nuclear waste disposal modelling : uses and needs at edf r&d f. dumortier (lnhe), m. eddi...
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Nuclear Waste Disposal Modelling :
uses and needs at EDF R&D
F. Dumortier (LNHE), M. Eddi (MFEE), S. Granet (AMA)
Journées scientifiques du GNR MOMAS : 23-25 Novembre2
Context and aimsContext 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.
Journées scientifiques du GNR MOMAS : 23-25 Novembre3
The repository concept 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
Evolution of thermal power for C2 waste package
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
0 50 100 150 200 250 300 350 400 450 500
Package age (years)T
her
mal
Po
wer
(W
/pac
kag
e)
Selected preliminary
storage
Thermal power of studied nuclear waste
ANDRA source
buffer to insure a better heat diffusion
Journées scientifiques du GNR MOMAS : 23-25 Novembre4
Thermal modellingThermal 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
Marnes du Kimméridgien
Calcaires oxfordiens
Argilites du Callovo-oxfordien
Calcaires du Dogger
0 m
120 m
420 m
550 m
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
Journées scientifiques du GNR MOMAS : 23-25 Novembre5
Numerical code and meshing toolNumerical 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/anisotropicRadiation (wall to wall) : all view
factors
SYRTHES (3D, transient process)
EDF-open source code
Using SIMAIL for meshing (parametrical studies)
Journées scientifiques du GNR MOMAS : 23-25 Novembre6
Modelling approachModelling 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
=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
Waste package
Over-packSleeve (25 mm) Clearance
(55 mm)
Criterion Tmax 90°C
over
Local modelling
Journées scientifiques du GNR MOMAS : 23-25 Novembre7
Improvement of numerical parameters
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 (Lb)
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
Journées scientifiques du GNR MOMAS : 23-25 Novembre8
Next main challengesNext 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
Journées scientifiques du GNR MOMAS : 23-25 Novembre9
The near field THM modelingThe 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 ?
Journées scientifiques du GNR MOMAS : 23-25 Novembre10
The near field THM modelingThe near field THM modelingGoals
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)
Journées scientifiques du GNR MOMAS : 23-25 Novembre11
T.H.M coupling descriptionT.H.M coupling description
Mechanic -> Hydraulic Fully saturated medium : Terzaghi relation
Partially saturated medium : Coussy formulation
Iσσ
1
3
2lS
c dSSppS
Iσσ wbp
Mechanic -> Hydraulic
Permeability affected by damage
Practically :
homogenisationdamage K
300. kfK
Thermic/Hydraulic : soft
Thermic->Mechanic (Temperatures generates dilatation effects and mechanical stresses)
M
TH
EDF’s FE Software : Code_aster (www.code_aster .org)
Journées scientifiques du GNR MOMAS : 23-25 Novembre12
S(Pc)
00,10,20,30,40,50,60,70,80,9
1
0,00E+00 1,00E+08 2,00E+08 3,00E+08 4,00E+08
Pc (Pa)
S
Colis
Béton rempl.
ZF
ZE
Cox
The classical two-phase flow modelThe classical two-phase flow modelHypothesis :
Porous media constituted by 2 phases (liquid + gas) et 2 components (ex. H2O et H2)
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
wres
mn
r
cwresl S
P
PSS
11 mmwewe
grel SSk
2/111 2/111mm
wewelrel SSk
Perméabilités relatives
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 0,2 0,4 0,6 0,8 1
S
k(S
)
S close to 1
Journées scientifiques du GNR MOMAS : 23-25 Novembre13
Questions and perspectives reliated to the near field THM modelingQuestions 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
Journées scientifiques du GNR MOMAS : 23-25 Novembre14
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 Long term safety assessment studies
Eau du sol Particules solides du sol
Atmosphère
Ingestion
Ingestion
Ingestion
Evapotranspiration
Précipitation
Irrigation
Transfert
Irrigation Lait Viande
Transfert
Ingestion
Eau de la nappe
contaminée
Saulx
ANDRA source
Journées scientifiques du GNR MOMAS : 23-25 Novembre15
Long term safety assessment studies 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
Journées scientifiques du GNR MOMAS : 23-25 Novembre16
Long term safety assessment studies 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 2DSUPG, CVFE
3DSUPG, ELLAM
2005Transport module
2010
3DSUPG
?
Journées scientifiques du GNR MOMAS : 23-25 Novembre17
General conclusionGeneral 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 ?