HDR J.-R. de Dreuzy Géosciences Rennes-CNRS

PhD. Etienne Bresciani ( ) 2 Risk assessment for High Level Radioactive Waste storage

Predictions for a complex system Mean behavior Uncertainty Relevant knowledge from a lack of data Determinism of large-scale structures Stochastic modeling of smaller-scale structures Relation between geological structures and hydraulic complexity What are the key hydro-geological structures? How to identify them (directly & inversely)? J.-R. de Dreuzy, HDR3

1. Framework Field observations 2. What is the relevant flow structure? (1996-) From fracture characteristics to hydraulic properties 3. Operative modeling approach (2006-) Discrete double-porosity models 4. Inverse problem (2005-) Channel identifications Optimal use of a data network 5. Numerical simulations (1996-) 6. Transport (2000-) 7. Mid- to long-term projects (2009-) J.-R. de Dreuzy, HDR4

1. Framework Field observations 2. What is the relevant flow structure? (1996-) From fracture characteristics to hydraulic properties 3. Operative modeling approach (2006-) Discrete double-porosity models 4. Inverse problem (2005-) Channel identifications Optimal use of a data network 5. Numerical simulations (1996-) 6. Transport (2000-) 7. Mid- to long-term projects J.-R. de Dreuzy, HDR5

3 site-scale examples Livingstone Yucca Mountain Mirror Lake Blueprint of fracture flow Channeling Permeability scaling Fracture geological characteristics 6

J.-R. de Dreuzy, HDR7 Mixed built-in and natural wastes confinement [Hanor,1994] Artificial large-scale permeameter What is really permeability?

J.-R. de Dreuzy, HDR8 Consequence of data scarcity Fractures in the confining clay layer have not been observed but are dominant

Influence of fractures on the permeability of the clay layer a

J.-R. de Dreuzy, HDR10 36 Cl Permeability increases with scale High flow channeling

PERMEABILITY SCALING FLOW STRUCTURE 11 Permeability decreases with scale High flow channeling

12 a=2.75 Odling, N. E. (1997), Scaling and connectivity of joint systems in sandstones from western Norway, Journal of Structural Geology, 19(10), Bour, O., et al. (2002), A statistical scaling model for fracture network geometry, with validation on a multiscale mapping of a joint network (Hornelen Basin, Norway), Journal of Geophysical Research, 107(B6). O. Bour, Ph. Davy Hornelen, Norway

Ph. Davy, C. Darcel, O. Bour, R. Le Goc13 D 2D =1.7 Correlation between fracture positions PhD C. Darcel ( ) Joint set in Simpevarp (Sweden) Mechanical interactions between fractures Ph. Davy

1. Framework Field observations 2. What is the relevant flow structure? (1996-) From fracture characteristics to hydraulic properties 3. Operative modeling approach (2006-) Discrete double-porosity models 4. Inverse problem (2005-) Channel identifications Optimal use of a data network 5. Numerical simulations (1996-) 6. Transport (2000-) 7. Mid- to long-term projects (2009-) J.-R. de Dreuzy, HDR14

J.-R. de Dreuzy, HDR15 Simple flow equation Complex medium structure + Simple flow equation Complex parameters Identified flow structures Complex flow equation Simple parameters Flow structure? K~exp[ (p,a). (log K)/2]

J.-R. de Dreuzy, HDR16 Simple flow equation Complex medium structure + Simple flow equation Complex parameters Identified flow structures Complex flow equation Simple parameters Flow structure? K~exp[ (p,a). (log K)/2]

J.-R. de Dreuzy, HDR17 de Dreuzy, J. R., P. Davy, and O. Bour (2001), Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 1-Effective connectivity, Water Resources Research, 37(8).

Non correlated fractures D=1.75 a=2.75 D=d a=2.75 Correlated fractures At thresholdFar above threshold Same permeability Same flow structure Close Permeability Different flow structure de Dreuzy, J.-R., et al. (2004), Influence of spatial correlation of fracture centers on the permeability of two-dimensional fracture networks following a power law length distribution, Water Resources Research, 40(1).

J.-R. de Dreuzy, HDR19 Simple flow equation Complex medium structure + Simple flow equation Complex parameters Identified flow structures Complex flow equation Simple parameters Flow structure? K~exp[ (p,a). (log K)/2]

D=1 10 h 100 h 1<D<2 D=2 D : dimension fractale d w : dimension de transport anormal Transport dans les fractals

21 Well test in Ploemeur Le Borgne, T., O. Bour, J.-R. de Dreuzy, P. Davy, and F. Touchard, Equivalent mean flow models for fractured aquifers: Insights from a pumping tests scaling interpretation, Water Resources Research, normal fault zone contact zone Anomalous diffusion exponent d w = 2.8 Fractional flow dimension n=1.6 Fractional flow dimension n=1.6 Meaning of n and dw?

22 Inverse problem on (n,d w ) Ploemeur Integrated information on flow structure de Dreuzy, J.-R., et al. (2004), Anomalous diffusion exponents in continuous 2D multifractal media, Physical Review E, 70. de Dreuzy, J.-R., and P. Davy (2007), Relation between fractional flow and fractal or long-range permeability field in 2D, Water Resources Research, 43.

Blueprint of structures on data Sensitivity of well tests on structure organization Classical upscaled hydraulic approaches Strong homogenization Strong localization Intermediary flow structures Deterministic versus statistical structures depending on available data and objectives J.-R. de Dreuzy, HDR23

1. Framework Field observations 2. What is the relevant flow structure? (1996-) From fracture characteristics to hydraulic properties 3. Operative modeling approach (2006-) Discrete double-porosity models 4. Inverse problem (2005-) Channel identifications Optimal use of a data network 5. Numerical simulations (1996-) 6. Transport (2000-) 7. Mid- to long-term projects (2009-) J.-R. de Dreuzy, HDR24

J.-R. de Dreuzy, HDR25 From classical DFN and continuous approaches to an alternative hybrid approach

J.-R. de Dreuzy, HDR26 Geological data Fracture characteristics Hydraulic data geochemical data Geometrical structures DFN-stochastic Homogenized permeabilities Continuous models-deterministic DATA MODEL PREDICTIONS direct inverse Parameterization Calibration Mean behavior Uncertainty Equilibrium between data, model and predictions (objectives)

J.-R. de Dreuzy, HDR27 Geological data Fracture characteristics Hydraulic data geochemical data D ISCRETE DUAL - POROSITY MODEL Stochastic smaller fractures Deterministic larger fractures DATA MODEL PREDICTIONS direct I NVERSE Mean behavior Uncertainty Equilibrium between data, model and predictions (objectives) I NVERSE 0 I NVERSE

J.-R. de Dreuzy, HDR28 PhD Delphine Roubinet ( )

PhD D. Roubinet ( )29 Tensor EHM

30 Rough fracture experiments PhD. Laure Michel Importance of gravity LB pore-scale simulation of advection, diffusion and gravity With L. Talon, H. Auradou (FAST) Gravity dominantAdvection dominant

1. Framework Field observations 2. What is the relevant flow structure? (1996-) From fracture characteristics to hydraulic properties 3. Operative modeling approach (2006-) Discrete double-porosity models 4. Inverse problem (2005-) Channel identifications Optimal use of a data network 5. Numerical simulations (1996-) 6. Transport (2000-) 7. Mid- to long-term projects (2009-) J.-R. de Dreuzy, HDR31

32 Non convex objective functions Gradient algorithms Monté-Carlo inverse algorithms like simulated annealing, genetic algorithms, taboo search,… PhD. Romain Le Goc ( ) Minimization of an objective function = mismatch between data and model

PhD. Romain Le Goc ( )33 Inversion algorithm Iterative parameterization of the channels First step Objective Function (classical least- square formulation): Solving direct problem Parameter estimation in optimizing F obj using simulated annealing

PhD. Romain Le Goc ( )34 Second step Objective Function with regularization term Regularization term: values from previous step as a priori values

PhD. Romain Le Goc ( )35 i-th step Objective Function with regularization term Regularization term is build at each iteration The refinement level is controlled by the information included in the data (accounting for under- and over-parameterization)

36 PhD. Romain Le Goc ( ) FLOW Flow structure in a 2D synthetic fracture network

1. Framework Field observations 2. What is the relevant flow structure? (1996-) From fracture characteristics to hydraulic properties 3. Operative modeling approach (2006-) Discrete double-porosity models 4. Inverse problem (2005-) Channel identifications Optimal use of a data network 5. Numerical simulations (1996-) 6. Transport (2000-) 7. Mid- to long-term projects (2009-) J.-R. de Dreuzy, HDR37

38 J. Bodin, G. Porel, F. Delay, University of Poitiers

39 Niveau piézométrique 105 m 14 m 17 m 3 m 34 m FRACTURES J. Bodin, G. Porel, F. Delay KARST

J.-R. de Dreuzy, CARI LARGE NUMBER OF WELLS J. Bodin, G. Porel, F. Delay Modeling exercise: Prediction of doublet test from all other available information

Collaboration with J. Erhel (INRIA) & A. Ben Abda (Tunis)

Point-wise head and flow data (PhD. Romain Le Goc) Monopole and dipole tests (with J. Erhel & A. Ben Abda) Dipole nets Tripoles do not bring additional facilities Flow-metry (with T. Le Borgne & O. Bour) Identification of 3D flow structures Use of travel-time and geochemical data (with L. Aquilina) In situ fracture-matrix interactions on 222 Rn and 4 He data on Ploemeur site (M2 N. Le Gall) Long-term chronicle of nitrates and sulfates on Ploemeur (C. Darcel & Ph. Davy) J.-R. de Dreuzy, HDR42

1. Framework Field observations 2. What is the relevant flow structure? (1996-) From fracture characteristics to hydraulic properties 3. Operative modeling approach (2006-) Discrete double-porosity models 4. Inverse problem (2005-) Channel identifications Optimal use of a data network 5. Numerical simulations (1996-) 6. Transport (2000-) 7. Mid- to long-term projects (2009-) J.-R. de Dreuzy, HDR43

Balance between precision and efficiency 3D fracture flow simulations B. Poirriez (PhD INRIA ) G. Pichot (Post-Doc Géosciences Rennes ) Transient-state simulations Large-scale intensive transport simulation A. Beaudoin (Univ. of Le Havre) Parallelization Sub domain methods D. Tromeur-Dervout (Univ. of Lyon) Platform development E. Bresciani (INRIA, 2007) N. Soualem (INRIA, ) J.-R. de Dreuzy, CARI

45 Broad power-law length distribution n(l)~l -a with l min <l<L Large number of fractures: ~10 3 to 10 5 a=3.4 L=50 l min ~ fractures Post-Doc Géraldine Pichot ( ) PhD Baptiste Poirriez ( )

Post-Doc G. Pichot ( ) 46 Head distribution in a simple fracture network Matching Fracture meshesNon-Matching Fracture meshes

1. Framework Field observations 2. What is the relevant flow structure? (1996-) From fracture characteristics to hydraulic properties 3. Operative modeling approach (2006-) Discrete double-porosity models 4. Inverse problem (2005-) Channel identifications Optimal use of a data network 5. Numerical simulations (1996-) 6. Transport (2000-) 7. Mid- to long-term projects (2009-) J.-R. de Dreuzy, HDR47

Transport in fractured media The example of percolation theory (2001) Pre-asymptotic to asymptotic regimes Collaboration with A. Beaudoin & J. Erhel (2006-) Velocity field structure Collaboration with T. Le Borgne & J. Carrera Reactive transport Simulation means Fluid-Solid and Fluid-Fluid reactivity J.-R. de Dreuzy, HDR48

J.-R. de Dreuzy, HDR49 Advection-diffusion in highly heterogeneous media ( 2 =9)

50 =1, n=0.9, D=0, Ka=1, 2 =1.5 Influence of heterogeneity on: - Sorption reactivity (PhD. K. Besnard ) - Dynamic of mixing (T. Le Borgne, M. Dentz, J. Carrera) ParticlesConcentration

1. Framework Field observations 2. What is the relevant flow structure? (1996-) From fracture characteristics to hydraulic properties 3. Operative modeling approach (2006-) Discrete double-porosity models 4. Inverse problem (2005-) Channel identifications Optimal use of a data network 5. Numerical simulations (1996-) 6. Transport (2000-) 7. Mid- to long-term projects (2009-) J.-R. de Dreuzy, HDR51

3D Theoretical studies Geological & physico-chemical complexities Chemical transport Multiphase flow Numerical Simulation tools Inverse problem Broader range of data and heterogeneity structures From flow to transport Connection between theory and field Application to existing well-documented fractured media field-scale models ORE H+ HLRW, CO2 sequestration, remediation FIELD SITES J.-R. de Dreuzy, HDR52

J.-R. de Dreuzy, HDR53

Gary Larson, The far side gallery 54

PhD. Etienne Bresciani ( ) advised by Ph. Davy55 Example of protection zone delineation Pochon, A., et al. (2008), Groundwater protection in fractured media: a vulnerability-based approach for delineating protection zones in Switzerland, Hydrogeology Journal, 16(7),

J.-R. de Dreuzy, HDR56 Essentially, all models are wrong, but some are useful Which ones? Box, George E. P.; Norman R. Draper (1987). Empirical Model-Building and Response Surfaces, p. 424