Mass Transfer & Porous Media (MTPM) - Andra

More documents

Recommendations

Info

P/MTPM/9Moreover, using another sample, radial and axial strains were recorded during each transient phase. Theeffective value of the relative humidity imposed by the saturated salt solutions was continuously recorded.A third set of samples was submitted to the same drying path allowing the determination, by destructivemeasurements, of the moisture content and the bulk density for each suction level. This study provides thecapillary curve of the argillite.INTERPRETATION OF THE RESULTSThe second part of the work concerns the permeability determination. More precisely, a coefficient formoisture transfer in the argillite is deduced from both experimental results and calculation. A model forwater transport in uniaxial conditions is proposed. This model is based on the following assumptions :isotropic permeability, linear behaviour (small suction variation), small transformation hypothesis, smallgas pressure variation, vapour relative diffusion into gas is neglected, strain and mass have same evolution,Darcy law is applicable [Olchitzky, 2002]. Using this model, the calculated behaviour is compared to theexperimental behaviour. Fitting the curves provides the value of the water permeability of the argillite.This method was developed by [Olchitzky, 2002] who studied a bentonite. A detailed presentation of themodel and the analytical solution can be found in [Imbert, 2005]. A similar experimental work has beenundertaken on a deep argillite by [Koriche, 2004]. The values of permeability they obtain are in goodagreement with those of the present paper. [Homand, 2004] and [Giraud, 2006] have improved the methodand proposed both a linear and a non-linear modelling approaches.Finally, these results of water permeability for partially saturated states are compared to the permeabilityof the saturated argillite.References:Giraud A. et al. (2006): Permeability identification of a weakly permeable partially saturated porous rock.Kluwer Academic Publishers.Imbert C., Olchitzky E., Lassabatère T., Dangla P., Courtois A. (2005): Evaluation of a thermal criterionfor an engineered barrier system.Olchitzky E. (2002): Couplage hydro-mécanique et perméabilité d’une argile gonflante non saturée soussolicitations hydriques et thermiques. Thesis, Ecole Nationale des Ponts et Chaussées, 213pp, in french.Homand F., et al. (2004): Permeability determination of a deep argillite in saturated and partially saturatedconditions. International Journal of Heat and Mass Transfer 47, pp 3517-3531.Koriche A. (2004): Caractérisation du comportement couplé des argilites de Meuse/Haute-Marne aux étatssaturé et partiellement saturé. Thesis, Ecole Nationale Supérieure de Géologie de Nancy, in french.Page 440INTERNATIONAL MEETING, SEPTEMBER 17...>...18, 2007, LILLE, FRANCECLAYS IN NATURAL & ENGINEERED BARRIERSFOR RADIOACTIVE WASTE CONFINEMENT
P/MTPM/10MIXED HEXAHEDRAL FINITE ELEMENTSFOR DARCY FLOW CALCULATIONIN CLAY POROUS MEDIAA. Sboui 1 , J. E. Roberts 2 , J. Jaffré 21. ANDRA DS/CS Parc de la Croix Blanche 1/7 rue Jean Monnet 92298 Chatenay-Malabry Cedex2. INRIA-Roquencourt, B.P 105, 78153 Le Chesnay Cedex, FranceWe are concerned with the problem of developing a numerical simulator for modeling flow andcontaminant transport in the vicinity of an underground nuclear waste repository for use in performanceassessment. Clearly reasonably accurate and reliable simulators are needed, but as performance assessmentrequires many simulations, it is also important that the simulators be very efficient. The method developedhere is the Kuznetsov-Repin mixed finite element method which is designed to handle nonrectangularhexahedral meshes for Darcy flow calculations.INTRODUCTIONThe Darcy flow equation is an elliptic equation coupling a conservation equation with Darcy’s law. As theDarcy velocity is the unknown of interest and we are concerned with problems with large changes in thepermeability coefficient, we use a mixed finite element method. However standard mixed finite elementsdo not work on general hexahedral grids because the space of discrete velocities does not contain theconstant velocities [5]. To correct this situation some solutions were proposed in two dimensions in [1, 2,7]. We will instead use a new mixed finite element method for hexahedrons proposed by Yu. Kuznetzovand S. Repin (KR) [3, 4].In this paper, following the ideas of Kuznetsov and Rapin, we develop a composite element specificallyfor a convex hexahedron. This element is obtained by dividing the hexahedron into five tetrahedra [6] .EXPERIMENTAL CONCEPTThe Kuznetsov-Repin mixed finite element method was proven to be convergent, it was used to calculatethe pressure and velocity field around a nuclear waste disposal. The domain of calculation is made up of13 geological subdomains with permeabilities changing with up to three orders of magnitude from onesubdomain to the other. The mesh was provided by engineers from ANDRA and is made of about 500 000hexahedrons which for the most part are not parallelepipeds.RESULTS AND INTERPRETATIONSince the Darcy velocity is actually the important quantity that is needed for the transport, we show inFigure 1 the norm of the velocity on an horizontal cross section, the velocity calculated with RTN finiteelements (left) and KR mixed finite elements (right).As one can observe, there are significant differences in the calculated velocity. In particular the norm ofthe velocity calculated with RTN mixed finite elements show a rough behaviour which is clearlyunphysical for regions with constant permeabilities. This will necessarily have a strong impact when thisvelocity will be used in transport calculations.We constructed a new mixed finite element for general hexahedral grids based on Kuznetsov’s and Repin’sgeneral procedure for composite mixed finite elements. This new mixed finite element provides an elegantand simple way to implement mixed finite elements for general hexahedral discretizations. Theoreticalconvergence was proven and numerical convergence was observed. The method was applied to thecalculation of a Darcy velocity which will be used for the simulation of the transport of radionuclidesaround a storage site.INTERNATIONAL MEETING, SEPTEMBER 17...>...18, 2007, LILLE, FRANCECLAYS IN NATURAL & ENGINEERED BARRIERSFOR RADIOACTIVE WASTE CONFINEMENTPage 441
Page 1: Poster [MTPM]Mass Transfer & Porous
Page 4 and 5: P/MTPM/1The free energy cost of for
Page 7 and 8: P/MTPM/3DIFFUSION OF IONS IN UNSATU
Page 9: P/MTPM/4POROUS MEDIA CHARACTERIZATI
Page 12 and 13: P/MTPM/5Oxalate ionsQuartzQuartz +P
Page 14 and 15: P/MTPM/6borehole was capped with a
Page 16 and 17: P/MTPM/7Initial state with glass an
Page 18 and 19: P/MTPM/8The mesh of the elementary
Page 22 and 23: P/MTPM/10Figure 1: Horizontal cross
Page 24 and 25: P/MTPM/11n t (mol)as received8 10 -
Page 26 and 27: P/MTPM/1210,9Degree of saturation (
Page 28 and 29: P/MTPM/13RESULTSFirst, we estimated
Page 30 and 31: P/MTPM/142.5Energy (M eV)1.6 1.7 1.
Page 32 and 33: P/MTPM/15C/Co10.90.80.70.60.50.40.3
Page 34 and 35: P/MTPM/16ModelIrmayvG-M1vG-M2vG-M3T
Page 36 and 37: P/MTPM/17Figure 1: Experimental HTO
Page 38 and 39: P/MTPM/18Diffusion experiments were
Page 40 and 41: P/MTPM/19Figure 1: Used mesh for co
Page 42 and 43: P/MTPM/201.81.61.41.2upstream compa
Page 44 and 45: P/MTPM/21490Pressure [bar]0 10 20 3
Page 46 and 47: 134P/MTPM/22through-diffusion exper
Page 48 and 49: P/MTPM/23HA (µg/g)3002001000(a):pH
Page 50 and 51: P/MTPM/24through each sample. The p
Page 52 and 53: P/MTPM/25FIRST RESULTSPreliminary c
Page 54 and 55: P/MTPM/26heterogeneous distribution
Page 56 and 57: P/MTPM/27Relative concentration (C-
Page 58 and 59: P/MTPM/280.75m0.25mTable 1: Cross s
Page 60 and 61: P/MTPM/29Figure 1: A. Scheme of the
Page 62 and 63: P/MTPM/30The presented theory is ex
Page 64 and 65: P/MTPM/31Furthermore, Van Loon et a
Page 66 and 67: P/MTPM/32RESULTSResults show that,
Page 68 and 69: P/MTPM/33Clay modellingPore size di
Page 70 and 71:
P/MTPM/341.60E-11f H2-d total (kg.m
Page 72 and 73:
P/MTPM/350.50η R ()0.400.300.200.1
Page 74 and 75:
P/MTPM/36200Bq/g1801601401201008060
Page 76 and 77:
P/MTPM/37Argilite (ionic strength 0
Page 78 and 79:
P/MTPM/38-Samples cored at 12m were
Page 80 and 81:
P/MTPM/39APPLICATIONSCORE 2D has be
Page 82 and 83:
P/MTPM/40Figure 1: Sketch drawing o
Page 84 and 85:
P/MTPM/41Figure 1: Thermal conducti
Page 86 and 87:
P/MTPM/42Figure 2: Model of pore st
Page 88 and 89:
P/MTPM/43The available data are con
Page 90 and 91:
P/MTPM/44Figure 1: Spatial extensio
Page 92 and 93:
P/MTPM/45Relative concentration / (
Page 94 and 95:
P/MTPM/46Figure 2: Swelling pressur
Page 96 and 97:
P/MTPM/47then used in the transport
Page 98:
P/MTPM/4820181614121086Gas pressure
show all

Mass Transfer & Porous Media (MTPM) - Andra

Create successful ePaper yourself

Delete template?

Save as template?