Bourgeat Siam

Modelling an Underground Nuclear waste Repository: 

Modelling an Underground Nuclear waste Repository From the Near Field To the Far Field Model Main steps and challenges Alain Bourgeat UCB-Lyon1, CNRS UMR 5028, GDR MoMaS

Slide2: 

What is a Nuclear waste site (exemple) Near Field versus Far Field modelling Some problems for Scaling Up the source terms Modelling an Underground Nuclear waste Repository

Geological Storage: 

Geological Storage where Host rock: Brine, Clay, Granite, Argilite, … Who (high level, long lived) high level of activity and/or long lived elements B Type : low or medium activity level, but long life time C Type : high activity level, T° > 80 °C come mainly from industrial activities(power plants)

Numbers:: 

Numbers: For instance (in France) Expected Total volume of nuclear waste (including containers) in 2020: 100 000 m3 Total length of galleries, tunnels,needed in 2020: 102 km Only the high activity waste will be stored in a geological repository : More than 25 isotopes Some of them have a life time of 1 000 000 years

Question before deciding a Geological Storage for Nuclear waste: 

Question before deciding a Geological Storage for Nuclear waste What is the possible evolution, and impact on the biosphere, of such an underground storage ? Real experiments are not possible at these scales of both time ( > 500 years) and space ( 1X25 X 25 km3) Only predictions based on numerical simulations are possible

Predictions based on numerical simulations ??: 

Predictions based on numerical simulations ?? There are well established models, but at usual scales of measurement (meters, years) Two types of simulations: One based on Near Field (mainly for performance assessement) and one based on Far Field models (mainly for safety analysis)

Far Field 1X25 X 25 km3 and > 500 years : 

Far Field 1X25 X 25 km3 and > 500 years Far field region Far field domain of computation Repository region

Slide8: 

Numerical simulations and predictions based on MACROmodels: Diffusion/Dispersion, Convection, Reaction ( by mean of a Retardation factor) The repository is reduced to a very thin homogeneous « source » zone Far Field 1X25 X 25 km3 and > 500 years Real size of the repository domain

Far Field Simulations: 

Far Field Simulations MACRO model: Diffusion/Dispersion, Convection, Reaction ( by mean of a Retardation factor)

Far Field Models: 

Far Field Models MACROSCOPIC models need to be derived from the mesoscopic level, including : geochimical effects in rocks with highly contrasted properties (possibly fractured) for various velocity ratio (reaction / diffusion/flow) geomechanical effects after drilling shafts and tunnels emission from each container or vault …….

Near Field: 

Near Field Waste Inside a matrix (glass, concrete, tar) Protected by a container (steel, concrete) Surrounded by manufactured barriers (bentonite, concrete, …) Containers grouped in a Vault Vaults are connected by tunnels, galleries, drifts and shafts

Near Field - Containers: 

Manufactured barrier One container Host rock biosphere A container inside a vault Near Field - Containers

Near Field - Vaults: 

Various types of Vaults , and haulage tunnels Open vault with a set of containers closed vault Near Field - Vaults

Near Field Modelling: 

Near Field Modelling Vault dimensions  » 1 m diameter, length: 10m Numerical simulations and predictions based on mesoscopic models including: T-H-M-C couplings Coupling of different materials ( steel, glass, concrete, bentonite, clay, ….) Adsorption / desorption Hydrogen production …..

Slide15: 

Containers set , vault, with a haulage tunnel Damaged zone of the host rock haulage tunnel Set of Containers Bentonite barrier Bentonite barrier after swelling Broken container and matrix Disturbed Containers set, (after n103 years) backfill

Near Field Models: 

Near Field Models These MESOSCOPIC models need to be derived from the microscopic level, specially : - geomechanical properties of rocks - coupling transport/reaction - adsorption/desorption - swelling of bentonites …….

Far Field versus Near Field: 

Far Field versus Near Field Near Field model to be derived from « microscopic » models Far Field model to be derived from Near Field models

Far Field vs. Near Field: 

Far Field vs. Near Field Container vault repository Far field region Unit Zone

Far Field vs. Near Field Scaling Up the Sources: 

Far Field vs. Near Field Scaling Up the Sources vault Unit / Zone Unit / Zone Far field Region Zone Repository Unit

Scaling Up the Sources: 

Scaling Up the Sources There are several levels of upscaling from waste packages to a storage unit global model from storage units to a zone model from similar zones to the repository global model One way would be to use Re-iterated Homogenization, but : the phenomena to be taken in account at each level are different leading to different equations parameters or boundary conditions

Slide21: 

Zone Repository Unit First example of Scaling Up: From the STORAGE UNITS to a “ZONE global model" OR, From Similar ZONES to the “REPOSITORY global model” A.B., O. Gipouloux, E. Marusic-Paloka. Mathematical Modeling of an underground waste disposal site by upscaling. Math. Meth. Appli. Sci., Volume 27, Issue 4; March 2004, p 381-403.

from storage units to a zone model (or from similar zones to the repository ): 

from storage units to a zone model (or from similar zones to the repository ) Rescaled domain section Real domain section

from storage units to a zone model (or from similar zones to the repository ): 

from storage units to a zone model (or from similar zones to the repository )

from storage units to a zone model (or from similar zones to the repository ): 

from storage units to a zone model (or from similar zones to the repository ) The Zone « global model »

from storage units to a zone model (or from similar zones to the repository ): 

from storage units to a zone model (or from similar zones to the repository ) Simulation of all the units Simulation of the zone « global model »

Slide26: 

Second example of Scaling Up: From a " WASTE PACKAGES model" to a “Storage UNIT Global model", including a possibly damaged zone (A. B, E. Marusic-Paloka. A homogenized model of an underground waste repository including a disturbed zone. To appear in SIAM J.on Multiscale Modeling and Simulation, 2005.)

From a " WASTE PACKAGES model" to a “Storage UNIT Global model", including a possibly damaged zone: 

From a " WASTE PACKAGES model" to a “Storage UNIT Global model", including a possibly damaged zone

From a " WASTE PACKAGES model" to a “Storage UNIT Global model", including a possibly damaged zone: 

From a " WASTE PACKAGES model" to a “Storage UNIT Global model", including a possibly damaged zone

From a " WASTE PACKAGES model" to a “Storage UNIT Global model", including a possibly damaged zone: 

From a " WASTE PACKAGES model" to a “Storage UNIT Global model", including a possibly damaged zone

Slide30: 

Third exemple of Scaling Up: From the LONG STORAGE UNITS to a “ZONE global model" A.B., jointly with A. Piatnitski and E. Marusic-Paloka. ; work in progress.

Slide31: 

Third exemple of Scaling Up: From the LONG STORAGE UNITS to a “ZONE global model" (A.B., jointly with A. Piatnitski and E. Marusic-Paloka. ; work in progress.) The repository zone, is made of a high number of similar long waste filled storage units, lying on a hypersurface S and linked by backfilled working and haulage drifts. . Like previously, the parameter b characterize de degree of damaging ( scaling the Darcy's velocity range) The main difference and difficulties compared to the previously studied situations, is the singular behavior of the only one damaged drift. In the first exemple there was no damaged zone at all, while in the second one the damaged drifts were periodically repeated, allowing to use the technique of singular measures. The global models only slightly differ; depending on b; the global model is independent of the choice of b and only higher order correctors terms differ, according to b.

Slide32: 

Fourth example of Scaling Up: The contents, and the leaking starting time of the Waste Packages are Random A.B., jointly with A. Piatnitski; work in progress The "local sources" f e are periodically repeated, lying on a plan S the contains, the leaking starting time and the emission time evolution, of each local source, are random :

THE END : 

THE END Thank you for your attention Finally !!