Dissertations / Theses on the topic 'Reactive porous flow'

Understanding the reactive-di usive turbulent ow inside porous media is interesting in many applications. It could have geochemical applications such as describing the rock dissolution patterns in river beds or the e ect of riparian zones in nitrate attenuation. Other applications could be, e.g. ow over and through vegetation, porous heat exchangers such as metal foams, gas and oil industry, etc. A limited number of studies have been carried out to understand the turbulent ow regime over a porous medium. This might be due to the fact that Darcy's law cannot be applied to turbulent ows. Therefore, the turbulent ow inside/above porous media needs to be done with expensive numerical simulations. This cost is much higher if one wants to solve the problem using Direct Numerical Simulation (DNS) in which the ow eld is completely and directly computed from Navier-Stokes equations. This needs much greater CPU power than other methods such as VANS(Volume-Averaged Navier-Stokes) equations or LES(Large Eddy Simulations), etc; however, solving the Navier-Stokes equation would eliminate any closure problems that appear in turbulence models, which could be considered as an advantage. Furthermore, DNS is able to detect the smallest length scales in turbulence structures which lead to highly accurate results. In addition to Navier-Stokes equations, scalar transport equation is also solved in order to model the transportation of reactive-di usive solutes. In our case, the porous medium is modeled by a packed bed of spheres and an Immersed Boundary Method (IBM) is used to apply the no-slip/no-penetration conditions on the spheres. The main objective of this work is to study how a reactive-di usive scalar is transported through porous media inspired by ows in river beds where micro-organisms and vegetation consume nutrients inside the ow besides the fact that porosity of the river beds a ect these activities as well as ow behavior.

Thesis (MSc)--Stellenbosch University, 2013.<br>ENGLISH ABSTRACT: Flow and reactive transport of chemical species is a very common phenomenon that occurs in natural and artificial systems. However in this study, the topic is related to acid mine drainage in the South African mining environment. Due to the hazards associated with acid mine drainage, prevention or treatment of mine effluent water before discharging to receiving waters and other environments is a necessity. A new time-dependent mathematical model is developed for a passive treatment method, based on multi-scale modelling of the coupled physico-chemical processes such as diffusion, convection, reactions and filtration, that are involved in the treatment process. The time-dependent model is simulated on a two-dimensional domain using finite volume discretization to obtain chemical species distributions.<br>AFRIKAANSE OPSOMMING: Vloei en reagerende transport van chemiese spesies is ’n baie algemene verskynsel wat in natuurlike en kunsmatige stelsels plaasvind. In hierdie studie is die onderwerp egter verwant aan suurmyndreinering in die Suid-Afrikaanse mynbou-omgewing. As gevolg van die gevare wat verband hou met suurmyndreinering, is die voorkoming of die behandeling van die afval-mynwater voor dit in opvangswaters en ander omgewings beland ’n noodsaaklikheid. ’n Nuwe tydafhanklike wiskundige model vir ’n passiewe behandelingsmetode is ontwikkel. Dit is gebaseer op die multi-skaal modulering van gekoppelde fisies-chemiese prosesse soos diffusie, konveksie, reaksies en filtrasie, wat by die behandelingsproses betrokke is. Die tydafhanklike model word gesimuleer op ’n twee-dimensionele domein met behulp van eindige volume diskretisasie om die verspreiding van chemiese spesies te bepaal.

In this work, we developed and applied computational methods for simulating flow, transport and reactive transport in porous media. This comprised four main components: single-phase flow calculation; chemical transport calculation; the coupling to reaction kinetics at mineral surfaces and resulting structural changes; and the use of parallel and GPU computing to make the calculation practicable on realistic rock geometries. Single phase flow was calculated using the Lattice Boltzmann (LB) method. We used the multi-relaxation-time (MRT) operator for its superior stability and viscosity-independence. A sparse memory approach was employed which improves the efficiency of calculations performed on low-permeability rock pore-space images. We also extended an idea proposed by Skordos in which the lattice Boltzmann densities were transformed to increase the number of floating point bits retained in the calculation. We showed that this enhances the numerical precision of the calculation considerably, where the original paper found no appreciable benefit. We showed how this now permits the 4-byte datatype to be used reliably in slow flowing, heterogeneous domains. The LB algorithm was implemented for the use of parallel GPUs (Graphics Processors) using the MPI (Message Passing Interface) and shown to give strong scaling on a cluster of 24 Tesla K40 GPUs. A study of single phase permeability on micro-CT images of sandstone and carbonate rock pore structures of varying degrees of heterogeneity was carried out. Good agreement with experiment was found for the simpler pore spaces, while discrepancies in the micro-porous samples was attributed to two causes: 1) the exclusion of flow through unresolved micro-porosity and 2) unrepresentative sample sizes used in the simulation. The effect of image resolution and segmentation was studied by comparing single phase permeability computed in 1) scans of the same volume obtained at different voxel sizes, individually segmented and 2) numerically coarsened images from a high resolution segmented image. Numerical coarsening from a high resolution segmented image was found to be much more consistent than 1) and was shown to preserve porosity and permeability down to lower voxel size images unlike the images scanned and segmented at different voxel sizes. Finally, representative elementary volume (REV) was investigated for the rock samples. A statistical method was used in which porosity and permeability were obtained from sub-volumes sampled from the domain. The convergence of these parameters with sub-volume size was used to obtain characteristic length scales and measures of heterogeneity. The image sizes used were found to be unrepresentative for the complex microporous carbonates. Transport curves (propagators) were computed in three different porous media samples of increasing heterogeneity (a bead-pack; sandstone; and carbonate) and found to agree with experiment. Questions about the origins of stagnant transport zones in the microporous carbonate were pursued by investigating the effects of image segmentation. The effects of the image segmentation techniques, in which grey-scale micro-porosity in a scanned pore image is binarised into fluid or mineral, were quantified by computing the fraction of trapped solute (stagnant zones) for segmentations of varying porosity. Physical differences between experiment and calculation were clarified, and we suggest alternative approaches for the treatment of micro-porous rocks. A pore-scale reactive flow model was put together by coupling flow calculation and solute transport methods with changes in pore-structure through chemical kinetics. Convection and diffusion in this model was solved using a finite-volume approach: a second order transport model with a flux limiter function made the model suitable for high Peclet number transport calculations. We also proposed a method for counteracting errors associated with the staircase representation of diagonal surfaces in the Cartesian grid in which exposed grid surfaces are associated with a rescaling factor. First order reaction kinetics were included at mineral surfaces and the dissolution of a sphere was shown to give different dissolution profiles with different dimensionless transport and reaction parameters. The dissolution model was applied to the reaction between HCl acid and calcite mineral under the assumption that products of the reaction could be neglected. An experimental system in which HCl acid was injected through a flow cell containing a calcite block was simulated and the normalised volume of undissolved calcite was compared with the experimental data, as well as resulting morphologies obtained by micro-CT scanning. Good agreement with the experimental dissolution rate was obtained, however some differences in the resulting morphologies were found. This was attributed to neglecting the influence of product ions on the diffusion behaviour of the reactant and was discussed. By obtaining the concentration of H+ reactant on the surface of calcite block, the process could be concluded to be strongly transport-controlled. This enabled the definition of a new effective Damkohler number in terms of the reactant surface concentration which no longer required approximating length scales or separating convection or diffusion rates. Finally, the dissolution of a Ketton carbonate sample was computed. The injection process mirrored that of a strong acid flowing through the pore-space at a given flow rate, and having an intrinsic surface reaction rate with the rock mineral. It was found that the flow rate strongly affected the resulting dissolution pattern, in line with experimental observation. This lead to drastically altered flow properties, including single-phase permeability which was quantified.

Tableau d’honneur de la Faculté des études supérieures et postdoctorales, 2005-2006<br>Un modèle numérique tridimensionnel a été développé pour la simulation du système chimique quartz-eau couplé avec l’écoulement à densité et viscosité variable dans les milieux poreux discrètement fracturés. Le nouveau modèle simule aussi le transfert de chaleur dans les milieux poreux fracturés en supposant que l’expansion thermique du milieu est négligeable. Les propriétés du fluide, densité et viscosité, ainsi que les constantes chimiques (constant de taux de dissolution, constant d’équilibre, coefficient d’activité) sont calculées en fonction de la concentration des ions majeurs et de la température. Des paramètres de réaction et d’écoulement, comme la surface spécifique du minéral et la perméabilité sont mis jour à la fin de chaque pas de temps avec des taux de réaction explicitement calculés. Le modèle suppose que des changements de la porosite et des ouvertures de fractures n’ont pas d’impact sur l’emmagasinement spécifique. Des pas de temps adaptatifs sont utilisés pour accélérer et ralentir la simulation afin d’empêcher des résultats non physiques. Les nouveaux incréments de temps dépendent des changements maximum de la porosité et/ou de l’ouverture de fracture. Des taux de réaction au niveau temporel L+1 (schéma de pondération temporelle implicite) sont utilisés pour renouveler tous les paramètres du modèle afin de garantir la stabilité numérique. Le modèle a été vérifié avec des problèmes analytiques, numériques et physiques de l’écoulement à densité variable, transport réactif et transfert de chaleur dans les milieux poreux fracturés. La complexité de la formulation du modèle permet d’étudier des réactions chimiques et l’écoulement à densité variable d’une façon plus réaliste qu’auparavant possible. En premier lieu, cette étude adresse le phénomène de l’écoulement et du transport à densité variable dans les milieux poreux fracturés avec une seule fracture à inclinaison arbitraire. Une formulation mathématique générale du terme de flottabilité est dérivée qui tient compte de l’écoulement et du transport à densité variable dans des fractures de toute orientation. Des simulations de l’écoulement et du transport à densité variable dans une seule fracture implanté dans une matrice poreuse ont été effectuées. Les simulations montrent que l’écoulement à densité variable dans une fracture cause la convection dans la matrice poreuse et que la fracture à perméabilité élevée agit comme barrière pour la convection. Le nouveau modèle a été appliqué afin de simuler des exemples, comme le mouvement horizontal d’un panache de fluide chaud dans un milieu fracturé chimiquement réactif. Le transport thermohalin (double-diffusif) influence non seulement l’écoulement à densité variable mais aussi les réactions chimiques. L’écoulement à convection libre dépend du contraste de densité entre le fluide (panache chaud ou de l’eau salée froide) et le fluide de référence. Dans l’exemple, des contrastes de densité sont généralement faibles et des fractures n’agissent pas comme des chemins préférés mais contribuent à la dispersion transverse du panache. Des zones chaudes correspondent aux régions de dissolution de quartz tandis que dans les zones froides, la silice mobile précipite. La concentration de silice est inversement proportionnelle à la salinité dans les régions à salinité élevée et directement proportionnelle à la température dans les régions à salinité faible. Le système est le plus sensible aux inexactitudes de température. Ceci est parce que la température influence non seulement la cinétique de dissolution (équation d’Arrhenius), mais aussi la solubilité de quartz.<br>A three-dimensional numerical model is developed that couples the quartz-water chemical system with variable-density, variable-viscosity flow in fractured porous media. The new model also solves for heat transfer in fractured porous media, under the assumption of negligible thermal expansion of the rock. The fluid properties density and viscosity as well as chemistry constants (dissolution rate constant, equilibrium constant and activity coefficient) are calculated as a function of the concentrations of major ions and of temperature. Reaction and flow parameters, such as mineral surface area and permeability, are updated at the end of each time step with explicitly calculated reaction rates. The impact of porosity and aperture changes on specific storage is neglected. Adaptive time stepping is used to accelerate and slow down the simulation process in order to prevent physically unrealistic results. New time increments depend on maximum changes in matrix porosity and/or fracture aperture. Reaction rates at time level L+1 (implicit time weighting scheme) are used to renew all model parameters to ensure numerical stability. The model is verified against existing analytical, numerical and physical benchmark problems of variable-density flow, reactive solute transport and heat transfer in fractured porous media. The complexity of the model formulation allows chemical reactions and variable-density flow to be studied in a more realistic way than previously possible. The present study first addresses the phenomenon of variable-density flow and transport in fractured porous media, where a single fracture of an arbitrary incline can occur. A general mathematical formulation of the body force vector is derived, which accounts for variable-density flow and transport in fractures of any orientation. Simulations of variable-density flow and solute transport are conducted for a single fracture, embedded in a porous matrix. The simulations show that density-driven flow in the fracture causes convective flow within the porous matrix and that the highpermeability fracture acts as a barrier for convection. The new model was applied to simulate illustrative examples, such as the horizontal movement of a hot plume in a chemically reactive fractured medium. Thermohaline (double-diffusive) transport impacts both buoyancy-driven flow and chemical reactions. Free convective flow depends on the density contrast between the fluid (hot brine or cool saltwater) and the reference fluid. In the example, density contrasts are generally small and fractures do not act like preferential pathways but contribute to transverse dispersion of the plume. Hot zones correspond to areas of quartz dissolution while in cooler zones, precipitation of imported silica prevails. The silica concentration is inversely proportional to salinity in high-salinity regions and directly proportional to temperature in low-salinity regions. The system is the most sensitive to temperature inaccuracy. This is because temperature impacts both the dissolution kinetics (Arrhenius equation) and the quartz solubility.

Dans cette thèse, nous développons le modèle phénoménologique optimisé de lessivage chimique in situ (ISL) de l'uranium par l'injection d'acide sulfurique, en prenant en compte la précipitation des espèces non-solubles telles que le gypse, qui réduisent la récupération de l'uranium. Le modèle proposé décrit le transport de masse avec des réactions chimiques hétérogènes entre le liquide et les roches solides, qui mènent à la dissolution des oxydes d'uranium et à la récupération de l'uranium sous forme liquide. Ce modèle comprend à la fois des réactions utiles, qui décrivent la dissolution de divers types d'oxydes d'uranium, et les réactions néfastes qui conduisent à la précipitation des sédiments solides (gypse), dont les flocons couvrent la surface de canaux poreux et réduisent l'efficacité des réactions utiles. Parmi les résultats qualitatifs, nous avons révélé l'existence d'un taux critique de sédimentation de gypse, en dessous duquel la récupération ultime de l'uranium est complète. En revanche, elle tend à une valeur limite inférieure à 100% lorsque le taux de sédimentation est supérieur à la valeur critique. Ce taux de récupération limite dépend de divers paramètres du processus. La théorie et la méthodologie développées dans ce travail peuvent être facilement étendues et appliquées aux autres types de minerais qui sont récupérés par la méthode de lessivage in situ, et autres types de solvant<br>In the present thesis we develop the optimized phenomenological model of in-situ chemical leaching (ISL) of uranium by the injection of sulfuric acid, with special account for the precipitation of non-soluble species as gypsum, which reduces the uranium recovery. The suggested model describes the mass transport with heterogeneous chemical reactions between liquid and solid rocks, leading to dissolve uranium oxides and recover uranium in liquid form. It includes both useful reactions, describing the dissolution of various kinds of uranium oxides, and detrimental reactions, leading to the precipitation of solid sediments (gypsum), whose flakes cover the surface of porous channels and reduce the efficiency of useful reactions. Among the qualitative results we revealed the existence of a critical rate of gypsum sedimentation, below which the ultimate uranium recovery is complete. In contrast, it tends to a limit value lower than 100% when the sedimentation rate is higher than the critical value. This limit recovery depends on various parameters of the process. The theory and the methodology developed in this work can be easily extended and applied on other type of ores that are recovered by in-situ leaching method and other types of solvents

La modélisation du transport réactif est utilisée dans de nombreuses applications énergétiques et environnementales liées aux écoulements souterrains. La modélisation de tels problèmes conduit à un système hautement non linéaire d'EDP couplées à des équations différentielles ordinaires ou algébriques. Deux types d'approches pour la résolution numérique des problèmes de transport réactif sont largement utilisés dans la littérature. L'une est l'approche de séparation des opérateurs qui consiste à découpler les problèmes d'écoulement et de transport réactif. Ces derniers sont résolus séquentiellement à chaque pas de temps. L'autre stratégie est basée sur une approche entièrement couplée dans laquelle le système entier est résolu simultanément. Le but de la thèse de doctorat est le développement d'un schéma implicite en volumes finis pour la modélisation numérique d'écoulements multicomposants monophasiques et diphasiques avec transport réactif en milieu poreux.Deux nouveaux modules de transport réactif seront implémentés dans DuMuX, un simulateur libre pour les problèmes d'écoulements et de transport dans les milieuw poreux. Des simulations numériques bi et tridimensionnels comprenant des benchmarks et du calcul haute performance, seront effectuées pour valider les modules<br>Reactive transport modeling is used in many energy and environmental applications related to subsurface flows. Modeling such problems leads to a highly nonlinear system of PDEs coupled with algebraic or ODEs. Two types of approaches for the numerical solving of reactive transport problems are widely used in the literature. One is the operator-splitting approach which consists in splitting the flow and reactive transport problems. These latter are solved sequentially at each time step. The other strategy is based on the fully coupled approach in which the entire system is solved simultaneously. The goal of the PhD thesis is the development of a fully coupled fully implicit finite volume scheme for numerical modeling of single and two-phase multicomponent flows with reactive transport in porous media. New reactive transport modules will be implemented in DuMuX, a free and open-source simulator for flow and transport processes in porous media. Numerical simulations for 2D and 3D including benchmark tests and high performance computing will be performed to validate the modules

Ce travail vise à étudier le couplage entre écoulement et interactions physico-chimiques dans les sols, dans différentes conditions de saturation en eau, afin d’améliorer la prédiction du devenir des polluants. Il s’agit de comprendre en quoi le taux de saturation du milieu affecte la réactivité du sol vis-à-vis des polluants, et d’évaluer le pouvoir prédictif du transport de solutés réactifs étudié en milieu saturé sur la réactivité en conditions non saturées. Différents processus sont considérés : l’échange de cations calcium-zinc sur un milieu poreux modèle (sable-kaolinite), la sorption et désorption d’un composé organique sur une terre non contaminée, le transport de polluants prioritaires tels que les HAP sur une terre de friche industrielle. Dans chaque cas, des expériences en colonne de laboratoire ont été conduites en conditions d’écoulement saturé et non saturé permanent, permettant tout d’abord la caractérisation de l’hydrodynamique, puis l’étude du couplage avec la réactivité. Les courbes de percée obtenues ont été ensuite modélisées avec des codes tels que CXTFIT. On a montré l’influence de la teneur en eau du milieu sur le transport réactif, variable suivant le type de réaction considéré, la structure des milieux jouant également un rôle important. L’échange d’ions sur le milieu modèle n’est globalement pas affecté par la teneur en eau, dans une gamme proche de la saturation. En revanche, une plus forte sorption et une plus faible mobilisation des polluants organiques ont été observées en conditions non saturées. Le transport réactif de ces composés ne peut donc pas être prédit en conditions non saturées à partir de mesures en milieu saturé, qui peuvent surestimer le transport<br>The aim of this work was to study the link between water flow and physical and chemical interactions in soils under variably water flow conditions, in order to improve the prediction of contaminants fate. It deals with understanding how the porous media water content can modify soil reactivity towards contaminants, and assessing the possibility to predict reactivity under unsaturated conditions with reactive solute transport studied in saturated porous media. Various processes were considered: cations exchange calcium-zinc on a model porous media (sand-kaolinite), sorption and desorption of an organic compound on a non polluted soil, transport of priority contaminants such as PAHs on an industrial contaminated soil. In each case, experiments were carried out with soil columns at the laboratory scale under saturated and unsaturated steady-state flow conditions, in order to characterize at first hydrodynamics and then to study the link with reactivity. Modeling of the breakthrough curves was then performed with codes such as CXTFIT. We showed an influence of porous media water content on reactive transport which was different as a function of the interaction. Porous media structure must also be taken into account. Ions exchange on a model porous media was not globally modified by the water content varying in a range close to saturation. On the contrary, higher sorption and lower migration of organic contaminants were observed under unsaturated conditions. Reactive transport of these compounds cannot therefore be predicted under unsaturated conditions with tests performed on saturated porous media which may overestimate transport

Environmental noise has for decades been a well known problem, especially in urban areas. As noise requirements for vehicles are sharpened, noise reducing concepts are needed in early design stages requiring accurate simulations to support the design. Specifically for optimization of noise treatments, the absorber performance must be simulated correctly. So called noise encapsulations are placed below the powertrain on heavy vehicles to enclose the engine and reduce noise radiation. The attenuation of the absorbers on these shields must be represented correctly in simulations, even in environments with complex sound field, cooling flow and high temperature variations which may affect the absorber performance. This thesis studies the performance variation due to different absorber representations and due to these factors and how to include this in simulations. It is shown that the material representation significantly affects the attenuation performance in the simulations. Assuming locally reacting absorbers neglects the full interaction between the sound field and the material, which was shown to affect the noise reduction considerably. A measurement method to determine the angular dependent surface impedance was evaluated. It was shown sensitive to small samples and a method to improve accuracy was suggested. Including the angular dependence, either by full resolution or an angular dependent impedance, the field-absorber interaction is included in the simulations and more accurate results are obtained. The influence of flow and temperature fields on the absorber performance was also investigated. A method to include these effects was developed and the attenuation performance shown significant, especially for materials with bulk reaction. In conclusion, thorough knowledge of the material behavior and the field in the applications is required to choose appropriate material representation to enable reliable simulation results.​<br><p>QC 20160311</p>

Les processus magmatiques qui régissent l'accrétion crustale au niveau des dorsales médio-océaniques à expansion lente restent à l'heure actuelle mal contraints. Parmi les processus potentiellement impliqués dans l'évolution des réservoirs de magma de la croûte inférieure, les réactions associées à des écoulements poreux réactifs au travers de bouillies cristallines - ou mush - tendent à supplanter les processus classiques de cristallisation simple des magmas. La part de ces processus dans la formation des gabbros cumulatifs de base de croûte est dépendante des modes de migration des liquides, qui sont eux-mêmes corrélés à la géométrie des réservoirs considérés. En combinant des études structurales, pétrographiques et géochimiques à haute résolution de sections in situ forées dans un corps complexe océanique de la dorsale Sud-Ouest indienne, j'ai pu apporter de nouvelles contraintes sur les modes de formation et d'évolution des réservoirs magmatiques impliqués lors de l'accrétion crustale. Le modèle de réservoir développé est généralisable, au moins en partie, à d'autres portions de croûte inférieure océanique. Ce modèle, ainsi que les nouvelles contraintes de l'étude expérimentale couplée des processus de cristallisation, ouvre la voie vers de nouvelles quantifications des processus d'interaction liquides-roches dans la différenciation des lithologies gabbroïques, et de manière plus générale dans l'évolution des liquides magmatiques de la croûte océanique. Ces développements vont de pair avec l'évolution au cours des dernières décennies de la vision des systèmes magmatiques crustaux, passant de chambres magmatiques constituées de liquides vers des modèles de réservoirs magmatiques majoritairement constitués de mush cristallins<br>Magmatic processes that govern crustal accretion at mid-ocean ridges still need to be better constrained. Among the processes potentially involved in the evolution of the lower crust magma reservoirs, reactions associated with reactive porous flow through crystal mushes tend to be considered as one of the predominant processes together with simple crystallization of magmas. The share of these processes during magma differentiation is dependent on the modes of melt migration and is thus correlated to the geometry of the reservoirs considered. By combining high-resolution structural, petrographic and geochemical studies of in situ sections drilled in an oceanic core complex of the Southwest Indian Ridge, I was able to bring new constraints on the formation and evolution of magmatic reservoirs involved in crustal accretion. All or part of the igneous reservoir model developed herein can be applied to other sections of lower oceanic crust. This model, together with additional constraints obtained by the coupled experimental petrology study of crystallization processes, paves the way for new quantifications of the involvement of melt-rock reactions in the differentiation of gabbroic lithologies, and more generally in the evolution of melts within the oceanic crust. Those developments are consistent with the constant evolution in recent decades of the understanding of crustal magmatic systems, which shifted from melt-filled magma chambers to igneous reservoir models mostly composed of crystal mushes

Le présent travail consiste en l'étude et la modélisation d'un procédé dans lequel un réacteur hétérogène est traversé, à débit variable, par un gaz sous haute pression (plusieurs centaines de bars) provenant d'un réservoir fermé. Le gaz, qui réagit avec le solide poreux de manière exothermique, est collecté, à sa sortie du réacteur, dans un second réservoir initialement vide, connecté au réacteur par un tube long et de faible section. Un modèle et un outil de simulation du procédé, prenant en compte le couplage du transfert de matière avec la réaction chimique et le transfert thermique, ont été développés. Les paramètres physico-chimiques qui caractérisent le système et interviennent dans le modèle ont été mesurés (perméabilité et conductivité thermique effective du réacteur, cinétiques d'échange de matière, dispersion axiale, construction de la courbe de Van Deemter à vitesse variable). Une maquette instrumentée du procédé, incluant le couplage du réacteur et d'un spectromètre de masse quadripolaire, a été mise au point. Ce dispositif, qui permet de suivre en continu la pression, la température et la composition du système au cours de la détente rapide du gaz, a été utilisé pour valider le modèle. L’outil de simulation a été exploité pour étudier la sensibilité du procédé à certains paramètres opératoires (pression initiale du gaz, porosité du réacteur, etc. . . . ). Les simulations ont de plus permis de prévoir l'influence de la dégradation du solide poreux sur les performances du système.

Les activités humaines dans la subsurface se développent rapidement (stockage de déchets,nouvelles techniques minières, stockage à haute fréquence de l’énergie), alors que dans le même temps les attentes du public et des autorités s’intensifient. L’évaluation de chaque étape de ces opérations souterraines repose sur des études détaillées de la sûreté et des impacts environnementaux.Elles reposent sur des simulateurs élaborés et sur de la modélisation multiphysique. Avec leur approche orientée processus, les simulations en transport réactifs proposent une méthode efficace pour comprendre et prévoir le comportement de ces systèmes complexes, à différentes échelles de temps et d’espace.Le but de ce travail est d’intégrer la résolution de l’écoulement diphasique compressible dans le cadre de codes de transport réactifs à l’aide d’une méthode de séparation d’opérateurs. Un module multiphasique a été créé dans le code de transport réactif HYTEC. Une nouvelle approche a ensuite été développée pour coupler écoulement multicomposant multiphasique compressible, description de propriétés thermo-dynamiques complexes pour les fluides, avec des codes de transport réactif. La méthode a été intégrée dans HYTEC. Des cas de validation sont proposés, puis des exemples d’application pour la simulation du stockage souterrain de CO2 et des impuretés associées<br>Human activity in the subsurface has rapidly been expanding and diversifying (waste disposal, new mining technologies, high-frequency storage of energy), while the public and regulatory expectations keep growing. The assessment of each step of underground operations requires careful safety and environmental impact evaluations. They rely on elaborate simulators and multiphysics modeling. With its process-based approach, reactive transport simulation provides an effective way to understand and predict the behavior of such complex systems at different time and spatial scale.This work aims at incorporating a compressible multiphase flow into conventional reactive transport framework by an operator splitting approach. A multiphase flow module is developed in the HYTEC reactive transport software. A new approach is then developed to fully couple multiphase multicomponent compressible flow, the complex thermodynamic description of the fluid properties, with existing reactive transport codes. The method is implemented in HYTEC. Some validation is provided, before application to the simulation of underground storage of CO2 and associated impurities

Les travaux de cette thèse portent sur des méthodes de volumes finis sur maillages quelconque pour la discrétisation de problèmes d'évolution non linéaires modélisant le transport de contaminants en milieu poreux et les écoulements diphasiques.Au Chapitre 1, nous étudions une famille de schémas numériques pour la discrétisation d'une équation parabolique dégénérée de convection-reaction-diffusion modélisant le transport de contaminants dans un milieu poreux qui peut être hétérogène et anisotrope. La discrétisation du terme de diffusion est basée sur une famille de méthodes qui regroupe les schémas de volumes finis hybrides, de différences finies mimétiques et de volumes finis mixtes. Le terme de convection est traité à l'aide d'une famille de méthodes qui s'appuient sur les inconnues hybrides associées aux interfaces du maillage. Cette famille contient à la fois les schémas centré et amont. Les schémas que nous étudions permettent une discrétisation localement conservative des termes d'ordre un et d'ordre deux sur des maillages arbitraires en dimensions d'espace deux et trois. Nous démontrons qu'il existe une solution unique du problème discret qui converge vers la solution du problème continu et nous présentons des résultats numériques en dimensions d'espace deux et trois, en nous appuyant sur des maillages adaptatifs.Au Chapitre 2, nous proposons un schéma de volumes finis hybrides pour la discrétisation d'un problème d'écoulement diphasique incompressible et immiscible en milieu poreux. On suppose que ce problème a la forme d'une équation parabolique dégénérée de convection-diffusion en saturation couplée à une équation uniformément elliptique en pression. On considère un schéma implicite en temps, où les flux diffusifs sont discrétisés par la méthode des volumes finis hybride, ce qui permet de pouvoir traiter le cas d'un tenseur de perméabilité anisotrope et hétérogène sur un maillage très général, et l'on s'appuie sur un schéma de Godunov pour la discrétisation des flux convectifs, qui peuvent être non monotones et discontinus par rapport aux variables spatiales. On démontre l'existence d'une solution discrète, dont une sous-suite converge vers une solution faible du problème continu. On présente finalement des cas test bidimensionnels.Le Chapitre 3 porte sur un problème d'écoulement diphasique, dans lequel la courbe de pression capillaire admet des discontinuité spatiales. Plus précisément on suppose que l'écoulement prend place dans deux régions du sol aux propriétés très différentes, et l'on suppose que la loi de pression capillaire est discontinue en espace à la frontière entre les deux régions, si bien que la saturation de l'huile et la pression globale sont discontinues à travers cette frontière avec des conditions de raccord non linéaires à l'interface. On discrétise le problème à l'aide d'un schéma, qui coïncide avec un schéma de volumes finis standard dans chacune des deux régions, et on démontre la convergence d'une solution approchée vers une solution faible du problème continu. Les test numériques présentés à la fin du chapitre montrent que le schéma permet de reproduire le phénomène de piégeage de la phase huile.

In the mantle section of many ophiolite sequences, dunite dikes are present. Around dunite dikes at the Josephine and Trinity ophiolite, a sequence of lithologies consisting of plagioclase lherzolite, lherzolite, and harzburgite is present. This sequence of rocks has been interpreted to be the result of reactive porous flow. From trace element data, the mafic melt has been interpreted to flow both into and out of the dunite dikes. Whether the melt emanates from the dunite bodies or is collected by them has implications for the mechanisms of melt extraction beneath ridge systems. The determination of the flow direction based on tracer distributions is difficult and therefore additional constraints are important. Reactive transport theory predicts that lithological zonations around dunite bodies can indicate the direction of flow. To date no reactive transport model has been developed to test these hypotheses, and therefore I have built a reactive transport model using COMSOL v. 4.1. I developed a model for an orthopyroxene dissolution front based on the model of Chadam et al. (1986, Reactive infiltration instabilities, IMA Journal of Applied Mathematics, v. 36, p.207-221). This model includes the strong nonlinearity feedback that has been invoked to lead to the channelization of melt flow. The instability leads to the formation of elongated regions where orthopyroxene is depleted. This model predicts that the melt is focused into the dunite bodies, most flow is parallel to the dunite boundaries, and exits the fingers at the tip of the column.<br>text

CO₂ injection in oil reservoirs provides the dual benefit of increasing oil recovery as well as sequestration. Compositional simulations using phase behavior calculations are used to model miscibility and estimate oil recovery. The injected CO₂, however, is known to react with brine. The precipitation and dissolution reactions, especially with carbonate rocks, can have undesirable consequences. The geochemical reactions can also change the mole numbers of components and impact the phase behavior of hydrocarbons. A Gibbs free energy framework that integrates phase equilibrium computations and geochemical reactions is presented in this dissertation. This framework uses the Gibbs free energy function to unify different phase descriptions - Equation of State (EOS) for hydrocarbon components and activity coefficient model for aqueous phase components. A Gibbs free energy minimization model was developed to obtain the equilibrium composition for a system with not just phase equilibrium (no reactions) but also phase and chemical equilibrium (with reactions). This model is adaptable to different reservoirs and can be incorporated in compositional simulators. The Gibbs free energy model is used for two batch calculation applications. In the first application, solubility models are developed for acid gases (CO₂ /H2 S) in water as well as brine at high pressures (0.1 - 80 MPa) and high temperatures (298-393 K). The solubility models are useful for formulating acid gas injection schemes to ensure continuous production from contaminated gas fields as well as for CO₂ sequestration. In the second application, the Gibbs free energy approach is used to predict the phase behavior of hydrocarbon mixtures - CO₂ -nC₁₄ H₃₀ and CH₄ -CO₂. The Gibbs free energy model is also used to predict the impact of geochemical reactions on the phase behavior of these two hydrocarbon mixtures. The Gibbs free energy model is integrated with flow using operator splitting to model an application of cation exchange reactions between aqueous phase and the solid surface. A 1-D numerical model to predict effluent concentration for a system with three cations using the Gibbs free energy minimization approach was observed to be faster than an equivalent stoichiometric approach. Analytical solutions were also developed for this system using the hyperbolic theory of conservation laws and are compared with experimental results available at laboratory and field scales.<br>text

A mathematical model has been developed to describe the simultaneous transport of water, heat, and multicomponent reactive chemicals in saturated-unsaturated subsurface soils. The water movement equation takes into account vapor transport in the unsaturated zone, as well as the fluxes caused by the gradients of temperature and solute concentration. The solute transport equations are formulated in terms of the total analytical concentration of each component species. Chemical reactions that can be dealt with in this model include complexation, acid base reaction, ion exchange, and precipitation-dissolution. The mathematical model has been solved by the Galerkin finite element method. The chemical transport equations are solved sequentially and separately from the chemical reaction equations, which are solved by the Newton-Raphson method. An iterative procedure is used among water flow equation, heat transfer equation, solute transport equations and chemical reaction equations. Three methods of solving the resulting systems of linear equations are implemented: the banded matrix method, the sparse matrix method, and the iterative methods. Two efficient and reliable iterative methods are provided: the conjugate gradient method for symmetric matrix equations and the bi-conjugate gradient squared method for general nonsymmetric matrix equations. The chemical system can be considered as either an open or a closed system. It has been demonstrated that the computer model can be used to solve one-, two-, and three dimensional problems. The model was used to simulate processes of salinization and leaching of soils under irrigation with realistic conditions. The soil solution included 48 chemical species in total. The computer model was used to simulate salinization of the soil if the irrigation rate was set equal to the crop uptake so that there was no leaching taking place. The simulation continued with increased rate and improved quality of irrigation water so that leaching of the saline soil took place. During both stages of the simulation, the computer model was shown to provide reason able results as how the dissolved concentrations changed in the soil solution during the salinization and leaching processes, how the composition on the exchange sites adjusted to new equilibrium, and how minerals dynamically precipitated and dissolved depending on degree of saturation of the soil solution with respect to each mineral.

Non-isothermal compositional two-phase flow is considered to be one of the fundamental physical processes in the field of water resources research. The strong non-linearity and discontinuity emerging from phase transition phenomena pose a serious challenge for numerical modeling. Recently, Lauser et al.[1] has proposed a numerical scheme, namely the Nonlinear Complementary Problem (NCP), to handle this strong non-linearity. In this work, the NCP is implemented at both local and global levels of a Finite element algorithm. In the former case, the NCP is integrated into the local thermodynamic equilibrium calculation. While in the latter one, it is formulated as one of the governing equations. The two different formulations have been investigated through several well established benchmarks and analyzed for their efficiency and robustness. In the second part of the thesis, the presented numerical formulations are applied for application and process studies in the context of nuclear waste disposal in Switzerland. Application studies comprehend the coupling between multiphase transport model and complex bio-geo-chemical process to investigate the degradation of concrete material due to two major reactions: carbonation and Aggregate Silica Reaction(ASR). The chemical processes are simplified into a lookup table and cast into the transport model via source and sink term. The efficiency and robustness of the look-up table are further compared with a fully reactive transport model.

La modélisation du transport réactif est utilisée dans de nombreuses applications énergétiques et environnementales liées aux écoulements souterrains. La modélisation de tels problèmes conduit à un système hautement non linéaire d'EDP couplées à des équations différentielles ordinaires ou algébriques. Deux types d'approches pour la résolution numérique des problèmes de transport réactif sont largement utilisés dans la littérature. L'une est l'approche de séparation des opérateurs qui consiste à découpler les problèmes d'écoulement et de transport réactif. Ces derniers sont résolus séquentiellement à chaque pas de temps. L'autre stratégie est basée sur une approche entièrement couplée dans laquelle le système entier est résolu simultanément. Le but de la thèse de doctorat est le développement d'un schéma implicite en volumes finis pour la modélisation numérique d'écoulements multicomposants monophasiques et diphasiques avec transport réactif en milieu poreux.Deux nouveaux modules de transport réactif seront implémentés dans DuMuX, un simulateur libre pour les problèmes d'écoulements et de transport dans les milieuw poreux. Des simulations numériques bi et tridimensionnels comprenant des benchmarks et du calcul haute performance, seront effectuées pour valider les modules<br>Reactive transport modeling is used in many energy and environmental applications related to subsurface flows. Modeling such problems leads to a highly nonlinear system of PDEs coupled with algebraic or ODEs. Two types of approaches for the numerical solving of reactive transport problems are widely used in the literature. One is the operator-splitting approach which consists in splitting the flow and reactive transport problems. These latter are solved sequentially at each time step. The other strategy is based on the fully coupled approach in which the entire system is solved simultaneously. The goal of the PhD thesis is the development of a fully coupled fully implicit finite volume scheme for numerical modeling of single and two-phase multicomponent flows with reactive transport in porous media. New reactive transport modules will be implemented in DuMuX, a free and open-source simulator for flow and transport processes in porous media. Numerical simulations for 2D and 3D including benchmark tests and high performance computing will be performed to validate the modules

In this study we are concerned with the modelling of multi-component, multiphase chemically reacting flows in porous media, with particular application to the spontaneous combustion of coal and the extraction of coalbed methane. These two related problems involve complex multiphase, multi-component flow in a porous medium. Chemical reactions, adsorption, gaseous diffusion and changes in porosity and permeability are important in one or both of these problems. These matters are discussed in general in the first few chapters of the thesis. Several models for the spontaneous combustion of coal that include the effect of a diminishing reaction rate are investigated and a new formulation in the form of a generic power law model is introduced. A numerical module for modelling the spontaneous combustion of coal is described, based on the TOUGH2 code. A new equation of state (EOS) module is developed including realistic physical properties for all gases involved. The modified version of TOUGH2 is used for modelling the adiabatic method for testing the reactivity of coal samples. The results agree very well with experimental measurements for coal samples from different mines in New Zealand and Australia. Moisture effect on the reaction rate was then introduced to TOUGH2 using a new twophase EOS module with water and air broken into its main components (Nitrogen, Oxygen, Carbon dioxide and Argon). Finally the production of methane from low rank coalbeds is investigated. A new EOS for mixture of water and methane is developed and incorporated into the TOUGH2 code to produce a new and versatile coalbed methane simulator. It is validated by running some simple test problems and comparing results with those obtained with the commercial COMET simulator.

MSc (Mathematics)<br>Department of Mathematics and Applied Mathematics<br>The unsteady hydromagnetic chemically reacting mixed convection MHD ow over a permeable stretching sheet embedded in a porous medium with thermal radiation and heat source/sink is investigated numerically. The original partial di erential equations are converted into ordinary di erential equations by using similarity transformation. The governing non-linear partial di erential equations of Momentum, Energy, and Concentration are considered in this study. The e ects of various physical parameters on the velocity, temperature, and species concentration have been discussed. The parameters include the Prandtl number (Pr), Magnetic parameter (M), the Schmidt number (Sc), Unsteady parameter (A), buoyancy forces ratio parameter (N), Chemical reaction (K), Radiation parameter (Nr), Eckert number (Ec), local heat source/sink parameter (Q) and buoyancy parameter due to temperature ( ). The coe cient of Skin friction and Heat transfer are investigated. The coupled non-linear partial di erential equations governing the ow eld have been solved numerically using the Spectral Relaxation Method (SRM). The results that are obtained in this study are then presented in tabular forms and on graphs and the observations are discussed.<br>NRF