Modélisation des écoulements dans un réseau ... - Cast3M - CEA
Modélisation des écoulements dans un réseau ... - Cast3M - CEA
Modélisation des écoulements dans un réseau ... - Cast3M - CEA
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© IFPRéserves prolongées | Raffinage propre | Véhicules économes | Carburants diversifiés | CO 2 maîtriséModélisation <strong>des</strong> écoulements <strong>dans</strong><strong>un</strong> réseau discret de fractures par <strong>un</strong>eapproche continueA. Fourno, C. Grenier, F. Delay,H. Benabderrahmane, B. NoetingerR03 Fourno et. al. Club CAST3M 11/2012
© IFPGeological contextComplex geological structuresDifferent Rock typesHigh heterogeneities (porosity, permeability)2R03 Fourno et. al. Club CAST3M 11/2012
© IFPFractured reservoirSome reservoirs present complex fracture networkLocal scale (well)Field scale3Fracture logR03 Fourno et. al. Club CAST3M 11/2012Faults and structural maps
© IFPFlow simulation model :equivalent propertiesReservoir modeling softwares don't model flow on discrete fracturenetwork.Equivalent flow properties have to be computed for each cellFrom M. Verscheure PHD work (2010)4R03 Fourno 11/2010R03 Fourno et. al. Club CAST3M 11/2012
© IFPGoal :to propose a new equivalent permeabilityFlow :qfracfQik h ni.fractures. Sfik.hQ K h.n . SeqiiiK(cosk.asincos)cosLzcossin sinLz012 2 2 2zsin sinLzcosL cos00005R03 Fourno et. al. Club CAST3M 11/2012
© IFPSome commentsK(cosk.asincos)cosLzcossin sinLz012 2 2 2zsin sinLzcosL cos0000• To correctly take into acco<strong>un</strong>t a fracture,a full tensor have to be used by cellsNevertheless• If the dip or azimuth is closed to 0,K can be approximated by a diagonal tensor.6R03 Fourno et. al. Club CAST3M 11/2012
© IFPSmeared FracturesThis work was initiated by <strong>CEA</strong>(DEN/DM2S/MTMS)The idea behind this approach is torepresent a fracture networkby heterogeneous propertieson a regular meshFrom A. Fourno PHD work (2005)7R03 Fourno 11/2010R03 Fourno et. al. Club CAST3M 11/2012KSFKSF100K0SF20K00SF2
© IFPExemple for the 2D• Two sets of cell areidentified8R03 Fourno et. al. Club CAST3M 11/2012
© IFPEquivalent permeability K MHFEQ11K. h.n s QihiMijMij. Thji i.• Mixed and Hybrid Finite Element scheme (MHFE) FlowjjQMHFEKMHFEhQMHFE32KMHFEh9R03 Fourno et. al. Club CAST3M 11/2012
© IFP2D: equivalent permeability K MHFEThe flow balance give the equivalent permeabilitya = fracture aperturek = fracture permeabilityL = fracture lengthh = head differenceLNb x = number of X cellsNb y = number of Y cellsQMHFE3NbX32NbYKMHFEhQ refaLkh10R03 Fourno et. al. Club CAST3M 11/2012
© IFP3D fracture meshS Cells (green)FractureC Cells (blue)11R03 Fourno 11/2010R03 Fourno et. al. Club CAST3M 11/2012
© IFPAnalytical and MHFE flowKSFKSF10K0SF20 0K00SF2S (simple) cellC (complex) cells S Cells (green)MHFEX ,Q . K .1 1hQMHFEX ,Q . K . h Q2 2 C Cells (blue)QQMHFE , Y23N.4. K2.2K22) K3Nref , X1ref , X2h43Na coscncosa cosc cosn. k.. k.. K .MHFE , Y1 1( N 12K1.hhhQref , cosY N . a.kcos.2Qref , 1 cosY1a.k.N cosc nhh(cos2sin2Ncostantan2)1212R03 Fourno et. al. Club CAST3M 11/2012
© IFPA 3D equivalent permeabilityKSFKSF100K0SF20K00SF2SCellsKSF1ccoscosnakKSF2cosc cosnakSf SfK3K2CCellsKSF1ccos.cosn(1tantan(22 tan3 tan2sin)2sin22)akKSF243cosc cosnakSf SfK3K213R03 Fourno et. al. Club CAST3M 11/2012
© IFPValidation caseSensitivity study on the dip and azimuth value.Numerical and analytical equivalent permeabilitiesare compared• Single fracture : dip and strike• Regular fracture network : cubic element size14R03 Fourno et. al. Club CAST3M 11/2012
© IFPPrecision of the results :single fractureErr % Strike (°)Dip(°)k max 0 15 30 45k mink int00000.0.60.1001.18.70.2.80.05.14.42008.59.20.13.80.015.23.7024.213.9300.22.411.9K(cosk.asincos)cosLzcossin sinLz012 2 2 2zsin sinLzcosL cos0As attempted, error depends on dip and strikevalues due to extra diagonal terms that areneglected in our approach00015R03 Fourno et. al. Club CAST3M 11/2012
© IFPPrecision of the results :regular fracture network16R03 Fourno et. al. Club CAST3M 11/2012Huge and minor connectivity changesdue to the spatial cell size
© IFPConclusions Performance of the method Fractured media mesh easily obtained Quick results and low computer cost (coarse discretizations) Precision depends on head gradient orientation, discretization. Modeler point of view For huge fracture density, weak space discretization have to berequired (increase the computer cost). The number of cell required is frequently an handicap17R03 Fourno et. al. Club CAST3M 11/2012
© IFPPerspectives☼ Perspectives : Reduce the number of cells Simulations of transfers in the fractured media BenchmarkApproche « explicite optimisée »MD, NK,[1] (100 mailles)Approche « Voxel »AF et al., (10 6 mailles)Approche « explicite fin »AF et al. [2] (2.10 5 mailles)Approche extérieure18 JRD, [3].R03 Fourno et. al. Club CAST3M 11/2012[1] N. Khvoenkova & M. Delorme (2011), méthode pour construire le maillage d'<strong>un</strong> réseau defractures a partir de diagrammes de voronoï,FR11/01.686[2] A. Fourno, B. Noetinger, C. La Borderie. Publication prévue[3] G. Pichot, J. Erhel and J. R. de Dreuzy, A mixed hybrid Mortar method for solving flow indiscrete fracture networks, Applicable Analysis An International Journal, 89 Issue 10,1629, doi:10.1080/00036811.2010.495333
© IFPBibliography• 2012. A. Fourno, C. Grenier, F. Delay, H. Benabderrahmane. A continuum voxel approach to model flowin 3D fault networks: a new way to obtain up-scaled hydraulic conductivity tensors of grid cells.Accepté <strong>dans</strong> Journal Of Hydology.• 2011. A. Fourno, C. Grenier, F. Delay, H. Benabderrahmane. A novel and efficient 3D fracturecontinuum model for flow in fracture networks. MAMERN11: 4th International Conference onApproximation Methods and Numerical Modelling in Environment and Natural Resources. Saidia(Morocco).• 2007. A. Fourno, C. Grenier, F. Delay and H. Benabderrahmane. Development and qualification of asmeared fracture modelling approach for transfers in fractured media. Gro<strong>un</strong>water in fractured rocks,IAH selected papers volume 9, section 6; Numerical modelling of fractured environment.• 2005. A. Fourno, directeur de thèse F. Delay, responsable C. Grenier. Modélisation multi-échellesde l'écoulement et du transport <strong>dans</strong> <strong>un</strong> milieu granitique ; application au site d‘Äspö en Suède.Thèse financée par l'ANDRA et effectuée au <strong>CEA</strong>/DEN <strong>dans</strong> le laboratoire de Modélisation <strong>des</strong>Transferts en Milieux Soli<strong>des</strong>.19R03 Fourno et. al. Club CAST3M 11/2012
© IFP20R03 Fourno et. al. Club CAST3M 11/2012
© IFPSpatial sensitivity studyThe DFN was generated using J.R. de Dreuzy tools21R03 Fourno et. al. Club CAST3M 11/2012
© IFPSpatial sensitivity studyEquivalent permeability tensor(m)Equivalent permeabilityK (mD)Kmin0.007 313.37 -88.67 -36.6 211-56.381 289.64 -174.20 374Diagonal tensor (mD)Kmax-38.72 41.92 540.78 5590.01 320 -90 -37.5 2180.02cell number(1.628.973)-56.5 298.6 -173.5 382-37.7 42 548 566351 -92 -43 243-57 326 182 413-37 35 580 6010.04 386 -115 74 296-53 425 166 491KzFracture conductivitiesCf = 1000 mD.m-45 33 633 6570.08 590 -59 -14 495-35 533 -175 61522-9 54 821 833R03 Fourno et. al. Club CAST3M 11/2012
© IFPSpatial sensitivity studysensitivity analysis600500400300K(mD)200KxKyKz10000 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09Δ(m)Huge and minor connectivity changesdue to the spatial cell size23R03 Fourno et. al. Club CAST3M 11/2012
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