah River Site. Results show that recharge changes significantly affect well concentrations: after an initial slight dilution we identify a significant concentration increase at different observation wells some years after the recharge increase and/or the cap failure, as a consequence of contaminants' mobilization. This effect is generally emphasized and occurs earlier as the recharge increases. Under decreased aquifers' recharge the concentration could slightly increase for some years, due to a decrease of dilution, depending on the magnitude of the negative recharge shift. We identify trigger levels of recharge above which the concentration/export breakthrough curves and the time of exceedance of the Maximum Contaminant Level for tritium are remarkably affected. Moreover, we observe that the contaminant export at the control plane, identified as the risk pathway to the downgradient population, may only be minimally affected by shifts in the natural recharge regime, except for some extreme cases. We conclude that more frequent sampling and in-situ monitoring near the source zone should be adopted to better explain concentrations' anomalies under changing climatic conditions. Moreover, the maintenance of the cap is critical not only to sequester residual contaminants in the vadose zone, but also to reduce the uncertainty associated with future precipitation changes. Finally, realistic flow and transport simulations achieved through proper calibration processes, rather than conservative modeling, should be adopted to identify non-trivial trade-offs which enable better allocation of resources towards reducing uncertainty in decision making., (Copyright © 2019 Elsevier B.V. All rights reserved.)

The deformation of elementary fluid volumes by velocity gradients is a key process for scalar mixing, chemical reactions and biological processes in flows. Whilst fluid deformation in unsteady, turbulent flow has gained much attention over the past half century, deformation in steady random flows with complex structure - such as flow through heterogeneous porous media - has received significantly less attention. In contrast to turbulent flow, the steady nature of these flows constrains fluid deformation to be anisotropic with respect to the fluid velocity, with significant implications for e.g. longitudinal and transverse mixing and dispersion. In this study we derive an ab initio coupled continuous time random walk (CTRW) model of fluid deformation in random steady three-dimensional flow that is based upon a streamline coordinate transform which renders the velocity gradient and fluid deformation tensors upper-triangular. We apply this coupled CTRW model to several model flows and find these exhibit a remarkably simple deformation structure in the streamline coordinate frame, facilitating solution of the stochastic deformation tensor components. These results show that the evolution of longitudinal and transverse fluid deformation for chaotic flows is governed by both the Lyapunov exponent and power-law exponent of the velocity PDF at small velocities, whereas algebraic deformation in non-chaotic flows arises from the intermittency of shear events following similar dynamics as that for steady two-dimensional flow.

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., (Copyright © 2017 Elsevier B.V. All rights reserved.)

We investigate how the uncertainty stemming from disordered porous media that display long-range correlation in the hydraulic conductivity (K) field propagates to predictions of environmental performance metrics (EPMs). In this study, the EPMs are quantities that are of relevance to risk analysis and remediation, such as peak flux-averaged concentration, early and late arrival times among others. By using stochastic simulations, we quantify the uncertainty associated with the EPMs for a given disordered spatial structure of the K-field and identify the probability distribution function (PDF) model that best captures the statistics of the EPMs of interest. Results indicate that the probabilistic distribution of the EPMs considered in this study follows lognormal PDF. Finally, through the use of information theory, we reveal how the persistent/anti-persistent correlation structure of the K-field influences the EPMs and corresponding uncertainties., (Copyright © 2016 Elsevier B.V. All rights reserved.)