Modelling radionuclide distribution and transport in the environment

Mathematical models of radionuclide distribution and transport in the environment have been developed to assess the impact on people of routine and accidental releases of radioactivity from a variety of nuclear activities, including: weapons development, production, and testing; power production; and waste disposal. The models are used to estimate human exposures and doses in situations where measurements have not been made or would be impossible or impractical to make. Model results are used to assess whether nuclear facilities are operated in compliance with regulatory requirements, to determine the need for remediation of contaminated sites, to estimate the effects on human health of past releases, and to predict the potential effects of accidental releases or new facilities. This paper describes the various applications and types of models currently used to represent the distribution and transport of radionuclides in the terrestrial and aquatic environments, as well as integrated global models for selected radionuclides and special issues in the fields of solid radioactive waste disposal and dose reconstruction. Particular emphasis is placed on the issue of improving confidence in the model results, including the importance of uncertainty analysis and of model verification and validation.     

Fast method for simulation of radionuclide chain migration in dual porosity fracture rocks

In fractured rocks with a porous rock matrix such as granites, radionuclides will flow with the water in the fracture network. The nuclides will diffuse in and out the rock matrix where they can sorb and be considerably retarded compared to the water velocity. A water parcel entering the network will mix and split at the fracture intersections and parts of the original parcel will traverse a multitude of different fractures. The flowrates, velocities, sizes and apertures of the fractures can vary widely. Normally one must solve the transport equations for every fracture and use the effluent concentration as inlet condition to the next fracture and so on. It is shown that under some weakly simplified conditions it suffices to determine one single parameter group containing information on the flow wetted surface that a water parcel contacts along the entire path. It is also shown how this can be obtained. Then, solving the transport equations only once for time and location along the path gives the concentration and nuclide flux of every nuclide in the chain everywhere along a path. The same solution actually is valid for every path in the network. This dramatically reduces the computation effort. The same approach can be used for models based on streamtubes.     

An overview of uncertainties in modelling groundwater solute transport

Model predictions are uncertain because of uncertainties on future and/or anthropogenic stresses, parameter values and conceptual models. The first two groups of problems can be addressed through rather systematic methods (scenario analysis, error transmission techniques, automatic calibration algorithms, etc.). However, conceptual uncertainties are rarely given adequate attention. The objective of this paper is to synthesize conceptual difficulties associated with transport. These include: (1) processes that are significant at small scales may not be relevant at large scales; (2) inversely, new processes (e.g., dispersion) emerge in response to increase in scale and the way to represent them may depend on the assumed model structure; (3) the observed shapes of both breakthrough curves and pollutant plumes are not well represented by the classical transport equation; (4) porosities and dispersivities derived from field tracer tests often exhibit a directional dependence; etc. Though not directly related to solute transport, scale effects on hydraulic conductivity may also affect solute transport modelling. When these anomalies are examined, it is concluded that they are directly or indirectly caused by heterogeneity. Current approaches for dealing with heterogeneity can be divided into stochastic and deterministic. Stochastic methods have been successful in explaining qualitatively some anomalies of solute transport, but they appear to be far from reaching a stage at which they can be used routinely for solving realistic field problems. On the other hand, when applied with care, deterministic methods have been successfully used in actual problems. Yet, it can be argued that they fail to account for small-scale variability of concentrations so that they would become ineffective when dealing with nonlinear processes, such as chemical reactions. Relevance of on-going research for overcoming these difficulties is discussed.     

The Grimsel (Switzerland) migration experiment: integrating field experiments, laboratory investigations and modelling

For several years tracer migration experiments are performed at Nagra's Grimsel Test Site in the Swiss Alps as a joint undertaking of Nagra, PNC and PSI. The aim is to develop methods for field experiments at possible sites for nuclear waste repositories and to test radionuclide transport models.A hydraulic dipole field is generated in a well-defined fracture zone in granite. The tracers used are non-sorbing (uranine, ³He, ⁴He, ⁸²Br⁻, ¹²³I⁻), mildly sorbing (²²Na⁺, ²⁴Na⁺), and more strongly sorbing (⁸⁵Sr²⁺, ⁸⁶Rb⁺, ¹³⁴Cs⁺, ¹³⁷Cs⁺). These experiments have been complemented by extensive laboratory investigations on petrography, on water-rock and nuclide-rock interaction as well as by migration experiments with bore cores.The main questions addressed are: What are the relevant geometric factors and mechanisms for transport, how well can breakthrough curves be extrapolated from one dipole arrangement to another, which parameters are scale dependent, is there a difference in sorption values between laboratory and field experiments or between static and dynamic experiments. Evaluating the experimental results for the non-sorbing uranine and the mildly sorbing tracers sorption, Strontium, we show that a consistent picture of tracer transport, and specifically of tracer sorption, is obtained when exploiting all available experimental information and using not too simplistic models.     

Kinetic modeling of microbially-driven redox chemistry of radionuclides in subsurface environments: coupling transport, microbial metabolism and geochemistry

Microbial reactions play an important role in regulating pore water chemistry as well as secondary mineral distribution in many subsurface systems and, therefore, may directly impact radionuclide migration in those systems. This paper presents a general modeling approach to couple microbial metabolism, redox chemistry, and radionuclide transport in a subsurface environment. To account for the likely achievement of quasi-steady state biomass accumulations in subsurface environments, a modification to the traditional microbial growth kinetic equation is proposed. The conditions for using biogeochemical models with or without an explicit representation of biomass growth are clarified. Based on the general approach proposed in this paper, the couplings of uranium reactions with biogeochemical processes are incorporated into computer code BIORXNTRN Version 2.0. The code is then used to simulate a subsurface contaminant migration scenario, in which a water flow containing both uranium and a complexing organic ligand is recharged into an oxic carbonate aquifer. The model simulation shows that Mn and Fe oxyhydroxides may vary significantly along a flow path. The simulation also shows that uranium(VI) can be reduced and therefore immobilized in the anoxic zone created by microbial degradation.     

A natural analogue of high-pH cement pore waters from the Maqarin area of northern Jordan: Comparison of predicted and observed trace-element chemistry of uranium and selenium

Current design concepts for low-/intermediate-level radioactive waste disposal in many countries involve emplacement underground in a cementitious repository. The highly alkaline groundwaters at Maqarin, Jordan, are a good analogue for the cementitious pore waters that will be present within such a repository. A geochemical modelling study of these groundwaters has been carried out in order to test the applicability of equilibrium models in geochemical programs and their associated thermodynamic databases in such hyperalkaline conditions. This was achieved by comparison of elemental solubilities and speciations predicted by the programs with observations in the natural system. Five organisations took part in the study: AEA Technology, U.K.; Chalmers University of Technology, Sweden; MBT Tecnología Ambiental, Spain; Nagra, Switzerland; and SKB, Sweden. The modelling study was coordinated by the University of Berne.The results of the study showed good agreement between the predictions of the programs employed. Comparison of the observed solids with those predicted by the models has allowed limited validation of the databases. The results for U and Se are presented here.     

Application of genetic algorithms for the design of ozone control strategies

Designing air quality management strategies is complicated by the difficulty in simultaneously considering large amounts of relevant data, sophisticated air quality models, competing design objectives, and unquantifiable issues. For many problems, mathematical optimization can be used to simplify the design process by identifying cost-effective solutions. Optimization applications for controlling nonlinearly reactive pollutants such as tropospheric ozone, however, have been lacking because of the difficulty in representing nonlinear chemistry in mathematical programming models. We discuss the use of genetic algorithms (GAs) as an alternative optimization approach for developing ozone control strategies. A GA formulation is described and demonstrated for an urban-scale ozone control problem in which controls are considered for thousands of pollutant sources simultaneously. A simple air quality model is integrated into the GA to represent ozone transport and chemistry. Variations of the GA formulation for multiobjective and chance-constrained optimization are also presented. The paper concludes with a discussion of the practically of using more sophisticated, regulatory-scale air quality models with the GA. We anticipate that such an approach will be practical in the near term for supporting regulatory decision-making.     

The long range transport of ozone within Europe and its control

It is widely accepted that the ozone concentrations experienced during photochemical episodes over large areas of Europe may exceed levels at which adverse environmental effects could be expected. These peak ozone concentrations can be reduced by controlling atmospheric emissions of the hydrocarbon and nitrogen oxide precursors. For ozone control to be successful over the spatial scale of Europe, long term international cooperation is required in the formulation of emission abatement strategies. A significant barrier to rapid progress has been the complexity of the processes that describe ozone formation. Highly sophisticated computer models of chemistry and transport have, up to now, been the only means to study the impact of abatement strategies. An alternative approach has been adopted here involving the development of a simplified long range transport model for ozone based on the analysis of over 60 experimental runs of a photochemical trajectory model applied to a wide range of hydrocarbon-nitrogen oxide emission combinations. Using the ozone-precursor relationship obtained, it has been possible to examine various policy options in the European context. Although taken together, three illustrative emission control scenarios reduce NO(x) and hydrocarbon emissions substantially through controls on motor vehicle exhaust, large combustion plant and solvent usage, a significant potential for photochemical ozone formation and long range transport may still remain after their implementation. The extents of precursor emission abatement that will be required, if the potential for ozone formation is to be reduced below published air quality criteria guidelines or critical levels, have been determined for each European country. The implied reductions in NO(x) and hydrocarbons relative to current levels amount to between 50 and 90%.     

The application of predictive models in the environmental risk assessment of ECONOR

Environmental risk assessment of products requires information on the physico-chemical properties, persistence and ecotoxicity of the product, its constituents and possible metabolic and degradation products. Experimental investigations are usually required to generate this information and consequently risk assessment can be costly and time consuming. One possible approach to minimising the amount of experimental testing is to supplement experimental data with data predicted using models such as quantitative structure-activity relationships (QSARs). Using these models, information can be generated based primarily on the knowledge of the chemical structure of the substance(s) under investigation. In this study predictive models were used to assess the environmental risk of the veterinary medicine, ECONOR which contains the active ingredient valnemulin. Available experimental data on the properties, degradability and ecotoxicity of valnemulin was supplemented with predicted data. Where possible, experimental data was used to validate the predicted approaches and this indicated that the predictions were accurate. Information on usage, properties and degradability was input to fate models to predict environmental concentrations (PECs) of valnemulin in soil, pore water and groundwater. Comparison of PECs with experimental and predicted ecotoxicity data for valnemulin indicated that that even under 'worst case' scenarios the environmental risk posed by valnemulin was low.     

Global-scale environmental transport of persistent organic pollutants

In order to realistically simulate both chemistry and transport of atmospheric organic pollutants, it is indispensable that the applied models explicitly include coupling between different components of the global environment such as atmosphere, hydrosphere, cryosphere and soil system. A model with such properties is presented.

The atmospheric part of the model is based on the equations in a general contravariant form which permits easy changes of the coordinate system by redefining the metric tensor of a specifically employed coordinate system. Considering a need to include explicitly the terrain effects, the terrain following spherical coordinate system is chosen from among many possible coordinate systems. This particular system is a combination of the Gal-Chen coordinates, commonly employed in mesoscale meteorological models, and the spherical coordinates, typical for global atmospheric models.

In addition to atmospheric transport, the model also simulates the exchange between air and different types of underlying surfaces such as water, soil, snow, and ice. This approach permits a realistic representation of absorption and delayed re-emission of pollutants from the surface to the atmosphere and, consequently, allows to capture hysteresis-like effects of the exchange between the atmosphere and the other components of the system. In this model, the most comprehensive numerical representation of the exchange is that for soil. In particular, the model includes a realistic soil module which simulates both diffusion and convection of a tracer driven by evaporation from the soil, precipitation, and gravity.

The model is applied to a long-term simulation of the transport of pesticides (hexachlorocyclohexanes in particular). Emission fluxes from the soil are rigorously computed on the basis of the realistic data of the agricultural application. All four modelled systems, i.e. atmosphere, soil, hydrosphere and cryosphere, are driven by objectively analysed meteorological data supplemented, when necessary, by climatological information. Therefore, the verification against the observed data is possible. The comparison of the model results and the observations taken at remote stations in the Arctic indicates that the presented global modelling system is able to capture both trends and short-term components in the observed time series of the concentrations, and therefore, provides a useful tool for the evaluation of the source–receptor relationships.     

Contribution to a more realistic approach in assessing the release of C-14 from low-level radioactive waste repositories

The contribution of C-14 to radiation exposure in the biosphere can be significant as compared to that of other radionuclides disposed in a repository for low-level radioactive waste. The release pathways of C-14 and processes relevant to its release from a closed final repository for low-level radioactive waste are discussed. Because a conservative approach may lead to undue overestimation of the potential radiation exposure, a more realistic approach is outlined. At the present level of refinement, our approach helps to provide a sufficient safety margin to German dose limits for radiation exposure of 0.3 mSv and can thus facilitate licence approval.     

Using chemical models for evaluating the geochemical confinement capacity of a geological barrier application to the Centre de Stockage de l'Aube (France)

The feasibility of using a chemical reaction-based approach for evaluating and modelling the role of adsorption reactions in determining the geochernical confinement capacity of natural geological barriers is being studied as part of an on-going R & D programme. The confined superficial aquifer underlying the Centre de Stockage de l'Aube facility, a geological barrier for this site, has been used as a case study with the following aims. First, development of a site characterisation protocol and demonstration of its use to determine the principal geochemical characteristics of aquifer materials using batch experiments and to represent the information obtained in terms of a chemical model. The experimental results obtained for Ni²⁺ partitioning as a function of total Ni, pH, total Ca and total solid can be satisfactorily represented in terms of reactions with an ion exchange site and a single amphoteric surface hydroxyl site with ferrihydrite reaction constants. A second objective is the incorporation of the reactions in a coupled geochemistry/transport code, and to verify the applicability of the coupled code predictions for Ni²⁺ mass transfer by comparison with the results obtained during column tracer experiments. The breakthrough curve and equilibrium solid phase Ni loading, predicted by a one-dimensional coupled model for a column tracer experiment, agree closely with observed data.Additional studies are underway to reduce model conditionality, to extend the adsorption model to other analogue cations and anions, to incorporate the effect of natural organic matter and to take into consideration precipitation/dissolution of amorphous Fe surface phases.     

CityDelta: A model intercomparison study to explore the impact of emission reductions in European cities in 2010

This paper gives an overview of the set up, methodology and the obtained results of the CityDelta (phase 1 and 2) project. In the context of the Clean Air For Europe programme of the European Commission, the CityDelta project was designed to evaluate the impact of emission-reduction strategies on air quality at the European continental scale and in European cities. Ozone and particulate matter (PM) are the main components that have been studied. To achieve this goal, a model intercomparison study was organized with the participation of more than 20 modelling groups with a large number of modelling configurations. Two following main topics can be identified in the project. First, in order to evaluate their strengths and weaknesses, the participating models were evaluated against observations in a control year (1999). An accompanying paper will discuss in detail this evaluation aspect for four European cities. The second topic is the actual evaluation of the impact of emission reductions on levels of ozone and PM, with particular attention to the differences between large-scale and fine-scale models. An accompanying paper will discuss this point in detail. In this overview paper the main input to the intercomparison is described as well as the use of the ensemble approach. Finally, attention is given to the policy relevant issue on how to implement the urban air quality signal into large-scale air quality models through the use of functional relationships.     

Application of Genetic Algorithms for the Design of Ozone Control Strategies

ABSTRACT

Designing air quality management strategies is complicated by the difficulty in simultaneously considering large amounts of relevant data, sophisticated air quality models, competing design objectives, and unquantifiable issues. For many problems, mathematical optimization can be used to simplify the design process by identifying cost-effective solutions. Optimization applications for controlling nonlinearly reactive pollutants such as tropospheric ozone, however, have been lacking because of the difficulty in representing nonlinear chemistry in mathematical programming models.

We discuss the use of genetic algorithms (GAs) as an alternative optimization approach for developing ozone control strategies. A GA formulation is described and demonstrated for an urban-scale ozone control problem in which controls are considered for thousands of pollutant sources simultaneously. A simple air quality model is integrated into the GA to represent ozone transport and chemistry. Variations of the GA formulation for multiobjective and chance-constrained optimization are also presented. The paper concludes with a discussion of the practicality of using more sophisticated, regulatory-scale air quality models with the GA. We anticipate that such an approach will be practical in the near term for supporting regulatory decision-making.     

Estimating contaminant-flushing rates for heterogeneous aquifers

Groundwater remediation evaluations typically include cleanup time projections. Current batch flushing-rate equations and analytical models often used to estimate groundwater cleanup rates typically underestimate cleanup times, with a major factor the flawed assumption of aquifer homogeneity. Numerical modelling of groundwater flow and contaminant transport is a time-intensive and costly alternative. An analytical modelling approach has been developed to quickly and cost effectively approximate realistic contaminant cleanup rates, factoring aquifer heterogeneity into the process. The mathematical relationships predict residual dissolved concentrations and average pumped concentrations over time, and also the time required to meet a concentration standard.     

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.     

Laboratory migration experiments with radionuclides and natural colloids in a granite fracture

Natural colloids in groundwater could facilitate radionuclide transport, provided the colloids are mobile, are present in sufficient concentrations and can adsorb radionuclides. This paper describes the results of a laboratory migration study carried out with combinations of radionuclides and natural colloids within a fracture in a large granite block to experimentally determine the impact of colloids on radionuclide transport. The 85Sr used in this study is an example of a moderately sorbing radionuclide, while the 241Am is typical of a strongly sorbed radionuclide with very low solubility. The natural colloids used in this study were isolated from granite groundwater from Atomic Energy of Canada (AECL) Underground Research Laboratory (URL), and consisted of mostly 1-10 nm organic colloids, along with lesser amounts of 10-450 nm colloids (organics and aluminosilicates). The measured coefficients for radionuclide sorption onto these colloids were between 3 x 10(2) and 1 x 10(3) ml/g for 85Sr, and between 7 x 10(4) and 7 x 10(5) mg/l for 241Am. The 85Sr sorption on the natural colloids appeared to be reversible. Migration experiments in the granite block were carried out by establishing a flow field between two boreholes (out of a total of nine) intersecting a main horizontal fracture. These experiments showed that dissolved 85Sr behaved as a moderately sorbing tracer, while dissolved 241Am was completely adsorbed by the fracture surfaces and showed no evidence of transport. However, when natural colloids were injected together with dissolved 241Am, a small amount of 241Am transport was observed, demonstrating the ability of natural colloids to facilitate the transport of radionuclides with low solubility. Natural colloids had only a minor effect on the transport of 85Sr. In a separate experiment to test the effect of higher colloid concentrations on 85Sr migration, synthetic colloids were produced from Avonlea bentonite. The introduction of a relatively high concentration of bentonite colloids actually reduced 85Sr transport because, compared to natural colloids, the bentonite colloids were less mobile and they sorbed 85Sr more strongly.