nuclear waste disposal modelling : uses and needs at edf r&d f. dumortier (lnhe), m. eddi...

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.


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


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


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)


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


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


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


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 ?


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)


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)


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


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


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


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


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

?


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 ?

nuclear waste disposal modelling : uses and needs at edf r&d f. dumortier (lnhe), m. eddi...

Documents

ultimate nuclear waste

optimized repository

developpement division

waste glass package

presentationthermal

respect of thermal criterion

technical options

near field thm modelling