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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Double Ended Guillotine Break in a Prismatic Block VHTR Lower Plenum Air Ingress Scenario

Hartley, Jessica 2011 August 1900 (has links)
The double ended guillotine break leading to density-driven air ingress has been identified as a low probability yet high consequence event for Very High Temperature Reactor (VHTR). The lower plenum of the VHTR contains the core support structure and is composed of graphite. During an air ingress event, oxidation of the graphite structure under high temperature conditions in an oxygen containing environment could degrade the integrity of the core support structure. Following this large break, air from the reactor containment will begin to enter the lower plenum via two mechanisms: diffusion or density driven stratified flow. The large difference in time scales between the mechanisms leads to the need to perform high fidelity experimental studies to investigate the dominant the air ingress mechanism. A scaled test facility has been designed and built that allows the acquisition of velocity measurements during stratification after a pipe break. A non-intrusive optical measurement technique provides full-field velocity measurements profiles of the two species Particle Image Velocimetry (PIV). The data allow a more developed understanding of the fundamental flow features, the development of improved models, and possible mitigation strategies in such a scenario.Two brine-water experiments were conducted with different break locations. Flow fronts were analyzed and findings concluded that the flow has a constant speed through the pipe after the initial lock exchange. The time in which the flow enters the lower plenum is an important factor because it provides the window of opportunity for mitigation strategies in an actual reactor scenario. For both cases the flow of the heavier density liquid (simulating air ingress from the reactor containment) from the pipe enters the reactor vessel in under 6 seconds. The diffusion velocity and heavy flow front of the stratified flow layer were compared for the SF6/He gas case. It is seen that the diffusion plays less of a role as the transport mechanism in comparison to the density-driven stratified flow since the velocity of the diffusion is two orders of magnitude smaller than the velocity of the stratified flow mechanism. This is the reason for the need for density-driven stratified flow investigations following a LOCA. These investigations provided high-quality data for CFD validation in order for these models to depict the basic phenomena occurring in an air ingress scenario.
2

Multi-scale Investigations of Geological Carbon Sequestration in Deep Saline Aquifers

Guo, Ruichang 25 May 2022 (has links)
Geological carbon dioxide (CO2) sequestration (GCS) in deep saline aquifers is viewed as a viable solution to dealing with the impact of anthropogenic CO2 emissions on global warming. The trapping mechanisms that control GCS include capillary trapping, structural trapping, dissolution trapping, and mineral trapping. Wettability and density-driven convection play an important role in GCS, because wettability significantly affects the efficiency of capillary trapping, and density-driven convection greatly decreases the time scale of dissolution trapping. This work focuses on the role of wettability on multiphase flow in porous media, density-driven convection in porous media, and their implications for GCS in deep saline aquifers. Wettability is a critical control over multiphase fluid flow in porous media. However, our understanding on the wettability heterogeneity of a natural rock and its effect on multiphase fluid flow in a natural rock is limited. This work innovatively models the heterogeneous wettability of a rock as a correlated random field. The realistic wetting condition of a natural rock can be reconstructed with in-situ measurements of wettability on the internal surfaces of the rock. A Bentheimer sandstone was used to demonstrate the workflow to model and reconstruct a wettability field. Relative permeability, capillary pressure-water saturation relation are important continuum-scale properties controlling multiphase flow in porous media. This work employed lattice Boltzmann method to simulate the displacement process. We found that pore-scale surface wettability heterogeneity caused noticeable local scCO2 and water redistributions under less water-wet conditions at the pore scale. At the continuum scale, the capillary pressure-water saturation curve under the heterogeneous wetting condition was overall similar to that under the homogeneous wetting condition. This suggested that the impact of local wettability heterogeneity on the capillary pressure-water saturation curve was averaged out at the entire-sample scale. The only difference was that heterogeneous wettability led to a negative entry pressure at the primary drainage stage under the intermediate-wet condition. The impact of pore-scale wettability heterogeneity was more noticeable on the relative permeability curves. Particularly, the variation of the scCO2 relative permeability curve in the heterogeneous wettability scenario was more significant than that in the homogenous wettability scenario. Results showed that higher wettability heterogeneity (i.e., higher standard deviation and higher correlation length) increased the variations in the CO2/brine relative permeability curves. Dissolution of CO2 into brine is a primary mechanism to ensure the long-term security of GCS. CO2 dissolved in brine increases the CO2-brine solution density and thus can cause downward convection. Onset of density-driven instability and onset of convective dissolution are two critical events in the transition process from a diffusion-dominated regime to a convection-dominated regime. In the laboratory, we developed an empirical correlation between light intensity and in-situ solute concentration. Based on the novel and well-controlled experimental methods, we measured the critical Rayleigh-Darcy number and critical times for the onset of density-driven instability and convective dissolution. To further investigate the impact of permeability heterogeneity on density-driven convection, a three-dimensional (3D) fluidics method was proposed to advance the investigation on density-driven convection in porous media. Heterogeneous porous media with desired spatial correlations were efficiently built with 3D-printed elementary porous blocks. In the experiments, methanol-ethylene-glycol (MEG), was used as surrogate fluid to CO2. The heterogeneous porous media were placed in a transparent tank allowing visual observations. Results showed that permeability structure controlled the migration of MEG-rich water. Permeability heterogeneity caused noticeable uncertainty in dissolution rates and uncertainty in dissolution rates increases with correlation length. To sum up, this work comprehensively employed novel experimental methods and large-scale direct simulations to investigate the sequestration of CO2 in saline aquifers at a pore scale and a continuum scale. The findings advanced our understanding on the role of wettability heterogeneity and permeability heterogeneity on GCS in deep saline aquifers. / Doctor of Philosophy / Global warming caused by anthropogenic CO2 emissions is a pressing issue to address of our time. The storage of CO2 in deep saline aquifers is a promising solution because of saline aquifers' vast storage capacity. Property heterogeneity exists extensively in saline aquifers from a continuum scale to a pore scale. The implications of pore-scale wettability heterogeneity and continuum-scale permeability heterogeneity for the storage of CO2 in saline aquifers are not clear. This work is to employ novel experimental methods and powerful simulation tools to investigate the role of wettability heterogeneity and permeability heterogeneity on the storage of CO2 in saline aquifers. This work measured contact angles on the scanned micro-CT images of a Bentheimer sandstone after a CO2 flooding. A correlated lognormal wettability model was put forward with the statistical information of the contact angle measurements. Simulations on the CO2/brine flow in the Bentheimer sandstone were performed. Results showed that the wettability heterogeneity caused noticeable redistributions of CO2/brine compared to scenarios under homogeneous wettability. Impact of wettability on capillary pressure-water saturation curve was not noticeable because the effects were averaged out through the entire rock sample. The standard deviation and correlation length caused variations on the relative permeabilities. This means that we need to take them into consideration in simulating the migration of CO2 in saline aquifers at a reservoir scale. After CO2 pools beneath the impermeable cap rock, dissolution of CO2 into brine dominates the trapping process. Convection caused by CO2 dissolution can greatly accelerate the dissolution rate. The onset of convection is a critical issue and lack of experimental evidence. This work firstly determined the onset time of instability. To further investigate the heterogeneity on the convection, this work proposed a 3D-print-based method to efficiently build heterogeneous porous media with a designed permeability distribution. The experiments were conducted, and results showed that heterogeneity structure of porous media can cause great variations on the dissolution rate of CO2. The findings of this work advanced our understanding on the migration of CO2 in saline aquifers, provided solid basis for assessment and decision on the storage of CO2 into saline aquifers.
3

Risk of subsidence and aquifer contamination due to evaporite dissolution : modelization of flow and mass transport in porous and free flow domains

Zidane, Ali 13 December 2012 (has links) (PDF)
The groundwater flow in aquifers contain evaporite rocks can cause problems such as geo-mechanical subsidence or collapse. In this work, we focus on the development of numerical models to simulate the flow in porous and non-porous domains in order to study the dissolution phenomenon and fractures evolution over time. The first part of this thesis is devoted to developing new solutions for the validation of numerical models to simulate density driven flow in porous media. The new procedure consist of solving simultaneously the flow and the transport equations using the Levenberg-Marquardt algorithm. The use of this technique allowed us to develop, for the first time, semi-analytical solutions of saltwater intrusion in the case of small diffusion and in the case of a large density contrast. In the second part of this work, we studied the flow in evaporitic rocks. A numerical code was developed to solve the nonlinear system using advanced numerical methods. To validate this new model, we have developed a semi-analytical solution for the density Stokes flow. The third part of this work is devoted to transport with dissolution of rock salt. As a first step, we studied the influence of various parameters on the dissolution of salt in Adlertunnel located at a depth of 160 m in the region of Basel in Switzerland. In a second step, we are interested in the simulation of the fracture's evolution as a result of the dissolution. The numerical model takes into account the Stokes flow and mass transport effects and dissolution of the fracture walls.
4

Fonctionnement hydrogéologique et hydrochimique du bassin crétacé de Tsagaan Els (Dornogobi, Mongolie) / Hydrogeology and hydrochemistry of the Tsagaan Els Cretaceous Basin (Dornogobi, Mongolia)

Grizard, Pierre 29 November 2017 (has links)
Le bassin crétacé de Tsagaan Els est situé dans le désert de Gobi en Mongolie. L’objectif de cette thèse est de mieux comprendre le fonctionnement hydrogéologique et hydrochimique de ce bassin endoréique afin de faciliter l’implantation de futurs projets miniers. Dans cette optique, un modèle hydrogéologique régional 3D a tout d’abord été développé sous MODFLOW. La calibration à partir des niveaux piézométriques mesurés sur les ouvrages présents au sein des licences et quelques puits nomades, aboutit à plusieurs solutions. Elles présentent chacune des conductivités hydrauliques en accord avec les tests de pompages, et des taux de recharge entre 0.6 et 3.1 mm/an, cohérents avec le climat actuel. Ce modèle a ainsi permis d’étendre nos connaissances piézométriques au-delà des licences et d’effectuer un bilan hydrique régional. Ensuite, l’âge des eaux a été estimé numériquement via ce modèle puis par des datations 14C. Une comparaison des résultats de ces méthodes a indiqué que les solutions présentant des taux de recharges élevés étaient plus probables que celles en présentant de plus faibles à conditions que les écoulements soient restés les mêmes durant les trente derniers milliers d’années. En parallèle, une étude hydrochimique portant sur les ions majeurs, le brome et les isotopes stable de l’eau (18O et 2H) a montré que l’origine de la salinité des eaux était principalement liée à la dissolution d’évaporites superficielles. En dernier lieu, un modèle 3D local, centré sur la playa terminale du bassin a permis de mieux comprendre le fonctionnement actuel et passé du bassin en s’appuyant sur l’évolution spatiotemporelle de la salinité. / The Tsagaan Els basin is located in the Gobi desert, in Mongolia. This thesis aims to better understand the hydrogeology and hydro-chemistry of the basin in order to optimize the future mining projects. To this end, a 3D groundwater flow model of the basin has first been developed under MODFLOW. The latter was calibrated using piezometric network data and levels in a few nomadic wells. Several solutions were found with hydraulic conductivity values in agreement with pumping tests and recharge rates between 0.6-3.1 mm/yr in agreement with the current climate. The model helped us to extend our piezometric knowledge beyond AREVA’s mining licenses and to establish a regional water balance model. Groundwater age was then estimated with this model and with 14C dating. A comparison of the results of these two methods showed that calibrated solutions with higher recharge are more likely than those with lower recharge under the hypothesis that groundwater flow has not changed significantly during the last 30 kyrs. Meanwhile, a hydrochemical study using major ions, bromines and the stable isotopes of water (18O and 2H) showed that groundwater salinity mainly comes from dissolution of surficial evaporites: likely gypsum and halite and possibly thenardite. Even though evaporation is the main driving force of the groundwater flow, this process, when taking place in subsurface, seems to have no real influence on δ18O and δ2H values of the groundwater. Last a 3D local groundwater flow model centered on the terminal playa and based on the spatiotemporal evolution of the salinity, led us to a better understanding of the past and current hydrogeological functioning of the basin.
5

Risk of subsidence and aquifer contamination due to evaporite dissolution : modelization of flow and mass transport in porous and free flow domains / Risque de subsidence et de contamination d'aquifère due à la dissolution des evaporites : modélisation d'écoulement et du transport du masse dans les milieux poreux et les milieux non-poreux

Zidane, Ali 13 December 2012 (has links)
La circulation de l’eau souterraine dans les aquifères contenants des roches évaporitiques peut provoquer des problèmes géo-mécaniques tels que l'affaissement du sol ou l'effondrement. Dans ce travail, nous nous intéressons au développement de modèles numériques permettant de simuler les écoulements dans les milieux poreux et non poreux ainsi que les phénomènes de dissolution et d’évolution des fractures dans le temps. La première partie de cette thèse est consacrée au développement de nouvelles solutions pour la validation des modèles numériques simulant les écoulements densitaires en milieux poreux. La nouvelle procédure consiste à résoudre simultanément les deux systèmes d’écoulement et de transport en utilisant l’algorithme de Levenberg-Marquardt. L’utilisation de cette technique nous a permis de développer, pour la première fois, des solutions semi-analytiques d’intrusion d’eau salée dans le cas de faible diffusion ainsi que dans le cas d’un grand contraste de densité. Dans la deuxième partie de ce travail, nous nous sommes intéressés aux écoulements dans les fractures des roches évaporitiques. Un code de calcul a été développé pour résoudre ce système non linéaire en utilisant des méthodes numériques adaptées. Pour valider ce nouveau modèle, nous avons développé une solution semi-analytique pour les écoulements densitaires de Stokes. La troisième partie de ce travail est consacrée au transport avec dissolution de la roche salée. Dans un premier temps, nous avons étudié l’influence de différents paramètres sur la dissolution du sel dans l’Adler tunnel situé à une profondeur de 160 m dans la région de Bâle en Suisse. Dans un second temps, nous nous sommes intéressés à la simulation de l’évolution dune fracture sous l’effet de la dissolution. Le modèle numérique développé prend en compte les écoulements de Stokes ainsi que le transport de masse avec effets densitaires et la dissolution des parois de la fracture. / The groundwater flow in aquifers contain evaporite rocks can cause problems such as geo-mechanical subsidence or collapse. In this work, we focus on the development of numerical models to simulate the flow in porous and non-porous domains in order to study the dissolution phenomenon and fractures evolution over time. The first part of this thesis is devoted to developing new solutions for the validation of numerical models to simulate density driven flow in porous media. The new procedure consist of solving simultaneously the flow and the transport equations using the Levenberg-Marquardt algorithm. The use of this technique allowed us to develop, for the first time, semi-analytical solutions of saltwater intrusion in the case of small diffusion and in the case of a large density contrast. In the second part of this work, we studied the flow in evaporitic rocks. A numerical code was developed to solve the nonlinear system using advanced numerical methods. To validate this new model, we have developed a semi-analytical solution for the density Stokes flow. The third part of this work is devoted to transport with dissolution of rock salt. As a first step, we studied the influence of various parameters on the dissolution of salt in Adlertunnel located at a depth of 160 m in the region of Basel in Switzerland. In a second step, we are interested in the simulation of the fracture’s evolution as a result of the dissolution. The numerical model takes into account the Stokes flow and mass transport effects and dissolution of the fracture walls.
6

Études théorique et expérimentale du transport de fluides miscibles en cellule Hele-Shaw / Theoretical and experimental study of fluid transport in miscible Hele-Shaw cell

Trieu, Hung Truong 04 May 2011 (has links)
Dans cette thèse, nous avons étudié expérimentalement, numériquement et théoriquement la sédimentation d’un soluté en cellule de Hele-Shaw, modèle analogue de milieu poreux, avec un écoulement zonal horizontal. Une cellule, alimentée par deux grands réservoirs assurant un écoulement zonal uniforme, a été réalisée au laboratoire. La vitesse a été mesurée par PIV. L’injection d’une solution saline dans cet écoulement permet de visualiser la propagation du panache de pollution, et de mesurer le champ de concentration par LIF. Trois configurations typiques ont été observées : panache sans digitation (« stable »), avec une seule digitation (« faiblement instable »), et avec de nombreuses digitations (« fortement instable »). L’influence du contraste de densité, de la vitesse zonale, et du débit d’injection sur la stabilité du panache a été analysée. Ces résultats ont été comparés à des simulations numériques sous COMSOL Multiphysics®. Les champs de concentration simulés sont en accord quantitatif avec les champs expérimentaux. Ces simulations ont de plus permis d’étudier l’influence de l’anisotropie du tenseur de dispersion sur la stabilité du panache. Une étude théorique linéaire, effectuée à partir d’un écoulement de base unidirectionnel et quasi-stationnaire, est venue compléter ces résultats. Elle montre que le panache est toujours convectivement instable pour les valeurs des paramètres considérées, et permet de retrouver et de quantifier les principaux résultats mis en évidence lors des études expérimentale et numérique, comme l’effet stabilisant de la dispersivité longitudinale ou l’effet déstabilisant du contraste de densité / This thesis is an experimental and numerical investigation of solute transport and sedimentation in a Hele-Shaw cell with zonal flow. A vertical cell joining two large tanks has been built to provide a uniform horizontal flow, the velocity of which has been measured by using PIV. The concentration field of a solute injected in this flow has been measured by using LIF. Three typical plume configurations have been observed: without digitations (“stable”), with a single digitation (“weakly unstable”), and with various digitations appearing at the lower interface (“unstable plume”). The influence of density contrast, zonal flow and solute flow rate on the appearance of the various configurations has been investigated. These results have been compared to numerical simulations using the COMSOL Multiphysics® software. The numerical concentration fields are in qualitative agreement with the experimental ones. In addition, these simulations allowed us to investigate the effect of the anisotropy of the dispersion tensor on the occurrence of unstable configurations. A linear stability analysis based on a uniform parallel flow superposed to a quasi-steady horizontal layer of solute has been performed. It shows that the plume is convectively unstable for the parameters considered here, and confirms the various behaviors observed in both the experimental and the numerical analyses, like the stabilizing effect of the longitudinal dispersivity or the destabilizing effect of the solute concentration
7

Transport de fluides miscibles à propriétés physiques variables en cellule Hele-Shaw.Comparaisons entre simulations numériques et mesures par LIF / Variable physical properties miscible fluids transport in Hele-Shaw cell. Comparison between numerical simulations and LIF measures

Mainhagu, Jon 01 July 2009 (has links)
L'étude décrite dans cette thèse porte sur l'injection ponctuelle d'une solution saline au sein d'une cellule dite de Hele-Shaw, afin de caractériser le comportement dispersif d'un polluant en milieu poreux. L'approche expérimentale employée est basée sur l'implémentation originale d'un dispositif de Fluorescence Induite par Laser (LIF) dans la cellule. La mise en place d'un protocole de mesure efficace permet de mener une analyse quantitative des résultats expérimentaux. En outre, en appliquant la méthode des moments, il est possible de caractériser avec précision le comportement dispersif de la zone de mélange de la solution injectée. Parallèlement aux expériences, à l'aide du code numérique FRIPE, les injections ont été simulées numériquement. L'analyse quantitative a été appliquée à ces dernières. Une comparaison poussée des résultats expérimentaux et numériques a donc été effectuée, du point de vue qualitatif mais aussi sur l'expression de la dispersion du panache de la zone de mélange de la solution / The study described in this thesis is about punctual injection of a saline solution inside a "Hele-Shaw cell" in order to characterize the dispersive behavior of a pollutant in porous media. The chosen experimental approach is based on the setup of an original Laser Induced Fluorescence (LIF) in the Hele-Shaw cell. The setting of the experimental apparatus allows quantitative data reduction of the experimental results. Moreover the "Moments Method" studied precisely the solution mixing dispersive behavior. Using the numerical code FRIPE the same injections have been simulated. The same quantitative data reductions have been applied to the numerical results. This led to an extensive comparison of the numerical and the experimental results, qualitatively but also of the dispersion in the mixing area of the injected solution
8

Apport de la stratigraphie séquentielle à la gestion et à la modélisation des ressources en eau des aquifères côtiers

Aunay, Bertrand 01 June 2007 (has links) (PDF)
Lieu de développement économique et démographique intense, les zones littorales font l'objet de pressions importantes sur l'environnement et, en particulier, sur les ressources en eau. Bien que la gestion des eaux souterraines côtières bénéficie de nombreux résultats issus de la recherche scientifique, une des problématiques majeures reste la connaissance de la géométrie des aquifères. Des interprétations géologiques de la genèse du bassin Plio-Quaternaire du Roussillon, issues de la stratigraphie séquentielle, sont confrontées, par l'intermédiaire d'une base données, à l'hydrogéologie de cet hydrosystème complexe localisé sur la partie littorale des Pyrénées-Orientales. L'étude statistique des points de prélèvement (distribution des crépines, productivité des forages...), l'analyse fonctionnelle (traitement du signal des chroniques piézométriques), l'hydrochimie et la géophysique électrique ont été utilisées afin d'élaborer un modèle conceptuel hydrogéologique des écoulements à l'échelle du bassin et de son prolongement vers le domaine offshore. La présence de la mer, de zones à salinité résiduelle et de cours d'eaux littoraux contribue à augmenter la salinité d'un aquifère libre supérieur (Quaternaire) sus-jacent aux différents aquifères captifs (Pliocène) exploités pour l'eau potable dans la zone littorale. La vulnérabilité face aux intrusions salines de cette ressource de bonne qualité, tant sur le point de vue quantitatif que qualitatif est appréhendée par modélisation. Dans le domaine offshore, le rôle protecteur des formations géologiques à faible et moyenne perméabilité est mis en évidence vis-à-vis de la préservation de la qualité de l'eau potable.
9

Méthodes numériques pour les écoulements et le transport en milieu poreux / Numerical methods for flow and transport in porous media

Vu Do, Huy Cuong 25 November 2014 (has links)
Cette thèse porte sur la modélisation de l’écoulement et du transport en milieu poreux ;nous effectuons des simulations numériques et démontrons des résultats de convergence d’algorithmes.Au Chapitre 1, nous appliquons des méthodes de volumes finis pour la simulation d’écoulements à densité variable en milieu poreux ; il vient à résoudre une équation de convection diffusion parabolique pour la concentration couplée à une équation elliptique en pression.Nous nous appuyons sur la méthode des volumes finis standard pour le calcul des solutions de deux problèmes spécifiques : une interface en rotation entre eau salée et eau douce et le problème de Henry. Nous appliquons ensuite la méthode de volumes finis généralisés SUSHI pour la simulation des mêmes problèmes ainsi que celle d’un problème de bassin salé en dimension trois d’espace. Nous nous appuyons sur des maillages adaptatifs, basés sur des éléments de volume carrés ou cubiques.Au Chapitre 2, nous nous appuyons de nouveau sur la méthode de volumes finis généralisés SUSHI pour la discrétisation de l’équation de Richards, une équation elliptique parabolique pour le calcul d’écoulements en milieu poreux. Le terme de diffusion peut être anisotrope et hétérogène. Cette classe de méthodes localement conservatrices s’applique àune grande variété de mailles polyédriques non structurées qui peuvent ne pas se raccorder.La discrétisation en temps est totalement implicite. Nous obtenons un résultat de convergence basé sur des estimations a priori et sur l’application du théorème de compacité de Fréchet-Kolmogorov. Nous présentons aussi des tests numériques.Au Chapitre 3, nous discrétisons le problème de Signorini par un schéma de type gradient,qui s’écrit à l’aide d’une formulation variationnelle discrète et est basé sur des approximations indépendantes des fonctions et des gradients. On montre l’existence et l’unicité de la solution discrète ainsi que sa convergence vers la solution faible du problème continu. Nous présentons ensuite un schéma numérique basé sur la méthode SUSHI.Au Chapitre 4, nous appliquons un schéma semi-implicite en temps combiné avec la méthode SUSHI pour la résolution numérique d’un problème d’écoulements à densité variable ;il s’agit de résoudre des équations paraboliques de convection-diffusion pour la densité de soluté et le transport de la température ainsi que pour la pression. Nous simulons l’avance d’un front d’eau douce assez chaude et le transport de chaleur dans un aquifère captif qui est initialement chargé d’eau froide salée. Nous utilisons des maillages adaptatifs, basés sur des éléments de volume carrés. / This thesis bears on the modelling of groundwater flow and transport in porous media; we perform numerical simulations by means of finite volume methods and prove convergence results. In Chapter 1, we first apply a semi-implicit standard finite volume method and then the generalized finite volume method SUSHI for the numerical simulation of density driven flows in porous media; we solve a nonlinear convection-diffusion parabolic equation for the concentration coupled with an elliptic equation for the pressure. We apply the standard finite volume method to compute the solutions of a problem involving a rotating interface between salt and fresh water and of Henry's problem. We then apply the SUSHI scheme to the same problems as well as to a three dimensional saltpool problem. We use adaptive meshes, based upon square volume elements in space dimension two and cubic volume elements in space dimension three. In Chapter 2, we apply the generalized finite volume method SUSHI to the discretization of Richards equation, an elliptic-parabolic equation modeling groundwater flow, where the diffusion term can be anisotropic and heterogeneous. This class of locally conservative methods can be applied to a wide range of unstructured possibly non-matching polyhedral meshes in arbitrary space dimension. As is needed for Richards equation, the time discretization is fully implicit. We obtain a convergence result based upon a priori estimates and the application of the Fréchet-Kolmogorov compactness theorem. We implement the scheme and present numerical tests. In Chapter 3, we study a gradient scheme for the Signorini problem. Gradient schemes are nonconforming methods written in discrete variational formulation which are based on independent approximations of the functions and the gradients. We prove the existence and uniqueness of the discrete solution as well as its convergence to the weak solution of the Signorini problem. Finally we introduce a numerical scheme based upon the SUSHI discretization and present numerical results. In Chapter 4, we apply a semi-implicit scheme in time together with a generalized finite volume method for the numerical solution of density driven flows in porous media; it comes to solve nonlinear convection-diffusion parabolic equations for the solute and temperature transport as well as for the pressure. We compute the solutions for a specific problem which describes the advance of a warm fresh water front coupled to heat transfer in a confined aquifer which is initially charged with cold salt water. We use adaptive meshes, based upon square volume elements in space dimension two.
10

Variable-Density Flow Processes in Porous Media On Small, Medium and Regional Scales

Walther, Marc 03 November 2014 (has links) (PDF)
Nowadays society strongly depends on its available resources and the long term stability of the surrounding ecosystem. Numerical modelling has become a general standard for evaluating past, current or future system states for a large number of applications supporting decision makers in proper management. In order to ensure the correct representation of the investigated processes and results of a simulation, verification examples (benchmarks), that are based on observation data or analytical solutions, are utilized to evaluate the numerical modelling tool. In many parts of the world, groundwater is an important resource for freshwater. While it is not only limited in quantity, subsurface water bodies are often in danger of contamination from various natural or anthropogenic sources. Especially in arid regions, marine saltwater intrusion poses a major threat to groundwater aquifers which mostly are the exclusive source of freshwater in these dry climates. In contrast to common numerical groundwater modelling, density-driven flow and mass transport have to be considered as vital processes in the system and in scenario simulations for fresh-saltwater interactions. In the beginning of this thesis, the capabilities of the modelling tool OpenGeoSys are verified with selected benchmarks to represent the relevant non-linear process coupling. Afterwards, variable-density application and process studies on different scales are presented. Application studies comprehend regional groundwater modelling of a coastal aquifer system extensively used for agricultural irrigation, as well as hydro-geological model development and parametrization. In two process studies, firstly, a novel method to model gelation of a solute in porous media is developed and verified on small scale laboratory observation data, and secondly, investigations of thermohaline double-diffusive Rayleigh regimes on medium scale are carried out. With the growing world population and, thus, increasing pressure on non-renewable resources, intelligent management strategies intensify demand for potent simulation tools and development of novel methods. In that way, this thesis highlights not only OpenGeoSys’ potential of density-dependent process modelling, but the comprehensive importance of variable-density flow and transport processes connecting, both, avant-garde scientific research, and real-world application challenges.

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