At many sites it has become apparent that most chemicals of concern (COCs) in groundwater are persistent and not effectively treated by conventional remediation methods. In recent years, the permeable reactive barrier (PRB) technology has proven to be more cost-efficient in the long-run and capable of rapidly reducing COC concentrations by up to several orders of magnitude. In its simplest form, the PRB is a vertically emplaced rectangular porous medium in which impacted groundwater passively enters a narrow treatment zone. In the treatment zone dissolved COCs are rapidly degraded as they come in contact with the reactive material. As a result, the effluent groundwater contains significantly lower solute concentrations as it re-enters the aquifer and flows towards the plane of compliance (POC). Effective implementation of the PRB relies on accurate site characterization to identify the existing COCs, their interactions, and their required residence time in the PRB and aquifer. Ensuring adequate residence time in the PRB-aquifer system allows COCs to react longer, hence improving the probability that regulatory concentrations are achieved at the POC. In this study, the Park and Zhan solution technique is used to derive steady-state analytical and transient semi-analytical solutions to multispecies reactive transport in a permeable reactive barrier-aquifer (dual domain) system. The advantage of the dual domain model is that it can account for the potential existence of natural degradation in the aquifer, when designing the required PRB thickness. Also, like the single-species Park and Zhan solution, the solutions presented here were derived using the total mass flux (third-type) boundary condition in PRB-aquifer system. The study focuses primarily on the steady-state analytical solutions of the tetrachloroethylene (PCE) serial degradation pathway and secondly on the analytical solutions of the parallel degradation pathway. Lastly, the solutions in this study are not restricted solely to the PRB-aquifer model. They can also be applied to other types of dual domain systems with distinct flow and transport properties, and up to four other species reacting in serial or parallel degradation pathways. Although the solutions are long, the results of this study are novel in that the solutions provide improved modeling flexibility. For example: 1) every species can have unique first-order reaction rates and unique retardation factors, 2) higher order daughter species can be modeled solely as byproducts by neglecting their input concentrations, 3) entire segments of the parallel degradation pathway can be neglected depending on the desired degradation pathway model, and 4) converging multi-parent reactions can be modeled. As part of the study, separate Excel spreadsheet programs were created to facilitate prompt application of the steady-state analytical solutions, for both the serial and parallel degradation pathways. The spreadsheet programs are included as supplementary material.

La modélisation du transport réactif dans les milieux poreux implique la simulation de plusieurs processus physico-chimiques : écoulement de phases fluides, transport de chaleur, réactions chimiques entre espèces en phases identiques ou différentes. La résolution du système d'équations qui décrit le problème peut être obtenue par une approche soit totalement couplée soit découplée. Les approches découplées simplifient le système d'équations en décomposant le problème sous-parties plus faciles à gérer. Chacune de ces sous-parties peut être résolue avec des techniques d'intégration appropriées. Les techniques de découplage peuvent être non‑itératives (operator splitting methods) ou itératives (fixed‑point iteration), chacunes ayant des avantages et des inconvénients. Les approches non‑iteratives génèrent une erreur associée à la séparation des sous­-parties couplées, et les approaches itératives peuvent présenter des problèmes de convergence. Dans cette thèse, nous développons un code sous licence libre en langage MATLAB (https://github.com/TReacLab/TReacLab) dédie à la modélisation du la problématique de la carbonatation atmosphérique du béton, dans le cadre du stockage de déchets de moyenne activité et longue vie en couche géologique profonde. Le code propose un ensemble d'approche découplée : classique, comme les approches de fractionnement séquentiel, alternatif ou Strang, et moins classique, comme les approches de fractionnement additif ou par répartition symétrique. En outre, deux approches itératives basées sur une formulation spécifique (SIA CC et SIA TC) ont également été implémentées. Le code été interfacé de manière générique avec différents solveurs de transport (COMSOL, pdepe MATLAB, FVTool, FD scripts) et géochimiques (iPhreeqc, PhreeqcRM). Afin de valider l'implémentations des différentes approches, plusieurs bancs d'essais classiques dans le domaine du transport réactif ont été utilises avec succès. L'erreur associée à la combinaison du fractionnement de l'opérateur et des techniques numériques étant complexe à évaluer, nous explorons les outils mathématiques existants permettant de l'estimer. Enfin, nous structurons le problème de la carbonatation atmosphérique et présentons des simulations préliminaires, en détaillant les problèmes pertinents et les étapes futures à suivre. / Reactive transport modeling in porous media involves the simulation of several physico‑chemical processes: flow of fluid phases, transport of species, heat transport, chemical reactions between species in the same phase or in different phases. The resolution of the system of equations that describes the problem can be obtained by a fully coupled approach or by a decoupled approach. Decoupled approaches can simplify the system of equations by breaking down the problem into smaller parts that are easier to handle. Each of the smaller parts can be solved with suitable integration techniques. The decoupling techniques might be non‑iterative (operator splitting methods) or iterative (fixed‑point iteration), having each its advantages and disadvantages. Non‑iterative approaches have an error associated with the separation of the coupled effects, and iterative approaches might have problems to converge. In this thesis, we develop an open‑source code written in MATLAB (https://github.com/TReacLab/TReacLab) in order to model the problematic of concrete atmospheric carbonation for an intermediate‑level long‑lived nuclear waste package in a deep geological repository. The code uses a decoupled approach. Classical operator splitting approaches, such as sequential, alternating or Strang splitting, and less classical splitting approaches, such as additive or symmetrically weighted splitting, have been implemented. Besides, two iterative approaches based on an specific formulation (SIA CC, and SIA TC) have also been implemented. The code has been interfaced in a generic way with different transport solvers (COMSOL, pdepe MATLAB, FVTool, FD scripts) and geochemical solvers (iPhreeqc, PhreeqcRM). In order to validate the implementation of the different approaches, a series of classical benchmarks in the field of reactive transport have been solved successfully and compared with analytical and external numerical solutions. Since the associated error due to the combination of operator splitting and numerical techniques may be complex to assess, we explore the existing mathematical tools used to evaluate it. Finally, we frame the atmospheric carbonation problem and run preliminary simulations, stating the relevant problems and future steps to follow.

The overarching goal of this thesis is to develop a diagnostic and predictive model to quantify the estuarine CO2 dynamics across scales – from catchment to the globe – using an approach that explicitly resolves the strong physical and biogeochemical gradients typically observed in these systems.Chapter 1 provides fundamental definitions and descriptions of estuaries, as well as an assessment of their role in the global carbon cycle. It also raises the specific objectives and research questions tackled in the present study. Chapter 2 presents the rationale behind the novel modelling approach (C-GEM, Carbon-Generic Estuary Model) developed in the framework of this thesis. First, the dominant processes that control the estuarine biogeochemistry in estuaries are discussed in detail. Then, the power of reactive-transport models (RTMs) in understanding and quantifying the estuarine biogeochemical functioning is illustrated on the basis of local modelling studies. Finally, trends in estuarine biogeochemical dynamics across different geometries and environmental scenarios are briefly explored with C-GEM and results are discussed in the context of improving the modelling of estuarine carbon dynamics at regional and global scales. In Chapter 3, a detailed description of C-GEM, both in terms of structure and set-up, is provided and model’s performance is successfully evaluated through comprehensive model-data and model-model comparisons in the macro-tidal Scheldt estuary (BE/NL). In Chapter 4, C-GEM is combined with a generic set of forcing conditions and parameter values to quantify the carbon dynamics (net ecosystem metabolism, CO2 exchange at the air-water interface, carbon filtering capacity) in three idealized estuaries subject to temperate climatic conditions. Their hydro-geometrical characteristics span the wide diversity of estuarine morphological characteristics. Model results are used to upscale the estuarine CO2 dynamics under present-day conditions and to quantify the response of the estuarine filter to future atmospheric CO2, land use and climate change scenarios. In Chapter 5, C-GEM is applied to derive estimations of carbon export and CO2 outgassing from all tidal estuaries discharging in the North Sea. Overall, our results suggest that the estuarine carbon filtering capacity and the contribution of these land-ocean transition systems to the atmospheric CO2 budget might not be as high as previously thought. Finally, a conclusive chapter (Chapter 6) provides a synthesis of the key findings and arguments projected by the present research work. Moreover, recommendations are given in the light of further applications of the modelling approach developed during this thesis. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

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

Pressure solution creep is a fundamental deformation mechanism in the upper crust. Overburden pressure that acts upon layers of sediment leaves grains densely packed. Nonhydrostatic stress distributed over the contacts between grains brings an enhancement effect on surface dissolution. As surface retreat over the contacts and hence grain repacking squeeze out pore water in the voids, the layers of sediment are deformed to become denser and denser. This work aims to identify what process slows down pressure solution creep over time. For this purpose, a new mechanistic model of pressure solution creep is developed, derived from the reaction rate law for nonhydrostatic dissolution kinetics under the hypothesis of a closed system. The present mechanistic model shows that (1) the creep rate goes down as a combined consequence of stress transfer across expanding contacts and concentration build-up in the interlayer of absorbed water; and (2) solute migration process acts as the primary rate-limiting process of pressure solution creep in the long run. This work then focuses on hydraulic evolution of channelling flow through a single deformable fracture which is simultaneously subjected to pressure solution creep. The developed 1-D reactive transport model is allowed to capture the strong interaction between channelling flow and pressure solution creep under crustal conditions. This numerical investigation provides a justified interpretation for the unusual experimental observation that fracture permeability reduction does not necessarily cause concentration enrichment. Temperature elevation contributes to accelerating the progression of pressure solution creep.

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In der vorliegenden Dissertation sollten die hydrogeochemischen Prozesse herausgearbeitet werden, die für die Wasserqualitätsänderung während eines ASR Experiments in Bolivar, Südaustralien und während der Versickerung in einem künstlichen Grundwasseranreicherungsbecken in Berlin von Bedeutung waren. Reaktive Stofftransportmodellierung des ASR Experiments in Bolivar, Südaustralien zeigte, dass die hydrochemischen Veränderungen in der direkten Umgebung des Injektionsbrunnens während der Speicherphase nur durch rapide Änderungen der Sauerstoff- und Nitrat reduzierenden Bakterienmasse erklärt werden können. Die hydrochemischen Veränderungen in größerer Distanz zum Injektionsbrunnen wurden überwiegend durch Ionenaustauschprozesse und Kalzitlösung verursacht. Geochemische und hydraulische Messungen unter einem Sickerbecken in Berlin zeigten, dass die beobachteten geochemischen Änderungen im Sickerwasser mit den periodisch auftretenden wassergesättigten/wasserungesättigen Bedingungen unter dem Becken einhergehen. Während der ungesättigten Periode wird Luft unter das Becken gezogen und führt zur plötzlichen Reoxidierung von bereits in der gesättigten Periode gebildeten Eisensulfiden und zur beschleunigten Mineralisation von sedimentärem organischem Kohlenstoff. Reaktive Stofftransportmodellierung auf größerer Skale zeigte, dass allein die saisonalen Temperaturunterschiede im Infiltrationswasser für die beobachtete zeitliche und räumliche Dynamik der Redoxzonen im weiteren Abstrom des Sickerbeckens verantwortlich sind. Das Abbauverhalten der Arzneimittelsubstanz Phenazon hängt ausschließlich von der Verfügbarkeit von gelöstem Sauerstoff und damit indirekt von der Wassertemperatur im Aquifer ab. In der vorliegenden Arbeit wird deutlich, dass ein adäquates Verständnis der wasserqualitätsändernden Prozesse in künstlichen Anreicherungsystemen nur dann erreicht werden kann wenn Strömung, Transport und reaktive Prozesse, im Feld als auch in der Modellierung, simultan betrachtet werden. / In this thesis, three major studies were carried out in order to understand the key factors controlling the water quality changes that occurred during a reclaimed water Aquifer Storage and Recovery (ASR) experiment at Bolivar, South Australia and during ponded infiltration in Berlin, Germany. Multi-component reactive transport modelling of the ASR experiment suggested that during the storage phase, dynamic changes in bacterial mass have a significant influence on the local geochemistry in the vicinity of the injection well. Water quality changes further away from the injection well were mainly driven by ion exchange and calcite dissolution. Geochemical and hydraulic measurements below an artificial recharge pond in Berlin, Germany, showed that the observed dynamic changes of the hydrochemistry within the seepage water are strongly linked to the periodic saturated/unsaturated hydraulic conditions below the pond. During unsaturated conditions, atmospheric oxygen penetrates from the pond margins to the centre below the pond, leading to (i) a sudden re-oxidation of sulphide minerals that have formed previously during saturated conditions and (ii) an enhanced mineralisation of sedimentary particulate organic carbon. Reactive transport modelling showed that at larger scale, seasonal temperature changes of the infiltration water are the key control for the observed temporal and spatial redox dynamics further downstream the recharge pond. Moreover, the degradation behaviour of the pharmaceutically residue phenazone solely depends on the availability of dissolved oxygen, and thus indirectly on the water temperature within the aquifer. Overall this thesis shows that a sound understanding and analysis of the key processes affecting the water quality changes during artificial recharge of groundwater could only be achieved when flow, transport and reactive processes are considered simultaneously, both in the field and during modelling.

Bio-deterioration of concrete, which is very common in sewer system and waste water treatment plant, results in significant structure degradation. Normally, the process can be described by the two following parts: 1) Biochemistry reactions producing biogenic aggressive species in biofilms which are spread on the surface of concrete. As one of the most significant biogenic acid in sewer pipes, sulfuric acid (H2SO4) is produced by sulfur oxidizing bacteria (SOB). 2) Chemical reactions between biogenic aggressive species and cement hydration products which is responsible for concrete deterioration. A reactive transport model is proposed to simulate the bio-chemical and chemical deterioration processes of cementitious materials in contact with SOB and H2S or sulfuric acid solution. This model aims at solving simultaneously transport and biochemistry/chemistry in biofilms and cementitious materials by a global coupled approach. To provide an appropriate environment for SOB to grow, the surface neutralization of concrete (i.e., the absorption of H2S and aqueous H2S corrosion) is considered. To obtain the amount of biogenic H2SO4, the bio-oxidation of H2S by the activation of bacteria is simulated via a simplified model. To provide a suitable environment for SOB to grow, the abiotic pH reduction of concrete process is introduced. The production rate of H2SO4 is governed by the pH in the biofilms and the content of H2S in gas.It is assumed that all chemical processes are in thermodynamical equilibrium. The dissolution of portlandite (CH) and calcium silicate hydrates (C-S-H) and the precipitation of gypsum (C¯S H2) and calcium sulfide are described by mass action law and threshold of ion activity products. To take into account the continuous decrease of the Ca/Si ratio during the dissolution of C-S-H a generalization of the mass action law is applied. By simplifying the precipitation process of gypsum, a damage model is introduced to characterize the deterioration of concrete due to the swelling of gypsum. Thus, the porosity evolution and deterioration depth during deterioration process are taken into account. Only diffusion of aqueous species are considered. Different diffusion coefficients are employed for various ions and Nernst-Planck equation was implemented. The effect of the microstructure change during deterioration on transport properties is considered as well. For both biofilms and cementitious materials, the balance equations of total mass of each atom (Ca, Si, S, K, Cl) are used to couple transport equations and (bio-)chemical reactions. The model is implemented within a finite-volume code, Bil. Following the introduction of principle of the finite volume method, the coupling of the bio-chemistry process in biofilms and chemistry process in cementitious materials is illustrated. By this model, some experiments reported in literature, including chemical immersion tests (statical solution condition and flow solution condition) and microbiological simulation tests, are simulated. The numerical results and the experimental observations are compared and discussed. The influence of properties of cementitious materials (initial porosity, carbonated layer, etc.) and environmental factors (concentration of H2SO4, content of H2S, etc.) are investigated by this model as well. Furthermore, a long term predictionis conducted

Doctor of Philosophy / Department of Civil Engineering / David R. Steward / Groundwater contamination with arsenic (As), a naturally occurring metalloid, is a worldwide problem. Over 100 million people are at health risk due to arsenic contaminated groundwater, especially in the Bengal Basin in south-east Asia. Dissolved organic matter (DOM), geology and geomicrobiology are important factors affecting arsenic mobility. This study focuses on interactions of different aspects of natural organic matter in arsenic-contaminated environments. A literature review specifically includes past studies done on fundamentals of arsenic geology, geomicrobiology, DOM characterization and relevant analytical methods and tools. Based on background information already collected, this research is focused on specific research questions and corresponding hypotheses. The overarching goal of this investigation is to better understand the mechanisms by which DOM influences arsenic mobilization. The specific goals of this research are: 1) to evaluate role of oxidized humic quinones in reductive dissolution of Fe-As minerals and subsequent arsenic mobilization via electron shuttling, 2) to quantify the rate of microbially mediated reductive dissolution in the presence of oxidized humic quinones, 3) to evaluate DOM-Fe-As ternary complex formation and its influence on arsenic mobility and 4) to characterize DOM in the arsenic-contaminated aquifers of West Bengal, India and evaluate its role in arsenic mobilization using groundwater flow and contaminant transport modeling approach. Results of this study revealed that oxidized quinone like moieties (such as fulvic acids) serve as an electron shuttle and enhance the reductive dissolution process under reducing conditions, hence mobilize the arsenic in groundwater. Another key result from this study suggested that arsenic binds with non-aromatic portion of the humic-like DOM under reducing conditions and increases its solution concentration. A field study conducted in West Bengal, India revealed that the mechanisms studied in the laboratory exists in reducing aquifer. A groundwater flow and reactive transport model was created to explain multiple interactions of DOM and arsenic spatial scales. Broader impacts of this study include significant addition to scientific knowledge about subsurface biogeochemistry and the role of DOM in biogeochemical reactions in the subsurface.