Transport In Heterogeneous Aquifers Research Articles

MODPATH-RW: A Random Walk Particle Tracking Code for Solute Transport in Heterogeneous Aquifers.

Random walk particle tracking (RWPT) is a discrete particle method that offers several advantages for simulating solute transport in heterogeneous geological systems. The formulation is a discrete solution to the advection-dispersion equation, yielding results that are not influenced by grid-related numerical dispersion. Numerical dispersion impacts the magnitude of concentrations and gradients obtained from classical grid-based solvers in advection-dominated problems with relatively large grid Péclet numbers. Accurate predictions of concentrations are crucial for reactive transport studies, and RWPT has been recognized for its potential benefits for this kind of application. This highlights the need for a solute transport program based on RWPT that can be seamlessly integrated with industry-standard groundwater flow models. This article presents a solute transport code that implements the RWPT method by extension of the particle tracking model MODPATH, which provides the base infrastructure for interacting with several variants of MODFLOW groundwater flow models. The implementation is achieved by developing a method for determining the exact cell-exit position of a particle undergoing simultaneous advection and dispersion, allowing for the sequential transfer of particles between flow model cells. The program is compatible with rectangular unstructured grids and integrates a module for the smoothed reconstruction of concentrations. In addition, the program incorporates parallel processing of particles using the OpenMP library, enabling faster simulations of solute transport in heterogeneous systems. Numerical test cases involving different applications in hydrogeology benchmark the RWPT model with well-known transport codes.

Facilitated transport of toluene and naphthalene with humic acid in high- and low-permeability systems: Role of ionic strength and cationic type

The occurrence of colloids on pollutants transport in groundwater has attracted more attention. However, the research on the regulation mechanism of colloids on combined pollutants transport in heterogeneous aquifers is limited. In this study, a series of tank experiments were conducted to systematically investigate the effects of ionic strength, and cation type on humic acid (HA) facilitated transport of toluene (TOL), and naphthalene (NAP) in high- and low-permeability systems. The results showed that HA facilitated pollutants transport in low Na+ solution. In Ca2+ solution, the presence of HA hindered pollutants transport, and the inhibition increased with the increase of ionic strength. Both in Na+ solution and low Ca2+ solution, the influence of heterogeneous structure on pollutant transport played a dominant role, and TOL and NAP had a greater transport potential in the high permeability zone (HPZ) due to the preferential flow. Whereas, deposition of HA aggregates, and electrostatic attractive interaction had negative effects on transport than groundwater flow in high Ca2+ solution. Pollutants were prone to accumulate at the bottom of the HPZ, and the top of the low permeability zone (LPZ). These new findings provide insights into the mechanism of colloids influence on the pollutants transport in heterogenous aquifer.

Stochastic Inversion of a Tomographic Pumping Test: Identifying Conductivity Horizontal Correlation and Longitudinal Macrodispersivity

AbstractTwo important properties for modeling flow and transport in heterogeneous aquifers are the horizontal integral scale (Ih) of hydraulic logconductivity (Y = ln K) and the longitudinal macrodispersivity (αL). Estimating the former generally requires K measurements in many wells, which are typically not available. In this work, we present a method for estimating Ih and αL from hydraulic tomography (HT) pumping tests. The approach is based on stochastic inversion, assuming head and K are stationary random space functions. Head variance and mean head gradient are calculated from measured head data at large distances from the pumping well and for large times from the start of pumping. These are then used in a theoretical formula for head variance in uniform mean flow to obtain Ih and subsequently αL, requiring only previous knowledge of the vertical integral scale (Iv) and the logconductivity variance . The method is applied to data from an HT pumping test at the Boise Hydrogeophysical Research site and results for Ih and αL are in the range previously reported in the literature. Particularly promising results are found for αL, which is seen to be robust, with relatively little variation for different values of Iv and .

Performance evaluation of surrogate models for simulating multiphase NAPL transport in heterogeneous aquifers

Abstract A better understanding of the distribution of nonaqueous phase liquid (NAPL) plumes is of great importance to groundwater pollution remediation and control. However, the efficiency of surrogate models in simulating the transport is still not well addressed. Selecting a leakage problem as an example, 50 sets of random permeability distributions are generated using the Monte Carlo method, and a numerical model is used to obtain benchmark data of NAPL transport. Four machine learning methods are employed to simulate dense NAPL transport under point leakage sources across spatiotemporal scales. The validation of the models demonstrate that the random forest model can also effectively capture the spatial-temporal distribution of the plume in heterogeneous aquifers, with a maximum mean absolute error and root mean square error smaller than 5.55 × 10−4 and 5.88 × 10−5, respectively. Meanwhile, the multiple phase outcome from the random forest model fits well with the numerical results under the scenarios of linear leakage sources and light NAPL transport. The total time consumed in the computation is reduced by over 150 times after using the surrogate models. The results suggest that surrogate models can provide a promising way to understand NAPL transport in heterogeneous aquifers.

A Dual Heterogeneous Domain Model for Upscaling Anomalous Transport With Multi‐Peaks in Heterogeneous Aquifers

AbstractNatural aquifers are often characterized by multiscale heterogeneity and complex flow networks, challenging the reliable simulation and prediction of contaminant transport. Classic stochastic transport models usually assume independent, identically distributed probability density functions when upscaling solute dynamics, but this assumption is not valid for media with multiscale heterogeneity. To address this issue, a dual heterogeneous domain model (DHDM) was proposed to quantify solute transport in heterogeneous aquifers where solute breakthrough curves (BTCs) exhibit multiple peaks and transient tailing behaviors. To efficiently solve the resultant DHDM, a Lagrangian solver was developed by combining the renewal‐reward process (to capture solute dynamics in each domain) and the state transition probability (to capture solute particle transfer between the two heterogeneous domains). The DHDM and its Lagrangian solver were then applied to simulate solute transport in three different aquifer settings (alluvial, fractured, and karst). Analyses showed that in the alluvial aquifer, early arrivals and bi‐peaks of the observed solute BTC might be caused by interconnected preferential flow paths consisting of high conductivity sediments, while the front edge or long tails of local peaks might be a result of small‐scale heterogeneity. Fracture networks and karst conduits also resulted in anomalous transport with multiple peaks, and mass transfer between the preferential flow channels and matrix led to solute retention. All these complex, coexisting anomalous transport characteristics can be simultaneously and accurately captured by the unifying DHDM approach, significantly expanding the capability of nonlocal transport models.

Contaminant transport in heterogeneous aquifers: A critical review of mechanisms and numerical methods of non-Fickian dispersion

Contaminant transport in heterogeneous aquifers: A critical review of mechanisms and numerical methods of non-Fickian dispersion

A field evidence model: how to predict transport in heterogeneous aquifers at low investigation level

Abstract. Aquifer heterogeneity in combination with data scarcity is a major challenge for reliable solute transport prediction. Velocity fluctuations cause non-regular plume shapes with potentially long-tailing and/or fast-travelling mass fractions. High monitoring cost and a shortage of simple concepts have limited the incorporation of heterogeneity into many field transport models up to now. We present an easily applicable hierarchical conceptualization strategy for hydraulic conductivity to integrate aquifer heterogeneity into quantitative flow and transport modelling. The modular approach combines large-scale deterministic structures with random substructures. Depending on the modelling aim, the required structural complexity can be adapted. The same holds for the amount of monitoring data. The conductivity model is constructed step-wise following field evidence from observations, seeking a balance between model complexity and available field data. The starting point is a structure of deterministic blocks, derived from head profiles and pumping tests. Then, subscale heterogeneity in the form of random binary inclusions is introduced to each block. Structural parameters can be determined, for example, from flowmeter measurements or hydraulic profiling. As proof of concept, we implemented a predictive transport model for the heterogeneous MADE site. The proposed hierarchical aquifer structure reproduces the plume development of the MADE-1 transport experiment without calibration. Thus, classical advection–dispersion equation (ADE) models are able to describe highly skewed tracer plumes by incorporating deterministic contrasts and effects of connectivity in a stochastic way without using uni-modal heterogeneity models with high variances. The reliance of the conceptual model on few observations makes it appealing for a goal-oriented site-specific transport analysis of less well investigated heterogeneous sites.

Heterogeneity-controlled uncertain optimization of pump-and-treat systems explained through geological entropy

Pump-and-treat (P&T) is a widely-adopted solution for the containment of solute plumes in contaminated aquifers. A cost-effective design of P&T systems requires optimizing (minimizing) the overall pumping rates (Q). This optimization is a stochastic process, as Q is a random variable linked to the randomness of the aquifer hydraulic conductivity (K). Previously presented stochastic approaches to minimize Q adopted two-dimensional (2D) Gaussian random spatial fields (r.s.f.) of log-transformed K. Recent studies based on geological entropy have demonstrated the limited ability of Gaussian r.s.f. to reproduce extreme K patterns, which mostly control transport in heterogeneous aquifers, when compared to non-Gaussian r.s.f. Moreover, 2D models generate different flow and transport connectivity than three-dimensional (3D) models. On these premises, this work aimed at extending previous works on P&T optimization in heterogeneous aquifers through Monte-Carlo groundwater simulations of 2D and 3D Gaussian and non-Gaussian r.s.f. The results indicated that the mean ( $$ \bar{Q}_{n} $$ ) and variance ( $$ \sigma_{Qn}^{2} $$ ) of the optimal Q distribution depend strictly on the chosen model dimensionality and r.s.f. generator. In particular, 2D models and models embedding indicator-based (i.e. non-Gaussian) r.s.f. tended to generate higher $$ \bar{Q}_{n} $$ and $$ \sigma_{Qn}^{2} $$ than 3D models with increasing number of model layers (KL) and Gaussian models. This behavior can be explained considering the spatial ordering of K clusters in the simulated aquifers, which is measured through metrics derived from the concept of geological entropy. It was found that 2D models and models embedding non-Gaussian r.s.f. displayed more spatially-persistent ordered K structures than 3D models and Gaussian models, resulting in higher $$ \bar{Q}_{n} $$ and $$ \sigma_{Qn}^{2} $$ . This is attributed to the relative amount of heterogeneity sampled by the solute source and the increased likelihood of more ordered K clusters to generate preferential flow and solute transport channeling than more disordered and chaotic systems, which enhance solute mixing. Combining P&T with physical barriers (i.e. cut-off walls) was helpful to reduce both $$ \bar{Q}_{n} $$ and $$ \sigma_{Qn}^{2} $$ in all tested scenarios, corroborating previous findings. However, the relative efficacy of a specific physical barrier geometry to reduce $$ \bar{Q}_{n} $$ and $$ \sigma_{Qn}^{2} $$ also depends on the chosen model dimensionality and r.s.f. generator.

Upscaling non-linear reactive transport in correlated velocity fields

While commonly non-local transport models have been shown to reproduce breakthrough curves resulting from transport in heterogeneous aquifers successfully, open questions include the formal link between the upscaled governing equations and the sub-scale heterogeneity, and the ability to account for the effect of heterogeneity on effective chemical reaction rates in the presence of non-linear multi-component reactions. Time-domain random walk approaches based on velocity Markov models provide a framework to resolve these issues by incorporating the spatial correlation of velocity of a solute particle in consecutive locations along its trajectory. These approaches often rely on particle tracking approaches, which, however, can be computationally burdensome especially when non-linear reactions are sought to be modeled. In this paper, an integro-differential equation is proposed for upscaling multi-component reactive transport in heterogeneous media that relies on copulas for representing the velocity correlation structure. For this purpose, we express concentration or flux of solutes as a distribution over their velocity. We then derive the integro-differential equation that governs the evolution of concentration distribution over a quantity defined as velocity-rank. In this way, the spatial evolution of breakthrough curves away from the source is predicted based on ergodic cross-sectional velocity distributions and a parameterized copula function which expresses the correlation between velocity-ranks of a solute particle along its trajectory. We demonstrate the validity of the proposed model by comparing breakthrough curves for conservative and non-linearly reacting solutes based on realizations of hydraulic conductivity fields to the results of the upscaled model.

Effects of local transverse dispersion on macro-scale coefficients of oxygen-limited biodegradation in a stratified formation

The correct characterization of macro-scale contaminant transport and transformation rates is an important issue for modeling reactive transport in heterogeneous aquifers. While previous studies have investigated field-scale heterogeneity of transport and biochemical properties, the effects of local transverse dispersion on macro-scale transport and transformation rates have not been well understood. In this paper, the process of oxygen-limited biodegradation in a stratified aquifer is analysed by spectral perturbation approach, and longitudinal macrodispersivity, effective biodegradation rate, effective retardation factor and effective velocity are derived for the coupled transport equations of a system consisting of a contaminant and an oxidizing agent (oxygen). The effects of local transverse dispersion on these macro-scale coefficients are studied. It is shown that local transverse dispersion can smooth the heterogeneity in biodegradation and sorption processes and enlarge effective biodegradation rate and retardation factor. The local transverse dispersion can also limit the effects of heterogeneity in biodegradation process on longitudinal macrodispersivities and effective velocities for the contaminant and dissolved oxygen. But the effects of heterogeneity in sorption process on the contaminant macrodispersivity is likely to be magnified by local transverse dispersion.

Experimental study of conservative solute transport in heterogeneous aquifers

Aquifer heterogeneity affects the characteristics of solute breakthrough curves (BTCs). A better understanding of the relationship between aquifer heterogeneity and BTCs will help improve prediction of the fate of contaminants in an aquifer. Previous studies have shown that systematic research of aquifer heterogeneity on solute transport is limited. Therefore, this study investigates the impacts of aquifer heterogeneity on conservative solute BTCs and transport mechanism via experimental and modeling approaches. Tracer experiments are conducted in four flow-through columns exhibiting different patterns of heterogeneities. Furthermore, this study also examines the influence of hydraulic conductivity on transport mechanism. In addition, this paper analyses the correlation between hydraulic conductivity and dispersivity, which are the key parameters of conservative solute transport in an aquifer. Experimental data indicates the impacts of aquifer heterogeneity on transport of tracer. Tracer BTCs in a homogeneous aquifer have the typical sigmoid shape without tailing. In a heterogeneous aquifer, tracer BTCs display a strong and persistent tailing. In a preferential flow aquifer, tracer BTCs have pronounced tailing and early arrival time. The hydraulic conductivity of an aquifer significantly affects the transport mechanism of tracer. When the hydraulic conductivity is higher than 1.53 cm/min, transport of tracer is applicable to the ADE. When the hydraulic conductivity is lower than 1.53 cm/min, transport of tracer is applicable to the TRM. This work offers insight into the correlation between the hydraulic conductivity of an aquifer and the dispersivity of a conservative solute. A critical finding is that hydraulic conductivity K and dispersivity $$\lambda$$ correspond to an exponential regression form $$\lambda = e^{{ - 0.24555 - 4.54413K + 2.27308K^{2} }}$$ (R 2 = 0.957).

Lagrangian scheme to model subgrid‐scale mixing and spreading in heterogeneous porous media

AbstractSmall‐scale heterogeneity of permeability controls spreading, dilution, and mixing of solute plumes at large scale. However, conventional numerical simulations of solute transport are unable to resolve scales of heterogeneity below the grid scale. We propose a Lagrangian numerical approach to implement closure models to account for subgrid‐scale spreading and mixing in Darcy‐scale numerical simulations of solute transport in mildly heterogeneous porous media. The novelty of the proposed approach is that it considers two different dispersion coefficients to account for advective spreading mechanisms and local‐scale dispersion. Using results of benchmark numerical simulations, we demonstrate that the proposed approach is able to model subgrid‐scale spreading and mixing provided there is a correct choice of block‐scale dispersion coefficient. We also demonstrate that for short travel times it is only possible to account for spreading or mixing using a single block‐scale dispersion coefficient. Moreover, we show that it is necessary to use time‐dependent dispersion coefficients to obtain correct mixing rates. On the contrary, for travel times that are large in comparison to the typical dispersive time scale, it is possible to use a single expression to compute the block‐dispersion coefficient, which is equal to the asymptotic limit of the block‐scale macrodispersion coefficient proposed by Rubin et al. (1999). Our approach provides a flexible and efficient way to model subgrid‐scale mixing in numerical models of large‐scale solute transport in heterogeneous aquifers. We expect that these findings will help to better understand the applicability of the advection‐dispersion‐equation (ADE) to simulate solute transport at the Darcy scale in heterogeneous porous media.

Oscillatory hydraulic testing as a strategy for NAPL source zone monitoring: Laboratory experiments

Non-aqueous phase liquids (NAPLs) have a complex mode of transport in heterogeneous aquifers, which can result in pools and lenses of NAPLs (the “source zone”) that are difficult to detect and can cause long-term contamination via slow dissolution into groundwater (the “dissolved plume”). Characterizing the extent and evolution of NAPL contamination within the source zone is a useful strategy for designing and adapting appropriate remedial actions at many contaminated sites. As a NAPL flows into a given aquifer volume, the effective hydraulic conductivity (K) and specific storage (Ss) of the volume changes associated with the viscosity and compressibility of the impinging fluid, meaning that NAPL movement may be detectable with hydraulic testing. Recently, the use of oscillatory pumping tests – in which sinusoidal pumping variations are implemented and oscillatory pressure changes are detected at monitoring locations – has been suggested as a low-impact hydraulic testing strategy for characterizing aquifer properties (Cardiff et al., 2013; Zhou et al., 2016). Here, we investigate this strategy in an experimental laboratory sandbox where dyed vegetable oil is injected and allowed to migrate as a NAPL. Initial qualitative analyses demonstrate that measurable changes in pressure signal amplitude and phase provide clear evidence for NAPL plume emplacement and migration. Using the approach developed in Zhou et al. (2016), we then apply tomographic analyses to estimate the location of effective K changes (representing fluid changes) and their movement throughout time. This approach provides a method for monitoring ongoing NAPL movement without net extraction or injection of fluid, making it advantageous in field remediation applications.

An analytical model for carrier-facilitated solute transport in weakly heterogeneous porous media

Carrier-facilitated solute transport in heterogeneous aquifers is studied within a Lagrangian framework. Dissolved solutes and carriers are advected by steady random groundwater flow, which is modeled by Darcy's law with uncertain hydraulic conductivity that is treated as a stationary random space function. We derive general expressions for the spatial moments of the dissolved concentration and the concentration associated with the carrier phase. In order to reduce the computational effort, we use previously derived solutions for the flow field. This enables us to obtain closed-form solutions for the spatial moments of the two concentration fields. The mass and center of gravity of the two propagating plumes depend only on the mean velocity field and chemical/degradation processes. The higher (second and third) moments are affected by the coupling between reactions (sorption/desorption and degradation) among the three phases (i.e., dissolved, carrier and sorbed concentrations) and the aquifer’s heterogeneity. We investigate the potentially enhancing effect of carriers by comparing spatial moments of the two propagating plumes. The forward/backward mass transfer rates between the liquid and carrier phases, and the degradation coefficients are identified as critical parameters. The carrier's role is most prominent when detachment from carrier sites is slow, provided that degradation on the carriers is smaller than that in the liquid phase.

Reply to comment by S. P. Neuman on “Advective transport in heterogeneous aquifers: Are proxy models predictive?”

AbstractIn this Reply we further comment on the main assumptions and the results of our recent manuscript “Advective transport in heterogeneous aquifers: Are proxy models predictive?”

Comment on “Advective transport in heterogeneous aquifers: Are proxy models predictive?” by A. Fiori, A. Zarlenga, H. Gotovac, I. Jankovic, E. Volpi, V. Cvetkovic, and G. Dagan

Fiori et al. [2015] examine the predictive capabilities of (among others) two “proxy” non-Fickian transport models, MRMT (Multi-RateMassTransfer) and CTRW (Continuous-Time Random Walk). In particular, they compare proxy model predictions of mean breakthrough curves (BTCs) at a sequence of control planes with near-ergodic BTCs generated through two- and three-dimensional simulations of nonreactive, mean-uniform advective transport in single realizations of stationary, randomly heterogeneous porous media. The authors find fitted proxy model parameters to be nonunique and devoid of clear physical meaning. This notwithstanding, they conclude optimistically that “i. Fitting the proxy models to match the BTC at [one control plane] automatically ensures prediction at downstream control planes [and thus] ii. … the measured BTC can be used directly for prediction, with no need to use models underlain by fitting.” I show that (a) the authors' findings follow directly from (and thus confirm) theoretical considerations discussed earlier by Neuman and Tartakovsky [2009], which (b) additionally demonstrate that proxy models will lack similar predictive capabilities under more realistic, non-Markovian flow and transport conditions that prevail under flow through nonstationary (e.g. multiscale) media in the presence of boundaries and/or nonuniformly distributed sources, and/or when flow/transport are conditioned on measurements. This article is protected by copyright. All rights reserved.

A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers

Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the concentration variance, used in moment methods. The mixing model, describing the transport of the PDF in concentration space, is essential for both methods. Finding a satisfactory mixing model is still an open question and due to the rather elaborate PDF methods, a difficult undertaking. Both the PDF equation and the concentration variance equation depend on the same mixing model. This connection is used to find and test an improved mixing model for the much easier to handle concentration variance. Subsequently, this mixing model is transferred to the PDF equation and tested. The newly proposed mixing model yields significantly improved results for both variance modelling and PDF modelling.

Advective transport in heterogeneous aquifers: Are proxy models predictive?

AbstractWe examine the prediction capability of two approximate models (Multi‐Rate Mass Transfer (MRMT) and Continuous Time Random Walk (CTRW)) of non‐Fickian transport, by comparison with accurate 2‐D and 3‐D numerical simulations. Both nonlocal in time approaches circumvent the need to solve the flow and transport equations by using proxy models to advection, providing the breakthrough curves (BTC) at control planes at any x, depending on a vector of five unknown parameters. Although underlain by different mechanisms, the two models have an identical structure in the Laplace Transform domain and have the Markovian property of independent transitions. We show that also the numerical BTCs enjoy the Markovian property. Following the procedure recommended in the literature, along a practitioner perspective, we first calibrate the parameters values by a best fit with the numerical BTC at a control plane at x1, close to the injection plane, and subsequently use it for prediction at further control planes for a few values of . Due to a similar structure and Markovian property, the two methods perform equally well in matching the numerical BTC. The identified parameters are generally not unique, making their identification somewhat arbitrary. The inverse Gaussian model and the recently developed Multi‐Indicator Model (MIM), which does not require any fitting as it relates the BTC to the permeability structure, are also discussed. The application of the proxy models for prediction requires carrying out transport field tests of large plumes for a long duration.

Combining 3D Hydraulic Tomography with Tracer Tests for Improved Transport Characterization.

Hydraulic tomography (HT) is a method for resolving the spatial distribution of hydraulic parameters to some extent, but many details important for solute transport usually remain unresolved. We present a methodology to improve solute transport predictions by combining data from HT with the breakthrough curve (BTC) of a single forced-gradient tracer test. We estimated the three dimensional (3D) hydraulic-conductivity field in an alluvial aquifer by inverting tomographic pumping tests performed at the Hydrogeological Research Site Lauswiesen close to Tübingen, Germany, using a regularized pilot-point method. We compared the estimated parameter field to available profiles of hydraulic-conductivity variations from direct-push injection logging (DPIL), and validated the hydraulic-conductivity field with hydraulic-head measurements of tests not used in the inversion. After validation, spatially uniform parameters for dual-domain transport were estimated by fitting tracer data collected during a forced-gradient tracer test. The dual-domain assumption was used to parameterize effects of the unresolved heterogeneity of the aquifer and deemed necessary to fit the shape of the BTC using reasonable parameter values. The estimated hydraulic-conductivity field and transport parameters were subsequently used to successfully predict a second independent tracer test. Our work provides an efficient and practical approach to predict solute transport in heterogeneous aquifers without performing elaborate field tracer tests with a tomographic layout.

Stochastic modeling of solute transport in aquifers: From heterogeneity characterization to risk analysis

AbstractThe article presents a few recent developments advanced by the authors in a few key areas of stochastic modeling of solute transport in heterogeneous aquifers. First, a brief review of the Lagrangian approach to modeling plumes longitudinal mass distribution and temporal (the breakthrough curve) mass arrival, is presented. Subsequently, transport in highly heterogeneous aquifers is analyzed by using a recently developed predictive model. It relates the non‐Gaussian BTC to the permeability univariate pdf and integral scale, with application to the MADE field observations. Next, the approach is extended to transport of reactive solute, combinnig the effects of the random velocity field and multirate mass transfer on the BTC, with application to mass attenuation. The following topic is modeling of the local concentration field as affected by mixing and dilution due to pore scale dispersion. The results are applied to the analysis of concentration measurements at the Cape Cod field experiment. The last section incorporates the results of the preceding ones in health risk assessment by analyzing the impact of concentration prediction on risk uncertainty. It is illustrated by assessing the effect of identification of macrodispersivity from field characterization and transport modeling, upon the probability of health risk.