1. Summary of results to date B. Garitte and A. Gens 2nd DECOVALEX 2011 workshop, 20 th of October 2008, Wakkanai, Japan Dept. of Geotechnical Engineering and Geosciences TECHNICAL UNIVERSITY OF CATALONIA (UPC)

2. Comparison of the modelling results

3. Schedule of Task A  Step 0: Identification of relevant processes and of Opalinus Clay parameters. Modelling of the laboratory drying test.  Step 1: Hydromechanical modelling up to the end of Phase 1.  Step 2: Hydromechanical modelling up to the end of Phase 2 using parameters backcalculated from step 1. Advanced features as permeability anisotropy, rock damage and permeability increase in the damaged zone may be considered.  Step 3: Hydromechanical and geochemical modelling of the full test. Conservative transport and one species considered.  Step 4: Hydromechanical and geochemical modelling of the full test. Reactive transport and full geochemical model (optional).

4.  (T)H(M) formulation  Parameters and constitutive equations  Model setup  Comparison of the modelling results  Summary of the mechanisms  Conclusions and discussion on future work Index

5. (T)H(M) formulation Variation of the water mass in a certain volume (variation of liquid density, gas density, water saturation, gas saturation and porosity) Main balance equation: water mass balance In- and outflux of water to/from that volume (flux of water in the liquid phase and flux of water in the gas phase) Source and sink terms CASCEAJAEAQuintessaUoE Energy balance Air mass balance Stress equilibrium

6. (T)H(M) formulation Variation of the water mass in a certain volume (variation of liquid density, gas density, water saturation, gas saturation and porosity) In- and outflux of water to/from that volume (flux of water in the liquid phase and flux of water in the gas phase) Source and sink terms CASCEAJAEAQuintessaUoE Main balance equation: water mass balance Energy balance Air mass balance Stress equilibrium

7. (T)H(M) formulation Variation of the water mass in a certain volume (variation of liquid density, gas density, water saturation, gas saturation and porosity) In- and outflux of water to/from that volume (flux of water in the liquid phase and flux of water in the gas phase) Source and sink terms CASCEAJAEAQuintessaUoE Main balance equation: water mass balance Energy balance Air mass balance Stress equilibrium

8. (T)H(M) formulation Variation of the water mass in a certain volume (variation of liquid density, gas density, water saturation, gas saturation and porosity) In- and outflux of water to/from that volume (flux of water in the liquid phase and flux of water in the gas phase) Source and sink terms CASCEAJAEAQuintessaUoE Main balance equation: water mass balance Energy balance Air mass balance Stress equilibrium

9. (T)H(M) formulation Variation of the water mass in a certain volume (variation of liquid density, gas density, water saturation, gas saturation and porosity) In- and outflux of water to/from that volume (flux of water in the liquid phase and flux of water in the gas phase) Source and sink terms CASCEAJAEAQuintessaUoE Energy balance Air mass balance Main balance equation: water mass balance Stress equilibrium CASCEAJAEAQuintessaUoE CASCEAJAEAQuintessaUoE CASCEAJAEAQuintessaUoE

10. Parameters and constitutive equations CASCEAJAEAQuint.UoE Physical Solid grain densityρ s [kg/m3]2710 2700 Porosityφ0.165 0.16 0.162 0.16 Hydraulic Intrinsic permeabilityk [m2] 7.5E-202E-20 1.69E-191.9E-20 Dynamic viscosityμ [Pa.s]1E-52.9E-4 Liquid relative permeabilityλ’ 0.4 0.68 0.650.3 Vapour diffusion coefficient 6E-6 5E-6 Mechanical Young modulusE [GPa] 6 1.5 Poisson coefficientν 0.27 0.3 Friction angleφ [º] Cohesionc [MPa] Hydro-Mech. coupling Suction bulk modulusK s [GPa] Air entry value (retention curve)P 0 [MPa] 3.9 8 Shape parameter (retention curve)λ0.128 0.150128 Maximum suction (retention curve)*P s [MPa]700 Second shape parameter (retention curve)*λsλs 2.73 Residual and maximum saturation (retention curve)S rl – S rs 0 – 1 0 - 1 * Modified Van Genuchten

11. Parameters and constitutive equations CASCEAJAEAQuint.UoE Physical Solid grain densityρ s [kg/m3]2710 2700 Porosityφ0.165 0.16 0.162 0.16 Hydraulic Intrinsic permeabilityk [m2] 7.5E-202E-20 1.69E-191.9E-20 Dynamic viscosityμ [Pa.s]1E-52.9E-4 Liquid relative permeabilityλ’ 0.4 0.68 0.650.3 Vapour diffusion coefficient 6E-6 5E-6 Mechanical Young modulusE [GPa] 6 0.15 Poisson coefficientν 0.27 0.3 Friction angleφ [º] Cohesionc [MPa] Hydro-Mech. coupling Suction bulk modulusK s [GPa] Air entry value (retention curve)P 0 [MPa] 3.9 8 Shape parameter (retention curve)λ0.128 1.5 0128 Maximum suction (retention curve)*P s [MPa]700 Second shape parameter (retention curve)*λsλs 2.73 Residual and maximum saturation (retention curve)S rl – S rs 0 – 1 0 - 1 * Modified Van Genuchten

12. Parameters and constitutive equations CASCEAJAEAQuint.UoE Physical Solid grain densityρ s [kg/m3]2710 2700 Porosityφ0.165 0.16 0.162 0.16 Hydraulic Intrinsic permeabilityk [m2] 7.5E-202E-20 1.69E-191.9E-20 Dynamic viscosityμ [Pa.s]1E-52.9E-4 Liquid relative permeabilityλ’ 0.4 0.68 0.650.3 Vapour diffusion coefficient 6E-6 5E-6 Mechanical Young modulusE [GPa] 6 0.15 Poisson coefficientν 0.27 0.3 Friction angleφ [º] Cohesionc [MPa] Hydro-Mech. coupling Suction bulk modulusK s [GPa] Air entry value (retention curve)P 0 [MPa] 3.9 8 Shape parameter (retention curve)λ0.128 1.5 0128 Maximum suction (retention curve)*P s [MPa]700 Second shape parameter (retention curve)*λsλs 2.73 Residual and maximum saturation (retention curve)S rl – S rs 0 – 1 0 - 1

13. Parameters and constitutive equations CASCEAJAEAQuint.UoE Physical Solid grain densityρ s [kg/m3]2710 2700 Porosityφ0.165 0.16 0.162 0.16 Hydraulic Intrinsic permeabilityk [m2] 7.5E-202E-20 1.69E-191.9E-20 Dynamic viscosityμ [Pa.s]1E-52.9E-4 Liquid relative permeabilityλ’ 0.4 0.68 0.650.3 Vapour diffusion coefficient 6E-6 5E-6 Mechanical Young modulusE [GPa] 6 0.15 Poisson coefficientν 0.27 0.3 Friction angleφ [º] Cohesionc [MPa] Hydro-Mech. coupling Suction bulk modulusK s [GPa] Air entry value (retention curve)P 0 [MPa] 3.9 8 Shape parameter (retention curve)λ0.128 0.150128 Maximum suction (retention curve)*P s [MPa]700 Second shape parameter (retention curve)*λsλs 2.73 Residual and maximum saturation (retention curve)S rl – S rs 0 – 1 0 - 1 * Modified Van GenuchtenBishop effective stress

14. Parameters and constitutive equations CASCEAJAEAQuint.UoE Physical Solid grain densityρ s [kg/m3]2710 2700 Porosityφ0.165 0.16 0.162 0.16 Hydraulic Intrinsic permeabilityk [m2] 7.5E-202E-20 1.69E-191.9E-20 Dynamic viscosityμ [Pa.s]1E-52.9E-4 Liquid relative permeabilityλ’ 0.4 0.68 0.650.3 Vapour diffusion coefficient 6E-6 5E-6 Mechanical Young modulusE [GPa] 6 0.15 Poisson coefficientν 0.27 0.3 Friction angleφ [º] Cohesionc [MPa] Hydro-Mech. coupling Suction bulk modulusK s [GPa] Air entry value (retention curve)P 0 [MPa] 3.9 8 Shape parameter (retention curve)λ0.128 0.150128 Maximum suction (retention curve)*P s [MPa]700 Second shape parameter (retention curve)*λsλs 2.73 Residual and maximum saturation (retention curve)S rl – S rs 0 – 1 0 - 1 * Modified Van Genuchten

15. Parameters and constitutive equations CASCEAJAEAQuint.UoE Physical Solid grain densityρ s [kg/m3]2710 2700 Porosityφ0.165 0.16 0.162 0.16 Hydraulic Intrinsic permeabilityk [m2] 7.5E-202E-20 1.69E-191.9E-20 Dynamic viscosityμ [Pa.s]1E-52.9E-4 Liquid relative permeabilityλ’ 0.4 0.68 0.650.3 Vapour diffusion coefficient 6E-6 5E-6 Mechanical Young modulusE [GPa] 6 0.15 Poisson coefficientν 0.27 0.3 Friction angleφ [º] Cohesionc [MPa] Hydro-Mech. coupling Suction bulk modulusK s [GPa] Air entry value (retention curve)P 0 [MPa] 3.9 8 Shape parameter (retention curve)λ0.128 0.150128 Maximum suction (retention curve)*P s [MPa]700 Second shape parameter (retention curve)*λsλs 2.73 Residual and maximum saturation (retention curve)S rl – S rs 0 – 1 0 - 1 * Modified Van Genuchten

16. Parameters and constitutive equations CASCEAJAEAQuint.UoE Physical Solid grain densityρ s [kg/m3]2710 2700 Porosityφ0.165 0.16 0.162 0.16 Hydraulic Intrinsic permeabilityk [m2] 7.5E-202E-20 1.69E-191.9E-20 Dynamic viscosityμ [Pa.s]1E-52.9E-4 Liquid relative permeabilityλ’ 0.4 0.68 0.650.3 Vapour diffusion coefficient 6E-6 5E-6 Mechanical Young modulusE [GPa] 6 0.15 Poisson coefficientν 0.27 0.3 Friction angleφ [º] Cohesionc [MPa] Hydro-Mech. coupling Suction bulk modulusK s [GPa] Air entry value (retention curve)P 0 [MPa] 3.9 8 Shape parameter (retention curve)λ0.128 0.150128 Maximum suction (retention curve)*P s [MPa]700 Second shape parameter (retention curve)*λsλs 2.73 Residual and maximum saturation (retention curve)S rl – S rs 0 – 1 0 - 1 * Modified Van Genuchten

17. Parameters and constitutive equations CASCEAJAEAQuint.UoE Physical Solid grain densityρ s [kg/m3]2710 2700 Porosityφ0.165 0.16 0.162 0.16 Hydraulic Intrinsic permeabilityk [m2] 7.5E-202E-20 1.69E-191.9E-20 Dynamic viscosityμ [Pa.s]1E-52.9E-4 Liquid relative permeabilityλ’ 0.4 0.68 0.650.3 Vapour diffusion coefficient 6E-6 5E-6 Mechanical Young modulusE [GPa] 6 0.15 Poisson coefficientν 0.27 0.3 Friction angleφ [º] Cohesionc [MPa] Hydro-Mech. coupling Suction bulk modulusK s [GPa] Air entry value (retention curve)P 0 [MPa] 3.9 8 Shape parameter (retention curve)λ0.128 0.150128 Maximum suction (retention curve)*P s [MPa]700 Second shape parameter (retention curve)*λsλs 2.73 Residual and maximum saturation (retention curve)S rl – S rs 0 – 1 0 - 1 * Modified Van Genuchten

18. Parameters and constitutive equations CASCEAJAEAQuint.UoE Physical Solid grain densityρ s [kg/m3]2710 2700 Porosityφ0.165 0.16 0.162 0.16 Hydraulic Intrinsic permeabilityk [m2] 7.5E-202E-20 1.69E-191.9E-20 Dynamic viscosityμ [Pa.s]1E-52.9E-4 Liquid relative permeabilityλ’ 0.4 0.68 0.650.3 Vapour diffusion coefficient 6E-6 5E-6 Mechanical Young modulusE [GPa] 6 0.15 Poisson coefficientν 0.27 0.3 Friction angleφ [º] Cohesionc [MPa] Hydro-Mech. coupling Suction bulk modulusK s [GPa] Air entry value (retention curve)P 0 [MPa] 3.9 8 Shape parameter (retention curve)λ0.128 0.150128 Maximum suction (retention curve)*P s [MPa]700 Second shape parameter (retention curve)*λsλs 2.73 Residual and maximum saturation (retention curve)S rl – S rs 0 – 1 0 - 1 * Modified Van Genuchten

19. Model setup 10cm 28cm 1D No flux Evaporation is the process by which molecules in a liquid state (e.g. water) spontaneously become gaseous (e.g. water vapour) Relative Humidity is a measurement of the amount of water vapour that exists in a gaseous mixture of air and water Psychrometric law

20. Model setup CASCEAJAEAQuintessaUoE Relative humidity [%] 20% 50% 30%

21. Model setup CASCEAJAEAQuintessaUoE Relative humidity [%] 20% 50% 30% Psychrometric law Suction Consequences:  water outflow under liquid form  fixed degree of saturation on boundary

22. Model setup CASCEAJAEAQuintessaUoE Relative humidity [%] 20% 50% 30% Relative Humidity Consequences:  Evaporation boundary condition  Possibility to take the rock-air interface, wind velocity, etc into account (β coefficient). Comparison with free water surface evaporation.

23. Comparison of the modelling results CASCEAJAEAQuintessaUoE 21 days

24. Comparison of the modelling results CASCEAJAEAQuintessaUoE 99 days

25. Comparison of the modelling results CASCEAJAEAQuintessaUoE 142 days

26. Comparison of the modelling results CASCEAJAEAQuintessaUoE

27. Summary of the mechanisms Evaporation Desaturation Reduction of the permeability Dominant water transport mode: vapour diffusion in the gas phase (non advective) Dominant water transport mode: Darcy flow in the liquid phase (advective)

28. Summary of the mechanisms Quintessa

29. Summary of the mechanisms Quintessa

30. Conclusions and future work  Objectives of step 0 are fulfilled:  Brainstorming about theoretical formulations to be used in Task A  Determination of a set of parameters for Opalinus Clay  Reproduction of a laboratory drying experiment (Floria et al, 2002)  Step 0 (second iteration): optional  Start of step 1 (defined in Oxford and in TaskA_description.doc)  Improvement of the models (diffusive flux of vapour and boundary condition)  Advised common parameters (retention curve, porosity,…)