Modelling Groundwater Contamination Above High-Level Nuclear-Waste Repositories in Salt, Granitoid and Clay

Modelling the groundwater contamination in the aquifer above a repository for high-level nuclear waste is a complex task. The usual procedure is based on modelling the transport of radionuclides in one or two dimensions only (NAGRA, 2002; Kosakowski, 2004; Keesmann et al., 2006; SKB, 2006; Nykyri et al., 2008). However, modern computing techniques allow to perform simulations in three dimensions, which are a more realistic representation of the geosphere or far field. This is shown for candidate repositories in salt (Gorleben, Germany) and granitoid (Olkiluoto, Finland). To date, is not possible to conduct similar threedimensional simulations for a repository in clay because the necessary input data are not available. Nevertheless, it can be shown that the results obtained from the simulations with a granitoid-hosted repository are useful for evaluating the performance of a clay-hosted repository. The objective of this comparative study is to provide tools that facilitate the identification of disposal sites and enhance the transparency of decision-making processes.


Introduction
Modelling the groundwater contamination in the aquifer above a repository for high-level nuclear waste is a complex task.The usual procedure is based on modelling the transport of radionuclides in one or two dimensions only (NAGRA, 2002;Kosakowski, 2004;Keesmann et al., 2006;SKB, 2006;Nykyri et al., 2008).However, modern computing techniques allow to perform simulations in three dimensions, which are a more realistic representation of the geosphere or far field.This is shown for candidate repositories in salt (Gorleben, Germany) and granitoid (Olkiluoto, Finland).To date, is not possible to conduct similar threedimensional simulations for a repository in clay because the necessary input data are not available.Nevertheless, it can be shown that the results obtained from the simulations with a granitoid-hosted repository are useful for evaluating the performance of a clay-hosted repository.The objective of this comparative study is to provide tools that facilitate the identification of disposal sites and enhance the transparency of decision-making processes.

Computer codes for flow-transport models
The generation of a gas phase is an important issue for a repository in salt.Therefore, both one-phase (liquid only) and two-phase (liquid and gas) simulations are performed for the salt-hosted Gorleben repository.The two-phase simulations are performed with the TOUGHREACT code (Xu et al., 2005).This is a numerical simulation program that calculates chemically reactive non-isothermal flows of multi-phase fluids and geochemical transport in porous and fractured media.The program was developed by introducing reactive chemistry into the multi-phase flow code TOUGH2 (Pruess et al., 1999).The code performs a fully coupled simultaneous solution of mass and energy balance for multicomponent fluids, combined with a multiphase extension of Darcy's Law and Fickian diffusion.The program consists of a number of functional units with flexible and transparent interfaces.The governing equations are discretised using integral finite difference for space and fully implicit first-order finite difference in time.The resulting nonlinear algebraic equations are solved by Newton-Raphson iteration.The simulations are performed with the ECO2 module, which treats the aqueous phase as a mixture of water and salt.The dependence of density, viscosity, enthalpy and vapour pressure on salt concentration is taken into account, as well as the effects of salinity on gas solubility in the liquid phase and related heat of solution.
The one-phase scenario for Gorleben is calculated with TOUGH2-MP (Zhang et al., 2008), the parallel version of the TOUGH2 code.The EOS7R module is used, which calculates the transport of a parent radionuclide and a daughter radionuclide.The aqueous phase is treated as a mixture of water and brine.
For a granitoid-hosted repository, the potential gas release is negligibly small.Therefore, only a one-phase scenario is calculated for the Olkiluoto repository.The TOUGHREACT code with the ECO2 module is used for these simulations.

Repository layout
The repository (Figs. 1 and 2) will accommodate 5,440 waste containers with a total of 8,550 t U of burnt fuel (Keesmann et al., 2005).The waste containers, which are made of Mn-Ni steel, have a length of 5.5 m and a diameter of 1.6 m (Javeri, 2006).They will be emplaced in horizontal disposal drifts, which will be connected to two or more shafts by a system of access drifts.The envisaged disposal depth is about 800 m.There are 260-280 m Quaternary-Tertiary siliciclastic sediments above the present mine workings within the Zechstein salt dome.

Near field
The near field is the hydrochemical regime of the backfilled underground workings in the salt dome and the far field is hydrochemical regime of the caprock and cover sediments.The Modelling Groundwater Contamination Above High-Level Nuclear-Waste Repositories in Salt, Granitoid and Clay 461 far-field simulations use the near-field releases as input.To date, only two near-field scenarios have been published.The first considers a single-phase case with liquid-phase transport only.The second considers a two-phase case with both liquid-phase and gas-phase transport.
The near-field release of the single-phase scenario (Fig. 3; Keesmann et al., 2005) is the latest update of the Early-Intrusion-Case of Storck et al. (1988).About 2,000 m 3 of brine is assumed to intrude into the repository and dissolve the waste up to the solubility limits shown in Table 1.The brine is squeezed out of the repository due to the convergence of the elastically deforming rock salt.The exit point of the contaminated brine is the contact between Quaternary sediments and the Main Anhydrite (Hauptanhydrit) of the Zechstein salt dome at the borehole location GoHy3020 (Fig. 2) on the -250-m level.The two-phase scenario for the release of C-14 in the presence of a gas phase is based on a case described by Javeri (2006).Brine squeezed out from a 1,000 m 3 brine pocket intrudes a backfilled disposal drift during 2,000 years following the closure of the repository.The disposal drift hosts 33 waste containers.At low oxygen fugacities, the container wall is subjected to corrosion dominated by the reaction 3Fe + 4H 2 O = Fe 3 O 4 + 4H 2 . (1) The corrosion process releases hydrogen gas at a rate that increases from zero to 3.84 kg/a in the period from year zero to year 100 and decreases from 3.84 kg/a to zero in the period from year 20,000 to year 40,000.The hydrogen gas leaves the repository via the backfilled shaft according to the release rates shown in Figure 4.

Two-phase scenario
Table 1.Gorleben model.Liquid-phase solubility in the near field Together with hydrogen, C-14 species are released.The average waste canister contains C-14 with an activity of 3 x 10 10 Bq (Keesmann et al., 2005).A fraction of 15 % is available for rapid release upon failure of the canister.This is assumed to result in a release of 13 % of the initial C-14 inventory out of the repository during a 100-year period starting in the year 1,000 after the closure of the repository.The corresponding release from the total of the 33 waste containers is 1.3 x 10 9 Bq/a.C-14 is the only radionuclide considered in the two-phase scenario because it is the only long-lived radionuclide that strongly partitions into the gas phase.
TOUGHREACT allows for injection of a single non-condensable gas, which is hydrogen in the case of the present study.Other gaseous species are introduced as secondary species via the corresponding primary liquid species according to a dissociation reaction such as The primary species are HCO 3 -, H + and O 2(aq) .The secondary species are CO 2(gas) , CH 4(gas) , CH 4(aq) , CO 2(aq) and CO 3 -2 .The initial and boundary solutions have a H + activity of 10 -7 and an O 2(aq) activity of 10 -67 .The source for the two-phase model is the near-field release shown in Figure 4. Hydrogen gas is injected into the primary central cell of shaft 2 on the -237.5-mlevel whereas a boundary solution with HCO 3 -is injected from a secondary boundary cell that is connected to this primary cell.

Geometry of the far-field model and initialisation
The irregular mesh has 290,435 elements and measures 22,400 m x 21,000 m x 400 m (Figs.5-7; Table 2).Three sets of nodal distances in the x and y direction are used.The backfilled shaft 2, which measures 6 x 6 m horizontally, and the area immediately surrounding shaft 2 (shaft wall and bedrock) have horizontal nodal distances of 2 m.An intermediate zone (only bedrock) has horizontal nodal distances of 20 m.The remaining part of the primary mesh (only bedrock) has nodal distances of 200 m.
The top layer has nodal z values representing the head (between 12.7 m and 22.1 m altitude; Fig. 8).The second layer has nodes located 0.1 m vertically below those of the top layer.The vertical nodal distance between the following 32 layers is 12.5 m.The top layer, which serves to maintain constant pressure and salinity, exclusively consists of infinite-volume boundary elements (10 45 m 3 ).Other boundary cells are the rock-salt cells and the bottomlayer cells of the -375-m level.They have a volume of 10 14 m 3 .This volume is large enough for maintaining nearly constant salinity throughout the simulation period but is simultaneously flexible enough to account for pressure adjustments.The volume of the remaining cells is calculated according to their nodal positions.A secondary boundary cell is connected to the primary cell in the centre of shaft 2 at the top of the salt dome (-237.5-mlevel).The boundary cell is used for injecting HCO 3 -whereas the primary cell is used for injecting hydrogen gas.
The initialisation starts with a pressure of 10 5 Pa in all models cells.The infinite-volume elements of the top layer have zero salinity.The large-volume elements (10 14 m 3 ) for the rock-salt unit and the bottom layer have an initial salinity of X brine = 1 (X salt = 0.25).Based on these boundary conditions, the diffusivity of brine is estimated in a trial-and-error procedure.Suitable vertical salinity gradients at the end of the 100,000-year initialisation period are obtained with a diffusivity 10 -7 m 2 /s (Fig. 9).These salinity gradients, which are close to the present-day values (Klinge et al., 2007), are maintained with insignificant variations throughout the following 7,000-year and 200,000-year simulation periods.

Hydrostratigraphy and hydraulic properties
The hydrostratigraphic information of 197 drill hole logs is transferred to the nearest model node at the corresponding z-position (Figs. 6 and 8;Ludwig et al., 1989;Beushausen & Ludwig, 1990;Ludwig et al., 1993;Klinge et al., 2001).Based on this information, the hydrostratigraphic units for the remaining nodes are assigned by interpolation and extrapolation.
The saturated hydraulic properties of the hydrostratigraphic units of the caprock and cover sediments (Table 3) are assigned according to Vogel (2005).This scheme is based on the geometric mean of empirical maximum and minimum values.No decision has been taken yet with respect to the saturated hydraulic properties of the backfill of shaft 2. Therefore, various permeability cases are calculated (base-case permeability of 1 x 10 -12 ; sensitivity cases of 3 x 10 -13 , 5 x 10 -13 , 2 x 10 -12 and 3 x 10 -12 m 2 ).The porosity is 0.3 for all cases.

Sorption and diffusion
The distribution coefficients for the radionuclides in the one-phase scenario are taken from Suter et al. (1998).C-14 in the two-phase scenario is assumed to be non-sorbing under low oxygen fugacities compatible with the release of hydrogen gas.The aqueous phase diffusivity is 10 -9 m 2 /s for all species (Keesmann et al., 2005).

Simulated far-field transport
The simulation period is from year 1,000 to year 200,000 for the single-phase scenario and from year 1,000 to year 8,000 for the two-phase scenario.The input for the one-phase simulations is the near-field release of 17 radionuclides, of which five are the parents for daughter radionuclides (Am-241, Pu-239, Pu-240, Pu-242 and Th-230; Fig. 3; Table 4).The biosphere is represented by the -37.5-m level, which approximately is the limit between fresh water and saline water (1 g/L salt or 0.0034 brine fraction).The radioactive plume reaches its highest vertical extent in the year 200,000 (end of the simulation period) and in the year 7,000 for the one-phase and two-phase scenario, respectively (Figs. 10 and 11).
The calculation of the radioactive dose is based on Dose Conversion Factors (DCFs; Table 4; Hirsekorn et al., 1991).The annual dose D D (Sv/a) is calculated according to the equation where X i is the concentration (Bq/L) of the radionuclide i and C i is the DCF (Sv/a:Bq/L) of the radionuclide i.For the single-phase scenario, the peak doses on the -37.5-m level is 1 x 10 -17 Sv/a.For the two-phase scenario, the peak dose varies strongly depending on the assumptions for the permeability of the backfill of shaft 2. For the base-case permeability (1 x 10 -12 m 2 ) and lower permeabilities, the peak dose is above the German regulatory limit of 1 x 10 -4 Sv/a.The planned repository is located in granitoid at 420 m depth at the island of Olkiluoto off the south-west coast of Finland (POSIVA, 2009).It can accommodate 3,000 containers with a total of 5,800 t U of burnt fuel (Löfman, 2005).According to the KBS-3V concept, the containers will be emplaced in vertical deposition holes driven from the floor of deposition tunnels, which are connected to a nearly horizontal system of access tunnels and transport tunnels.The containers that host the waste have a 5 cm thick corrosion-resistant copper shell around an inner deformation-resistant cast-iron canister; they are embedded in a 35 cm thick bentonite buffer.The horizontal dimensions of the repository are 1,600 m x 1,400 m.

Near-field
The near field is the hydrochemical regime of the underground workings and engineered barrier around the radioactive waste, consisting of the container wall and bentonite buffer.The reference failure mode for a defective canister and release of radioactivity from the near field to the undisturbed rock of the far field (geosphere) is the near-field base case (Nykyri et al., 2008).The canister is assumed to have a production defect with a diameter of 1 mm through which water enters into the canister causing dissolution of the fuel up to the solubility limits shown in Table 5.The near-field release of radionuclides (Fig. 12) is used as source for the contaminant injection cells in the far-field model.
As opposed to the easily corrodible steel canisters in the salt repository (see above), the copper shell of the canisters in the granitoid repository (KBS-3V concept) has an extraordinary chemical stability (Schwartz, 2008).Among the various candidate materials for waste packages, copper has unique oxidation characteristics.The conversion from native metal (Cu°) to metal oxide (Cu 2 O) occurs in a mildly oxidising to mildly reducing environment (positive Eh for pH <7.7 at 25°C; Fig. 13) whereas the conversion of steel, titanium or nickel-chromium alloy already is possible under strongly reducing conditions, i.e., below the stability field of liquid water.Native copper is present as natural occurrence in the Earth's crust.The largest deposits are located on the Keweenaw Peninsula of Michigan, where they have been mined to a depth of 2.2 km (Schwartz, 1996).These deposits formed one billion years ago at temperatures of 100-200°C.The mineralising fluids were slightly less reducing but had much higher copper concentrations than common present-day groundwater.
Fig. 13.Eh-pH diagrams for the system Cu-S-Cl-O-H at 25°C and 100°C for 0.1-0.3mol/L Cl (Schwartz, 2008).Shaded area = Eh-pH range in which the Keweenaw native-copper deposits have formed (Schwartz, 1996).Point symbols = groundwater in crystalline rock of envisaged disposal sites in Sweden, Finland and Switzerland.(A and C) Diagrams for ΣS of 10 -2 and 10 -5 , and ΣCu/Cl 2 = 10 -3 .(B and D) Diagrams for ΣS = 10 -5 and ΣCu/Cl 2 of 10 -3 , 10 -4 and 10 -5 Under the envisaged repository conditions, CuCl 2 -is the dominant aqueous copper species.Accordingly, the thermodynamically relevant parameter is the ΣCu/Cl 2 ratio, which refers to the sum of activities of all dissolved copper species divided by the Cl -activity raised to the second power.Mine waters in the Keweenaw district have ΣCu/Cl 2 ratios in the range from 10 -4 to 10 -5 .Similar conditions are achievable in the bentonite buffer around the copper container if the bentonite contains artificial admixtures of fine-grained native copper.This is a technically feasible variant of the KBS-3V concept, which simulates the environment of a natural native-copper deposit.Thus thermodynamic equilibrium between container and fluid on the high Eh side of the native-copper stability field is implemented in the repository-container system as analogue to the natural counterparts.
The low-Eh and low-pH side of the native-copper stability field is the copper-sulphide phase boundary (CuS and CuS 2 ).The position of this boundary depends on the total activity of aqueous sulphur species (ΣS).The groundwater in the envisaged repositories in Finland, Sweden and Canada has ΣS in the range from <10 -5 to 10 -2 .This implies conditions partly below the stability field of native copper, pH being in the range of 7-9 and Eh in the range from -0.03 to -0.4 V. Provided the bentonite contains no sulphur-bearing minerals, the corrosion of the copper container is constrained by the diffusion of aqueous sulphide from the granitoid aquifer through the bentonite to the container surface.This situation is quite different from corrosion of other package materials such as steel, titanium or nickelchromium alloy, which all corrode by reaction with omnipresent water.It is not possible to control corrosion of these materials by a diffusion barrier around the container.
The reference buffer of the KBS-3V concept is the pyrite-bearing MX-80 bentonite (0.3 % sulphide sulphur).Another option is the Avonlea bentonite, which has no sulphides but a high content of gypsum (2 %).Neither the presence of pyrite (FeS 2 ) nor gypsum (CaSO 4 .2H 2 O) is desirable because ΣS of the system should be as low as possible.The Czech EKOBENT bentonite (Prikryl & Woller, 2002), which has a total sulphur concentration of less than 0.05 % and does not contain sulphides, would be the better choice although it has not been tested as thoroughly as MX-80 or Avonlea.The original idea behind the use of a sulphide-bearing bentonite in the KBS-3V repository was to accelerate the transition from oxidising conditions (during the construction phase) towards a final anoxic regime.This scheme, however, has been called in question (SKI, 2006).There are alternatives such as the implementation of saturated conditions in the shortest possible time.This can be achieved by incremental flooding of those parts of the slightly inclined emplacement tunnels where waste packages are already in place.
In the case of a sulphur-free buffer, general corrosion of the copper container can be determined by a simple calculation.The experimentally derived diffusion coefficient of aqueous sulphide in bentonite is approximately 7 x 10 -8 cm 2 /s (King & Stroes-Gascoyne, 1995;King et al., 2002).The groundwater of the envisaged repositories in Finland, Sweden and Canada has sulphide concentrations in the range from <3 x 10 -7 to 3 x 10 -5 mol/L.Assuming sulphide concentrations at the upper limit, 6 x 10 -17 mol/(s cm 2 ) are transported through the 35 cm thick bentonite to the container surface.This is equivalent to a general corrosion rate of 3 x 10 -8 cm/a, when Cu° is transformed to Cu 2 S. Allowing for localised corrosion by multiplying the general rate with a correction factor of 5, the maximum corrosion depth is less than 0.2 cm within one million years.A service time for the 5-cm thick copper shell beyond one million years is a realistic possibility (Schwartz, 2008).The mass-transport assumption in this case sets an upper corrosion limit because some of the diffusing sulphide reacts with disseminated native-copper in the buffer and, therefore, is not available for corrosion of the copper container.Thus the near-field release for a canister that has no production defect and has not suffered mechanical damage is assumed to be zero for the 200,000-year simulation period.Table 5. Olkiluoto model.Liquid-phase solubility (mol/L) in the near-field

Geometry of the far-field model and initialisation
The model has a total of 323,657 elements.The irregular rectangular primary mesh is the fracture continuum, which measures 7,700 m x 5,500 m x 750 m (Figs.14-16) and consists of 27 layers with 168,048 cubic or cuboid cells.The nodal distance in the x and y direction is 66.6 m.The top layer has nodal z values representing the head (-8 m to 10 m altitude).The second layer has nodes located 0.1 m vertically below those of the top layer.The vertical nodal distance between the following 25 layers is 30 m.The top layer, which serves to maintain constant temperature, pressure and salinity, exclusively consists of infinite-volume boundary elements (10 45 m 3 ).The bottom layer cells have a volume of 10 14 m 3 .This volume is large enough for maintaining nearly constant temperature and salinity throughout the simulation period but is simultaneously flexible enough to account for pressure adjustments.The volume of the remaining cells is calculated according to their nodal positions.The secondary matrix continuum comprises the layers 2 to 26.The detailed geometric relationships between fracture and matrix continuum are determined on the basis of a parameter estimation procedure (see "Parameter estimation").
The infinite-volume elements of the top layer have a pressure of 10 5 Pa, a temperature of 6°C and zero salinity.The bottom-layer large-volume elements (10 14 m 3 ) have an initial temperature of 14°C and an initial salinity of 0.025 mass fraction salt (corresponding to 0.44 mol/L Cl).The remaining layers have initial values along the gradients defined by the top and bottom layers.These boundary conditions and initial conditions, together with a high diffusivity of salt (10 -3 m 2 /s), allow to maintain suitable vertical gradients throughout the simulation, unless disturbed by radioactive heat sources.These gradients include temperature and salinity gradients that are close to the present-day values (Pitkänen et al., 2004;Löfman, 2005).

477
The simulation period is 200,000 years.During the first 10,000 years, the terrain is subjected to glacio-isostatic uplift (POSIVA, 2006;Löfman & Poteri, 2008) and the transient head conditions are translated into transient mesh geometries.The head reference point, which is the vertical projection of the north-western corner of the repository, is fixed at a constant value (2 m).The z values of the top layer change from simulation year zero to year 1,000 and 10,000 according to the z values in Figure 17.The rising terrain implies a retreating shoreline of the Baltic Sea, indicated by the <0-m head contours moving away from the present island of Olkiluoto.
There are nine contaminant-injection cells evenly distributed over the repository area on the -420 m level (Fig. 16).These source cells have only one connection to a fracture element.The near-field releases of the radionuclides shown in Figure 12 are used as input (see "Near field").Transport paths and, hence, travel times for the radionuclides strongly depend on the location within the repository from which they are released.An ideal simulation would include all repository cells but this is too expensive computationally.Scoping calculations indicate that the relevant results such as median, mean and maximum doses change little when more than nine source cells are used.

Hydraulic properties
The geometry of the Hydrogeological Zones (HZs) of high permeability and surrounding Sparsely Fractured Rock (SFR) of low permeability corresponds to the hydrogeological structure model of Vaittinen et al. (2009).Permeability and flow porosity (Figs. 15 and 16) are based on POSIVA (2009).The only exception is the repository area on the -420 m level, where the permeability is based on Vaittinen et al. (2009) and POSIVA ( 2009) but the flow porosity is 0.01; this flow porosity value is derived from a backfilled repository volume of 1,310,000 m 3 (Kirkkomäki, 2007) and an average backfill porosity of 0.35.

Heat sources
The heat production of the radioactive waste in a single canister is shown for the first 2,000 years after deposition in Figure 18.These values are multiplied by a factor of 8.8, which is the number of canisters in a model cell, and are used as heat-generation data for the repository area on the -420 m level.

Parameter estimation
The retention of radionuclides in a fractured medium is caused by diffusion from the fracture into the stagnant fluid of the matrix adjacent to the fracture.An ideal simulation of a fracture media problem would require the discretisation of the matrix continuum (multiple-interacting continua or MINC model; Pruess, 1983;Pruess & Narasimhan, 1985;Pruess, 1992;Xu & Pruess, 2001;Liou, 2007).
Ten or more matrix continua are necessary for accurately simulating diffusive transport between fracture and matrix as the comparisons between numerical and analytical solutions have shown (Tang et al., 1981;Sudicky & Frind, 1982;Wu & Pruess, 2000;Diersch, 2009).However, the resulting problem size would be too large in the case of a three-dimensional simulation.Therefore, the problem size has to be reduced by replacing the model with a finely discretised matrix by an equivalent dual-continuum model (one matrix continuum).This is achieved by parameterising two variables among the three variables that control the retention of radionuclides; these are the diffusive transport distance between fracture and matrix, fluid volume of the fracture and effective diffusivity.The equivalent model is designed as conventional double-porosity model (Hantush et al., 2000(Hantush et al., , 2002;;Lichtner, 2000).
The critical step in designing the model with a single matrix continuum (equivalent dualcontinuum model) is the estimation of the parameters that justify to replace the corresponding finely discretised model (with a multi-continua matrix).The MINC preprocessor program of the TOUGHREACT code (Pruess et al., 1999) is suitable for models with up to 34 matrix continua.Scoping calculations have shown that models with 14 matrix continua have nearly the same retention properties as those of a model with the maximum number of continua.Thus, a two-dimensional 15-continua model has been designed that contains the fracture continuum of a 2,000-m long vertical subsection of the threedimensional model enclosing the radioactive source element 1 (Figs.15 and 16).A row of 14 matrix elements is connected to each fracture element with the exception of the fracture elements of the top and bottom layers.The detailed geometry of the MINC mesh is calculated with the ONE-D proximity function of the MINC pre-processor program of the TOUGHREACT code.The fracture spacing is set at 5.0 m, which is the reciprocal of the weighted mean of the fracture intensity (Nykyri et al., 2008).The element volume fraction of the matrix continuum is derived from a matrix porosity of 0.001 for anions (Cl-36 and I-129) and 0.005 for neutral species and cations (C-14, Cs-135 and Ni-59) (Nykyri et al., 2008).According to the anion exclusion concept, anions and cations do not occupy the same pore system in low-porosity rocks, due to electrical forces caused by the usually negative charge of the mineral surfaces.Anions experience repulsion close to the mineral surfaces whereas cations are adsorbed on the surfaces (Rasilainen, 1997).
Fig. 18.Olkiluoto model.Heat output (J/s) from a canister with 1.93 t U burnt fuel from year 10 to year 2,000 after disposal (Löfman, 2005) The near-field releases of radionuclides (Fig. 12) are used as input.The decay, diffusion and sorption data for the radionuclides (Tables 4 and 6; Nykyri et al., 2008) are the same as those for the three-dimensional far-field model.
Sorption of radionuclides takes place in the matrix continuum of the 15-continua model but not in the fracture continuum.The retardation factor R m,i of the radionuclide i (dimensionless) for the matrix continuum is calculated according to the equation where n m is the matrix porosity (dimensionless), d is the rock density (kg/dm 3 ) and K d,i is the distribution coefficient (dm 3 /kg) of the radionuclide i for the rock matrix (Table 6).
TOUGHREACT calculates diffusion according to Fick's first law.The retention of radionuclides is controlled by the diffusivity, the fluid volume and transport distance between fracture and matrix.A dual-continuum model can almost perfectly substitute the 15-continua model if only two variables are parameterised; e.g., the fluid volume of the fracture together with the transport distance between fracture and matrix (as applied here) or the fluid volume of the fracture together with the diffusivity (producing similar results).
The fluid volume of the fracture continuum is adjusted by parameterising the retardation factor of the fracture continuum (which equals unity in the 15-continua model).The diffusive transport distance is parameterised by multiplying the fracture spacing of the 15continua model (5 m) with a distance factor.The parameters are determined by the logleast-squares method.This method minimises the squared deviations between the annual far-field releases of the dual-continuum model and those of the 15-continua model (Fig. 19; Table 6).Note that the annual far-field release of a radionuclide (Bq/a) is the annual transport of the radionuclide from the second topmost layer to the topmost layer of the twodimensional model.
The parameters obtained from this optimised two-dimensional model are used for the threedimensional model that has one fracture continuum and one matrix continuum.This equivalent dual-continuum model is used for the subsequent transport simulations.The radionuclide releases of the near-field base case are used as input for the far-field simulations.The biosphere is represented by the second topmost layer of the far-field model, which has fresh-water quality for most of the simulation period.The near-field base case assumes that one canister randomly chosen in the repository layout has a defect.There is a strong variability of radioactivity released to the biosphere depending on the location of the defective canister (Fig. 20).The canister locations 1-4, 6 and 8 in the north-eastern and central part of the repository imply a relatively large amount of radioactivity released to the biosphere whereas canisters located at the positions 5, 7 and 9 in the south-western part imply low or insignificant amounts of radioactivity.Figures 21A and 21B show the contaminant plumes for the source 3 at the NE corner and source 5 at the SE corner of the repository, respectively.The plumes emanating from the remainder of the canister locations have shapes that are intermediate between those shown.The maximum dose, which is produced by the canister position 6 (1.2 x 10 -7 Sv/a), is far below the Finish regulatory limit of 1 x 10 -4 Sv/a.

The Opalinus-Clay repository
The current scenarios assume that the repository will be located in the Jurassic Opalinus Clay in the Zürcher Weinland region, Switzerland (Fig. 1; NAGRA 2002).The claystone formation is gently dipping and has a thickness of 105-125 m.It is overlain by Middle Jurassic through Pleistocene sediments of approximately 600 m thickness.About 2,800 waste canisters containing 3,200 t U burnt fuel will be deposited in near-horizontal emplacement tunnels, which are connected to an access ramp via operational tunnels.
Two types of waste containers are considered for the repository.The first option is a steel canister, which is similar to that envisaged for the Gorleben repository.The second option is a container with a corrosion-resistant copper shell, such as the canisters for the Olkiluoto repository.So far, only the near-field release for the first option has been published (NAGRA, 2002;Kosakowski, 2004).For the second option, which considers improved safety standards, there are no near-field data available.The hydrochemical regime of a clay repository is similar to that of a granitoid repository but totally different from the highly corrosive regime of a salt repository.The performance of a copper-cast iron canister in a clay repository is as good as the performance of such a canister in a granitoid repository.Except for the case of a production defect or mechanical damage, the canister can assumed to be isolating the waste for a period of more than one million years.The permeability of a clay host rock is less than the permeability of a granitoid host rock.Thus it can be assumed that the potential groundwater contamination caused by a defective canister in the Opalinus-Clay repository is not higher than that for the Olkiluoto granitoid repository if the same type of waste canister is used.

Conclusions
The quality of models for groundwater contamination above high-level repositories in granitoid, salt and clay is not uniform.The most problematic case is a salt repository for two main reasons.First, the plastic behaviour of the host rock (salt) is a variable that introduces a high degree of uncertainty in any model attempt.Second, there is the inevitable generation of hydrogen gas caused by the corrosion of the steel waste canisters in high-salinity environments at low oxygen fugacities.The conditions of gas release constitute a great source of uncertainty.There is the possibility of unsteady or explosive release of hydrogen gas transporting short-lived radionuclides (Schulze, 2002).Furthermore, the permeability of the backfill of the shaft, through which the gas is assumed to flow, has a strong influence on the performance of the repository.
For a steady (non-explosive) gas release, a backfill permeability of <10 -12 m 2 results in a radioactive dose of about 1 mSv/a.A higher permeability would decrease the radioactive dose to values below the German regulatory limit (0.1 mSv/a).A relatively high permeability favours the flow of liquid with respect to the flow of gas whereas a relatively low permeability has the opposite effect.A low permeability is the appropriate safety concept for a one-phase scenario (only liquid); however, a high permeability is the appropriate concept for a two-phase scenario (liquid and gas).As both scenarios are equally realistic, there is a typical conflict of targets.Such problems are not an important issue for the standard concept of a granitoid-hosted repository and the non-standard concept of a clay-hosted repository (both with copper-cast iron waste containers).

Fig. 2 .
Fig. 2. Map of the Gorleben area with model mesh

Fig. 10 .
Fig.10.Gorleben model.Peak values of the radioactive dose (Sv/a) on the -37.5 m level for the one-phase scenario and two-phase scenario (base case with a permeability of 1 x 10 -12 m 2 for the backfill of Shaft 2 and sensitivity cases with a permeability of 3 x 10 -13 m 2 , 5 x 10 -13 m 2 , 2 x 10 -12 m 2 and 3 x 10 -12 m 2 )

Fig. 17 .
Fig. 17.Olkiluoto model.Vertical nodal positions (z coordinates; m) of the top layer in the simulation year zero, 1,000 and 10,000

Fig. 19 .4. 7
Fig. 19.Parameter estimation for the Olkiluoto model.The far-field release of radionuclides is shown for a 15-continua model and the equivalent dual-continuum model (optimised model)

Fig. 21 .
Fig. 21.Olkiluoto model.(A and B) Maps of the second topmost layer with radioactive dose (Sv/a) in the simulation year 200,000 for the sources 3 and 5

Table 3 .
Saturated hydraulic properties of rocks and structural material of the Gorleben farfield model www.intechopen.comModellingGroundwaterContaminationAbove High-Level Nuclear-Waste Repositories in Salt, Granitoid and Clay 467

Table 6 .
Set-up of the Olkiluoto model www.intechopen.comModelling Groundwater Contamination Above High-Level Nuclear-Waste Repositories in Salt, Granitoid and Clay