MODELING REACTIVE
TRANSPORT IN NUCLEAR WASTE
GEOLOGICAL DISPOSAL:
2 benchmark problems :
- Glass/iron/clay interactions
- Atmospheric Carbonation of
concrete
SES BENCH – OCT. 27 - NOV. 2 2012
O. Bildstein, P. Thouvenot, J.E. Lartigue, I. Pointeau
CEA (French Alternative Energies and Atomic Energy Commission)
B. Cochepin, I. Munier ANDRA (French Radioactive Waste Management Agency)
20 avril 2023 | PAGE 1CEA | 10 AVRIL 2012
DISPOSAL CONCEPT IN A CLAYSTONE FORMATION AT 500 m DEPTH
Current design of deep underground repository for high and intermediate level long-lived waste
S.S.BENCH - November 16-18. 2011
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 2
Just a few words aboutthe glass/iron/clay
benchmark…
S.S.BENCH - November 16-18. 2011
DRD/EAP/11-0219
HLW DISPOSAL CELL
20 avril 2023 5th Andra International Conference - Montpellier | 22 Oct 2012 | PAGE 4
• different types of material in physical contact, technological gaps
long term calculations of geochemical evolution (100 000 years)
Vitrified wastepackages
Cross section
3 cm gap steel liner
disposal package
0.8 cm gap
3 cm gap
scale
• 1D radial domain
• transport: diffusion only
• water saturated, constant porosity
• glass
Φ = 0.42 m, H = 1 m
porosity = 0.12
• metallic components
total thickness = 0,095 m,
porosity = 0.25
• connected fractured zone
0.4 * excavation diameter = 0.268 m
porosity = 0.20; Deff(25°C) = 5.2 10-11 m2/s
• undisturbed claystone (50 m)
porosity = 0.18; Deff(25°C) = 2,6 10-11 m2/s
GEOMETRY AND TRANSPORT PROPERTIES
argilites (50 m – 183 cells)
glass (21cm – 21 cells)
overpack + lining + gaps
(13,8cm – 14 cells)
5th Andra International Conference - Montpellier | 22 Oct 2012 | PAGE 5
- reactive-transport codes: Crunch/Hytec
Isothermal conditions
- H2(g) produced from anoxic corrosion p(H2)max = 60 bar
RESULTS IN THE BASE CASE (2)
20 avril 2023 5th Andra International Conference - Montpellier | 22 Oct 2012 | PAGE 6
Corrosion products (volume%, 45 000 yrs, end of corrosion)
magnetite, Ca-siderite, and greenalite dominate
(oxide) (carbonte) (silicate)
also smaller amounts of aluminosilicates
(nontronites and saponites)
no significant changes after corrosion phase
POROSITY CLOGGING
modeling vs. experimental results (Schlegel at al. 2007)
iron/claystone at 90°C for 1 year small amount of magnetite
siderite(-Ca), Fe-silicates
more phenomenological model for corrosion
Canister zone
0,1 µm
Now to theconcrete carbonation
benchmark…
S.S.BENCH - November 16-18. 2011
DRD/EAP/11-0219
DESIGN: ILLW CELLS, SHAFTS (AND SEALS), ILLW DISPOSAL OVERPACK
Atmospheric carbonation of overpack during the operating period
S.S.BENCH - November 16-18. 2011
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 8
• Bitumized waste• Compacted metallic waste• Organic waste
CARBONATION ISSUE FOR RADWASTE DISPOSAL
S.S.BENCH - November 16-18. 2011
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 9
Ventilation (100 years)
DRYING AND CARBONATION PROCESSES OF ILLW OVERPACK
S.S.BENCH - November 16-18. 2011
Dry air
(Rh = 40 %)
T = 25°C to 50°C
SlWater vapor diffusion
CO2 gas diffusion
T
Aqueous diffusion of reactants
Two phase water/air flow
Dissolution/precipitation : porosity reduction, permeability variations
Brine formation
CO2 gas dissolution
Dry air
(Rh = 40 %)
T = 25°C to 50°C
SlWater vapor diffusion
CO2 gas diffusion
T
Aqueous diffusion of reactants
Two phase water/air flow
Dissolution/precipitation : porosity reduction, permeability variations
Brine formation
CO2 gas dissolution
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 10
MODELING ISSUES
S.S.BENCH - November 16-18. 2011
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 11
• CO2 gas diffusion and reactivity
MODELING ISSUES
S.S.BENCH - November 16-18. 2011
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 12
benchmark emphasizes the coupling aspects
• CO2 gas diffusion and reactivity
GEOMETRY
1D Cartesian – 5.5 cm divided in 11 x 5 mm cells
Boundary conditions (EOS 4)
S.S.BENCH - November 16-18. 2011
Concrete
Symmetry axis
Dry air Dry air
Wall package 110 mm
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 13
CASE 1DRYING OF CONCRETE OVERPACK
S.S.BENCH - November 16-18. 2011
DRD/EAP/11-0219
DRYING PHENOMENON (TOUGHREACT EOS4)
Flow law: Generalized Darcy law
Lowering of the dew point due to capillary effects (Kelvin equation in EOS 4)
Water relative permeability (Van Genuchten)
Gas relative permeability (Corey)
Klinkenberg effect (gas flow at low pressure)
S.S.BENCH - November 16-18. 2011
)(
gPkkF r
))(ln()( lrw
wrcap ShM
RThP
21
11)(
m
mrrrrl SSSk
lrls
lrlr SS
SSS
22 ˆ1ˆ1 SSk rg grlr
lrl
SS
SSS
1
ˆ
rgg kp
kk
1int
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 15
DRYING PHENOMENON (TOUGHREACT)
Air and water gases diffusion
CO2 and other gases
Aqueous diffusion
Effective diffusion
Tortuosity
S.S.BENCH - November 16-18. 2011
15,273
15,273,, 000,,0,,0
T
P
PTPdTPd ii
M
RT
PNd
RTd i
8
23 2,,0
TR
Edd a
KOHi
1
15,298
1exp15,298,,,0 2
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 16
0,,0, ii dD
baS 0
DRYING PHENOMENON (TOUGHREACT)
Air and water gases diffusion
CO2 and other gases
Aqueous diffusion
Effective diffusion
Tortuosity
S.S.BENCH - November 16-18. 2011
15,273
15,273,, 000,,0,,0
T
P
PTPdTPd ii
M
RT
PNd
RTd i
8
23 2,,0
TR
Edd a
KOHi
1
15,298
1exp15,298,,,0 2
0,,0, ii dD
baS 0
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 17
DRYING PHENOMENON : PARAMETERS IN REFERENCE CASE
BHP CEM I
S.S.BENCH - November 16-18. 2011
ROCK1
Density (kg/m3) 2700
Porosity 0.12
Intrinsic permeability to liquid (m²) 1e-19
Intrinsic permeability to gas (m²) 1e-17
Relative permeability m – Slr – Sls - Sgr
0.424 – 0.0 – 1.0 – 0.0
Capillarity pressurem – P0 (MPa) – Pmax (MPa) 0.424 – 15 - 1500
Molecular diffusion coefficient in gaseous phase (m²/s)
2.4e-5
Molecular diffusion coefficient in aqueous phase (m²/s)
1.9e-9
Millington-Quirk a parameter 2
Millington-Quirk b parameter 4.2
Klinkenberg parameter (MPa) 0.45
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 18
RESULTS
S.S.BENCH - November 16-18. 2011
Drying results
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 19
RESULTS with RICHARDS’ EQUATION
S.S.BENCH - November 16-18. 2011
Drying results
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 20
OK to use Richards’ equation for benchmarking exercise
CASE 2CARBONATION WITH CONSTANT SATURATION
S.S.BENCH - November 16-18. 2011
DRD/EAP/11-0219
PHENOMENOLOGY
Constant saturation but unsaturated + diffusion of gas
S.S.BENCH - November 16-18. 2011
Sliq = 0.3
CO2 gas diffusion
Diffusion of aqueous species
Dry AirRH = 60%
25°CpH = 13
CO2 dissolution
Precipitation/dissolution reactions
Sliq = 0.3
CO2 gas diffusion
Diffusion of aqueous species
Dry AirRH = 60%
25°CpH = 13
CO2 dissolution
Precipitation/dissolution reactions
Sliq = 0.3
CO2 gas diffusion
Diffusion of aqueous species
Dry AirRH = 60%
25°CpH = 13
CO2 dissolution
Precipitation/dissolution reactions
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 22
CHEMICAL PARAMETERS
Primary phases
Secondary phases
Kinetics of dissolution / precipitation
nnnn Akr 1
15,298
11exp15,298 TR
EkTk a
n
Phase Volume %
Calcite 72.12
Portlandite 5.73
CSH 1.6 13.76
Monocarboaluminate 2.26
Ettringite 3.60
Hydrotalcite 0.39
Hydrogarnet-Fe (C3FH6) 2.05
Phase type Phases
Oxides Magnetite, Amorphous silica
Hydroxides Brucite, Gibbsite, Fe(OH)3
Sheet silicates Sepiolite
Other silicates CSH 1.2, CSH 0.8, Straetlingite, Katoite_Si
Sulfates, chlorides, other salts Gypsum, Anhydrite, Burkeite, Syngenite, Glaserite, Arcanite, Glauberite, Polyhalite
Carbonates Calcite, Nahcolite
Other Hydrotalcite-CO3, Ettringite, Dawsonite
CHEMICAL PARAMETERS
Primary and Secondary phases characteristics
Phase Kinétic
Constant (298.15 K)
Activation Energy
(kJ.mol-1)
Specific Surface (m2.g-1)
C3FH6 1 10-12 30 1
Calcite 1.6 10-6 23.4 1
CSH 0.8 1.6 10-9 50 1
CSH 1.2 1.6 10-9 50 1
CSH 1.6 1.6 10-9 30 1
Ettringite 1.6 10-9 30 1
Gibbsite_am 1.6 10-9 30 1
Gypsum 1.6 10-5 20 1
Hydrotalcite 1.6 10-9 30 1
Iron Hydroxyde 1.6 10-8 30 10
Monocarboaluminate 1.6 10-9 10 1
Portlandite 1.6 10-8 20 1
Sépiolite 1.6 10-12 50 10
Amorphous SiO2 1.6 10-9 30 1
Straetlingite 1.6 10-9 50 1
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 24
CASE 3FULLY COUPLED CARBONATION
S.S.BENCH - November 16-18. 2011
DRD/EAP/11-0219
Input parameters
CARBONATION RESULTS
pH decrease, portlandite dissolution and calcite formation over a thickness of about 2 cm after 100 years
CARBONATION RESULTS
Dissolution of CSH 1.6, ettringite, monocarboaluminate and hydrotalcite on 2 cm after 100 years
Precipitation of CSH 1.2, CSH 0.8, straetlingite, amorphous silica and gypsum on the same thickness
Precipitation of small amounts of sepiolite, gibbsite and katoïte-Si is also predicted
CARBONATION: CPU CONCERNS…
CO2 diffusion (gas phase) and reactivity are very fast!
No SIA small time steps CPU times go up!
POSSIBLE EXTENSION:SATURATION DEPENDENT REACTIVITY
Considerable reduction in the amplitude of carbonation (less dissolution of portlandite and CSH 1.6 and less precipitation of amorphous silica and other secondary CSH)
Lower reactivity accompanied by a greater penetration of carbonation front due to lower consumption of CO2 at the surface
Effect of water content on reactivity (Bazant type function)
CONCLUSIONS
Drying process of 11 cm thick waste packages depends strongly on the concrete nature and slightly on the flow model (Richards or full multiphase)
Considering full multiphase model, carbonated depth is about 2 cm after 100 years for the Intermediate Performance Concrete. degraded thickness is totally carbonated (total dissolution of primary mineral phases)
If we consider a chemical reactivity depending on the liquid saturation (Bazant type function), a considerable reduction in the amplitude of carbonation and a greater penetration of carbonation front are observed.
Progress areas include:
• taking into consideration a protective effect of secondary minerals
• improving knowledge on kinetics parameters and thermodynamic data, especially for CSH with low Ca/Si ratio
• coupling this system with corrosion of rebars
NUMERICAL RESOURCES
S.S.BENCH - November 16-18. 2011
SeS BENCH – Taipei, Taiwan | NOV. 2012 | PAGE 32
And now: - EOS9- Crunchflow- Hytec- … more?
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| PAGE 33
CEA | 10 AVRIL 2012
AcknowlegementToughreact development team (LBNL)
C. Steefel (LBNL, Crunchflow)
Hytec developement team (Mines Paristech, PGT consortium) for technical support on codes
THANK YOU FOR YOUR ATTENTION