1. Dubrovnik meeting, 13/10/2008 1 Different approaches to simulate flow and transport in a multi scale fractured block October 2008 Bernard-Michel G. Grenier C. Khvoenkova N. IFP Different approaches to simulate flow and transport in a multi scale fractured block October 2008 Bernard-Michel G. CEA/DEN – DM2S/SFME/MTMS Grenier C. CEA/DSM – LSCE Khvoenkova N. IFP

2. Dubrovnik meeting, 13/10/2008 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. Dubrovnik meeting, 13/10/2008 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. Dubrovnik meeting, 13/10/2008 4 Semi synthetic fractured 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. Dubrovnik meeting, 13/10/2008 5 Fracture complexity

6. Dubrovnik meeting, 13/10/2008 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  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. 1 2

7. Dubrovnik meeting, 13/10/2008 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. Dubrovnik meeting, 13/10/2008 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. Dubrovnik meeting, 13/10/2008 9 First step – determine the main fractures  50 or 70 larger conductors are sufficient for flow !  Network at the percolation threshold Flow flux function of the amount of large fractures Flow–flux converged with 50 fractures‏ only

10. Dubrovnik meeting, 13/10/2008 10 Head and Flow field

11. Dubrovnik meeting, 13/10/2008 11 Transport first level and second level, increased matrix diffusion First level : T max = 10 7 y Second level T max = 10 9 y 4.8 10 8 2.2 10 8 5.5 10 6 X5 (level 2)‏ 3 10 6 5.63 10 5 2.25 10 5 X5 (level 1)‏ 56001200100.8X1 (level 2)‏ 181.2543.7513.75X1 (level 1)‏ T95%T50%T5%(Time in years)‏ Water transit time = 5.9 years Matrix zone 1 m

12. Dubrovnik meeting, 13/10/2008 12 Single fracture system for equivalent model Meshing of matrix zones Conc. profiles Conc. field 3 levels of PA time scale flow velocities 3 tracers (non sorbing to intermediate)‏

13. Dubrovnik meeting, 13/10/2008 13 Main transport paths Preferential path for the convection and short time flow => need to mesh the main features

14. Dubrovnik meeting, 13/10/2008 14 Half way conclusions  Strong influence of matrix diffusion and sorption for slow velocities: almost diffusive transport regime  Large storage volume of RNs in the matrix combined with retardation (retention) factor, and the small background fractures => Need for an accurate modelisation of background fractures in the vicinity of main features.  Green function techniques won’t be sufficient in two cases :  difficulty to determine Deq (influence of the small fractures)  Too many major features (percolation).  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.

15. Dubrovnik meeting, 13/10/2008 Asymptotic approach – for the matrix Scaling : Strong « not so physical » hypothesis : Strong bimodal periodic fracture distribution hypothesis

16. Dubrovnik meeting, 13/10/2008 Scaled equations  Darcy law  Transport f : fractures m : matrix 

17. Dubrovnik meeting, 13/10/2008 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. Dubrovnik meeting, 13/10/2008 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. Dubrovnik meeting, 13/10/2008 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. Dubrovnik meeting, 13/10/2008 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. Dubrovnik meeting, 13/10/2008 21 Model at fracture scale