Choice of dispersion coefficients in reactive transport calculations on smoothed fields

Local dispersion dominates the mixing of compounds that are introduced separately into the subsurface and do not partition into any other than the aqueous phase. Thus, reactions between these compounds are controlled by dispersive mixing if they are not limited by kinetics. I quantify longitudinal dispersive mixing by the longitudinal effective dispersion coefficient of a conservative tracer introduced by a point-like injection [Water Resour. Res. 36 (12) (2000) 3591-3604]. In the upscaling of mixing-controlled reactive transport, I apply the mean velocity and the effective dispersion coefficient to the macroscopic transport calculations, whereas the reactive parameters on the macro-scale are identical to those on the local scale. The applicability of the approach is demonstrated for the transport of compounds undergoing a second-order irreversible bimolecular reaction. Ten realizations of a two-dimensional heterogeneous log-conductivity field are considered. Using the effective dispersion parameters, the overall mass balance is met in the ensemble average, whereas solute spreading is underestimated. I assess the lack of spreading by the difference between the expected macrodispersion and effective dispersion coefficients. I extend the approach to simulations on log-conductivity fields obtained by kriging of regularly spaced conductivity measurements. These fields contain the large-scale features of the true fields but do not resolve the small-scale variability. For the calculations on the kriged fields, the corresponding conditional covariance is substituted into the analytical expressions of effective dispersion, yielding a correction effective dispersion coefficient. The comparison between simulations on the fully resolved fields and on the kriged fields indicates that the approach is valid for wide plumes meeting the ergodicity condition. The high variability of mixing on small scales unresolved by kriging, however, leads to severe uncertainty when mixing-controlled reactions are predicted for narrow plumes.     

Estimating spatially-variable first-order rate constants in groundwater reactive transport systems

Numerical reactive transport models are often used as tools to assess aquifers contaminated with reactive groundwater solutes as well as investigating mitigation scenarios. The ability to accurately simulate the fate and transport of solutes, however, is often impeded by a lack of information regarding the parameters that define chemical reactions. In this study, we employ a steady-state Ensemble Kalman Filter (EnKF), a data assimilation algorithm, to provide improved estimates of a spatially-variable first-order rate constant λ through assimilation of solute concentration measurement data into reactive transport simulation results. The methodology is applied in a steady-state, synthetic aquifer system in which a contaminant is leached to the saturated zone and undergoes first-order decay. Multiple sources of uncertainty are investigated, including hydraulic conductivity of the aquifer and the statistical parameters that define the spatial structure of the parameter field. For the latter scenario, an iterative method is employed to identify the statistical mean of λ of the reference system. Results from all simulations show that the filter scheme is successful in conditioning the λ ensemble to the reference λ field. Sensitivity analyses demonstrate that the estimation of the λ values is dependent on the number of concentration measurements assimilated, the locations from which the measurement data are collected, the error assigned to the measurement values, and the correlation length of the λ fields.     

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.     

Contaminant transport in groundwater in the presence of colloids and bacteria: Model development and verification

Colloids and bacteria (microorganisms) naturally exist in groundwater aquifers and can significantly impact contaminant migration rates. A conceptual model is first developed to account for the different physiochemical and biological processes, reaction kinetics, and different transport mechanisms of the combined system (contaminant–colloids–bacteria). All three constituents are assumed to be reactive with the reactions taking place between each constituent and the porous medium and also among the different constituents. A general linear kinetic reaction model is assumed for all reactive processes considered. The mathematical model is represented by fourteen coupled partial differential equations describing mass balance and reaction processes. Two of these equations describe colloid movement and reactions with the porous medium, four equations describe bacterial movement and reactions with colloids and the porous medium, and the remaining eight equations describe contaminant movement and its reactions with bacteria, colloids, and the porous medium. The mass balance equations are numerically solved for two-dimensional groundwater systems using a third-order, total variance-diminishing scheme (TVD) for the advection terms. Due to the complex coupling of the equations, they are solved iteratively each time step until a convergence criterion is met. The model is tested against experimental data and the results are favorable.     

Concentration statistics for mixing-controlled reactive transport in random heterogeneous media

Uncertainty in the distribution of hydraulic parameters leads to uncertainty in flow and reactive transport. Traditional stochastic analysis of solute transport in heterogeneous media has focused on the ensemble mean of conservative-tracer concentration. Studies in the past years have shown that the mean concentration often is associated with a high variance. Because the range of possible concentration values is bounded, a high variance implies high probability weights on the extreme values. In certain cases of mixing-controlled reactive transport, concentrations of conservative tracers, denoted mixing ratios, can be mapped to those of constituents that react with each other upon mixing. This facilitates mapping entire statistical distributions from mixing ratios to reactive-constituent concentrations. In perturbative approximations, only the mean and variance of the mixing-ratio distribution are used. We demonstrate that the second-order perturbative approximation leads to erroneous or even physically impossible estimates of mean reactive-constituent concentrations when the variance of the mixing ratio is high and the relationship between the mixing ratio and the reactive-constituent concentrations strongly deviates from a quadratic function. The latter might be the case in biokinetic reactions or in equilibrium reactions with small equilibrium constant in comparison to the range of reactive-constituent concentrations. When only the mean and variance of the mixing ratio is known, we recommend assuming a distribution that meets the known bounds of the mixing ratio, such as the beta distribution, and mapping the assumed distribution of the mixing ratio to the distributions of the reactive constituents.     

Temporal evolution of DNAPL source and contaminant flux distribution: impacts of source mass depletion

We investigated, using model simulations, the changes occurring in the distribution of dense non-aqueous phase liquid (DNAPL) mass (Sn) within the source zone during depletion through dissolution, and the resulting changes in the contaminant flux distribution (J) at the source control plane (CP). Two numerical codes (ISCO3D and T2VOC) were used to simulate selected scenarios of DNAPL dissolution and transport in three-dimensional, heterogeneous, spatially correlated, random permeability fields with emplaced sources. Data from the model simulations were interpreted based on population statistics (mean, standard deviation, coefficient of variation) and spatial statistics (centroid, second moments, variograms). The mean and standard deviation of the Sn and J distributions decreased with source mass depletion by dissolution. The decrease in mean and standard deviation was proportional for the J distribution resulting in a constant coefficient of variation (CV), while for the Sn distribution, the mean decreased faster than the standard deviation. The spatial distributions exhibited similar behavior as the population distribution, i.e., the CP flux distribution was more stable (defined by temporally constant second moments and range of variograms) than the Sn distribution. These observations appeared to be independent of the heterogeneity of the permeability (k) field (variance of the log permeability field=1 and 2.45), correlation structure (positive vs. negative correlation between the k and Sn domains) and the DNAPL dissolution model (equilibrium vs. rate-limited), for the cases studied. Analysis of data from a flux monitoring field study (Hill Air Force Base, Utah) at a DNAPL source CP before and after source remediation also revealed temporal invariance of the contaminant flux distribution. These modeling and field observations suggest that the temporal evolution of the contaminant flux distribution can be estimated if the initial distribution is known. However, the findings are preliminary and broader implications to sampling strategies for remediation performance assessment need to be evaluated in additional modeling and experimental studies.     

Modelling of physical and reactive processes during biodegradation of a hydrocarbon plume under transient groundwater flow conditions

Numerical experiments of non-reactive and reactive transport were carried out to quantify the influence of a seasonally varying, transient flow field on transport and natural attenuation at a hydrocarbon-contaminated field site. Different numerical schemes for solving advective transport were compared to assess their capability to model low transversal dispersivities in transient flow fields. For the field site, it is shown that vertical plume spreading is largely inhibited, particularly if sorption is taken into account. For the reactive simulations, a biodegradation reaction module for the geochemical transport model PHT3D was developed. Results of the reactive transport simulations show that under the site-specific conditions the temporal variations in groundwater flow do, to a modest extent, affect average biodegradation rates and average total (dissolved) contaminant mass in the aquifer. The model simulations demonstrate that the seasonal variability in groundwater flow only results in significantly enhanced biodegradation rates when a differential sorption of electron donor (toluene) and electron acceptor (sulfate) is assumed.     

Contaminant transport in dual-porosity media with dissolved organic matter and bacteria present as mobile colloids

In riverbank filtration, contaminant transport is affected by colloidal particles such as dissolved organic matter (DOM) and bacterial particles. In addition, the subsurface heterogeneity influences the behavior of contaminant transport in riverbank filtration. A mathematical model is developed to describe the contaminant transport in dual-porosity media in the presence of DOM and bacteria as mobile colloids. In the model development, a porous medium is divided into the mobile and immobile regions to consider the presence of ineffective micropores in physically heterogeneous riverbanks. We assume that the contaminant transport in the mobile region is controlled by the advection and dispersion while the contaminant transport in the immobile region occurs due to the molecular diffusion. The contaminant transfer between the mobile and immobile regions takes place by diffusive mass transfer. The mobile region is conceptualized as a four-phase system: two mobile colloidal phases, an aqueous phase, and a solid matrix. The complete set of governing equations is solved numerically with a fully implicit finite difference method. The model results show that in riverbank filtration, the contaminant can migrate further than expected due to the presence of DOM and bacteria. In addition, the contaminant mobility increases further in the presence of the immobile region in aquifers. A sensitivity analysis shows that in dual-porosity media, earlier breakthrough of the contaminant takes place as the volumetric fraction of the mobile region decreases. It is also demonstrated that as the contaminant mass transfer rate coefficient between the mobile and immobile regions increases, the contaminant concentration gradient between the two regions reverses at earlier pore volumes. The contaminant mass transfer coefficient between the mobile and immobile regions mainly controls the tailing effect of the contaminant breakthrough. The contaminant breakthrough curves are sensitive to changes in contaminant adsorption and desorption rate coefficients on DOM and bacteria. In situations where the contaminant is released in the presence of DOM and bacteria in dual-porosity media, the early breakthrough and tailing occur due to the colloidal facilitation and presence of immobile regions.     

Convergent-flow tracer tests in heterogeneous media: combined experimental-numerical analysis for determination of equivalent transport parameters

In modeling transport within naturally heterogeneous aquifers, it is usually assumed that the transport equations valid at local scales can also be applied at larger scales. At larger scales, the heterogeneous domain is represented by an equivalent homogeneous medium. Convergent-flow tracer tests constitute one of the most frequently used field tests to estimate effective input parameters of equivalent homogeneous aquifers. Traditionally, statistical approaches applied to groundwater flow and solute transport have provided tools to estimate these equivalent parameters. These approaches are based on a number of simplifications including the assumption that the point transmissivity values follow a multilog-normal random function. Several investigators have found that this assumption may not be valid in many field cases. In order to study the applicability of the equivalent homogeneous formulation in a nontraditional stochastic field, a number of experimental and numerical studies were conducted. The results are used to determine the apparent values of porosity and dispersivity that would be obtained if convergent-flow tracer tests were conducted in a deterministically generated heterogeneous transmissivity field displaying anisotropy in the correlation structure. It is shown that in this particular heterogeneous media, apparent porosity strongly depends on connectivity rather than on transmissivity. This dependence on connectivity questions the theoretical results obtained in continuum equivalent fields to estimate effective porosity.     

Stochastic-convective transport with nonlinear reaction and mixing: application to intermediate-scale experiments in aerobic biodegradation in saturated porous media

Aerobic biodegradation of benzoate by Pseudomonas cepacia sp. in a saturated heterogeneous porous medium was simulated using the stochastic-convective reaction (SCR) approach. A laboratory flow cell was randomly packed with low permeability silt-size inclusions in a high permeability sand matrix. In the SCR upscaling approach, the characteristics of the flow field are determined by the breakthrough of a conservative tracer. Spatial information on the actual location of the heterogeneities is not used. The mass balance equations governing the nonlinear and multicomponent reactive transport are recast in terms of reactive transports in each of a finite number of discrete streamtubes. The streamtube ensemble members represent transport via a steady constant average velocity per streamtube and a conventional Fickian dispersion term, and their contributions to the observed breakthroughs are determined by flux-averaging the streamtube solute concentrations. The resulting simulations were compared to those from a high-resolution deterministic simulation of the reactive transport, and to alternative ensemble representations involving (i) effective Fickian travel time distribution function, (ii) purely convective streamtube transport, and (iii) streamtube ensemble subset simulations. The results of the SCR simulation compare favorably to that of a sophisticated high-resolution deterministic approach.     

Contamination potential of nitrogen compounds in the heterogeneous aquifers of the Choushui River alluvial fan, Taiwan

This study aimed to analyze the contamination potential associated with the reactive transport of nitrate-N and ammonium-N in the Choushui River alluvial fan, Taiwan and to evaluate a risk region in developing a groundwater protection policy in 2021. In this area, an aquifer redox sequence provided a good understanding of the spatial distributions of nitrate-N and ammonium-N and of aerobic and anaerobic environments. Equiprobable hydraulic conductivity (K) fields reproduced by geostatistical methods characterized the spatial uncertainty of contaminant transport in the heterogeneous aquifer. Nitrogen contamination potential fronts for high and low threshold concentrations based on a 95% risk probability were used to assess different levels of risk. The simulated result reveals that the spatial uncertainty of highly heterogeneous K fields governs the contamination potential assessment of the nitrogen compounds along the regional flow directions. The contamination potential of nitrate-N is more uncertain than that for ammonium-N. The high nitrate-N concentrations (> or =3 mg/L) are prevalent in the aerobic environment. The low concentration nitrate-N plumes (0.5-3 mg/L) gradually migrate to the mid-fan area and to a maximum distance of 15 km from the aerobic region. The nitrate-N plumes pose a potential human health risk in the aerobic and anaerobic environments. The ammonium-N plumes remain stably confined to the distal-fan and partial mid-fan areas.     

Influence of temporally variable groundwater flow conditions on point measurements and contaminant mass flux estimations

Monitoring of contaminant concentrations, e.g., for the estimation of mass discharge or contaminant degradation rates, often is based on point measurements at observation wells. In addition to the problem, that point measurements may not be spatially representative, a further complication may arise due to the temporal dynamics of groundwater flow, which may cause a concentration measurement to be not temporally representative. This paper presents results from a numerical modeling study focusing on temporal variations of the groundwater flow direction. “Measurements” are obtained from point information representing observation wells installed along control planes using different well frequencies and configurations. Results of the scenario simulations show that temporally variable flow conditions can lead to significant temporal fluctuations of the concentration and thus are a substantial source of uncertainty for point measurements. Temporal variation of point concentration measurements may be as high as the average concentration determined, especially near the plume fringe, even when assuming a homogeneous distribution of the hydraulic conductivity. If a heterogeneous hydraulic conductivity field is present, the concentration variability due to a fluctuating groundwater flow direction varies significantly within the control plane and between the different realizations. Determination of contaminant mass fluxes is also influenced by the temporal variability of the concentration measurement, especially for large spacings of the observation wells. Passive dosimeter sampling is found to be appropriate for evaluating the stationarity of contaminant plumes as well as for estimating average concentrations over time when the plume has fully developed. Representative sampling has to be performed over several periods of groundwater flow fluctuation. For the determination of mass fluxes at heterogeneous sites, however, local fluxes, which may vary considerably along a control plane, have to be accounted for. Here, dosimeter sampling in combination with time integrated local water flux measurements can improve mass flux estimates under dynamic flow conditions.     

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.     

Monitoring groundwater contamination and delineating source zones at industrial sites: uncertainty analyses using integral pumping tests

Field-scale characterisations of contaminant plumes in groundwater, as well as source zone delineations, are associated with uncertainties that can be considerable. A major source of uncertainty in environmental datasets is due to variability of sampling results, as a direct consequence of the heterogeneity of environmental matrices. We develop a methodology for quantifying uncertainties in field-scale mass flow and average concentration estimations, using integral pumping tests (IPTs), where the contaminant concentration is measured as a function of time in a pumping well. This procedure increases the sampling volume and reduces the effect of small-scale variability that may bias point-scale measurements. In particular, using IPTs, the interpolation uncertainty of conventional point-scale measurements is transformed to a quantifiable uncertainty related to the (unknown) plume position relative to the pumping well. We show that this plume position uncertainty generally influenced the predicted mass flows and average concentrations (of acenapthene, benzene and CHCs) to a greater extent than a boundary condition uncertainty related to the local water balance, considering 19 control planes at a highly heterogeneous industrial site in southwest Germany. Furthermore, large (order of magnitude) uncertainties only occurred if the conditions were strongly heterogeneous in the nearest vicinity of the well. We also develop a consistent methodology for an assessment of the combined effect of uncertainty in hydraulic conditions and uncertainty in reactive transport parameters for delimiting of both contaminant source zones and zones absent of source, based on (downgradient) IPTs.     

A novel two-dimensional model for colloid transport in physically and geochemically heterogeneous porous media

A two-dimensional model for colloid transport in geochemically and physically heterogeneous porous media is presented. The model considers patchwise geochemical heterogeneity, which is suitable to describe the chemical variability of many surficial aquifers with ferric oxyhydroxide-coated porous matrix, as well as spatial variability of hydraulic conductivity, which results in heterogeneous flow field. The model is comprised of a transient fluid flow equation, a transient colloid transport equation, and an equation for the dynamics of colloid deposition and release. Numerical simulations were carried out with the model to investigate the colloid transport behavior in layered and randomly heterogeneous porous media. Results demonstrate that physical and geochemical heterogeneities markedly affect the colloid transport behavior. Layered physical or geochemical heterogeneity can result in distinct preferential flow paths of colloidal particles. Furthermore, the combined effect of layered physical and geochemical heterogeneity may result in enhanced or reduced preferential flow of colloids. Random distribution of physical heterogeneity (hydraulic conductivity) results in a random flow field and an irregularly distributed colloid concentration profile in the porous medium. Contrary to random physical heterogeneity, the effect of random patchwise geochemical heterogeneity on colloid transport behavior is not significant. It is mostly the mean value of geochemical heterogeneity rather than its distribution that governs the colloid transport behavior.     

Optimal design of pump-and-treat systems under uncertain hydraulic conductivity and plume distribution

In this work, we present a stochastic optimal control framework for assisting the management of the cleanup by pump-and-treat of polluted shallow aquifers. In the problem being investigated, hydraulic conductivity distribution and dissolved contaminant plume location are considered as the uncertain variables. The framework considers the subdivision of the cleanup horizon in a number of stress periods over which the pumping policy implemented until that stage is dynamically adjusted based upon new information that has become available in the previous stages. In particular, by following a geostatistical approach, we study the idea of monitoring the cumulative contaminant mass extracted from the installed recovery wells, and using these measurements to generate conditional realizations of the hydraulic conductivity field. These realizations are thus used to obtain a more accurate evaluation of the initial plume distribution, and modify accordingly the design of the pump-and-treat system for the remainder of the remedial process. The study indicates that measurements of contaminant mass extracted from pumping wells retain valuable information about the plume location and the spatial heterogeneity characterizing the hydraulic conductivity field. However, such an information may prove quite soft, particularly in the instances where recovery wells are installed in regions where contaminant concentration is low or zero. On the other hand, integrated solute mass measurements may effectively allow for reducing parameter uncertainty and identifying the plume distribution if more recovery wells are available, in particular in the early stages of the cleanup process.     

Analytical model of solute transport by unsteady unsaturated gravitational infiltration

Penetration of reactive solute into a soil during a cycle of water infiltration and redistribution is investigated by deriving analytical closed form solutions for fluid flux, moisture content and contaminant concentration. The solution is developed for gravitational flow and advective transport and is applied to two scenarios of solute applications encountered in the applications: a finite pulse of solute dissolved in irrigation water and an instantaneous pulse broadcasted onto the soil surface. Through comparison to simulations of Richards' flow, capillary suction is shown to have contrasting effects on the upper and lower boundaries of the fluid pulse, speeding penetration of the wetting front and reducing the rate of drying. This leads to agreement between the analytical and numerical solutions for typical field and experimental conditions. The analytical solution is further incorporated into a stochastic column model of flow and transport to compute mean solute concentration in a heterogeneous field. An unusual phenomenon of plume contraction is observed at long times of solute propagation during the drying stage. The mean concentration profiles match those of the Monte-Carlo simulations for capillary length scales typical of sandy soils.     

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.     

Effects of pore volume-transmissivity correlation on transport phenomena

The relevant velocity that describes transport phenomena in a porous medium is the pore velocity. For this reason, one needs not only to describe the variability of transmissivity, which fully determines the Darcy velocity field for given source terms and boundary conditions, but also any variability of the pore volume. We demonstrate that hydraulically equivalent media with exactly the same transmissivity field can produce dramatic differences in the displacement of a solute if they have different pore volume distributions. In particular, we demonstrate that correlation between pore volume and transmissivity leads to a much smoother and more homogeneous solute distribution. This was observed in a laboratory experiment performed in artificial fractures made of two plexiglass plates into which a space-dependent aperture distribution was milled. Using visualization by a light transmission technique, we observe that the solute behaviour is much smoother and more regular after the fractures are filled with glass powder, which plays the role of a homogeneous fault gouge material. This is due to a perfect correlation between pore volume and transmissivity that causes pore velocity to be not directly dependent on the transmissivity, but only indirectly through the hydraulic gradient, which is a much smoother function due to the diffusive behaviour of the flow equation acting as a filter. This smoothing property of the pore volume-transmissivity correlation is also supported by numerical simulations of tracer tests in a dipole flow field. Three different conceptual models are used: an empty fracture, a rough-walled fracture filled with a homogeneous material and a parallel-plate fracture with a heterogeneous fault gouge. All three models are hydraulically equivalent, yet they have a different pore volume distribution. Even if piezometric heads and specific flow rates are exactly the same at any point of the domain, the transport process differs dramatically. These differences make it important to discriminate in situ among different conceptual models in order to simulate correctly the transport phenomena. For this reason, we study the solute breakthrough and recovery curves at the extraction wells. Our numerical case studies show that discrimination on the basis of such data might be impossible except under very favourable conditions, i.e. the integral scale of the transmissivity field has to be known and small compared to the dipole size. If the latter conditions are satisfied, discrimination between the rough-walled fracture filled with a homogeneous material and the other two models becomes possible, whereas the parallel-plate fracture with a heterogeneous fault gouge and the empty fracture still show identifiability problems. The latter may be solved by inspection of aperture and pressure testing.     

Three-dimensional density-dependent flow and multicomponent reactive transport modeling of chlorinated solvent oxidation by potassium permanganate

A popular method for the treatment of aquifers contaminated with chlorinated solvents is chemical oxidation based on the injection of potassium permanganate (KMnO₄). Both the high density (1025 gL^− 1) and reactivity of the treatment solution influence the fate of permanganate (MnO₄) in the subsurface and affect the degree of contaminant treatment. The MIN3P multicomponent reactive transport code was enhanced to simulate permanganate-based remediation, to evaluate the pathways of MnO₄ utilization, and to assess the role of density contrasts for the delivery of the treatment solution. The modified code (MIN3P-D) provides a direct coupling between density-dependent fluid flow, solute transport, contaminant treatment, and geochemical reactions. The model is used to simulate a field trial of TCE oxidation in a sandy aquifer that is underlain by an aquitard. Three-dimensional simulations are conducted for a coupled reactive system comprised of ten aqueous components, two mineral phases, TCE (dissolved, adsorbed, and NAPL), reactive organic matter, and including ion exchange reactions. Model parameters are constrained by literature data and a detailed data set from the field site under investigation. The general spatial and transient evolution in observed concentrations of the oxidant, dissolved TCE, and reaction products are adequately reproduced by the simulations. The model elucidates the important role of density-induced flow and transport on the distribution of the treatment solution into NAPL containing regions located at the aquifer–aquitard interface. Model results further suggest that reactions that do not directly affect the stability of MnO₄ have a negligible effect on solution density and MnO₄ delivery.