1. REACTIVE-TRANSPORT PARAMETERS ADJUSTMENT AND SENSITIVITY ANALYSIS: APPLICATION TO CONCRETE CARBONATION TREPRO III – MARCH 5.-7. 2014 O. Bildstein, P. Thouvenot, A. Marrel CEA (French Alternative Energies and Atomic Energy Commission) I. Munier, B. Cochepin ANDRA (French Radioactive Waste Management Agency) 24 novembre 2015 | PAGE 1 CEA | 10 AVRIL 2012

2. OUTLINE PLAN Context of this study Concrete carbonation: phenomenology and modeling parameters Modeling of accelerated concrete carbonation experiments: Direct vs. inverse modeling Choice of parameters (with uncertainty) Building and calibration of the metamodel Results: optimal values for the parameters Sensitivity analysis (identify most influential parameters) Conclusion and perspectives TRePro III – Karlsruhe | March 2013 | PAGE 2

3. CONTEXT : 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 TRePro III – Karlsruhe | March 2013 | PAGE 3

4. DESIGN: ILLW CELLS, SHAFTS (AND SEALS), ILLW DISPOSAL OVERPACK Atmospheric carbonation of overpack during the operating period S.S.BENCH - November 16-18. 2011 | PAGE 4 Bitumized waste Compacted metallic waste Organic waste TRePro III – Karlsruhe | March 2013

5. DRYING AND CARBONATION PROCESSES OF ILLW OVERPACK S.S.BENCH - November 16-18. 2011 | PAGE 5 Major challenge comes from: -coupled multiphase flow-reaction- transport process -large number of parameters TRePro III – Karlsruhe | March 2013

6. MODELLING ACCELERATED CARBONATION EXPERIMENTS S.S.BENCH - November 16-18. 2011 | PAGE 6 TRePro III – Karlsruhe | March 2013 -experimental conditions: carbonation of concrete at 20°C with pCO 2 = 1atm; different experiments at constant RH (33%, 54%, 63%, 70%, 80%; Drouet, 2010) depth (mm) relative humidity intensity (a.u.)

7. MODELLING ACCELERATED CARBONATION EXPERIMENTS S.S.BENCH - November 16-18. 2011 | PAGE 7 TRePro III – Karlsruhe | March 2013 -coupled reaction-transport modeling with Toughreact (EOS4): 1D Cartesian – 30 mm divided in 10 cells (3 mm) for concrete, 1 extra cell for “atmosphere” Symmetry axis constant RH concrete sample 60 mm concrete

8. TRANPORT PARAMETERS BHP CEM I S.S.BENCH - November 16-18. 2011 ROCK1 Density (kg/m 3 )2700 Porosity0.12 Intrinsic permeability to liquid (m ² ) 1e-19 Intrinsic permeability to gas (m ² ) 1e-17 Relative permeability m – Slr – Sls - Sgr 0.424 – 0.0 – 1.0 – 0.0 Capillarity pressure m – P 0 (MPa) – Pmax (MPa) 0.424 – 15 - 1500 Molecular diffusion coefficient in gaseous phase (m ² /s) 2.4e-5 Molecular diffusion coefficient in aqueous phase (m ² /s) 1.9e-9 Millington-Quirk a parameter2 Millington-Quirk b parameter4.2 Klinkenberg parameter (MPa)0.45 | PAGE 8 TRePro III – Karlsruhe | March 2013 coupling equation (Millington-Quirk relationship):

9. CHEMICAL REACTION PARAMETERS (1) Primary phases Secondary phases Kinetics of dissolution / precipitation Phase Volume % Calcite72.12 Portlandite5.73 CSH 1.613.76 Monocarboaluminate2.26 Ettringite3.60 Hydrotalcite0.39 Hydrogarnet-Fe (C3FH6)2.05 Phase typePhases OxidesMagnetite, Amorphous silica HydroxidesBrucite, Gibbsite, Fe(OH) 3 Sheet silicatesSepiolite Other silicatesCSH 1.2, CSH 0.8, Straetlingite, Katoite_Si Sulfates, chlorides, other saltsGypsum, Anhydrite, Burkeite, Syngenite, Glaserite, Arcanite, Glauberite, Polyhalite CarbonatesCalcite, Nahcolite OtherHydrotalcite-CO 3, Ettringite, Dawsonite

10. CHEMICAL REACTION PARAMETERS (2) Primary and Secondary phases kinetics parameters | PAGE 10 TRePro III – Karlsruhe | March 2013 coupling equation (chemical reactivity coefficient R s depending on RH): 0 ≤ R s (RH) ≤ 1

11. DIRECT CARBONATION MODELING RESULTS (MANUAL PARAMETER FITTING) calcite and portlandite volume fraction profiles at 20 °C with k(CH) x 180 %, k(CSH 1.6) x 10 %, a = 2.6 and b = 5.4, and Rs(S liq ) = 0.10, 0.70, 0.95, 1.00 (resp. 33%, 54%, 70%, 80%RH) results are not satisfactory : carbonation fronts and effect of liquid saturation are not correctly predicted S.S.BENCH - November 16-18. 2011 | PAGE 11 TRePro III – Karlsruhe | March 2013 mineral volume fraction

12.  Uncertainty quantification : Domain of variation of uncertain parameters  Sampling design : Latin Hypercube Sample with optimal recovering properties  Metamodel : Replace Toughreact code with a faster surrogate model, called metamodel  Gaussian process metamodels for 3 curve indicators  Sensitivity analysis : Computation of Sobol indices (variance-based importance mesures)  Calibration : metamodels used to determine the optimal set of parameters that matches the experimental results (by minimizing an objective function) Uncertainty quantification Simulator (Toughreact code) Learning sample: N simulations Sampling design : N points Statistical modelling : Metamodel Calibration Global sensitivity analysis Metamodel Validation Interpretation STOCHASTIC APPROACH FOR CALIBRATION

13. INVERSE MODELING: BUILDING A GAUSSIAN PROCESS METAMODEL use a kriging or GP metamodel to approximate the results of the numerical model (build an interpolated response surface) perform a “large number” of simulations (300) to build a “learning sample” in the specified domain of variation for selected “uncertain” parameters TRePro III – Karlsruhe | March 2013 | PAGE 13

14. RESULTS OF THE GP METAMODEL 54%RH 63%RH70%RH 80%RH depth (mm) mineral volume fraction the set of parameters are sampled using space-filling design (optimized LHS method) which enables to efficiently explore the variation domain of parameters LHS : Latin Hypercube Sampling TRePro III – Karlsruhe | March 2013 | PAGE 14

15. ASSESSING GP METAMODEL QUALITY Gp metamodels are built for 3 indicators (characteristic of the output curves) and the Gp qualities are assessed using predictivity coefficients Q 2 : Q 2 values are good for #1 and fairly good for #3 Q 2 values are low for #2 (acceptable because of low variance)  overall quality is good CARBONATION CONCRETE 3. carbonation front mineral fraction profile 1. mineral quantity at the surface of the concrete 2. mineral quantity at depth in the concrete mineral volume fraction TRePro III – Karlsruhe | March 2013 | PAGE 15 Q² for HR – Mineral 1. Mineral quantity at surface 2. Mineral quantity at depth 3. Carbo- nation front position HR 54% - Portlandite0,982830,334490,70532 HR 54% - Calcite0,883480,361110,33442 HR 63% - Portlandite0,982030,235240,69678 HR 63% - Calcite0,886920,377880,48120 HR 70% - Portlandite0,982980,123340,67919 HR 70% - Calcite0,883270,204250,49888 HR 80% - Portlandite0.98144S.O.*0.47861 HR 80% - Calcite0.849780.729380.38123

16. INVERSE MODELING TO FIT PARAMETERS (1) Gp metamodels are used to determine the optimal set of parameters that matches the experimental results (minimization of an objective function) TRePro III – Karlsruhe | March 2013 | PAGE 16 PG metamodel prédictions are quite good !  Toughreact results with the PG model set of parameters are not satisfactory  representativity of the metamodel needs some improvement

17. GLOBAL SENSITIVITY ANALYSIS (1) The influence of the different parameters is determined using Sobol’ indices (based on variance decomposition) Estimation of Sobol’ indices with Gp metamodels and Monte Carlo approach TRePro III – Karlsruhe | March 2013 | PAGE 17 direct effect effect with interactions no effect !

18. GLOBAL SENSITIVITY ANALYSIS (2) “Experimentalist expert judgment” also helps redefine the variation intervals of uncertain parameters TRePro III – Karlsruhe | March 2013 | PAGE 18 15 plots for each RH … Satisfactory behaviour (non flat curves in red) vs. never-observed behaviour (flat curves in blue) plotted in the different parameter variation domain nothing to say for x2, x3, x4, x5, x6… for the kinetics of portlandite (x1), all results in the [-10;-6] interval give flat curves  redefine this interval to [-8,5;-4,5]

19. CONCLUSIONS A stochastic approach is used to determine optimal parameters to fit concrete carbonation experiments: Gp metamodel predictions match the experimental data but Toughreact simulations with the PG model set of parameters are not satisfactory  representativity of the metamodel should however be improved  need for a greater number of more “meaningful” simulations (no flat curves) The (preliminary) global sensitivity analysis shows that: the kinetics of portlandite is a key parameter (direct or primary influence) some parameters may play a role when interacting with others (secondary influence), e.g. diffusion parameters with portlandite or CSH1,6 dissolution kinetics the reactivity parameter is not very influential (counter-intuitive result !)  need for simulations with improved intervals (portlandite dissolution kinetics) and without non-influential parameters (calcite) TRePro III – Karlsruhe | March 2013 | PAGE 19

20. Direction de l’Energie Nucléaire Département des Technologies Nucléaires Service de Modélisation des Transferts et de Mesures Nucléaires Commissariat à l’énergie atomique et aux énergies alternatives Centre de Cadarache | 13108 Saint Paul-lez-Durance T. +33 (0)4 42 25 37 24 | F. +33 (0)4 42 25 62 72 Etablissement public à caractère industriel et commercial | RCS Paris B 775 685 019 24 novembre 2015 | PAGE 20 CEA | 10 AVRIL 2012 THANK YOU FOR YOUR ATTENTION

21. GLOBAL SENSITIVITY ANALYSIS  Sensitivity analysis : "Study of influence of inputs on the output of the simulator" Saltelli [1999] Global Sensitivity Analysis (GSA) based upon variance decomposition: 1 st index: Influence of an input, independently from the others Total index:total influence of an input and all its interactions Weight of input uncertainties on the output Primary effect of X i Interaction effect between X i and X j Several thousands of simulations required  use of the GP metamodels Estimation techniques: Monte Carlo (MC) based upon random sampling