Conditional Probability Density Functions of Concentrations for Mixing-Controlled Reactive Transport in Heterogeneous Aquifers

The increasing presence of toxic chemicals released in the subsurface has led to a rapid growth of social concerns and the need to develop and employ models that can predict the impact of groundwater contamination on human health risk under uncertainty. Monitored natural attenuation is a common remediation action in many contamination cases. However, natural attenuation can lead to the production of daughter species of distinct toxicity that may pose challenges in pollution management strategies. The actual threat that these contaminants pose to human health depends on the interplay between the complex structure of the geological media and the toxicity of each pollutant byproduct. This work addresses human health risk for chemical mixtures resulting from the sequential degradation of a contaminant (such as a chlorinated solvent) under uncertainty through high-resolution three-dimensional numerical simulations. We systematically investigate the interaction between aquifer heterogeneity, flow connectivity, contaminant injection model, and chemical toxicity in the probabilistic characterization of health risk. We illustrate how chemical-specific travel times control the regime of the expected risk and its corresponding uncertainties. Results indicate conditions where preferential flow paths can favor the reduction of the overall risk of the chemical mixture. The overall human risk response to aquifer connectivity is shown to be nontrivial for multispecies transport. This nontriviality is a result of the interaction between aquifer heterogeneity and chemical toxicity. To quantify the joint effect of connectivity and toxicity in health risk, we propose a toxicity-based Damk€ ohler number. Furthermore, we provide a statistical characterization in terms of low-order moments and the probability density function of the individual and total risks.

Section: Probability Density Functionssupporting

confidence: 90%

Probabilistic human health risk assessment of degradation‐related chemical mixtures in heterogeneous aquifers: Risk statistics, hot spots, and preferential channels

Henri

Fernàndez-García

Barros

2015

“…Similar findings have been published for the turbulent transport of scalars by Girimaji [1991]. The choice of the beta distribution for the probability density function (pdf) of concentration in heterogeneous porous media has recently been supported with theoretical evidence based on an Ito Stochastic Differential Equation for local concentration dynamics [e.g., Bellin and Tonina , 2007; Sanchez‐Vila et al , 2009].…”

Section: Introductionsupporting

confidence: 55%

“…The present contribution does not cover mixing‐controlled reactions themselves. However, it is possible to derive improved statistical concentration distributions of mixing‐controlled reactive species under specific conditions of the reactive systems, when using our concentration pdfs as input to adequate statistical studies of reactive transport [e.g., Cirpka et al , 2008; Sanchez‐Vila et al , 2009; Bellin et al , 2011].…”

Section: Introductionmentioning

confidence: 99%

Probability density function of steady state concentration in two‐dimensional heterogeneous porous media

Cirpka

Barros

Chiogna

et al. 2011

[1] Spatial variability of hydraulic aquifer parameters causes meandering, squeezing, stretching, and enhanced mixing of steady state plumes in concentrated hot-spots of mixing. Because the exact spatial distribution of hydraulic parameters is uncertain, the spatial distribution of enhanced mixing rates is also uncertain. We discuss how relevant the resulting uncertainty of mixing rates is for predicting concentrations. We develop analytical solutions for the full statistical distribution of steady state concentration in two-dimensional, statistically uniform domains with log-hydraulic conductivity following an isotropic exponential model. In particular, we analyze concentration statistics at the fringes of wide plumes, conceptually represented by a solute introduced over half the width of the domain. Our framework explicitly accounts for uncertainty of streamline meandering and uncertainty of effective transverse mixing (defined at the Darcy scale). We make use of existing low-order closed-form expressions that lead to analytical expressions for the statistical distribution of local concentration values. Along the expected position of the plume fringe, the concentration distribution strongly clusters at its extreme values. This behavior extends over travel distances of up to tens of integral scales for the parameters tested in our study. In this regime, the uncertainty of effective transverse mixing is substantial enough to have noticeable effects on the concentration probability density function. At significantly larger travel distances, intermediate concentration values become most likely, and uncertainty of effective transverse mixing becomes negligible. A comparison to numerical Monte Carlo simulations of flow and solute transport show excellent agreement with the theoretically derived expressions.

“…Regardless of the above mentioned limitations, a continuous formulation based on the ADRE is still used as a basis modeling tool for reactive transport problems [see, e.g., Fernández‐Garcia et al , 2008; Sanchez‐Vila et al , 2009, and references therein]. As such, it is embedded in a variety of codes [e.g., Cederberg et al , 1985; Mangold and Tsang , 1991; Yeh and Tripathi , 1991; Steefel and Lasaga , 1994; Walter et al , 1994; Saaltink et al , 2004; De Simoni et al , 2005; Bea et al , 2009 and references therein] and is at the core of benchmark problems comparing the results provided by different numerical models to identify their similarities and critical differences [e.g., Cochepin et al , 2008].…”

Section: Introductionmentioning

confidence: 99%

Interpretation of column experiments of transport of solutes undergoing an irreversible bimolecular reaction using a continuum approximation

Sánchez-Vila

Fernàndez-García

Guadagnini

2010

121

[1] We provide a quantitative interpretation of the column experiment reported by Gramling et al. (2002). The experiment involves advection-dominated transport in porous media of three dissolved species, i.e., two reactants undergoing a fast irreversible reaction and the resulting product. The authors found that their observations could not be properly fitted with a model based on an advection-dispersion-reaction equation (ADRE) assuming the reaction was instantaneous, the actual measured total reaction product being lower than predictions for all times. The data have been recently well reproduced by Edery et al. (2009Edery et al. ( , 2010) by means of a particle tracking approach in a continuous time random walk framework. These and other authors have questioned the use of partial differential equation (PDE)-based approaches to quantify reactive transport because of the difficulty in capturing local-scale mixing and reaction. We take precisely this approach and interpret the experiments mentioned by means of a continuum-scale model based on the ADRE. Our approach differs from previous modeling attempts in that we imbue effects of incomplete mixing at the pore scale in a time-dependent kinetic reaction term and show that this model allows quantitative interpretation of the experiments in terms of both reaction product profiles and time-dependent global production rate. The time dependence of the kinetic term presented accounts for the progressive effects of incomplete mixing due to pore-scale rate-limited mass transfer, and follows a power law, which is consistent with the compilation of existing experiments reported by Haggerty et al. (2004). Our interpretation can form the basis for further research to assess the potential use of PDE approaches for the interpretation of reactive transport problems in moderately heterogeneous media.Citation: Sanchez-Vila, X., D. Fernàndez-Garcia, and A. Guadagnini (2010), Interpretation of column experiments of transport of solutes undergoing an irreversible bimolecular reaction using a continuum approximation, Water Resour.