This thesis focuses on solutions of reactive transport problems in porous media. The principle mechanisms of flow and reactive mass transport in porous media are investigated. Global implicit approach (GIA), where transport and reaction are fully coupled, and sequential noniterative approach (SNIA) are implemented into the software OpenGeoSys (OGS6) to couple chemical reaction and mass transport. The reduction scheme proposed by Kräutle is used in GIA to reduce the number of coupled nonlinear differential equations. The reduction scheme takes linear combinations within mobile species and immobile species and effectively separates the reaction-independent linear differential equations from coupled nonlinear ones (i.e. reducing the number of primary variables in the nonlinear system). A chemical solver is implemented using semi-smooth Newton iteration which employs complementarity condition to solve for equilibrium mineral reactions. The results of three benchmarks are used for code verification. Based on the solutions of these benchmarks, it is shown that GIA with the reduction scheme is faster (ca. 6.7 times) than SNIA in simulating homogeneous equilibrium reactions and (ca. 24 times) in simulating kinetic reaction. In simulating heterogeneous equilibrium mineral reactions, SNIA outperforms GIA with the reduction scheme by 4.7 times.:Declaration of Authorship iii Acknowledgements iv Abstract v List of Figures viii Symbols ix 1 Introduction 1 1.1 State of the Art 1 1.2 Thesis Objectives 3 1.3 Thesis Outline 4 2 Mathematical Models 5 2.1 Introduction 5 2.2 Mass Balance Equations 5 2.2.1 Groundwater Flow 6 2.2.2 Mass Transport 7 2.2.3 Chemical Reaction 8 2.2.3.1 Equilibrium Reaction 8 2.2.3.2 Kinetic Reaction 10 2.3 Reactive Mass Transport 10 2.4 Initial and Boundary Conditions 11 3 Numerical Solutions 12 3.1 Introduction 12 3.2 Coupling Schemes 12 3.2.1 Operator Splitting 13 3.2.2 Global Implicit 13 3.2.2.1 Standard Reduction Schemes 14 3.2.2.2 Kräutle’s Reduction Scheme 14 3.2.2.3 Local Chemical Solver 21 3.3 Space and Time Discretization 23 3.3.1 Finite Element Method 23 3.3.2 Time Discretization 25 3.3.3 Jacobian Matrix 26 3.4 Code Implementation 29 4 Benchmarks 30 4.1 Introduction 30 4.2 Cation Exchange 30 4.3 Dissolution and Precipitation 32 4.4 Mixing Controlled Biodegradation 33 5 Conclusions and Outlooks 38 5.1 Conclusions 38 5.2 Outlooks 39 / Diese Arbeit konzentriert sich auf die numerische Berechnung reaktiver Transportprobleme in porösen Medien. Es werden prinzipielle Mechanismen von Fluidströmung und reaktive Stofftransport in porösen Medien untersucht. Um chemische Reaktionen und Stofftransport zu koppeln, wurden die Ansätze Global Implicit Approach (GIA) sowie Sequential Non-Iterative Approach (SNIA) in die Software OpenGeoSys (OGS6) implementiert. Das von Kräutle vorgeschlagene Reduzierungsschema wird in GIA verwendet, um die Anzahl der gekoppelten nichtlinearen Differentialgleichungen zu reduzieren. Das Reduzierungsschema verwendet Linearkombinationen von mobilen und immobile Spezies und trennt die reaktionsunabhngigen linearen Differentialgleichungen von den gekoppelten nichtlinearen Gleichungen (dh Verringerung der Anzahl der Primärvariablen des nicht-linearen Gleichungssystems). Um die Gleichgewichtsreaktionen der Mineralien zu berechnen, wurde ein chemischer Gleichungslaser auf Basis von ”semi-smooth Newton-Iterations” implementiert. Ergebnisse von drei Benchmarks wurden zur Code-Verifikation verwendet. Diese Ergebnisse zeigen, dass die Simulation homogener Equilibriumreaktionen mit GIA 6,7 mal schneller und bei kinetischen Reaktionen 24 mal schneller als SNIA sind. Bei Simulationen heterogener Equilibriumreaktionen ist SNIA 4,7 mal schneller als der GIA Ansatz.:Declaration of Authorship iii Acknowledgements iv Abstract v List of Figures viii Symbols ix 1 Introduction 1 1.1 State of the Art 1 1.2 Thesis Objectives 3 1.3 Thesis Outline 4 2 Mathematical Models 5 2.1 Introduction 5 2.2 Mass Balance Equations 5 2.2.1 Groundwater Flow 6 2.2.2 Mass Transport 7 2.2.3 Chemical Reaction 8 2.2.3.1 Equilibrium Reaction 8 2.2.3.2 Kinetic Reaction 10 2.3 Reactive Mass Transport 10 2.4 Initial and Boundary Conditions 11 3 Numerical Solutions 12 3.1 Introduction 12 3.2 Coupling Schemes 12 3.2.1 Operator Splitting 13 3.2.2 Global Implicit 13 3.2.2.1 Standard Reduction Schemes 14 3.2.2.2 Kräutle’s Reduction Scheme 14 3.2.2.3 Local Chemical Solver 21 3.3 Space and Time Discretization 23 3.3.1 Finite Element Method 23 3.3.2 Time Discretization 25 3.3.3 Jacobian Matrix 26 3.4 Code Implementation 29 4 Benchmarks 30 4.1 Introduction 30 4.2 Cation Exchange 30 4.3 Dissolution and Precipitation 32 4.4 Mixing Controlled Biodegradation 33 5 Conclusions and Outlooks 38 5.1 Conclusions 38 5.2 Outlooks 39

Although climate change is a global problem, specific mitigation measures are frequently applied on regional or national scales only. This is the case in particular for measures to reduce the emissions of land-based transport, which is largely characterized by regional or national systems with independent infrastructure, organization, and regulation. The climate perturbations caused by regional transport emissions are small compared to those resulting from global emissions. Consequently, they can be smaller than the detection limits in global three-dimensional chemistry-climate model simulations, hampering the evaluation of the climate benefit of mitigation strategies. Hence, we developed a new approach to solve this problem. The approach is based on a combination of a detailed three-dimensional global chemistry-climate model system, aerosol-climate response functions, and a zero-dimensional climate response model. For demonstration purposes, the approach was applied to results from a transport and emission modeling suite, which was designed to quantify the present-day and possible future transport activities in Germany and the resulting emissions. The results show that, in a baseline scenario, German transport emissions result in an increase in global mean surface temperature of the order of 0.01 K during the 21st century. This effect is dominated by the CO2 emissions, in contrast to the impact of global transport emissions, where non-CO2 species make a larger relative contribution to transport-induced climate change than in the case of German emissions. Our new approach is ready for operational use to evaluate the climate benefit of mitigation strategies to reduce the impact of transport emissions.

Les mécanismes responsables du transport hydrodynamique anormal (non-Fickéen) peuvent être rattachés à la complexité de la géométrie du milieu à l'échelle des pores. Dans cette thèse, nous étudions la dynamique des vitesses de particules à l'échelle des pores. À l'aide de simulations de suivi de particules effectuées sur un échantillon numérisé de grès de Berea, nous présentons une analyse détaillée de l'évolution Lagrangienne et Eulérienne et de leur dépendance aux conditions initiales. Le long de leur ligne de courant, la vitesse des particules montre un signal intermittent complexe, alors que leur sériede vitesses spatiales présente des fluctuations régulières. La distribution spatiale des vitesses des particules converge rapidementvers l'état stationnaire. Ces résultats dénotent un processus Markovienqui permet de prédire les fluctuations de vitesse dans le réseau poral.Ces processus, associés à la tortuosité et à la distance de corrélation de vitesse permettent de paramétrer un modèle de marche aléatoire dans le temps (CTRW) et de réaliser le changement d’échelle pour simuler le transport à l’échelle de Darcy. Le modèle, comme tout modèle issu d’un changement d'échelle, repose sur la définition d'un volume élémentaire représentatif (VER). Nous montrons qu’un VER basé sur les statistiques de vitesse permet de définir un support pertinent pour la modélisation du transport hydrodynamique pré-asymptotique à asymptotique, et ainsi d’éviter les limitations associées à l’équation d’advection-dispersionFickéenne. Cette approche est utilisée pour étudier l’impact de l’hétérogénéité du réseau poral sur le volume de mélange et la masse du produit d’une réaction bimoléculaire. / The mechanisms responsible for anomalous (non-Fickian) hydrodynamictransport can be traced back to the complexity of the medium geometry atthe pore-scale. In this thesis, we investigate the dynamics of pore-scaleparticle velocities. Using particle tracking simulations performed on adigitized Berea sandstone sample, we present a detailed analysis of theevolution of the Lagrangian and Eulerian evolution and their dependenceon the initial conditions. The particles experience a complexintermittent temporal velocity signal along their streamline while theirspatial velocity series exhibit regular fluctuations. The spatialvelocity distribution of the particles converges quickly to thesteady-state. These results lead naturally to Markov processes for theprediction of these velocity series.These processes, together with the tortuosity and the velocitycorrelation distance that are properties of the medium, allow theparameterization of a continuous time random walk (CTRW) for theupscaling of the transport. The model, like any upscaled model, relieson the definition of a representative elementary volume (REV). We showthat an REV based on the velocity statistics allows defining a pertinentsupport for modeling pre-asymptotic to asymptotic hydrodynamictransport at Darcy scale using, for instance, CTRW, thus overcomingthe limitations associated with the Fickian advection dispersionequation. Finally, we investigate the impact of pore-scale heterogeneityon a bimolecular reaction and explore a methodology for the predictionof the mixing volume and the chemical mass produced.