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. / 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.

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

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Listening comprehension and listening strategies plays a crucial role in the process of acquiring a language. This study aims to investigate to what extent the listening skill is practised in upper secondary schools in the south of Sweden. Research studies within the field of listening are few which indicates that the listening skill is not considered as essential in second language teaching as the other three skills: reading, writing and speaking. Previous studies indicate that teachers should educate students metacognitive awareness when teaching listening. The results summarize the teachers’ answers, reflections and attitudes conducted from semi-structured interviews. The analysis of the results focuses on the four categories distinguished from the teachers’ answers: Teaching Approaches, National Exams, The Individual Student and Metacognitive Awareness. Some of the teachers do not possess the knowledge of how to teach listening that develops students' listening proficiency. As a conclusion, the study shows that a hierarchy exists among the four skills to which teachers adjust to, and this may be detrimental in achieving educational aims.