Context – waste repository

1. Differentapproaches to simulate flow and transport in a multi scale fractured blockOctober2008Bernard-Michel G. CEA/DEN – DM2S/SFME/MTMSGrenier C.CEA/DSM – LSCEKhvoenkova N.IFP

2. Context – waste repository • Study the possibility to bury nuclear wastes deep undergroung • We are insterested in fractured rocks : scale or granite • It a is multiscale problem: fracture size from cm to hundreds of meters • Physical parameters are based on in-situ measures (ASPO, Cadarache) • We limite ourselves to a cubic block of 200 m. • The goal is to predict the flux of pollutants exaping the storage facility

3. The User Context • Industrials : answers to practical problems • No time to develop fancy theories • We try to develop very simplified approach taking into account most of the important physical phenomena • We nevertheless try to appropriate ourselves accademic developpement for a better understanding of the phenomena => This presentation’s goal is to show the limitations of our engineer approach but also to underline the praticle difficulties encountered when using more evoluate accademic approach

4. Semi syntheticfractured block Main features (mainly intersecting the gallery, above 10 meters): Measured features & Simulated features according to statistics Background features (cm to few meters) : Simulated features according to statistics

5. Fracture complexity

6. Modeling strategies • Explicit modeling of major fractures ( + sensitivity)‏ • Matrix diffusion treated by means of semi analytic approach and equivalent properties • Computation of flow and eulerian transport with Cast3m (Mixed hybrid Finite Element code), fractures as discretized planes 1 • Matrix diffusion may also be calculated with homogeneization techniques. For the moment developped only in 2D. • Major fractures either meshed or homogeneized with smeared fractures techniques. 2

7. Model at fracture scale First level : include zones in the vicinity of the flow path by means of retention coefficients (fracture coating, infilling materials, mylonite)‏

8. Model at fracture scale Second level : include zones in the depth of the matrix blocks (altered and non altered diorite) by means of a semi analytic simulation of diffusion in the matrix

9. First step – determine the main fractures Flow–flux converged with 50 fractures‏ only Flow flux function of the amount of large fractures • 50 or 70 larger conductors are sufficient for flow ! • Network at the percolation threshold

10. Head and Flow field

11. (Time in years)‏ T5% T50% T95% X1 (level 1)‏ 13.75 43.75 181.25 X1 (level 2)‏ 100.8 1200 5600 X5 (level 1)‏ 2.25 105 5.63 105 3 106 X5 (level 2)‏ 5.5 106 2.2 108 4.8 108 Transport first level and second level, increased matrix diffusion Water transit time = 5.9 years Matrix zone 1 m Second level Tmax = 109 y First level : Tmax = 107 y

12. Single fracture system for equivalent model Conc. field Meshing of matrix zones 3 levels of PA time scale flow velocities 3 tracers (non sorbing to intermediate)‏ Conc. profiles

13. Main transport paths Preferential path for the convection and short time flow => need to mesh the main features

14. Half way conclusions • Strong influence of the main fractures(when below the percolation threshold) => Impossible to have a full homogeneization approach. Main fractures are to be meshed (or smeared). Only the viscinity of the main path is containing concentrations. • Strong influence of matrix diffusionand sorption for slow velocities: almost diffusive transport regime • Large storage volume of RNsin the matrix combined with retardation (retention) factor, and the small background fractures => Need for anaccurate modelisation of background fracturesin the vicinity of main features. • Green function techniques won’t be sufficientin two cases : • difficulty to determine Deq (influence of the small fractures) • Too many major features (percolation).

15. Asymptotic approach – for the matrix Strong bimodal periodic fracture distribution hypothesis Scaling : Strong « not so physical » hypothesis :

16. Scaled equations • Darcy law • Transport f : fractures m : matrix a

17. Homogeneization (Nina Khvoenkova PhD 2007) The Ym integral is the matrix/fracture exchange term. Very important, it is the extra information we are looking for

18. How to use it • We varied the “scaling exponents” m,teta and alpha • The previous expressions are simplified accordingly • We select the case for which the equations are the closest expression of our physical intuition (or mesurement of the problem). There’s no other way since the scaling exponents are math based and not physical. • In the case of the granite rock : m=2, alpha=1, teta=3 or m=1, alpha=0, teta=3 give correct exchange terms => We can test this set of equations on a simplified geometry for validation.

19. Conclusions • Needs to be numerically improved (interpolation on local problems, parallelism for local problems). • Needs to be coded in 3D and coupled with main fractures, difficulties for the meshing. • Eventually use this approach on simple geometry to predict echange coef. In Barenblatt double porosity model. • For some species Am=1, then the matrix/fracture exchange is unstationnary. Taking into account the background fracturation improves the tracer time release evaluation (over Green functions, simple porosity approach). • For species where Am <<1 (Iodine) homogeneization approach shows an instantaneous exchange (for long times). No improvement.

20. Validation • We mesh explicitly a periodic network of fracture/matrix (sugar-box). We compare the output flux with the homogeneized approach • Good agreement (5-20%) for the different parameters, on transient calculations.

21. Model at fracture scale