Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model

International audienceThis paper considers the problem of a fluid-driven fracture propagating in a permeable poroelastic medium. We develop a zero-thickness finite element to model the fracture. The fracture propagation is governed by a cohesive zone model and the flow within the fracture by the lubrication equation. The hydro-mechanical equations are solved with a fully coupled approach, using the developed zero-thickness element for the propagating fracture and conventional bulk finite elements for the surrounding medium. The numerical results are compared to analytical asymptotic solutions under zero fluid lag assumption in the four following limiting propagation regimes: toughness-fracture storage, toughness-leak-off, viscosity-fracture storage and viscosity-leak-off dominated. We demonstrate the ability of our cohesive zone model in simulating the hydraulic fracture in all these propagation regimes

A damage model for transversely isotropic materials

International audienceIn a nuclear disposal project, the damage of the hosting rock is a capital issue that should be studied and understood. This problem is even more complex when the studied rock is anisotropic. In the present paper, a damage model that takes into account both initial and induced anisotropy is introduced using equivalence relations between the real material and a fictitious isotropic one on which we can take all the advantages of the well established isotropic theory. Numerical simulations using a Finite Element Method (FEM) code shows an agreement between the theoretical predictions and the experimental data of Brazilian tests with different orientation angles

Coupled Chemo-Hydro-Mechanical analysis of Bituminized Waste swelling due to water up-taking

Bituminized Waste materials (BW) were produced by an industrial reprocessing of radioactive waste qualified low or medium activity and long life (LA-LL and MA-LL). BW is composed of precipitation sludge from the chemical reprocessing of spent nuclear fuel, immobilised in bitumen matrix. Geological storage is the reference solution for this kind of wastes. Under geological disposal conditions, and after a period of hundred thousand years, BW will undergo water re-saturation from host rock. Water up-tacking by BW will first induced free swelling in order to fill all different types of void existing in the storage disposal (void in primary canister, void in concrete container and void in rock vault). Then eventually swelling in contact with host rock and under special stress conditions. That's why the study of the behaviour of this type of material is very-important. Bituminized waste can be considered as a very-low permeable material containing one or several salt crystals. In order to describe the behaviour of such a material in contact of water, several mechanisms has to be coupled. The aim of this work is to study theses coupling during water up-tacking. Swelling behaviour in contact of water is govern by two principal mechanisms. First mechanism is the solvent transport leading to the dissolution of salt crystals. During dissolution, salt crystals volume increases, leading to global swelling of the bitumen matrix. Second mechanism is osmotic flow, which is leading directly to an overpressure in pore water due to chemical gradient (osmotic pressure) A model based on classical poromechanical approach has been developed in order to evaluate which is the leading mechanism and to study all the coupling. The chemical part of this model manage the precipitation/dissolution of salt crystals present in the bitumen matrix. It is the principal driving force of water up-taking, leading to salt saturation in pore water and increasing the porosity. That create a chemical gradient (salt concentration gradient) between pore water and host rock's water. Which initiate osmotic phenomenon: the bitumen matrix play the role of semi-permeable membrane allowing increasing of pore water pressure in the bituminized waste (osmotic overpressure). Over wise the porosity created by the salt crystals dissolution allow advectif and diffusive transport of water and salt through the bitumen matrix. The mechanical behaviour is strongly dominated by creep-deformation needing viscoplastic deformation management. A chemo-hydro mechanical numerical model in one dimension has been implemented (finite volume) in order to evaluate all mechanisms and coupling. This numerical model has shown that osmosis is the principal mechanism of water up-taking and that other mechanisms are not negligible. Moreover the difference of behaviour and coupling importance has been studied during both free swelling and water up-taking under constant volume. This work permitted us to find which parameters are needed to be identified experimentally

Modélisation et étude numérique des transferts en milieux fissurés

L'ETUDE DES RESERVOIRS FISSURES REPRESENTE ACTUELLEMENT UN ASPECT FONDAMENTAL DE L'INDUSTRIE PETROLIERE. CES RESERVOIRS A HAUT RENDEMENT SE CARACTERISENT PAR L'EXTREME COMPLEXITE DE LEUR STRUCTURE INTERNE ET PAR LA COEXISTENCE DE MILIEUX DE CARACTERISTIQUES TRES DIFFERENTES. POUR SIMULER LES ECOULEMENTS DANS DE TELS MILIEUX, LES INGENIEURS UTILISENT DES MODELES PARTICULIERS BASES SUR UNE IDEALISATION (DITE DE WARREN & ROOT) ET UN MODELE DOUBLE-MILIEU. DANS CE MODELE, L'ECHANGE MATRICE-FISSURE EST REPRESENTEE PAR UNE EQUATION DE TRANSFERT QUASI-STATIONNAIRE FAISANT INTERVENIR UN COEFFICIENT D'ECHANGE. LE CHOIX DE CE FACTEUR D'ECHANGE EST ENCORE SUJET A CONTROVERSE. EN OUTRE, DE NOMBREUX PHENOMENES PHYSIQUES SONT NEGLIGES ET LES PROCESSUS RESTENT ENCORE MAL COMPRIS. AFIN D'AMELIORER CES MODELES, UN SIMULATEUR FOURNISSANT DES SOLUTIONS DE REFERENCE EST NECESSAIRE. C'EST POURQUOI NOUS PROPOSONS ICI DE SIMULER A L'ECHELLE FINE LES ECOULEMENTS MONOPHASIQUES ET DIPHASIQUES DANS LA MATRICE ET LES FISSURES. DANS CE BUT NOUS AVONS DEVELOPPE UNE METHODE PARTICULIERE APPELEE METHODE DES ELEMENTS FISSURES. CELLE-CI REPOSE SUR UN MAILLAGE PARTICULIER DU MILIEU (ELEMENTS LINEAIRES POUR LES FISSURES, TRIANGLES POUR LA MATRICE) ET SUR DES SCHEMAS DE TYPE VOLUMES FINIS APPROPRIES. CETTE THESE PRESENTE LE DEVELOPPEMENT DETAILLE DE CETTE NOUVELLE METHODE NUMERIQUE. A L'ISSU DE CE TRAVAIL, UN CODE DE CALCUL A ETE REALISE ET DES SIMULATIONS ONT PU ETRE EFFECTUEES. ELLES NOUS ONT PERMIS DE REALISER DES COMPARAISONS ENTRE DIVERS MODELES DOUBLE-MILIEU. L'EXPLOITATION DE CE CODE NOUS A AINSI CONDUIT A MENER UNE REFLEXION SUR LE CHOIX DU FACTEUR D'ECHANGE, DETERMINANT POUR LA FORMULATION DU MODELE DOUBLE-MILIEU.BORDEAUX1-BU Sciences-Talence (335222101) / SudocLILLE1-BU (590092102) / SudocSudocFranceF

Finite element modeling of fluid-driven fracture in permeable medium

International audienceIn this article, we present a numerical method to model the propagation of a fluid-driven fracture in a poroelastic medium in the finite element framework. We developed a zero-thickness finite element to model the fracture. The fracture propagation is governed by a cohesive zone model. The fluid flow within the crack is described by the lubrication equation and the fluid pressure in the fracture acts as an hydraulic and mechanical boundary condition on the lips of the crack. The bi-dimensional pressure diffusion equation and the equilibrium equation in the surrounding porous medium are fully solved numerically. We compare the results of our numerical model with asymptotic analytical solutions. Our numerical model captures very well the analytical solutions in all the asymptotic propagation regimes. In addition, our zero-thickness element method gives access to a finer description of the fluid diffusion in the porous medium and of its coupled mechanical response

Territoires en miroir. Espaces d'en haut et espaces d'en bas dans les montagnes européennes (XVIe -XXIe siècles)

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A transversely isotropic thermo-poroelastic model for claystone: parameter identification and application to a 3D underground structure

International audienceA transversely isotropic thermo-poroelastic constitutive law is developed and implemented in the finite element code Code_Aster (EDF, France). It is then validated using an analytic solution for an inclined borehole in a transversely isotropic medium. A strategy for identifying the parameters of the transversely isotropic thermo-poroelastic model based on an inverse method is proposed on the basis of different laboratory tests. To demonstrate the efficiency and applicability of the model, it is then applied in a three-dimensional numerical model of an underground structure in a parameter sensitivity study. The results of the modelling highlight the importance of accounting for anisotropic phenomena when determining the dimensions of underground facilities. The whole approach is presented in the paper, from model development to application to 3D numerical modelling to an engineering case study

Stress and flux reconstruction in Biot's poro-elasticity problem with application to a posteriori error analysis

International audienceWe derive equilibrated reconstructions of the Darcy velocity and of the total stress ten-sor for Biot's poro-elasticity problem. Both reconstructions are obtained from mixed finite element solutions of local Neumann problems posed over patches of elements around mesh vertices. The Darcy velocity is reconstructed using Raviart–Thomas finite elements and the stress tensor using Arnold–Winther finite elements so that the reconstructed stress tensor is symmetric. Both reconstructions have continuous normal component across mesh interfaces. Using these reconstructions, we derive a posteriori error estimators for Biot's poro-elasticity problem, and we devise an adaptive space-time algorithm driven by these estimators. The algorithm is illustrated on test cases with analytical solution, on the quarter five-spot problem , and on an industrial test case simulating the excavation of two galleries

Numerical modelling of the swelling of clayey geomaterials: A comparative study between Barcelona Basic model (BBM) and a multiscale approach

International audienceClay swelling occurs at diffrent scales and is governed by two phenomena: crystalline and osmotic swelling. In this work, we propose a comparative study between two numerical models. The first one is a multiscale constitutive law, based on a phenomenological approach conducted to formulate the different interactions that occur in the interlayer space with respect to the disjoining pressure (crystalline swelling) and the interparticular porous space to account for capillarity effects. The model is freshly developed and implemented in Code_Aster Finite Element software for hydro-mechanical coupling and showed a good consistency with experimental results. The second model is the highly acknowledged Barcelona Basic model already existing in Code_Aster. BBM model is already validated in the literature showing a good tendency with the experimental results. The idea of this paper is to compare between the two models as they have both reproduced the real swelling behaviour of clayey geomaterials comparing to the experimental results. To this aim, we will be focusing on the swelling mechanism existing in constant volume conditions in terms of swelling pressure