1. Nuclear Waste Disposal Modelling : uses and needs at EDF R&D F. Dumortier (LNHE), M. Eddi (MFEE), S. Granet (AMA)

2. Journées scientifiques du GNR MOMAS : 23-25 Novembre 2 Context and aims Context  ANDRA (French National Radioactive Waste Management Agency), in charge of the design and building of the repository for nuclear waste, has set out a « design concept 2005 », but technical options may still be modified,  EdF, responsible for its ultimate nuclear waste, has undertaken analysis of this ANDRA « repository reference concept » under various technical fields in order to control the cost Aims of the presentation 1. Thermal modelling allows : the dimensioning of the repository taking into account the respect of thermal criterion and the optimisation of the compactness of the disposal installation to reduce the cost. 2. Near Field THM modelling allows to estimate the extension of Excavation Damage Zone, to understand the comportment of plugs and sealings, to evaluate the Maximal Hydrogen pressure and its preferential pathway 3. Long term safety assessment studies are then conducted to ensure that radiological impacts linked to optimized repository are low enough for different evolution scenarii.

3. Journées scientifiques du GNR MOMAS : 23-25 Novembre 3 The repository concept Architecture : a single horizontal level at the depth of 500 m HL waste glass package C1 to C4 packages cell drift 500 m Selected preliminary storage Thermal power of studied nuclear waste ANDRA source buffer to insure a better heat diffusion

4. Journées scientifiques du GNR MOMAS : 23-25 Novembre 4 Thermal modelling The thermal modelling allows : - the dimensioning that respects the thermal criterion of 90°C on the geological barrier to prevent it from any damage + - the optimisation of the compactness of the disposal installation to reduce the cost. + - the thermal profiles evolution useful for the other phenomena modelling Application examples : - Stretching out the length of the tunnel (30 m -> 120 m) - Getting longer the package storage (60 -> 90 years) Technical improvement : reduce gas released by corrosion => Reducing the steel thickness of the over-pack Cost improvement densification

5. Journées scientifiques du GNR MOMAS : 23-25 Novembre 5 Numerical code and meshing tool Conduction F.E.M.: on unstructured grids for solids Thermo-physical parameters and heat generation : f(time, space and T) conductivity : iso/ortho/anisotropic Radiation (wall to wall) : all view factors SYRTHES (3D, transient process) EDF-open source code Using SIMAIL for meshing (parametrical studies)

6. Journées scientifiques du GNR MOMAS : 23-25 Novembre 6 Modelling approach for ¼ cell  = 0 ½ cell = “long term modelling” (t> 1000 ans) ¼ cell = “short term modelling” : to respect the thermal criterion -3500 m Free surface Text = 10.7°C 0m  =0 Dy/2  =0 T= 78.6°C 500 m -- Px/2  =0 Heat generation Kimmeridgian Oxfordien Callovo Oxfordien Dogger Heat transfer simplified assumptions Clearances (Clearances ~15 mm each) Waste package Over-pack Sleeve (25 mm) Clearance (55 mm) Criterion Tmax 90°C over Local modelling

7. Journées scientifiques du GNR MOMAS : 23-25 Novembre 7 Improvement of numerical parameters  Spatial meshing refinement Conduction : 3D- about 6*4 meshes (length*height for a disposal package) Radiation : 2D ~ similar refinement to the solid meshes adopted  Time step refinement Calculated (defined according to the variation of temperature) or prescribed (by the user ): hours to years Methodology for dimensioning optimisation For a fixed length of cell (30m), 1.choose N packages (Np) per cell to be installed => the length of buffer is determined (L b ) 2.then vary the spacing (Px) between two cells that respect the thermal criterion (90°C) 3.calculate the related excavated volume (Vexc/package), then Np varies to get the minimal Vexc => economical optimisation : “best estimate dimensioning“ =minimal Vexc (Np, Px) => “long term” modelling In 3 steps with 2 iterative loops Thermal optimisation

8. Journées scientifiques du GNR MOMAS : 23-25 Novembre 8 Next main challenges 3 « nested » modelling : site (km) > module(m) > local tunnel modelling (cm) More realistic modelling of the clearances (+ chemical, mechanical and hydraulic phenomena) Taking into account saturation for argillite physical properties (porous media) Uncertainties analysis Syrthes parallelization (in progress) = > smallest CPU time

9. Journées scientifiques du GNR MOMAS : 23-25 Novembre 9 The near field THM modeling  Different stages in the “life” of a nuclear waste repository :  Work stage (2 years) Excavation of galleries and wells Apparition of fractures and increase in permeability : EDZ  Exploitation stage (100 years) Positioning of waste containers and galleries ventilation Thermal loading and water expansion Closing of the cells with bentonite and concrete Unsaturated problem : resaturation of plugs and barriers How to predict mechanical evolution of plugs and sealings  Post closure stage (1 million years …) Thermal loading Corrosion of steel pieces (production of hydrogen) Evolution of EDZ due to hydrogen high pressures ?

10. Journées scientifiques du GNR MOMAS : 23-25 Novembre 10 The near field THM modeling  Goals  Estimation of the Excavation Damage Zone (EDZ) around galleries and cells  Understanding and prediction of the comportment of sealing and plugs  Understand the saturation/desaturation mechanisms  Estimate the Hydrogen pressure and the preferential pathways  Specificities  A fully coupled T.H.M problem on a Complex geometry  Heterogeneous materials with high contrasts Intact or damaged rock, engineered barriers (sealings, plugs, concrete), gaps between materials, steel (liners, jacketing, containers)  High contrast of initial saturation : clay initially saturated  engineered materials => stiff fronts  Multiphysic and multiscale (time, space) problem under hydraulic specificities (high level of capillary pressure and high level of gas pressure due to corrosion)

11. Journées scientifiques du GNR MOMAS : 23-25 Novembre 11 T.H.M coupling description  Mechanic -> Hydraulic Fully saturated medium : Terzaghi relation Partially saturated medium : Coussy formulation  Mechanic -> Hydraulic Permeability affected by damage Practically : homogenisation damage K  Thermic/Hydraulic : soft  Thermic->Mechanic (Temperatures generates dilatation effects and mechanical stresses) M TH EDF’s FE Software : Code_aster (www.code_aster.org)

12. Journées scientifiques du GNR MOMAS : 23-25 Novembre 12 The classical two-phase flow model  Hypothesis : Porous media constituted by 2 phases (liquid + gas) et 2 components (ex. H 2 O et H 2 ) Component mass conservation Darcy’s Law on each phase  High non linearities due to biphasic transfer term Diffusion term for mixture laws (Fick) Capillary pressure and relative permeabilities terms Example : Mualem Van-Genuchten model S close to 1

13. Journées scientifiques du GNR MOMAS : 23-25 Novembre 13 Questions and perspectives reliated to the near field THM modeling  Physical questions : What happen when S close to 1 : permeabilities ? Capillary pressure ? Limit or validity of two-phase flow model Good knowledge of data in EDZ : K(  v ), S(Pc) Effective stress/Total stress model : validity and limit (dilatant material)  Numerical questions : Hydraulic problem : Appearance and disappearance of a phase, stiff front treatment Contact problem : possible opening of gaps between plugs and rock Regularization methods (to avoid mesh dependency) - extension to viscoplastic model 3D modeling : High performance computations (decomposition domain, parallelism) Fully coupling vs strategy of couplings between mechanic software/scheme and two- phase flow software/scheme

14. Journées scientifiques du GNR MOMAS : 23-25 Novembre 14 Computations : 3D modelling to evaluate hydraulic head array (far field) 2D modelling around galleries containing waste packages : water flow + transport (near field) 1D/2D convective transport in galleries / shafts / aquifers (different scenarii) Transfer in the biosphere : human dose limited to 0,25 mSv/year Long term safety assessment studies Saulx ANDRA source

15. Journées scientifiques du GNR MOMAS : 23-25 Novembre 15 Long term safety assessment studies Tools : 1D OSIRIS : transport 2D ESTEL : water flow (saturated and non saturated zone) + transport (SUPG, CVFE, RWPT) 3D ESTEL : water flow (saturated and non saturated zone) + transport (SUPG, RWPT) On progress for 3D : MHFE + ELLAM 500 m  Taken into account : radiaoctive decay, sorption, precipitation, radioactive filiation (1D Osiris)  Not taken into account : multiphase transfers, coupling with chemistry Phenomenons

16. Journées scientifiques du GNR MOMAS : 23-25 Novembre 16 Long term safety assessment studies Tools (évolution) : Complexification of the studies for transport model Generalization of use of domain decompositions and parallel computations (till 25 millions elements for 3D hydro simulations) Next main challenge : take into account other phenomena (2 phases …) 1D 2D SUPG, CVFE 3D SUPG, ELLAM 2005 Transport module 2010 3D SUPG ?

17. Journées scientifiques du GNR MOMAS : 23-25 Novembre 17 General conclusion Nuclear waste disposal modeling = A very complete and multidisciplinary problem ! Geometry and phenomena to take into account : more an more complex  Multiphysic  Multiscale (space and time)  Each phenomena has to be well understand ! A better knowledge of the physic is required  With experimental results Improvement of numerical tool required  High performance computations (decomposition domain, parallelism, using of clusters, etc.)  Numerical schemes adapted to each phenomena  Uncertainties analysis  Fully coupled schemes vs coupling of tools adapted to each phenomena ?