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Flow and transport in highly heterogeneous and fractured media

This research explores the characterization and consequences of heterogeneity in complex systems, including the identification of key hydro-geological structures and the development of stochastic modeling approaches. It also addresses the uncertainty and lack of data in predicting flow behavior in fractured media.

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Flow and transport in highly heterogeneous and fractured media

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  1. Flow and transport in highly heterogeneous and fractured media HDR J.-R. de Dreuzy Géosciences Rennes-CNRS

  2. Risk assessment for High Level Radioactive Waste storage PhD. Etienne Bresciani (2008-2010)

  3. OBJECTIVES: Characterization and consequences of heterogeneity • 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, HDR

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

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

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

  7. Livingstone hazardous waste landfill Mixed built-in and natural wastes confinement [Hanor,1994] Artificial large-scale permeameter What is really permeability? J.-R. de Dreuzy, HDR

  8. Livingstone hazardous waste landfill Consequence of data scarcity Fractures in the confiningclay layer have not been observed but are dominant J.-R. de Dreuzy, HDR

  9. a Influence of fractures on the permeability of the clay layer

  10. Yucca mountain Permeability increases with scale High flow channeling 36Cl J.-R. de Dreuzy, HDR

  11. Mirror Lake Permeabilityscaling Flow structure Permeability decreases with scale High flow channeling

  12. 1st Fracture geologicalcharacteristic: Fracture length distribution Odling, N. E. (1997), Scaling and connectivity of joint systems in sandstones from western Norway, Journal of Structural Geology, 19(10), 1257-1271. 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). Hornelen, Norway a=2.75 O. Bour, Ph. Davy

  13. Organization of fractures Correlation between fracture positions PhD C. Darcel (1999-2002) Mechanical interactions between fractures Ph. Davy D2D=1.7 Joint set in Simpevarp (Sweden) Ph. Davy, C. Darcel, O. Bour, R. Le Goc

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

  15. Reduce complexity from geology to hydraulicsFracture network simulation Complex medium structure Simple flow equation + Simple flow equation Complex parameters Identified flow structures Complex flow equation Simple parameters Flow structure? K~exp[w(p,a).s2(log K)/2] J.-R. de Dreuzy, HDR

  16. Reduce complexity from geology to hydraulicsFracture network simulation Complex medium structure Simple flow equation + Simple flow equation Complex parameters Identified flow structures Complex flow equation Simple parameters Flow structure? K~exp[w(p,a).s2(log K)/2] J.-R. de Dreuzy, HDR

  17. 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). a modeling paradigm J.-R. de Dreuzy, HDR

  18. Influence of fracture organization At threshold Far above threshold Non correlated fractures D=d a=2.75 Correlated fractures D=1.75 a=2.75 Close Permeability Different flow structure Same permeability Same 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).

  19. Reduce complexity from geology to hydraulicsFracture network simulation Complex medium structure Simple flow equation + Simple flow equation Complex parameters Identified flow structures Complex flow equation Simple parameters Flow structure? K~exp[w(p,a).s2(log K)/2] J.-R. de Dreuzy, HDR

  20. Well test interpretation models D=2 10 h Transport dans les fractals 100 h 1<D<2 D : dimension fractale dw : dimension de transport anormal D=1

  21. Well test in Ploemeur Fractional flow dimension n=1.6 Fractional flow dimension n=1.6 contact zone normal fault zone Anomalous diffusion exponent dw= 2.8 Meaning of n and dw? Le Borgne , T., O. Bour, J.-R. de Dreuzy, P. Davy, and F. Touchard, Equivalent mean flow models for fracturedaquifers: Insights from a pumping tests scalinginterpretation, Water ResourcesResearch, 2004.

  22. Inverse problem on (n,dw) Ploemeur Integrated information on flow structure de Dreuzy, J.-R., et al. (2004), Anomalous diffusion exponents in continuous 2D multifractal media, PhysicalReview 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.

  23. Conclusion on the influence of fracture characteristics on hydraulic properties • 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, HDR

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

  25. From classical DFN and continuous approaches to an alternative hybrid approach PhD DelphineRoubinet 2008-2010 PhD Romain Le Goc 2007-2009 J.-R. de Dreuzy, HDR

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

  27. Alternative: identifiable hybridmodelingapproach Geological data Fracture characteristics Hydraulic data geochemical data DATA Inverse Inverse direct Inverse 0 MODEL Discrete dual-porosity model Stochastic smaller fractures Deterministic larger fractures Mean behavior PREDICTIONS Uncertainty Equilibrium between data, model and predictions (objectives) J.-R. de Dreuzy, HDR

  28. Discrete Dual-Porosity modelsPhD DelphineRoubinet 2008-2010 PhD DelphineRoubinet (2008-2010) J.-R. de Dreuzy, HDR

  29. Equivalent hydraulic matrix (EHM) permeability Tensor EHM PhD D. Roubinet (2008-2010)

  30. Increasing the relevance of fracture-matrix exchanges (experiments )Y. Méheust, J. de Brémondd’ArsPhD of L. Michel (2005-2008) and J. Bouquain (2008-2010) Rough fracture experiments PhD. Laure Michel LB pore-scale simulation of advection, diffusion and gravity With L. Talon, H. Auradou (FAST) Advection dominant Gravity dominant Importance of gravity

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

  32. Identification of major flow channels from head data (PhD Romain Le Goc 2007-2009) Minimization of an objective function = mismatch between data and model Non convex objective functions Gradient algorithms Monté-Carlo inverse algorithms like simulated annealing, genetic algorithms, taboo search,… PhD. Romain Le Goc (2007-2009)

  33. Inversion algorithmIterative parameterization of the channels First step Objective Function (classical least-square formulation): Solving direct problem Parameter estimation in optimizing Fobj using simulated annealing PhD. Romain Le Goc (2007-2009)

  34. Second step Inversion algorithm Objective Function with regularization term Regularization term: values from previous step as a priori values PhD. Romain Le Goc (2007-2009)

  35. Inversion algorithm 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)‏ PhD. Romain Le Goc (2007-2009)

  36. Knowledge content of dataData sensitivity to heterogeneity FLOW Flow structure in a 2D synthetic fracture network PhD. Romain Le Goc (2007-2009)

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

  38. Field perspective on the inverse problemLimestone aquifer example (SEH)J. Bodin, G. Porel, F. Delay, Univ. of Poitiers, MACH-1 M2 AlexandreBoisson 2007 J. Bodin, G. Porel, F. Delay, University of Poitiers

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

  40. LARGE NUMBER OF WELLS Modeling exercise: Prediction of doublet test from all other available information J.-R. de Dreuzy, CARI 2008 J. Bodin, G. Porel, F. Delay

  41. Sensitivity depends on stimulation configuration Collaboration with J. Erhel (INRIA) & A. Ben Abda (Tunis)

  42. Inverse problem on a broader range of hydraulic data • 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 222Rn and 4He 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, HDR

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

  44. Intensive development and use of numerical methods10-years collaboration with J. Erhel (INRIA) • Balance between precision and efficiency • 3D fracture flow simulations • B. Poirriez (PhD INRIA 2008-2010) • G. Pichot (Post-Doc Géosciences Rennes 2008-2009) • 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, 2008-2010) J.-R. de Dreuzy, CARI 2008

  45. 3D flow and transport simulation in fractured media Broad power-law length distribution n(l)~l-a with lmin<l<L Large number of fractures: ~103 to 105 a=3.4 L=50 lmin ~15 103fractures Post-Doc GéraldinePichot (2008-2009) PhD BaptistePoirriez (2008-2010)

  46. Relaxing mesh generation difficulties by using Mortar-like methods Non-Matching Fracture meshes Matching Fracture meshes Head distribution in a simple fracture network Post-Doc G. Pichot (2008-2009)

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

  48. Transport • 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, HDR

  49. Pre-asymptotic and asymptotic laws for inert transport Advection-diffusion in highly heterogeneous media (s2=9) J.-R. de Dreuzy, HDR

  50. Reactive transport a=1, n=0.9, D=0, gKa=1, s2=1.5 Particles Concentration Influence of heterogeneity on: - Sorption reactivity (PhD. K. Besnard 2001-2003) - Dynamic of mixing (T. Le Borgne, M. Dentz, J. Carrera)

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