Modelling radionuclide transport for time varying flow in a channel network

Water flowrates and flow directions may change over time in the subsurface for a number of reasons. In fractured rocks flow takes place in channels within fractures. Solutes are carried by the advective flow. In addition, solutes may diffuse in and out of stagnant waters in the rock matrix and other stagnant water regions. Sorbing species may sorb on fracture surfaces and on the micropore surfaces in the rock matrix. We present a method by which solute particles can be traced in flowing water undergoing changes in flowrate and direction in a complex channel network where the solutes can also interact with the rock by diffusion in the rock matrix. The novelty of this paper is handling of diffusion in the rock matrix under transient flow conditions. The diffusive processes are stochastic and it is not possible to follow a particle deterministically. The method therefore utilises the properties of a probability distribution function for a tracer moving in a fracture where matrix diffusion is active. The method is incorporated in a three dimensional channel network model. Particle tracking is used to trace out a multitude of flowpaths, each of which consists of a large number of channels within fractures. Along each channel the aperture and velocity as well as the matrix sorption properties can vary. An efficient method is presented whereby a particle can be followed along the variable property flowpath. For stationary flow conditions and a network of channels with advective flow and matrix diffusion, a simple analytical solution for the residence time distribution along each pathway can be used. Only two parameter groups need to be integrated along each path. For transient flow conditions, a time stepping procedure that incorporates a stochastic Monte-Carlo like method to follow the particles along the paths when flow conditions change is used. The method is fast and an example is used for illustrative purposes. It is exemplified by a case where land rises due to glacial rebound. It is shown that the effects of changing flowrates and directions can be considerable and that the diffusive migration in the matrix can have a dominating effect on the results.     

Description of hydrogeologic heterogeneity and evaluation of radionuclide transport at an underground nuclear test

Realistic models of contaminant transport in groundwater demand detailed characterization of the spatial distribution of subsurface hydraulic properties, while at the same time programmatic constraints may limit collection of pertinent hydraulic data. Fortunately, alternate forms of data can be used to improve characterization of spatial variability. We utilize a methodology that augments sparse hydraulic information (hard data) with more widely available hydrogeologic information to generate equiprobable maps of hydrogeologic properties that incorporate patterns of connected permeable zones. Geophysical and lithologic logs are used to identify hydrogeologic categories and to condition stochastic simulations using Sequential Indicator Simulation (SIS). The resulting maps are populated with hydraulic conductivity values using field data and Sequential Gaussian Simulation (SGS). Maps of subsurface hydrogeologic heterogeneity are generated for the purpose of examining groundwater flow and transport processes at the Faultless underground nuclear test, Central Nevada Test Area (CNTA), through large-scale, three-dimensional numerical modeling. The maps provide the basis for simulation of groundwater flow, while transport of radionuclides from the nuclear cavity is modeled using particle tracking methods. Sensitivity analyses focus on model parameters that are most likely to reduce the long travel times observed in the base case. The methods employed in this study have improved our understanding of the spatial distribution of preferential flowpaths at this site and provided the critical foundation on which to build models of groundwater flow and transport. The results emphasize that the impacts of uncertainty in hydraulic and chemical parameters are dependent on the radioactive decay of specific species, with rapid decay magnifying the effects of parameters that change travel time.     

Development and testing of radionuclide transport models for fractured rock: examples from the Nagra/JNC Radionuclide Migration Programme in the Grimsel Test Site, Switzerland

The joint Swiss National Co-operative for the Disposal of Radioactive Waste (Nagra)/Japan Nuclear Cycle Development Institute (JNC) Radionuclide Migration Programme has now been on-going for over a decade in Nagra's Grimsel Test Site (GTS). The main aim of the programme has been the direct testing of radionuclide transport models in as realistic manner as possible. Although it will never be possible to fully test these models due to the large time and distance scales involved, tests of the model assumptions in scaled down but otherwise realistic conditions will contribute to developing confidence in the predictive power of the models. In this paper, the Nagra/JNC approach is highlighted with examples from a large programme of field, laboratory and natural analogue studies based around the GTS. The successes and failures are discussed as in the general approach to the thorough testing of predictive transport codes which will be used in repository performance assessment (PA). Some of the work is still on-going and this represents the first presentation of a unique set of results and conclusions.     

Modelling the fate of organic chemicals in the soil plant environment: Model study of root uptake of pesticides

The fate of organic chemicals in the soil-plant-atmosphere environment and the governing processes were studied with a coupled dynamic soil transport and plant compartment model. Scenarios with applications of pesticides on sand and loam soils with chemical uptake in barley and wheat were used in the model calculations. Root uptake and concentrations in the plant compartments stem, leave and fruit were calculated for the pesticides terbuthylazine, isoproturon and carbofuran.

The effectivity of uptake from soils with different soil sorption coefficients had been shown for sand and loam soils. The processes degradation in plant and volatilization from leaves to atmosphere are especially effective for carbofuran and terbuthylazine. Although the concentrations in corn at harvest are lower than the maximum allowed concentrations, the peak concentrations in the course of the vegetation period are significantly higher (factor ≤ 200).     

Modelling photochemical oxidant formation, transport, deposition and exposure of terrestrial ecosystems

The chemical processes responsible for production of photochemical oxidants within the troposphere have been the subject of laboratory and field study throughout the last three decades. During the same period, models to simulate the atmospheric chemistry, transport and deposition of ozone (O(3)) from individual urban sources and from regions have been developed. The models differ greatly in the complexity of chemical schemes, in the underlying meteorology and in spatial and temporal resolution. Input information from land use, spatial and temporally disaggregated emission inventories and meteorology have all improved considerably in recent years and are not fully implemented in current models. The development of control strategies in both North America and Europe to close the gaps between current exceedances of environmental limits, guide values, critical levels or loads and full compliance with these limits provides the focus for policy makers and the support agencies for the research. The models represent the only method of testing a range of control options in advance of implementation. This paper describes currently applied models of photochemical oxidant production and transport at global and regional scales and their ability to simulate individual episodes as well as photochemical oxidant climatology. The success of current models in quantifying the exposure of terrestrial surfaces and the population to potentially damaging O(3) concentrations (and dose) is examined. The analysis shows the degree to which the underlying processes and their application within the models limit the quality of the model products.     

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.     

Solute transport in crystalline rocks at Äspö — II: Blind predictions, inverse modelling and lessons learnt from test STT1

Based on the results from detailed structural and petrological characterisation and on up-scaled laboratory values for sorption and diffusion, blind predictions were made for the STT1 dipole tracer test performed in the Swedish Äspö Hard Rock Laboratory. The tracers used were nonsorbing, such as uranine and tritiated water, weakly sorbing ²²Na⁺, ⁸⁵Sr²⁺, ⁴⁷Ca²⁺and more strongly sorbing ⁸⁶Rb⁺, ¹³³Ba²⁺, ¹³⁷Cs⁺.Our model consists of two parts: (1) a flow part based on a 2D-streamtube formalism accounting for the natural background flow field and with an underlying homogeneous and isotropic transmissivity field and (2) a transport part in terms of the dual porosity medium approach which is linked to the flow part by the flow porosity.The calibration of the model was done using the data from one single uranine breakthrough (PDT3). The study clearly showed that matrix diffusion into a highly porous material, fault gouge, had to be included in our model evidenced by the characteristic shape of the breakthrough curve and in line with geological observations.After the disclosure of the measurements, it turned out that, in spite of the simplicity of our model, the prediction for the nonsorbing and weakly sorbing tracers was fairly good. The blind prediction for the more strongly sorbing tracers was in general less accurate. The reason for the good predictions is deemed to be the result of the choice of a model structure strongly based on geological observation. The breakthrough curves were inversely modelled to determine in situ values for the transport parameters and to draw consequences on the model structure applied. For good fits, only one additional fracture family in contact with cataclasite had to be taken into account, but no new transport mechanisms had to be invoked. The in situ values for the effective diffusion coefficient for fault gouge are a factor of 2–15 larger than the laboratory data. For cataclasite, both data sets have values comparable to laboratory data. The extracted K_d values for the weakly sorbing tracers are larger than Swedish laboratory data by a factor of 25–60, but agree within a factor of 3–5 for the more strongly sorbing nuclides. The reason for the inconsistency concerning K_ds is the use of fresh granite in the laboratory studies, whereas tracers in the field experiments interact only with fracture fault gouge and to a lesser extent with cataclasite both being mineralogically very different (e.g. clay-bearing) from the intact wall rock.     

Coupled modeling of cement/claystone interactions and radionuclide migration

The interactions between cement and a clayey host-rock of an underground repository for intermediate-level radioactive waste are studied with the reactive transport code HYTEC for supporting performance assessment. Care is taken in using relevant time scales (100,000 years) and dimensions. Based on a literature review, three hypotheses are considered with respect to the mineralogical composition of the claystone and the neo-formed phases. In the long term, the pH is buffered for all hypotheses and important mineral transformations occur both in cement and the host-rock. The destruction of the primary minerals is localized close to the cement/claystone interface and is characterized by the precipitation of secondary phases with retention properties (illite, zeolite). However, beyond the zone of intense mineral transformations, the pore water chemistry is also disturbed over a dozen meters due to an attenuated but continuous flux of hydroxyl, potassium and calcium ions. Four interdependent mechanisms control the profile in the whole system: diffusion of the alkaline plume, mineralogical buffering, ion exchange and clogging of the pore space at the cement/claystone interface. The migration of a selected group of radionuclides (Cs, Ra, Tc and U) is explicitly integrated in the simulations of the strongly coupled system. Theoretical profiles of distribution coefficient (Kd) and solubility limit values are derived from the simulations, and their sensitivity with respect to the system evolution is estimated.     

Modelling of diffusion-limited retardation of contaminants in hydraulically and lithologically nonuniform media

A new reactive transport modelling approach and examples of its application are presented, dealing with the impact of sorption/desorption kinetics on the spreading of solutes, e.g. organic contaminants, in groundwater. Slow sorption/desorption is known from the literature to be strongly responsible for the retardation of organic contaminants. The modelling concept applied in this paper quantifies sorption/desorption kinetics by an intra-particle diffusion approach. According to this idea, solute uptake by or release from the aquifer material is modelled at small scale by a "slow" diffusion process where the diffusion coefficient is reduced as compared to the aqueous diffusion coefficient due to (i) the size and shape of intra-particle pores and (ii) retarded transport of solutes within intra-particle pores governed by a nonlinear sorption isotherm. This process-based concept has the advantage of requiring only measurable model parameters, thus avoiding fitting parameters like first-order rate coefficients.In addition, the approach presented here allows for modelling of slow sorption/desorption in lithologically nonuniform media. Therefore, it accounts for well-known experimental findings indicating that sorptive properties depend on (i) the grain size distribution of the aquifer material and (ii) the lithological composition (e.g. percentage of quartz, sandstone, limestone, etc.) of each grain size fraction. The small-scale physico-chemical model describing sorption/desorption is coupled to a large-scale model of groundwater flow and solute transport. Consequently, hydraulic heterogeneities may also be considered by the overall model. This coupling is regarded as an essential prerequisite for simulating field-scale scenarios which will be addressed by a forthcoming publication.This paper focuses on mathematical model formulation, implementation of the numerical code and lab-scale model applications highlighting the sorption and desorption behavior of an organic contaminant (Phenanthrene) with regard to three lithocomponents exhibiting different sorptive properties. In particular, it is shown that breakthrough curves (BTCs) for lithologically nonuniform media cannot be obtained via simple arithmetic averaging of breakthrough curves for lithologically uniform media. In addition, as no analytical solutions are available for model validation purposes, simulation results are compared to measurements from lab-scale column experiments. The model results indicate that the new code can be regarded as a valuable tool for predicting long-term contaminant uptake or release, which may last for several hundreds of years for some lithocomponents. In particular, breakthrough curves simulated by pure forward modelling reproduce experimental data much better than a calibrated standard first-order kinetics reactive transport model, thus indicating that the new approach is of high quality and may be advantageously used for supporting the design of remediation strategies at contaminated sites where some lithocomponents and/or grain size classes may provide a long-term pollutant source.     

Radionuclide transport and retardation in rock fracture and crushed rock column experiments

Transport and retardation of non-sorbing tritiated water and chloride and slightly sorbing sodium was studied in Syyry area SY-KR7 mica gneiss, in altered porous tonalite and in fresh tonalite. Experiments were performed using dynamic fracture and crushed rock column methods. Static batch method for sodium was introduced to compare retardation values from static and dynamic experiments. The ¹⁴C-PMMA method was used to study the pore structure of matrices. The pore aperture distribution was evaluated from Hg-porosimetry determinations and the surface areas were determined using the B.E.T. method. The flow characteristics and transport behavior of tracers were interpreted using a numerical compartment model for dispersion. The effect of matrix diffusion was calculated using an analytical solution to the advection-matrix diffusion problem in which surface retardation was taken into account. Radionuclide transport behavior in rock fractures was explained on the basis of rock structure.     

The effect of coupled transport phenomena in the Opalinus Clay and implications for radionuclide transport

In this study, the potential effects of coupled transport phenomena on radionuclide transport in the vicinity of a repository for vitrified high-level radioactive waste (HLW) and spent nuclear fuel (SF) hosted by the Opalinus Clay in Switzerland, at times equal to or greater than the expected lifetime of the waste canisters (about 1000 years), are addressed. The solute fluxes associated with advection, chemical diffusion, thermal and chemical osmosis, hyperfiltration and thermal diffusion have been incorporated into a simple one-dimensional transport equation. The analytical solution of this equation, with appropriate parameters. shows that thermal osmosis is the only coupled transport mechanism that could, on its own, have a strong effect on repository performance. Based on the results from the analytical model, two-dimensional finite-difference models incorporating advection and thermal osmosis, and taking conservation of fluid mass into account, have been formulated. The results show that, under the conditions in the vicinity of the repository at the time scales of interest, and due to the constraints imposed by conservation of fluid mass, the advective component of flow will oppose and cancel the thermal-osmotic component. The overall conclusion is that coupled phenomena will only have a very minor impact on radionuclide transport in the Opalinus Clay, in terms of fluid and solute fluxes, at least under the conditions prevailing at times equal to or greater than the expected lifetime of the waste canisters (about 1000 years).     

Role of magnetite and humic acid in radionuclide migration in the environment

Sorption of ¹³⁷Cs, ⁹⁰Sr, ¹⁵⁴Eu and ¹⁴¹Ce by magnetite has been studied at varying pH (4 to 11) in the presence and absence of humic acid. The sorption studies have also been carried out at varying ionic strength (0.01 to 0.2 M NaClO₄) and humic acid concentration (2 to 20 mg/L). Percentage sorption of ¹³⁷Cs and ⁹⁰Sr was found to be pH dependent, with the sorption increasing with increasing pH of the suspension. At any pH, the percentage sorption of ⁹⁰Sr was higher than that of ¹³⁷Cs. The results have been explained in terms of the electrostatic interaction between the positively charged metal ions and the surface charge of the magnetite which becomes increasingly negative with increasing pH. On the other hand, ¹⁵⁴Eu and ¹⁴¹Ce were found to be strongly sorbed by the magnetite at all pH values, with the sorption being independent of pH. The strong sorption of trivalent and tetravalent metal ions suggests the role of complexation reactions during sorption, apart from the electrostatic interactions. However, in the case of ¹⁴¹Ce surface precipitation of Ce(III) formed by reduction of Ce(IV) in the presence of magnetite cannot be ruled out. Presence of humic acid (2 mg/L) was found to have negligible effect on sorption of all metal ions.     

The influence of colloid formation in a granite groundwater bentonite porewater mixing zone on radionuclide speciation

In the context of deep geological storage of high level nuclear waste the repository will be designed as multiple barrier system including bentonite as buffer/backfill material and the host rock formation as geological barrier. The engineered barrier (bentonite) will be in contact with the host rock formation and consequently it can be expected that bentonite porewater will mix with formation groundwater. We simulate in this study the mixing of Grimsel groundwater (glacial melt water) with synthetic Febex porewater (assuming already saturated state) in a batch-type study and investigate the formation of colloids by laser-induced breakdown detection (LIBD) and SEM-EDX as well as the changes in radionuclide (U, Th, Eu) speciation via ultrafiltration or via time-resolved laser fluorescence spectroscopy (TRLFS) analysis in the case of Cm(III). Based on PHREEQC saturation index (SI) calculations a precipitation of calcite might be expected at low Febex porewater (FPW) content (< 20%), fluorite precipitation at FPW contents < 60% and gibbsite precipitation at FPW contents above 10%. The colloids generated in the mixing zone aggregate when the synthetic FPW content exceeds 10%. LIBD analysis of the time-dependent colloid generation/aggregation revealed a low concentration of colloids to be stable with an estimated plateau value around 100–200 ppt and an average colloid diameter around 30 nm after 140 days reaction time at FPW admixture > 10%. SEM/EDX mostly identifies Al/Si containing colloidal phases and some sulfates could be found under certain admixture ratios. TRLFS studies show that the Cm speciation is strongly influenced by colloid formation in all solutions. In the Febex pore water/GGW mixing zone with high groundwater contents (> 80%) colloids are newly formed and Cm is almost quantitatively associated with most likely polysilicilic acid colloids.     

Data requirements of GREAT-ER: Modelling and validation using LAS in four UK catchments

Higher-tier environmental risk assessments on “down-the-drain” chemicals in river networks can be conducted using models such as GREAT-ER (Geography-referenced Regional Exposure Assessment Tool for European Rivers). It is important these models are evaluated and their sensitivities to input variables understood. This study had two primary objectives: evaluate GREAT-ER model performance, comparing simulated modelled predictions for LAS (linear alkylbenzene sulphonate) with measured concentrations, for four rivers in the UK, and investigate model sensitivity to input variables. We demonstrate that the GREAT-ER model is very sensitive to variability in river discharges. However it is insensitive to the form of distributions used to describe chemical usage and removal rate in sewage treatment plants (STPs). It is concluded that more effort should be directed towards improving empirical estimates of effluent load and reducing uncertainty associated with usage and removal rates in STPs. Simulations could be improved by incorporating the effect of river depth on dissipation rates.     

Modelling of atrazine transport in the presence of surfactants

Laboratory experiments were conducted to examine the effect of detergents on transport of atrazine [2-chloro-4-(ethylamino)-6-(isopropylamino)-s-triazine] through loam and sandy loam soils under saturation conditions. The Convection Dispersion Equation (CDE) was used to model and quantify the effects of detergents on atrazine model parameters: the retardation factor (R), pore velocity (v) and dispersion coefficient (D). The transport parameters were estimated using moment technique and partition coefficient obtained from batch experiments and compared with best-fitted parameters, R and D, keeping pore velocity constant. Results indicated the CDE model was not successful in predicting atrazine transport in the presence of surfactants at high concentrations. In the case of anionic surfactant with Elora loam, the average predicted R and D from moment technique of 3.4 and 11.1 cm2/h, respectively were significantly different than fitted parameters (R = 39 and D = 227 cm2/h). The poor performance of CDE in the presence of surfactants results from physiochemical changes in herbicide solubility and retention to the soil matrix rather than changes in soil hydraulic properties since the predicted pore water velocities from moment technique were similar to those measured during leaching experiments. Nevertheless, BTC analysis with CDE showed that land application of anionic surfactant (sulphonic) significantly increased R and D and decrease v for both soils. Addition of sulphonic increased R of atrazine by 12 and 26 folds for loam and sandy loam soils, respectively. On the other hand non-ionic surfactants seemed to decrease R, especially in sandy loam soil, thus facilitating atrazine leaching through soil. Non-equilibrium conditions seemed to govern atrazine transport in the presence of surfactants; double peaks in breakthrough curves were observed, indicating a need for mathematical models to account for such phenomena. Atrazine dispersion and tailing seemed to be higher through Elora loam compared to Caledon sandy loam due to higher aggregation of the Elora soil.     

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.     

Long-range transport and re-circulation of pollutants in the western Mediterranean during the project Regional Cycles of Air Pollution in the West-Central Mediterranean Area

During the warm season (March–September), high ozone concentrations have been reported at the coastal and mountain monitoring stations of the eastern Iberia coast (Millán et al., J. Geophys. Res. 102 (D7) 8811, J. Appl. Meteorol. 4 (2000) 487). The vegetation protection threshold of current Directive 92/72/EEC and the World Health Organisation guideline for the protection of crops and semi-natural vegetation are systematically exceeded during the whole period. The main objective of the present study is to search for the origin of these chronic pollution levels: to search for the reason(s) for such high O₃ concentrations during such a long period. A mesoscale model is used to reproduce the diurnal cycle of winds and stability/layering over the Western Mediterranean Basin (WMB), at a sufficient space/temporal resolution, under a typical recursive synoptic condition during the warm season: data from the flight tracks of the European Project—Regional Cycles of Air Pollution in the West-Central Mediterranean Area—are used to substantiate the model results. Times of residence and the final distribution of pollutants entering the WMB are estimated using single-particle Lagrangian trajectories and a multiple-particle dispersion model. Our results show that the marine boundary layer and the lower troposphere in the region between the Balearic Islands and eastern Iberia are subject to a flow regime that tends to accumulate pollutants within large circulations, covering the entire western basin. We have also shown a diurnal pulsation of the Tramontana/Mistral wind regime, which can transport new pollutants into the area (background concentrations of 50–65 ppb of O₃ of continental European origin) that are added to local emissions and re-circulated within the coastal breezes at eastern Iberia for periods of more than five days. Local emissions and wind configuration contribute to increase the O₃ concentrations up to 100 ppb and even more.     

Economic instruments, transport and the global environment

The use of economic instruments, such as charges, in abating climate change is assessed, with special reference to their application in the transport sector. The general strategies and instruments for global environmental policies are presented. The role of economic instruments in this context is highlighted, both in terms of theory and of application. Economic instruments are then analysed from the perspective of transport policies. Climate and transport appear to have different perspectives on economic instruments. The analysis leads to a framework for developing climate-related economic instruments in transport. These may result in substantial economic savings, especially if approached internationally and if distributional and institutional problems can be overcome. The integration of climate concerns into transport policies can be improved, and several suggestions are made in this respect.     

Modelling the spatial distribution of ammonia emissions in the UK

Ammonia emissions (NH3) are characterised by a high spatial variability at a local scale. When modelling the spatial distribution of NH3 emissions, it is important to provide robust emission estimates, since the model output is used to assess potential environmental impacts, e.g. exceedance of critical loads. The aim of this study was to provide a new, updated spatial NH3 emission inventory for the UK for the year 2000, based on an improved modelling approach and the use of updated input datasets. The AENEID model distributes NH3 emissions from a range of agricultural activities, such as grazing and housing of livestock, storage and spreading of manures, and fertilizer application, at a 1-km grid resolution over the most suitable landcover types. The results of the emission calculation for the year 2000 are analysed and the methodology is compared with a previous spatial emission inventory for 1996.