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HYDROGEOLOGIE ECOULEMENT EN MILIEU FRACTURE 2D

HYDROGEOLOGIE ECOULEMENT EN MILIEU FRACTURE 2D. J. Erhel – INRIA / RENNES J-R. de Dreuzy – CAREN / RENNES P. Davy – CAREN / RENNES Chaire UNESCO - Calcul numérique intensif TUNIS - Mars 2004. Modelling Flow and Transport in Subsurface Complex Fracture Networks.

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HYDROGEOLOGIE ECOULEMENT EN MILIEU FRACTURE 2D

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  1. HYDROGEOLOGIE ECOULEMENT EN MILIEU FRACTURE 2D J. Erhel – INRIA / RENNES J-R. de Dreuzy – CAREN / RENNES P. Davy – CAREN / RENNES Chaire UNESCO - Calcul numérique intensif TUNIS - Mars 2004

  2. Modelling Flow and Transport in Subsurface Complex Fracture Networks Jocelyne Erhel, Jean-Raynald de Dreuzy, Philippe Davy IRISA / INRIA Rennes Géosciences Rennes / CAREN 2D Model 3D Model

  3. Channeling in natural fractured media Flow arrival in a mine gallery at Stripa (Sweden) 50 m 10 m 100 % of flow Olsson [1992] 80 % of flow Fluid flows only in a very limited number of fractures

  4. Synthetic image 2D Outcrop 100 m 50 m Gylling et al. [2000] Hornelen Basin Fracture networks geometry Äspö

  5. Influence of geometry on hydraulics length distribution has a great impact power law n(l) = l-a 3 types of networks based on the moments of length distribution  mean  std variation 2 < a < 3 • mean  std variation 3 < a < 4 • mean  variation a > 4

  6. Flow in 2D fracture networks h = 1 dh/dn = 0 dh/dn = 0 Flow h = 0 • Darcy law and mass conservation law : Div(K grad h) = 0 • stochastic modelling • High numerical requirements : large sparse matrix Papers: Dreuzy and al, WRR, [2000a;2000b;2001]

  7. Linear solver infinite cluster Backbone CG - No preconditioning 370 PCG with Jacobi preconditioning 563 48 PCG with ILU preconditioning 175 19 Sparse LU from Petsc Sparse Multifrontal LU from UMFPACK 2 0.07 1 Linear solver for permanent flow computation CPU requirements a=2.5 - 10 000 points in infinite cluster - 4 000 points in backbone Paper: Dreuzy and Erhel, CG [20002]

  8. Permanent flow computation - PCG solver Eigenvalue distribution Convergence history About 400 nodes CG : ~6000 iterations for 10-5 PGC with ILU : ~50 iterations for 10-5 Solid : constant fracture permeability dashed : lognormal fracture permeability distribution

  9. Complexity analysis of linear solver Example : k = 5 , niter(CG)=1500, niter(PCG) = 50 Direct solver : 1 , CG : 400 , PCG : 20

  10. SOME RESULTS FOR PERMANENT FLOW Computation of equivalent permeability or network permeability Percolation parameter : p (related to the fracture mass density) percolation threshold : pc power law exponent : a constant aperture in fractures • Domain of validity of classical approaches • a > 3 : percolation theory • p > pc and a < 3 : homogeneous media • p < pc and a < 3 : unique fracture system • a < 2 and p ~ pc : network of infinite fractures • 2 < a < 3 and p ~ pc : multi-path multi-segment network

  11. Transient flow computation dh / dt = Div (K grad h) Boundary conditions : h = 0 Initial condition : h = 0 excepted h = -1 in centre BDF scheme and sparse linear solver LSODE package Complex model with simple equations How to get a simplified model with adapted equations ?

  12. e u 4 q i m i h c n o Homogeneous models 3 i s Ploemeur n Multiscale models e m i Percolation 2D 3D D 2 1 2 3 Dimension hydraulique Transient flows Simplified model adapted equations hydraulic dimension chemical dimension

  13. First approach : 3D finite element or finite volume method very high numerical requirements 3D models Objective : 100 000 fractures with 1 000 elements in each

  14. 3D models Second approach : network of links - not accurate enough Current work : multilevel method based on a subdomain approach

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