Contributions of advective and diffusive oxygen transport through multilayer composite caps over mine waste

The relative contributions of four mechanisms of oxygen transport in multilayer composite (MLC) caps placed over oxygen-consuming mine waste were evaluated using numerical and analytical methods. MLC caps are defined here as caps consisting of earthen and geosynthetic (polymeric) components where a composite barrier layer consisting of a geomembrane (1-2 mm thick polymeric sheet) overlying a clay layer is the primary barrier to transport. The transport mechanisms that were considered are gas-phase advective transport, gas-phase diffusive transport, liquid-phase advective transport via infiltrating precipitation and liquid-phase diffusive transport. A numerical model was developed to simulate gas-phase advective-diffusive transport of oxygen through a multilayer cap containing seven layers. This model was also used to simulate oxygen diffusion in the liquid phase. An approximate analytical method was used to compute the advective flux of oxygen in the liquid phase. The numerical model was verified for limiting cases using an analytical solution. Comparisons were also made between model predictions and field data for earthen caps reported by others. Results of the analysis show that the dominant mechanism for oxygen transport through MLC caps is gas-phase diffusion. For the cases that were considered, the gas-phase diffusive flux typically comprises at least 99% of the total oxygen flux. Thus, designers of MLC caps should focus on design elements and features that will limit diffusion of gas-phase oxygen.     

Modelling the transport of suspended particulate matter by the Rhone River plume (France). Implications for pollutant dispersion

A model to simulate the transport of suspended particulate matter by the Rhone River plume has been developed. The model solves the 3D hydrodynamic equations, including baroclinic terms and a 1-equation turbulence model, and the suspended matter equations including advection/diffusion of particles, settling and deposition. Four particle classes are considered simultaneously according to observations in the Rhone. Computed currents, salinity and particle distributions are, in general, in good agreement with observations or previous calculations. The model also provides sedimentation rates and the distribution of different particle classes over the sea bed. It has been found that high sedimentation rates close to the river mouth are due to coarse particles that sink rapidly. Computed sedimentation rates are also similar to those derived from observations. The model has been applied to simulate the transport of radionuclides by the plume, since suspended matter is the main vector for them. The radionuclide transport model, previously described and validated, includes exchanges of radionuclides between water, suspended matter and bottom sediment described in terms of kinetic rates. A new feature is the explicit inclusion of the dependence of kinetic rates upon salinity. The model has been applied to 137Cs and 239,240Pu. Results are, in general, in good agreement with observations.     

Application and test of a simple tool for operational footprint evaluations

We present a user-friendly tool for footprint calculations of flux measurements in the surface layer. The calculations are based on the analytical footprint model by Kormann, R. and Meixner, F.X. [2001. An analytical footprint model for Non-neutral Stratification. Boundary-Layer Meteorology 99, 207-224]. The footprint density function of a flux sensor is determined using readily available data from standard eddy covariance measurements. This footprint density function is integrated over defined surface areas given as quadrangular polygons representing e.g. agricultural fields. We illustrate the use and performance of the tool by applying it to CO2 flux measurements with three eddy covariance system at the Swiss CarboEurope grassland site. Two flux towers were positioned in the centre of two neighbouring fields, respectively, that showed a very different CO2 flux during the study period. The third tower was located near the border of the two fields and was frequently influenced by both fields to a similar degree. The calculated footprint fractions were used to simulate the latter flux from the other two systems. The measured and simulated fluxes showed a good agreement and thus support the reliability of the footprint calculation. The presented simple footprint tool can be used as a routine quality check for flux monitoring stations influenced by surface areas with varying vegetation covers and/or land-use.     

Analytical modelling of stable isotope fractionation of volatile organic compounds in the unsaturated zone

Analytical models were developed that simulate stable isotope ratios of volatile organic compounds (VOCs) near a point source contamination in the unsaturated zone. The models describe diffusive transport of VOCs, biodegradation and source ageing. The mass transport is governed by Fick's law for diffusion. The equation for reactive transport of VOCs in the soil gas phase was solved for different source geometries and for different boundary conditions. Model results were compared to experimental data from a one-dimensional laboratory column and a radial-symmetric field experiment. The comparison yielded a satisfying agreement. The model results clearly illustrate the significant isotope fractionation by gas phase diffusion under transient state conditions. This leads to an initial depletion of heavy isotopes with increasing distance from the source. The isotope evolution of the source is governed by the combined effects of isotope fractionation due to vaporisation, diffusion and biodegradation. The net effect can lead to an enrichment or depletion of the heavy isotope in the remaining organic phase, depending on the compound and element considered. Finally, the isotope evolution of molecules migrating away from the source and undergoing degradation is governed by a combined degradation and diffusion isotope effect. This suggests that, in the unsaturated zone, the interpretation of biodegradation of VOC based on isotopic data must always be based on a model combining gas phase diffusion and degradation.     

Fluid flow and solute transport in a network of channels

A new model to describe flow and transort in fractured rocks is proposed. It is based on the concept of a network of channels. The individual channel members are given stochastically selected conductances and volumes. Flow-rate calculations have been performed. For large standard deviations in conductances, channeling becomes pronounced with most of the water flowing in a few paths. The effluent patterns and flow-rate distributions obtained in the simulations have been compared to three field measurements in drifts and tunnels of flow-rate distributions. Standard deviations of channel conductances were between 1.6 and 2.4 in some cases. A particle-following technique was used to simulate solute transport in the network. Non-sorbing as well as sorbing solute transport can be simulated. By using a special technique, solutes that diffuse into the rock matrix can also be simulated.     

The Limitations of Air Quality Standards

This paper describes a diffusion model designed to permit calculation of seasonal average concentrations of an air pollutant, in particular, sulfur dioxide. The calculations can encompass multiple sources and multiple receptors. For each receptor location the model sums the effect of all sources over a wide range of meteorological conditions. Input data include source pollutant emissions, source configuration and location, receptor location, and meteorological data expressed as a joint frequency distribution of wind direction, wind speed, stability. To determine the model’s accuracy, concentration estimates for St. Louis, Mo., are compared with measured SO₂ concentrations. The overall correlation with observed data is satisfactory. A computer program to handle the numerous calculations was written in Fortran IV language for use on an IBM 1130 computer.     

Validation of the operational emergency response model at the Swedish Meteorological and Hydrological Institute using data from etex and the chernobyl accident

The Eulerian atmospheric tracer transport model MATCH (Multiscale Atmospheric Transport and Chemistry model) has been extended with a Lagrangian particle model treating the initial dispersion of pollutants from point sources. The model has been implemented at the Swedish Meteorological and Hydrological Institute in an emergency response system for nuclear accidents and can be activated on short notice to provide forecast concentration and deposition fields.The model has been used to simulate the transport of the inert tracer released during the ETEX experiment and the transport and deposition of ¹³⁷Cs from the Chernobyl accident. Visual inspection of the results as well as statistical analysis shows that the extent, time of arrival and duration of the tracer cloud, is in good agreement with the observations for both cases, with a tendency towards over-prediction for the first ETEX release. For the Chernobyl case the simulated deposition pattern over Scandinavia and over Europe as a whole agrees with observations when observed precipitation is used in the simulation. When model calculated precipitation is used, the quality of the simulation is reduced significantly and the model fails to predict major features of the observed deposition field.     

Multidimensional, multicomponent, subsurface reactive transport in nonuniform velocity fields: code verification using an advective reactive streamtube approach

High performance computing has made possible the development of high resolution, multidimensional, multicomponent reactive transport models that can be used to analyze complex geochemical environments. However, as increasingly complex processes are included in these models, the accuracy of the numerical formulation coupling the nonlinear processes becomes difficult to verify. Analytical solutions are not available for realistically complex problems and benchmark solutions are not generally available for specific problems. We present an advective reactive streamtube (ARS) transport technique that efficiently provides accurate solutions of nonlinear multicomponent reactive transport in nonuniform multidimensional velocity fields. These solutions can be compared with results from Eulerian-based advection-dispersion-reaction models to evaluate the accuracy of the numerical formulation used. The ARS technique includes mixed equilibrium and kinetic complexation and precipitation-dissolution reactions subject to the following assumptions: (1) transport is purely advective (i.e., no explicit diffusion or dispersion), and (2) chemistry is described by a canonical system of reactions that evolves with time and is unaffected by position in space. Results from the ARS technique are compared with results from the massively parallel, multicomponent reactive transport model MCTRACKER on a test problem involving irreversible oxidation of organic carbon and reaction of the oxidation products with two immobile mineral phases, gypsum and calcite, and fifteen aqueous complexes. Truncation error, operator splitting error, and the nonlinear transformation of these errors in the high-resolution reactive transport model are identified for this problem.     

Determination of spatially-resolved porosity, tracer distributions and diffusion coefficients in porous media using MRI measurements and numerical simulations

This work is focused on measuring the concentration distribution of a conservative tracer in a homogeneous synthetic porous material and in heterogeneous natural sandstone using MRI techniques, and on the use of spatially resolved porosity data to define spatially variable diffusion coefficients in heterogeneous media. The measurements are made by employing SPRITE, a fast MRI method that yields quantitative, spatially-resolved tracer concentrations in porous media. Diffusion experiments involving the migration of H(2)O into D(2)O-saturated porous media are conducted. One-dimensional spatial distributions of H(2)O-tracer concentrations acquired from experiments with the homogeneous synthetic calcium silicate are fitted with the one-dimensional analytical solution of Fick's second law to confirm that the experimental method provides results that are consistent with expectations for Fickian diffusion in porous media. The MRI-measured concentration profiles match well with the solution for Fick's second law and provide a pore-water diffusion coefficient of 1.75×10(-9)m(2)s(-1). The experimental approach was then extended to evaluate diffusion in a heterogeneous natural sandstone in three dimensions. The relatively high hydraulic conductivity of the sandstone, and the contrast in fluid density between the H(2)O tracer and the D(2)O pore fluid, lead to solute transport by a combination of diffusion and density-driven advection. The MRI measurements of spatially distributed tracer concentration, combined with numerical simulations allow for the identification of the respective influences of advection and diffusion. The experimental data are interpreted with the aid of MIN3P-D - a multicomponent reactive transport code that includes the coupled processes of diffusion and density-driven advection. The model defines local diffusion coefficients as a function of spatially resolved porosity measurements. The D(e) values calculated for the heterogeneous sandstone and used to simulate diffusive and advective transport range from 5.4×10(-12) to 1.0×10(-10)m(2)s(-1). These methods have broad applicability to studies of contaminant migration in geological materials.     

Simulations of physical nonequilibrium solute transport models: Application to a large-scale field experiment

Equations expressing the spatial moments of solute concentration distributions simulated by various models, in terms of model parameters, have recently been presented. Using independently obtained parameter values, these equations are used to compare simulations of physical non-equilibrium models with spatial moment data collected in a large-scale natural gradient experiment on solute transport. The physical nonequilibrium models examined postulate the existence of layered zones of immobile water through which solute is transported by a diffusion mechanism. It is found that the qualitative aspects of the measured moment behavior are simulated by the physical nonequilibrium models if the independently obtained parameters are modified somewhat on the basis of reasonable corrective assumptions. It is further demonstrated that the physical nonequilibrium models, using parameter values obtained from spatial data, can qualitatively simulate temporal behavior at individual well points in this relatively homogeneous aquifer.     

Modeling colloid transport for performance assessment

The natural system is expected to contribute to isolation at the proposed high-level nuclear waste (HLW) geologic repository at Yucca Mountain, NV (YM). In developing performance assessment (PA) computer models to simulate long-term behavior at YM, colloidal transport of radionuclides has been proposed as a critical factor because of the possible reduced interaction with the geologic media. Site-specific information on the chemistry and natural colloid concentration of saturated zone groundwaters in the vicinity of YM is combined with a surface complexation sorption model to evaluate the impact of natural colloids on calculated retardation factors (RF) for several radioelements of concern in PA. Inclusion of colloids into the conceptual model can reduce the calculated effective retardation significantly. Strongly sorbed radionuclides such as americium and thorium are most affected by pseudocolloid formation and transport, with a potential reduction in RF of several orders of magnitude. Radioelements that are less strongly sorbed under YM conditions, such as uranium and neptunium, are not affected significantly by colloid transport, and transport of plutonium in the valence state is only moderately enhanced. Model results showed no increase in the peak mean annual total effective dose equivalent (TEDE) within a compliance period of 10,000 years, although this is strongly dependent on container life in the base case scenario. At longer times, simulated container failures increase and the TEDE from the colloidal models increased by a factor of 60 from the base case. By using mechanistic models and sensitivity analyses to determine what parameters and transport processes affect the TEDE, colloidal transport in future versions of the TPA code can be represented more accurately.     

Calibration and validation of an integrated nitrate transport model within a well capture zone

Groundwater contamination by nitrate was investigated in an agricultural area in southern Quebec, Canada, where a municipal well is the local source of drinking water. A network of 38 piezometers was installed within the capture zone of the municipal well to monitor water table levels and nitrate concentrations in the aquifer. Nitrate concentrations were also measured in the municipal well. A Water flow and Nitrate transport Global Model (WNGM) was developed to simulate the impact of agricultural activities on nitrate concentrations in both the aquifer and municipal well. The WNGM first uses the Agriflux model to simulate vertical water and nitrate fluxes below the root zone for each of the seventy agricultural fields located within the capture zone of the municipal well. The WNGM then uses the HydroGeoSphere model to simulate three-dimensional variably-saturated groundwater flow and nitrate transport in the aquifer using water and nitrate fluxes computed with the Agriflux model as the top boundary conditions. The WNGM model was calibrated by reproducing water levels measured from 2005 to 2007 in the network of piezometers and nitrate concentrations measured in the municipal well from 1997 to 2007. The nitrate concentrations measured in the network of piezometers, however, showed greater variability than in the municipal well and could not be reproduced by the calibrated model. After calibration, the model was validated by successfully reproducing the decrease of nitrate concentrations observed in the municipal well in 2006 and 2007. Although it cannot predict nitrate concentrations in individual piezometers, the calibrated and validated WNGM can be used to assess the impact of changes in agricultural practices on global nitrate concentrations in the aquifer and in the municipal well.     

Modeling of non-reactive solute transport in fractured clayey till during variable flow rate and time

Fractures and biopores can act as preferential flow paths in clay aquitards and may rapidly transmit contaminants into underlying aquifers. Reliable numerical models for assessment of groundwater contamination from such aquitards are needed for planning, regulatory and remediation purposes. In this investigation, high resolution preferential water-saturated flow and bromide transport data were used to evaluate the suitability of equivalent porous medium (EPM), dual porosity (DP) and discrete fracture/matrix diffusion (DFMD) numerical modeling approaches for assessment of flow and non-reactive solute transport in clayey till. The experimental data were obtained from four large undisturbed soil columns (taken from 1.5 to 3.5 m depth) in which biopores and channels along fractures controlled 96-99% of water-saturated flow. Simulating the transport data with the EPM effective porosity model (FRACTRAN in EPM mode) was not successful because calibrated effective porosity for the same column had to be varied up to 1 order of magnitude in order to simulate solute breakthrough for the applied flow rates between 11 and 49 mm/day. Attempts to simulate the same data with the DP models CXTFIT and MODFLOW/MT3D were also unsuccessful because fitted values for dispersion, mobile zone porosity, and mass transfer coefficient between mobile and immobile zones varied several orders of magnitude for the different flow rates, and because dispersion values were furthermore not physically realistic. Only the DFMD modeling approach (FRACTRAN in DFMD mode) was capable to simulate the observed changes in solute transport behavior during alternating flow rate without changing values of calibrated fracture spacing and fracture aperture to represent the macropores.     

Transport of polar and non-polar volatile compounds in polystyrene foam and oriented strand board

Transport of hexanal and styrene in polystyrene foam (PSF) and oriented strand board (OSB) was characterized. A microbalance was used to measure sorption/desorption kinetics and equilibrium data. While styrene transport in PSF can be described by Fickian diffusion with a symmetrical and reversible sorption/desorption process, hexanal transport in both PSF and OSB exhibited significant hysteresis, with desorption being much slower than sorption. A porous media diffusion model that assumes instantaneous local equilibrium governed by a nonlinear Freundlich isotherm was found to explain the hysteresis in hexanal transport. A new nonlinear sorption and porous diffusion emissions model was, therefore, developed and partially validated using independent chamber data. The results were also compared to the more conventional linear Fickian-diffusion emissions model. While the linear emissions model predicts styrene emissions from PSF with reasonable accuracy, it substantially underestimates the rate of hexanal emissions from OSB. Although further research and more rigorous validation is needed, the new nonlinear emissions model holds promise for predicting emissions of polar VOCs such as hexanal from porous building materials.     

Direct coupling of a genome-scale microbial in silico model and a groundwater reactive transport model

The activity of microorganisms often plays an important role in dynamic natural attenuation or engineered bioremediation of subsurface contaminants, such as chlorinated solvents, metals, and radionuclides. To evaluate and/or design bioremediated systems, quantitative reactive transport models are needed. State-of-the-art reactive transport models often ignore the microbial effects or simulate the microbial effects with static growth yield and constant reaction rate parameters over simulated conditions, while in reality microorganisms can dynamically modify their functionality (such as utilization of alternative respiratory pathways) in response to spatial and temporal variations in environmental conditions. Constraint-based genome-scale microbial in silico models, using genomic data and multiple-pathway reaction networks, have been shown to be able to simulate transient metabolism of some well studied microorganisms and identify growth rate, substrate uptake rates, and byproduct rates under different growth conditions. These rates can be identified and used to replace specific microbially-mediated reaction rates in a reactive transport model using local geochemical conditions as constraints. We previously demonstrated the potential utility of integrating a constraint-based microbial metabolism model with a reactive transport simulator as applied to bioremediation of uranium in groundwater. However, that work relied on an indirect coupling approach that was effective for initial demonstration but may not be extensible to more complex problems that are of significant interest (e.g., communities of microbial species and multiple constraining variables). Here, we extend that work by presenting and demonstrating a method of directly integrating a reactive transport model (FORTRAN code) with constraint-based in silico models solved with IBM ILOG CPLEX linear optimizer base system (C library). The models were integrated with BABEL, a language interoperability tool. The modeling system is designed in such a way that constraint-based models targeting different microorganisms or competing organism communities can be easily plugged into the system. Constraint-based modeling is very costly given the size of a genome-scale reaction network. To save computation time, a binary tree is traversed to examine the concentration and solution pool generated during the simulation in order to decide whether the constraint-based model should be called. We also show preliminary results from the integrated model including a comparison of the direct and indirect coupling approaches and evaluated the ability of the approach to simulate field experiment.     

Development of the FMT chemical transport simulator: Coupling aqueous density and mineral volume fraction to phase compositions

The Fracture-Matrix Transport (FMT) code couples saturated porous medium advection and diffusion with mechanistic chemical models for speciation and interphase reactions. Previous versions of FMT simulated double-porosity transport in two dimensions on the continuum from advection- to diffusion-dominated, with a user-specified velocity field to allow double-porosity transport. However, aqueous density was assumed constant, and reactive minerals were assumed to occupy negligible volume. Both of these assumptions can be considered poor for evaporite systems, where large changes in porosity and aqueous density can result from high mineral solubilities. Further development of FMT has relaxed these restrictions, allowing aqueous density to vary with phase composition, and allowing void volume to change as minerals dissolve and precipitate. This paper describes the additional mathematical complexity and code modifications required to simulate such systems. The sensitivity of advection-dominated transport to these variables is explored briefly in a one-dimensional example.     

Competitive sorption and diffusion of chromate and sulphate in a flow system with goethite in gel beads

Column experiments and model simulations were employed to evaluate the processes involved in multicomponent solute transport in a system with heterogeneous flow. Column experiments were performed with goethite embedded in polyacrylamide gel beads. The gel forms an immobile water region that can be accessed by diffusion. A two-region transport model with diffusion into spheres was combined with a surface complexation model to predict reactive transport in the goethite-gel bead system. Chromate and sulphate breakthrough curves were measured in a set of transport experiments, along with corresponding changes in the pH of the effluent. Sorption and transport of sulphate and chromate in separate columns were predicted from independently measured sorption parameters. The model overestimated the pH changes in the effluent, possibly because of proton buffering by the polyacrylamide gel. The effect of competitive sorption on transport was examined in experiments with both anions present. The model predicted the effect of competition very well in a system initially equilibrated with sulphate, followed by infiltration with chromate. However, when sulphate was infiltrated after equilibration with chromate, chromate desorption and sulphate adsorption were clearly overestimated by the transport model. The exchange between the more strongly bound chromate and the sulphate added subsequently may be too slow to cause a substantial chromate peak in the effluent. This suggests that the local equilibrium assumption was not applicable in this case.     

The Change of Concentration Standard Deviations with Distance

Calculations of pollutant concentrations at various downwind and crosswind distances from an elevated point source are frequently based on diffusion models and parameter values contained in Turner’s Workbook of Atmospheric Dispersion Estimates.1 These calculations can be made much more speedily on a computer or on a currentgeneration, programmable desk calculator, if the values of the horizontal and vertical standard deviations of plume concentrations distributions are stated explicitly as a mathematical function of downwind distance. The alternative is to read the values from Turner’s Figures 3-2 and 3-3 and input them into the calculation for each individual value of downwind distance.     

Numerical simulation of scalar dispersion downstream of a square obstacle using gradient-transport type models

We present a numerical study of scalar transport released from a line source downstream of a square obstacle to investigate the capabilities and limitations of gradient-transport modeling in predicting atmospheric dispersion. The standard k–? and k–ω models and a Reynolds Stress Transport closure are employed and compared to predict the time-averaged turbulent flow field, while a standard gradient–diffusion model is initially adopted to relate the scalar flux to mean gradients of the concentration field. The analysis of two algebraic closures for turbulent scalar fluxes based on the generalized-gradient–diffusion hypothesis and its quadratic extension is also presented. In spite of the rather simple flow setup, where both the flow and the scalar fields can be assumed homogeneous in the spanwise direction, the analysis clarifies several critical issues concerning gradient-transport type models. We established the dominant role of predicted turbulent kinetic energy on scalar dispersion when a scalar diffusivity is employed, irrespectively of the Reynolds stress closure adopted for the averaged momentum equation. Moreover, the standard gradient–diffusion hypothesis failed to predict the streamwise component of the scalar flux, which is characterized by a counter-gradient-transport mechanism. Although the resulting contribution in the averaged scalar transport equation is small in the present flow configuration, this limitation can become severe for strongly inhomogeneous flows in the presence of point sources, where the spread of the scalar plume is essentially three-dimensional. The predictive capabilities of gradient-transport type modeling are found clearly improved using algebraic closures, which appear to represent a promising tool for predicting atmospheric dispersion in complex flows when unsteady transport mechanisms are not dominant.