Upscaling heterogeneity in aquifer reactivity via exposure-time concept: forward model

Reactive properties of aquifer solid phase materials play an important role in solute fate and transport in the natural subsurface on time scales ranging from years in contaminant remediation to millennia in dynamics of aqueous geochemistry. Quantitative tools for dealing with the impact of natural heterogeneity in solid phase reactivity on solute fate and transport are limited. Here we describe the use of a structural variable to keep track of solute flux exposure to reactive surfaces. With this approach, we develop a non-reactive tracer model that is useful for determining the signature of multi-scale reactive solid heterogeneity in terms of solute flux distributions at the field scale, given realizations of three-dimensional reactive site density fields. First, a governing Eulerian equation for the non-reactive tracer model is determined by an upscaling technique in which it is found that the exposure time of solution to reactive surface areas evolves via both a macroscopic velocity and a macroscopic dispersion in the artificial dimension of exposure time. Second, we focus on the Lagrangian approach in the context of a streamtube ensemble and demonstrate the use of the distribution of solute flux over the exposure time dimension in modeling two-dimensional transport of a solute undergoing simplified linear reversible reactions, in hypothetical conditions following prior laboratory experiments. The distribution of solute flux over exposure time in a given case is a signature of the impact of heterogeneous aquifer reactivity coupled with a particular physical heterogeneity, boundary conditions, and hydraulic gradient. Rigorous application of this approach in a simulation sense is limited here to linear kinetically controlled reactions.     

Design of aquifer remediation systems: (1) describing hydraulic structure and NAPL architecture using tracers

Aquifer heterogeneity (structure) and NAPL distribution (architecture) are described based on tracer data. An inverse modelling approach that estimates the hydraulic structure and NAPL architecture based on a Lagrangian stochastic model where the hydraulic structure is described by one or more populations of lognormally distributed travel times and the NAPL architecture is selected from eight possible assumed distributions. Optimization of the model parameters for each tested realization is based on the minimization of the sum of the square residuals between the log of measured tracer data and model predictions for the same temporal observation. For a given NAPL architecture the error is reduced with each added population. Model selection was based on a fitness which penalized models for increasing complexity. The technique is demonstrated under a range of hydrologic and contaminant settings using data from three small field-scale tracer tests: the first implementation at an LNAPL site using a line-drive flow pattern, the second at a DNAPL site with an inverted five-spot flow pattern, and the third at the same DNAPL site using a vertical circulation flow pattern. The Lagrangian model was capable of accurately duplicating experimentally derived tracer breakthrough curves, with a correlation coefficient of 0.97 or better. Furthermore, the model estimate of the NAPL volume is similar to the estimates based on moment analysis of field data.     

Design of aquifer remediation systems: (1) Describing hydraulic structure and NAPL architecture using tracers

Aquifer heterogeneity (structure) and NAPL distribution (architecture) are described based on tracer data. An inverse modelling approach that estimates the hydraulic structure and NAPL architecture based on a Lagrangian stochastic model where the hydraulic structure is described by one or more populations of lognormally distributed travel times and the NAPL architecture is selected from eight possible assumed distributions. Optimization of the model parameters for each tested realization is based on the minimization of the sum of the square residuals between the log of measured tracer data and model predictions for the same temporal observation. For a given NAPL architecture the error is reduced with each added population. Model selection was based on a fitness which penalized models for increasing complexity. The technique is demonstrated under a range of hydrologic and contaminant settings using data from three small field-scale tracer tests: the first implementation at an LNAPL site using a line-drive flow pattern, the second at a DNAPL site with an inverted five-spot flow pattern, and the third at the same DNAPL site using a vertical circulation flow pattern. The Lagrangian model was capable of accurately duplicating experimentally derived tracer breakthrough curves, with a correlation coefficient of 0.97 or better. Furthermore, the model estimate of the NAPL volume is similar to the estimates based on moment analysis of field data.     

Incorporating layer- and local-scale heterogeneities in numerical simulation of unsaturated flow and tracer transport

This study characterizes layer- and local-scale heterogeneities in hydraulic parameters (i.e., matrix permeability and porosity) and investigates the relative effect of layer- and local-scale heterogeneities on the uncertainty assessment of unsaturated flow and tracer transport in the unsaturated zone of Yucca Mountain, USA. The layer-scale heterogeneity is specific to hydrogeologic layers with layerwise properties, while the local-scale heterogeneity refers to the spatial variation of hydraulic properties within a layer. A Monte Carlo method is used to estimate mean, variance, and 5th, and 95th percentiles for the quantities of interest (e.g., matrix saturation and normalized cumulative mass arrival). Model simulations of unsaturated flow are evaluated by comparing the simulated and observed matrix saturations. Local-scale heterogeneity is examined by comparing the results of this study with those of the previous study that only considers layer-scale heterogeneity. We find that local-scale heterogeneity significantly increases predictive uncertainty in the percolation fluxes and tracer plumes, whereas the mean predictions are only slightly affected by the local-scale heterogeneity. The mean travel time of the conservative and reactive tracers to the water table in the early stage increases significantly due to the local-scale heterogeneity, while the influence of local-scale heterogeneity on travel time gradually decreases over time. Layer-scale heterogeneity is more important than local-scale heterogeneity for simulating overall tracer travel time, suggesting that it would be more cost-effective to reduce the layer-scale parameter uncertainty in order to reduce predictive uncertainty in tracer transport.     

An inverse system for incorporation of conditioning to pressure and streamline-based calibration

A streamline-based history matching technique is employed to perform fast and efficient permeability identification and to integrate tracer data into an inverse model. To incorporate tracer data into the inverse model, a given tracer breakthrough curve is interpreted as cumulative breakthrough along independent streamlines. Permeabilities are modified along each streamline to match the tracer breakthrough curve. In this way, there is no explicit computation of sensitivity coefficients, nor any matrix inversion. However, this approach is incomplete by itself. Since the modifications occur along the streamlines, the identified permeability distribution is often incompatible with the actual permeability distribution. Thus, streamlines should be positioned correctly before the streamline-based method is applied. To accomplish this, geostatistical methods such as kriging and sequential Gaussian simulation (SGS) are implemented to provide an appropriate disposition of streamlines at the beginning of the inverse process. Then, permeabilities are iteratively calibrated in a conventional grid system to satisfy pressure and permeability observation data, and simultaneously modified along streamlines to match tracer data. The two independent optimization processes assist mutually and lead to stable convergence to a minimum. By applying the proposed inverse system to synthetic reference fields, it is observed that identified fields satisfactorily reproduce the permeability distribution of the reference fields. In addition, the pressure distributions of the identified and the reference fields are fairly alike, and the identified tracer breakthrough curves are well fitted to those of the reference fields. With regard to spatial patterns of transport behaviors, the streamlines of the identified fields show similar trajectories to those of the reference fields, and the time of flight distributions of the inversed fields are also analogous to those of the reference fields. The proposed inverse system is capable of estimating the future performance of a two-dimensional aquifer from a constrained number of permeability and pressure observation data accompanied by tracer data.     

Stochastic-convective transport with nonlinear reactions and mixing: finite streamtube ensemble formulation for multicomponent reaction systems with intra-streamtube dispersion

An effective streamtube ensemble method is developed to upscale convective-dispersive transport with multicomponent nonlinear reactions in steady nonuniform flow. The transport is cast in terms of a finite ensemble of independent discrete streamtubes that approximate convective transport along macroscopically averaged pathlines and dispersive transport longitudinally as microscopic mixing within streamtubes. The representation of fate and transport via a finite ensemble of effective linear streamtubes, allows the treatment of arbitrarily complex reaction systems involving both homogeneous and heterogeneous reactions, and longitudinal dispersive/diffusive mixing within streamtubes. This allows the use of reactive-transport codes designed to solve such problems in an Eulerian framework, as opposed to reliance on closed-form (convolutional or canonical) expressions for reactive transport in exclusively convective streamtubes. The approach requires both reactive-transport solutions for a representative ensemble of one-dimensional convective-dispersive-reactive streamtubes and the distribution of flux over the streamtube ensemble variants, and it does not allow for lateral mixing between streamtubes. Here, the only ensemble variant is travel time. The discussion details the way that the conventional Eulerian fate and transport model is converted first into an ensemble of transports along three-dimensional streamtubes of unknown geometry, and then to approximate one-dimensional streamtubes that are designed to honor the important global properties of the transport. Conditions under which such an 'equivalent' ensemble of one-dimensional streamtubes are described. The breakthrough curve of a nonreactive tracer in the ensemble is expressed as a combined Volterra-Fredholm integral equation, which serves as the basis for estimation of the distribution of flux over the variant of the ensemble, travel time. Transient convective speed and the effects of errors in flux distributions are described, and the method is applied to a demonstration problem involving nonlinear multicomponent reaction kinetics and strongly nonuniform flow.     

A direct passive method for measuring water and contaminant fluxes in porous media

This paper introduces a new direct method for measuring water and contaminant fluxes in porous media. The method uses a passive flux meter (PFM), which is essentially a self-contained permeable unit properly sized to fit tightly in a screened well or boring. The meter is designed to accommodate a mixed medium of hydrophobic and/or hydrophilic permeable sorbents, which retain dissolved organic/inorganic contaminants present in the groundwater flowing passively through the meter. The contaminant mass intercepted and retained on the sorbent is used to quantify cumulative contaminant mass flux. The sorptive matrix is also impregnated with known amounts of one or more water soluble 'resident tracers'. These tracers are displaced from the sorbent at rates proportional to the groundwater flux; hence, in the current meter design, the resident tracers are used to quantify cumulative groundwater flux. Theory is presented and quantitative tools are developed to interpret the water flux from tracers possessing linear and nonlinear elution profiles. The same theory is extended to derive functional relationships useful for quantifying cumulative contaminant mass flux. To validate theory and demonstrate the passive flux meter, results of multiple box-aquifer experiments are presented and discussed. From these experiments, it is seen that accurate water flux measurements are obtained when the tracer used in calculations resides in the meter at levels representing 20 to 70 percent of the initial condition. 2,4-Dimethyl-3-pentanol (DMP) is used as a surrogate groundwater contaminant in the box aquifer experiments. Cumulative DMP fluxes are measured within 5% of known fluxes. The accuracy of these estimates generally increases with the total volume of water intercepted.     

Diffusive partitioning tracer test for the quantification of nonaqueous phase liquid (NAPL) in the vadose zone: Performance evaluation for heterogeneous NAPL distribution

A partitioning tracer test based on gas-phase diffusion in the vadose zone yields estimates of the residual nonaqueous phase liquid (NAPL) saturation. The present paper investigates this technique further by studying diffusive tracer breakthrough curves in the vadose zone for a heterogeneous NAPL distribution. Tracer experiments were performed in a lysimeter with a horizontal layer of artificial kerosene embedded in unsaturated sand. Tracer disappearance curves at the injection point and tracer breakthrough curves at some distance from the injection point were measured inside and outside of the NAPL layer. A numerical code was used to generate independent model predictions based on the physicochemical sand, NAPL, and tracer properties. The measured and modeled tracer breakthrough curves were in good agreement confirming the validity of important modeling assumptions such as negligible sorption of chlorofluorocarbon (CFC) tracers to the uncontaminated sand and their fast reversible partitioning between the soil air and the NAPL phase. Subsequently, the model was used to investigate different configurations of NAPL contamination. The experimental and model results show that the tracer disappearance curves of a single-well diffusive partitioning tracer test (DPTT) are dominated by the near-field presence of NAPL around the tip of the soil gas probe. In contrast, breakthrough curves of inter-well tracer tests reflect the NAPL saturation in between the probes, although there is no unique interpretation of the tracer signals if the NAPL distribution is heterogeneous. Numerical modeling is useful for the planning of a DPTT application. Simulations suggest that several cubic meters of soil can be investigated with a single inter-well partitioning tracer test of 24-hour duration by placing the injection point in the center of the investigated soil volume and probes at up to 1 m distance for the monitoring of gaseous tracers.     

The effect of entrapped nonaqueous phase liquids on tracer transport in heterogeneous porous media: laboratory experiments at the intermediate scale

This work considers the applicability of conservative tracers for detecting high-saturation nonaqueous-phase liquid (NAPL) entrapment in heterogeneous systems. For this purpose, a series of experiments and simulations was performed using a two-dimensional heterogeneous system (10x1.2 m), which represents an intermediate scale between laboratory and field scales. Tracer tests performed prior to injecting the NAPL provide the baseline response of the heterogeneous porous medium. Two NAPL spill experiments were performed and the entrapped-NAPL saturation distribution measured in detail using a gamma-ray attenuation system. Tracer tests following each of the NAPL spills produced breakthrough curves (BTCs) reflecting the impact of entrapped NAPL on conservative transport. To evaluate significance, the impact of NAPL entrapment on the conservative-tracer breakthrough curves was compared to simulated breakthrough curve variability for different realizations of the heterogeneous distribution. Analysis of the results reveals that the NAPL entrapment has a significant impact on the temporal moments of conservative-tracer breakthrough curves.     

Colloid transport in a geochemically heterogeneous porous medium: aquifer tank experiment and modeling

To examine colloid transport in geochemically heterogeneous porous media at a scale comparable to field experiments, we monitored the migration of silica-coated zirconia colloids in a two-dimensional layered porous media containing sand coated to three different extents by ferric oxyhydroxides. Transport of the colloids was measured over 1.65 m and 95 days. Colloid transport was modeled by an advection-dispersion-deposition equation incorporating geochemical heterogeneity and colloid deposition dynamics (blocking). Geochemical heterogeneity was represented as favorable (ferric oxyhydroxide-coated) and unfavorable (uncoated sand) deposition surface areas. Blocking was modeled as random sequential adsorption (RSA). Release of deposited colloids was negligible. The time to colloid breakthrough after the onset of blocking increased with increasing ferric oxyhydroxide-coated surface area. As the ferric oxyhydroxide surface area increased, the concentration of colloids in the breakthrough decreased. Model-fits to the experimental data were made by inverse solutions to determine the fraction of surface area favorable for deposition and the deposition rate coefficients for the favorable (ferric oxyhydroxide-coated) and unfavorable sites. The favorable deposition rate coefficient was also calculated by colloid filtration theory. The model described the time to colloid breakthrough and the blocking effect reasonably well and estimated the favorable surface area fraction very well for the two layers with more than 1% ferric oxyhydroxide coating. If mica edges in the uncoated sand were considered as favorable surface area in addition to the ferric oxyhydroxide coatings, the model predicted the favorable surface area fraction accurately for the layer with less than 1% ferric oxyhydroxide coating.     

Anthropogenic contaminants as tracers in an urbanizing karst aquifer

Karst aquifers are uniquely vulnerable to contamination. In the Barton Springs segment of the karstic Edwards aquifer (Texas, U.S.A.), urban contaminants such as pesticides and volatile organic compounds frequently are detected in spring base flow. To determine whether contaminant concentrations change in response to storms, and if they therefore might act as tracers of focused recharge, samples were collected from Barton Springs at closely spaced intervals following three storms. Two herbicides (atrazine and simazine), two insecticides (carbaryl and diazinon), and a solvent (tetrachloroethene) described breakthrough curves over a 1-week period following one or more storms. The breakthrough curves were decomposed into two to five log-normal subcurves, which were interpreted as representing pulses of contaminants moving through the aquifer. Each subcurve could be used in the same way as an artificial tracer to determine travel time to and recovery at the spring. The contaminants have several advantages over artificial tracers: they represent the actual compounds of interest, they are injected essentially simultaneously at several points, and they are injected under those conditions when transport is of the most interest, i.e., following storms. The response of storm discharge, specific conductance, and contaminant loading at the spring depended on initial aquifer flow conditions, which varied from very low (spring discharge of 0.48 m3/s) to high (spring discharge of 2.7 m3/s): concentrations and recovery were the highest when initial aquifer flow conditions were low. This behavior provides information about aquifer structure and the influence of aquifer flow condition on transport properties.     

Prediction of some in situ tracer tests with sorbing tracers using independent data

Some recent converging tracer tests with sorbing tracers at the Asp? Hard Rock Laboratory in Sweden, the TRUE tests, have been predicted using only laboratory data and hydraulic data from borehole measurements. No model parameters were adjusted to obtain a better fit with the experiments. The independent data were fracture frequency and transmissivity data obtained in the field and laboratory data on sorption and matrix diffusion. Transmissivity measurements in five boreholes in the rock volume containing the region surrounding the injection and collection points show that there is a high frequency of water conducting fractures. Of 162 packed off sections with 0.5 m packer distances, 112 were found to have a transmissivity above the detection limit. The specific flow-wetted surface (FWS) of the rock mass could be estimated from these data. The transmissivities were found to be reasonably well described by a lognormal distribution. Laboratory data on diffusion and sorption properties together with the hydraulic data were used to "predict" the residence time distribution (RTD) of the sorbing tracers. The results were compared with the experimental breakthrough curves. In these experiments, the water residence time is very small compared to the residence time of the sorbing tracers due to their diffusion and sorption within the rock matrix. We thus could neglect the influence of the water residence time in our predictions. Therefore, no information on water residence times or on "dispersion" was needed. The dispersion of the sorbing tracers is caused by the different sorbing tracer residence times in different pathways. The sorbing tracer residence time is determined by the ratio of flowrate to the flow-wetted surface in the different pathways and not by the water residence time. Assuming a three-dimensional flow pattern and using the observed fracture frequency and flowrate distribution, breakthrough curves for three strongly sorbing tracers were predicted. Only the laboratory data, the transmissivity measurements and the pumping flowrate were used in the predictions. No information on the water residence time as obtained by the nonsorbing tracers was used. The predictions were surprisingly accurate.     

Modelling tritium and phosphorus transport by preferential flow in structured soil

Subsurface solute transport through structured soil is studied by model interpretation of experimental breakthrough curves from tritium and phosphorus tracer tests in three intact soil monoliths. Similar geochemical conditions, with nearly neutral pH, were maintained in all the experiments. Observed transport differences for the same tracer are thus mainly due to differences in the physical transport process between the different monoliths. The modelling is based on a probabilistic Lagrangian approach that decouples physical and chemical mass transfer and transformation processes from pure and stochastic advection. Thereby, it enables explicit quantification of the physical transport process through preferential flow paths, honouring all independently available experimental information. Modelling of the tritium breakthrough curves yields a probability density function of non-reactive solute travel time that is coupled with a reaction model for linear, non-equilibrium sorption–desorption to describe the phosphorus transport. The tritium model results indicate that significant preferential flow occurs in all the experimental soil monoliths, ranging from 60–100% of the total water flow moving through only 25–40% of the total water content. In agreement with the fact that geochemical conditions were similar in all experiments, phosphorus model results yield consistent first-order kinetic parameter values for the sorption–desorption process in two of the three soil monoliths; phosphorus transport through the third monolith cannot be modelled because the apparent mean transport rate of phosphorus is anomalously rapid relative to the non-adsorptive tritium transport. The occurrence of preferential flow alters the whole shape of the phosphorus breakthrough curve, not least the peak mass flux and concentration values, and increases the transported phosphorus mass by 2–3 times relative to the estimated mass transport without preferential flow in the two modelled monoliths.     

Modelling of nonreactive tracer dipole tests in a shear zone at the Grimsel test site

The investigation of the migration of a high pH plume in a fractured shear zone is foreseen by a long-term experiment at the Grimsel rock laboratory. In order to characterise the initial conditions for the long-term experiment and to evaluate an optimal hydraulic in situ set-up, several dipole experiments with nonreacting tracers have been performed. The dipole experiments differ in geometry, pumping rates and orientation to the background water flow. Several single and double-porosity models have been applied to fit the results of these dipole tracer tests in order to extract values for some transport parameters and discriminate for certain transport processes. A two-dimensional porous medium approach was successfully used to fit tracer breakthrough curves measured for a dipole experiment. A model based on a one-dimensional dual porous medium approach was also successful, although the applied hydraulic dipole, with similar injection and extraction rates, suggests the existence of an extended two-dimensional flow field. For the two-dimensional porous medium approach, tracer breakthrough could only be fitted with a complex flow field geometry within the heterogeneous fractured shear zone. The heterogeneity was generated by heterogeneous porosity and hydraulic permeability distributions. Predictions for further dipole geometries and a sorbing tracer have been calculated by means of both models using the flow and transport parameters deduced from fits for a single dipole experiment. This allows for comparison with the measured breakthrough of sorbing tracers. The foreseen experiment with sorbing (radionuclide) tracers will help decide on the appropriate approach that should be used to describe such dipole experiments in this shear zone. Additionally, the migration and spreading of a solution with high pH has been calculated taking into account mineral dissolution and precipitation in a two-dimensional porous medium approach in order to estimate the amount and character of the mineral reactions induced by the interaction between the high pH solution and the rock.     

Analyses of locally measured bromide breakthrough curves from a natural gradient tracer experiment at Krauthausen

Solute travel time distributions were derived from breakthrough curves (BTCs) of bromide concentrations, which were measured during a large-scale tracer experiment in a quaternary fluviatile aquifer at Krauthausen. Travel time distributions to a specific point in the aquifer were derived from locally measured BTCs, using averaged absolute concentrations ?abs(x1,t), normalized concentrations ?norm(x1,t), and velocity-weighted normalized concentrations ?vw(x1,t). The travel time distributions were characterized in terms of equivalent convective-dispersive transport parameters: the equivalent solute velocity and equivalent dispersivity. Parameters were derived from BTCs using moment analyses and least-squares fits of the 1-D convection-dispersion equation (CDE). Both local and averaged BTCs showed pronounced tailing which was not well described by the 1-D CDE and which indicates the presence of macroscopic regions with low velocities in the aquifer. Therefore, dispersivities derived from CDE fits were significantly smaller than those derived from time moments. The BTCs of ?abs(x1,t) were dominated by only a few local BTCs with high concentrations and were less representative for the travel time distribution than BTCs of averaged normalized concentrations. Dispersivities derived from ?norm(x1,t) and ?vw(x1,t) were very similar. Finally, estimates of dispersivities and vertical correlation length of lnK, gamma 3, from BTCs were in agreement with a first-order estimate of the dispersivity and gamma 3 based on grain size data and flow meter measurements.     

Spatial and temporal distribution of solute leaching in heterogeneous soils: analysis and application to multisampler lysimeter data

Accurate assessment of the fate of salts, nutrients, and pollutants in natural, heterogeneous soils requires a proper quantification of both spatial and temporal solute spreading during solute movement. The number of experiments with multisampler devices that measure solute leaching as a function of space and time is increasing. The breakthrough curve (BTC) can characterize the temporal aspect of solute leaching, and recently the spatial solute distribution curve (SSDC) was introduced to describe the spatial solute distribution. We combined and extended both concepts to develop a tool for the comprehensive analysis of the full spatio-temporal behavior of solute leaching. The sampling locations are ranked in order of descending amount of total leaching (defined as the cumulative leaching from an individual compartment at the end of the experiment), thus collapsing both spatial axes of the sampling plane into one. The leaching process can then be described by a curved surface that is a function of the single spatial coordinate and time. This leaching surface is scaled to integrate to unity, and termed S can efficiently represent data from multisampler solute transport experiments or simulation results from multidimensional solute transport models. The mathematical relationships between the scaled leaching surface S, the BTC, and the SSDC are established. Any desired characteristic of the leaching process can be derived from S. The analysis was applied to a chloride leaching experiment on a lysimeter with 300 drainage compartments of 25 cm2 each. The sandy soil monolith in the lysimeter exhibited fingered flow in the water-repellent top layer. The observed S demonstrated the absence of a sharp separation between fingers and dry areas, owing to diverging flow in the wettable soil below the fingers. Times-to-peak, maximum solute fluxes, and total leaching varied more in high-leaching than in low-leaching compartments. This suggests a stochastic-convective transport process in the high-flow streamtubes, while convection dispersion is predominant in the low-flow areas. S can be viewed as a bivariate probability density function. Its marginal distributions are the BTC of all sampling locations combined, and the SSDC of cumulative solute leaching at the end of the experiment. The observed S cannot be represented by assuming complete independence between its marginal distributions, indicating that S contains information about the leaching process that cannot be derived from the combination of the BTC and the SSDC.     

Experiments on vertical transverse mixing in a large-scale heterogeneous model aquifer

Vertical transverse mixing is known to be a controlling factor in natural attenuation of extended biodegradable plumes originating from continuously emitting sources. We perform conservative and reactive tracer tests in a quasi two-dimensional 14 m long sand box in order to quantify vertical mixing in heterogeneous media. The filling mimics natural sediments including a distribution of different hydro-facies, made of different sand mixtures, and micro-structures within the sand lenses. We quantify the concentration distribution of the conservative tracer by the analysis of digital images taken at steady state during the tracer-dye experiment. Heterogeneity causes plume meandering, leading to distorted concentration profiles. Without knowledge about the velocity distribution, it is not possible to determine meaningful vertical dispersion coefficients from the concentration profiles. Using the stream-line pattern resulting from an inverse model of previous experiments in the sand box, we can correct for the plume meandering. The resulting vertical dispersion coefficient is approximately approximately 4 x 10(-)(9) m(2)/s. We observe no distinct increase in the vertical dispersion coefficient with increasing travel distance, indicating that heterogeneity has hardly any impact on vertical transverse mixing. In the reactive tracer test, we continuously inject an alkaline solution over a certain height into the domain that is occupied otherwise by an acidic solution. The outline of the alkaline plume is visualized by adding a pH indicator into both solutions. From the height and length of the reactive plume, we estimate a transverse dispersion coefficient of approximately 3 x 10(-)(9) m(2)/s. Overall, the vertical transverse dispersion coefficients are less than an order of magnitude larger than pore diffusion coefficients and hardly increase due to heterogeneity. Thus, we conclude for the assessment of natural attenuation that reactive plumes might become very large if they are controlled by vertical dispersive mixing.     

Estimating first-order reaction rate coefficient for transport with nonequilibrium linear mass transfer in heterogeneous media

A travel-time based approach is developed for estimating first-order reaction rate coefficients for transport with nonequilibrium linear mass transfer in heterogeneous media. Tracer transport in the mobile domain is characterized by a travel-time distribution, and mass transfer rates are described by a convolution product of concentrations in the mobile domain and a memory function rather than predefining the mass transfer model. A constant first-order reaction is assumed to occur only in the mobile domain. Analytical solutions in Laplace domain can be derived for both conservative and reactive breakthrough curves (BTCs). Temporal-moment analyses are presented by using the first and second moments of conservative and reactive BTCs and the mass consumption of the reactant for an inverse Gaussian travel-time distribution. In terms of moment matching, there is no need for one to specify the mass transfer model. With the same capacity ratio and the mean retention time, all mass transfer models will lead to the same moment-derived reaction rate coefficients. In addition, the consideration of mass transfer generally yields larger estimations of the reaction rate coefficient than models ignoring mass transfer. Furthermore, the capacity ratio and the mean retention time have opposite influences on the estimation of the reaction rate coefficient: the first-order reaction rate coefficient is positively linearly proportional to the capacity ratio, but negatively linearly proportional to the mean retention time.     

Analysis of groundwater contamination using concentration-time series recorded during an integral pumping test: bias introduced by strong concentration gradients within the plume

When only few monitoring wells are available to assess the extent and level of groundwater contamination, inversion of concentration breakthrough curves acquired during an integral pumping test can be used as an alternative quantification method. The idea is to use concentration-time series recorded during integral pumping tests through an inversion technique to estimate contaminant mass fluxes crossing a control plane. In this paper, we examine how a longitudinal concentration gradient along a contaminant plume length scale affects the estimated inversed-concentration distribution and its associated mass flux. The analytically inversed-concentration distribution at the imaginary control plane (ICP) is compared to a numerically generated concentration distribution, treating the latter one as a "real contaminant plume" characterized by the presence of a longitudinal concentration gradient. It is found that the analytically inversed-concentration can lead to overestimation or underestimation of concentration distribution values depending on the transport time period and dispersivity values. At lower dispersivity values, with shorter transport time periods, the analytically inversed-concentration distribution overestimates the "real" concentration distribution. A better fit of the estimated concentration distribution to the "real" one is observed when the transport time period increases, i.e. when the advective front has already crossed the ICP. However, for higher dispersivity values, underestimation of the real concentration distribution is observed. Deviation of the inversed-concentration distribution from the "real" one is assessed for a site-specific concentration gradient term. A concentration gradient adjusted contaminant mass flux is thus formulated to evaluate groundwater contamination levels at a given time period through an ICP. This concentration gradient ratio can indicate whether the ICP is well positioned to evaluate accurately contaminant mass fluxes which are representative of groundwater contamination levels.     

Inverse modeling of multicomponent reactive transport through single and dual porosity media

Compacted bentonite is foreseen as buffer material for high-level radioactive waste in deep geological repositories because it provides hydraulic isolation, chemical stability, and radionuclide sorption. A wide range of laboratory tests were performed within the framework of FEBEX (Full-scale Engineered Barrier EXperiment) project to characterize buffer properties and develop numerical models for FEBEX bentonite. Here we present inverse single and dual-continuum multicomponent reactive transport models of a long-term permeation test performed on a 2.5 cm long sample of FEBEX bentonite. Initial saline bentonite porewater was flushed with 5.5 pore volumes of fresh granitic water. Water flux and chemical composition of effluent waters were monitored during almost 4 years. The model accounts for solute advection and diffusion and geochemical reactions such as aqueous complexation, acid-base, cation exchange, protonation/deprotonation by surface complexation and dissolution/precipitation of calcite, chalcedony and gypsum. All of these processes are assumed at local equilibrium. Similar to previous studies of bentonite porewater chemistry on batch systems which attest the relevance of protonation/deprotonation on buffering pH, our results confirm that protonation/deprotonation is a key process in maintaining a stable pH under dynamic transport conditions. Breakthrough curves of reactive species are more sensitive to initial porewater concentration than to effective diffusion coefficient. Optimum estimates of initial porewater chemistry of saturated compacted FEBEX bentonite are obtained by solving the inverse problem of multicomponent reactive transport. While the single-continuum model reproduces the trends of measured data for most chemical species, it fails to match properly the long tails of most breakthrough curves. Such limitation is overcome by resorting to a dual-continuum reactive transport model.