Study of Algorithms for Fast Computation of Crack Expansion Problem

International audienceA problem of quasi-static growth of an arbitrary shaped-crack along an interface requires many times of iterations not only for finding a spatial distribution of discontinuity but also for determining the crack tip. This is crucial when refining model resolution and also when the phenomena progresses quickly from one step to another. We propose a mathematical reformu-lation of the problem as a nonlinear equation and adopt different numerical methods to solve it efficiently. Compared to a previous work of the authors, the resulting code shows a great improvement of performance. This gain is important for further application of aseismic slip process along the fault interface, in the context of plate convergence as well as the reactivation of fault systems in reservoirs

Two phase partially miscible flow and transport modeling in porous media: application to gas migration in a nuclear waste repository

We derive a compositional compressible two-phase, liquid and gas, flow model for numerical simulations of hydrogen migration in deep geological repository for radioactive waste. This model includes capillary effects and the gas high diffusivity. Moreover, it is written in variables (total hydrogen mass density and liquid pressure) chosen in order to be consistent with gas appearance or disappearance. We discuss the well possedness of this model and give some computational evidences of its adequacy to simulate gas generation in a water saturated repository

Non-isothermal compositional liquid gas Darcy flow: formulation, soil-atmosphere boundary condition and application to high energy geothermal simulations

International audienceThis article deals with the modelling and formulation of compositional gas liquid Darcy flow. Our model includes an advanced boundary condition at the interface between the porous medium and the atmosphere accounting for convective mass and energy transfer, liquid evaporation and liquid outflow. The formulation is based on a fixed set of unknowns whatever the set of present phases. The thermody-namic equilibrium is expressed as complementary constraints. The model and its formulation are applied to the simulation of the Bouillante high energy geothermal field in Guadeloupe characterized by a high temperature close to the surface

Simulation of CO2 storage in coal seams: Coupling of TOUGH2 with the solver for mechanics CODE_ASTER®

A symposium on applications and enhancements to the TOUGH codes for multiphase fluid, heat, and chemical transport at the Lawrence Berkeley National Laboratory (LBNL)International audienceAmongst the various geological storage options currently under consideration, CO2 storage in coal formations presents the most economic potential for middle-term spreading but also the most uncertainties and technical difficulties. This study (part of the CARBOLAB project) investigates coupled flow and mechanical processes that will take place around the injection point at the bottom of the Montsacro mine in Asturias, Spain. In order to quantify the strain and stress fields due to changes in the fluid pressure field and to account for stress/sorption dependent porosity/permeability effects, an efficient coupling between TOUGH2/EOS7C, a special module with an Extended Langmuir Sorption model, and the solver for mechanics CODE_ASTER® has been developed by BRGM

Non-isothermal Compositional Two-Phase Darcy Flow: Formulation and Outflow Boundary Condition

International audienceThis article deals with the modelling and formulation of compositional gasliquid Darcy flow. Our model includes an advanced boundary condition at the interface between the porous medium and the atmosphere accounting for convective mass and energy transfer, liquid evaporation, and liquid outflow. The formulation is based on a fixed set of unknowns whatever the set of present phases. The thermodynamical equilibrium is expressed as complementary constraints. The model and its formulation are applied to the simulation of the Bouillante high energy geothermal field in Guadeloupe characterized by a high temperature closed to the surface

Existence of solutions for a model of multiphase flow in porous media applied to gas migration in underground nuclear waste repository

International audienc

A model of multiphase flow and transport in porous media applied to gas migration in underground nuclear waste repository

International audienc

Development of mathematical and numerical tools for assessment of underground disposal concept

Ce travail est consacré à l’analyse et au développement de concepts et d’outils mathématiques en vue de leur application à des problématiques propres aux sites de stockage géologique profond de déchets radioactifs. La première partie porte sur l’estimation en champ lointain de la concentration de radionucléides issus du relâchement des colis de confinement, lorsque les incertitudes sur le relâchement sont prises en compte. En s’appuyant sur les travaux de A. Bourgeat et A. Piatniski sur l’homogénéisation d’une équation de convection-diffusion avec second membre aléatoire, on développe des outils numériques permettant d’approcher le comportement probabiliste du champ de concentration dans une configuration du type site de stockage. Dans une seconde partie, on s’intéresse à la migration de gaz dans et autour d’un site de stockage. Après une revue sur la modélisation physique des écoulements diphasiques de type eau/hydrogène en milieu poreux, on propose une nouvelle formulation mathématique du problème qui décrit, dans un même jeu d’équations, les écoulements à une (liquide) et deux (liquide/gaz) phases. Une étude de l’existence de solutions de cette formulation est menée à l’aide de la théorie générale des équations différentielles quasilinéaires elliptiques-paraboliques introduite par H.W. Alt et S. Luckhaus. Une méthode de résolution numérique du problème est mise en oeuvre pour la simulation de différents cas test, des plus simples au plus représentatif d’un site de stockage géologique. Enfin, l’homogénéisation périodique du modèle est effectuée et appliquée à la simulation de l’exercice Couplex-Gaz proposé par l’ANDRAThe purpose of this work is to analyze and develop mathematical concepts and tools in application to performance assessment of an underground nuclear waste disposal. The first part is concerned with estimating the far field concentration of radionuclides released by containers of waste when uncertainties on the release are taking in account. Using the work of A. Bourgeat and A. Piatniski about homogenization of a convection-diffusion equation with random source term, numerical tools are developed to approximate the random behavior of the concentration field in an underground disposal configuration. In a second part, we are interested in gas migration in and around an underground nuclear waste disposal. After a review on physical models of two-phase flow in porous media for water/hydrogen mixture, we propose a new mathematical formulation describing one- (liquid) and two- (liquid/gas) phase flow with a unique set of equation. Considering the general theory of quasilinear elliptic-parabolic differential equations introduced by H.W. Alt and S. Luckhaus, we study existence of solutions for this formulation. A numerical method to solve the problem is implemented to simulate several test cases. These test cases run from very simple situations to a representative configuration of an underground nuclear waste disposal. Finally, the periodic homogenization of the model is done and applied to simulate the Couplex-Gas exercise proposed by ANDRA

Développement d’outils mathématiques et numériques pour l’évaluation du concept de stockage géologique

The purpose of this work is to analyze and develop mathematical concepts and tools in application to performance assessment of an underground nuclear waste disposal. The first part is concerned with estimating the far field concentration of radionuclides released by containers of waste when uncertainties on the release are taking in account. Using the work of A. Bourgeat and A. Piatniski about homogenization of a convection-diffusion equation with random source term, numerical tools are developed to approximate the random behavior of the concentration field in an underground disposal configuration. In a second part, we are interested in gas migration in and around an underground nuclear waste disposal. After a review on physical models of two-phase flow in porous media for water/hydrogen mixture, we propose a new mathematical formulation describing one- (liquid) and two- (liquid/gas) phase flow with a unique set of equation. Considering the general theory of quasilinear elliptic-parabolic differential equations introduced by H.W. Alt and S. Luckhaus, we study existence of solutions for this formulation. A numerical method to solve the problem is implemented to simulate several test cases. These test cases run from very simple situations to a representative configuration of an underground nuclear waste disposal. Finally, the periodic homogenization of the model is done and applied to simulate the Couplex-Gas exercise proposed by ANDRA.Ce travail est consacré à l’analyse et au développement de concepts et d’outils mathématiques en vue de leur application à des problématiques propres aux sites de stockage géologique profond de déchets radioactifs. La première partie porte sur l’estimation en champ lointain de la concentration de radionucléides issus du relâchement des colis de confinement, lorsque les incertitudes sur le relâchement sont prises en compte. En s’appuyant sur les travaux de A. Bourgeat et A. Piatniski sur l’homogénéisation d’une équation de convection-diffusion avec second membre aléatoire, on développe des outils numériques permettant d’approcher le comportement probabiliste du champ de concentration dans une configuration du type site de stockage. Dans une seconde partie, on s’intéresse à la migration de gaz dans et autour d’un site de stockage. Après une revue sur la modélisation physique des écoulements diphasiques de type eau/hydrogène en milieu poreux, on propose une nouvelle formulation mathématique du problème qui décrit, dans un même jeu d’équations, les écoulements à une (liquide) et deux (liquide/gaz) phases. Une étude de l’existence de solutions de cette formulation est menée à l’aide de la théorie générale des équations différentielles quasilinéaires elliptiques-paraboliques introduite par H.W. Alt et S. Luckhaus. Une méthode de résolution numérique du problème est mise en oeuvre pour la simulation de différents cas test, des plus simples au plus représentatif d’un site de stockage géologique. Enfin, l’homogénéisation périodique du modèle est effectuée et appliquée à la simulation de l’exercice Couplex-Gaz proposé par l’ANDR

Repeating earthquake behavior due to fluid circulation through tough-biem simulation.

International audienceWe carry out TOUGH-BIEM simulations for modeling fault slip behavior triggered by fluid circulation in a geothermal context. The TOUGH2 code is used for modeling the pore pressure evolution within a fault and then a boundary integral equation method is applied for simulating fault slip, including aseismic slip on the entire fault plane and fast slip on seismogenic asperities. It is assumed that Coulomb friction and a slip-strengthening-then-weakening friction govern the fault slip. The pore pressure change due to injection is increasing logarithmically (fast at the beginning and later slow) so that the induced aseismic slip is fast at the beginning and slows down later. The fault slip on the asperities are periodic, and its recurrence depends on the previous aseismic slip in surrounding fault areas. When the two asperities are separated, their behavior is independent. When they are close each other, the recurrence timing of each asperity is disturbed. This feature is consistent with repeating earthquakes observed associated with geothermal stimulation experiments. The configuration of this study is simple for our demonstration, but the combination of TOUGH2-BIEM simulation would allow for studies of complex seismic fault behavior in different geological applications of fluid injections