I DENTIFICATION OF main flow structures for highly CHANNELED FLOW IN FRACTURED MEDIA by solving the inverse problem R. Le Goc (1)(2), J.-R. de Dreuzy (1) and P. Davy (1) (1) Geosciences Rennes, UMR 6118, CNRS, Université de Rennes 1, Rennes, France, (2) Itasca Consultants SAS, Lyon, France

16 April 2008R. Le Goc, EGU Purpose  Aquifer characterization Simplified flow model Preferential flow paths  Hydrologic data Piezometric heads Flow measurements  Difficulties Sparse and scarce data Heterogeneous media natural media

16 April 2008R. Le Goc, EGU Classical inverse problem methodology  Aquifer modeled as a coarse grid Parameters: grid permeability or geostatistical characteristics  Getting around the lack of data Less parameters  Small zone number  Homogenization More information  A priori values  Qualitative geological data  Problems for fractured media: Flow is channeled in a very few structures Importance of connectivity 128x128 permeability grid. Permeability values are log correlated with a correlation length = 10.

16 April 2008R. Le Goc, EGU Inverse problem for fractured media  Parameterization = 1-5 channels + background permeability channel position and transmissivity Background permeability representing all second-order structures  Getting around the lack of data Iterative parameterization (with an increasing number of channels). Iterative regularization based on previously identified structures.  Specificities : Identification of hydraulically predominant fractures Method relevant to highly channeled flow conditions Flow in a channeled media. Flow path width is proportional to the transmissivity.

16 April 2008R. Le Goc, EGU Inversion algorithm  First step Objective Function (classical least- square formulation): Solving direct problem using HYDROLAB, hydrogeological simulation platform Parameter estimation in optimizing F obj using simulated annealing

16 April 2008R. Le Goc, EGU Inversion process  Second step Objective Function with regularization term Regularization term: values from previous step as a priori values

16 April 2008R. Le Goc, EGU Inversion process  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)

16 April 2008R. Le Goc, EGU Stopping criteria for inversion  Classical stopping criteria  For each iteration we calculate (/Tsai et al., 2003/) The residual errors (RE) The parameters uncertainties (PU) The structure determination between parameterization n and n-1

16 April 2008R. Le Goc, EGU Presentation of synthetic test cases  Synthetic 2D fracture networks 5 x 5m square domains Boundary conditions : regional gradient + perturbations 25 steady hydraulic heads regularly spaced

16 April 2008R. Le Goc, EGU Results

16 April 2008R. Le Goc, EGU Results Solution analysis and generation of statistical results

16 April 2008R. Le Goc, EGU Conclusion  Efficient methodology Parameterization adapted to highly channeled media  Models based on flow channels  Iterative parameterization  Iterative regularization Results consistent with data  Global minima for models requiring few parameters  Local minima for more complex models  statistical solutions  Channel refinement controlled by data quantity Data partially sensitive to parameters Relation between model parameterization and data availability (planned work)