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Modelling in Aquatic Chemistry
Thermodynamic data are important for the modelling of the chemical processes in the engineering part on nuclear waste repository systems (the "near-field" region), and also to describe the effect of the "far-field", i.e. how the chemical change in ground and surface water systems may affect the transport of toxic elements from the repository to the biosphere. This publication contains guidelines on how to use the NEA-recommended Thermochemical Database (TDB) values, and on procedures to estimate values for cases where none can be recommended based on published experimental work. This volume is of interest to anyone involved in modelling of aqueous systems, including scientists working in non-nuclear activities. Each subject is introduced in an elementary way, including simple examples, and prior expert knowledge in the various subjects is not required. The text contains the scientific background, and references, to the various subject areas, and is therefore a reference source also for the experts working with modelling of aquatic systems. Emphasis is given to the advantages and limitations of the various models described in the frame of a simplified systems discussion. Some of the chapters are intended as guidelines for the chemical equilibrium modelling of aquatic systems (for example, ionic strength and temperature corrections). Other chapters are intended to introduce the reader to non-equilibrium modelling: mass transfer between phases and transport of solutes in aquatic systems. Each chapter has been written independently by the author(s), while the co-ordination of the different subjects has been the task of the editors. A peer-review procedure has been followed to ensure the quality of the text. (To download, click on each chapter title below) (by Ingmar GRENTHE and Ignasi PUIGDOMENECH) I.1 Models and modelling I.1.1 The need for models I.1.2 Verification and validation of models I.1.3 Modelling stages for complex systems I.2 Laboratory systems vs. complex systems encountered in nature and in science and technology I.3 Modelling methodologies for complex systems I.4 Some simple physical and chemical models I.5 Under what circumstances can we make predictions of the time evolution of chemical systems? I.6 Some additional considerations on chemical modelling I.6.1 Sources of thermodynamic data I.6.2 Using tabulated thermodynamic data I.7 Chapitre I: Introduction (French translation of Chapter I) II Symbols, Standards, and Conventions (by Ingmar GRENTHE and Ignasi PUIGDOMENECH) II.1 Symbols, terminology and nomenclature II.1.1 Symbols and terminology II.1.2 Reference codes II.1.3 Chemical formulae and nomenclature II.1.4 Phase designators II.1.5 Systems and their components II.1.5.1 Components in redox reactions II.1.6 Processes II.1.7 Thermodynamic data II.1.8 Equilibrium constants II.1.8.1 Protonation of a ligand II.1.8.2 Formation of metal ion complexes II.1.8.3 Solubility constants II.1.8.4 Equilibria involving the addition of a gaseous ligand II.1.8.5 Surface coordination reactions II.1.8.6 Redox equilibria II.1.9 pH II.2 Units and conversion factors II.3 Standard and reference conditions II.3.1 Standard state II.3.2 Standard state pressure II.3.3 Reference temperature II.4 Fundamental physical constants II.5 Graphical representations of equilibrium systems III Chemical Background for the Modelling of Reactions in Aqueous Systems (by Ingmar GRENTHE, Wolfgang HUMMEL and Ignasi PUIGDOMENECH) III.1 Introduction III.2 Factors that influence the equilibrium properties of chemical reactions in aqueous systems III.2.1 Chemical characteristics of metal ions III.2.2 Water as a solvent III.2.2.1 Solvation and complex formation, ion-ion and ion-dipole interactions III.2.2.2 Ion-ion and ion-dipole interactions III.2.2.3 Ligands and their chemical characteristics III.2.2.4 Qualitative features of complex formation reactions III.3 Classification of metal complexes III.4 The thermodynamics of complex formation reactions III.5 Complex formation, a competitive process III.5.1 The pH dependence of complex formation reactions III.5.2 Polynuclear complex formation III.5.3 The stoichiometry of hydroxide complexes III.5.4 Competition between different metal ions for the same ligand III.6 Theoretical framework for the estimation of equilibrium constants III.6.1 On the magnitude of equilibrium constants and the ratios between equilibrium constants for successive complex formation reactions III.6.2 Estimation of equilibrium constants for ternary complexes III.6.3 On the use of correlations for the prediction of equilibrium constants III.6.3.1 Correlations based on the size and charge of the metal ion III.6.3.2 Ligand field theory and III.6.4 Correlations based on properties of the ligand III.6.5 Correlations between equilibrium constants, log10 K, of different metal ions III.6.6 Correlations between successive equilibrium constants III.6.7 An example of the use of estimation methods for the modelling of a complex aquatic system, the influence of oxalate on U(VI) speciation III.7 Some aspects of chemical kinetics III.7.1 Reactions in homogeneous aqueous systems III.7.2 The temperature dependence of rate constants III.7.2.1 Dynamics of acid/base and complex formation reactions III.7.2.2 Dynamics of electron transfer reactions III.7.2.3 Catalysis and biologically mediated reactions III.7.2.4 Photochemical reactions III.7.3 The steady-state concept for flow systems III.7.4 Rates and mechanisms of heterogeneous equilibria IV Solubility Limitations: An "Old Timer's" View (by Rolf GRAUER) IV.1 Einleitung IV.2 Über Inhalt und Qualitaet von geochemischen Datenbasen IV.2.1 "The Law of Mythical Numbers" ... IV.2.2 ... and "The Handbook of Unstable, Exotic and Nonexistent Compounds" IV.2.3 Der Vergleich von Datenbasen: Ein Weg zu besseren Werten? IV.3 Löslichkeitslimiten im Nahfeld: Das Beispiel Americium IV.3.1 Löslichkeitsbestimmende Phasen IV.3.2 Die Rolle der Lanthaniden IV.3.3 Verglaste Abfaelle IV.3.4 Löslichkeitslimiten im Nahfeld: welche Festphasen? IV.4 Löslichkeitslimiten im Fernfeld: Das Beispiel Nickel IV.4.1 Die Modellierung der Nickel-Löslichkeit IV.4.2 Zur Geochemie des Nickels IV.4.3 Löslichkeitslimiten im Fernfeld? IV.5 Schlussbemerkungen IV.6 Solubility limitations: An "old timer's" view (English translation of Chapter IV) V Binding Models for Humic Substances (by Wolfgang HUMMEL) V.1 Introduction V.2 What are humic substances? V.3 Metal ion binding of humic substances V.3.1 The experimental data V.3.2 Variations in component concentration V.3.2.1 The simplest model V.3.2.2 Mixed-ligand models V.3.2.3 Variable stoichiometry models V.3.2.4 The multi-site models V.3.2.5 The continuous distribution models V.3.3 Variations in pH V.3.3.1 Empirical functions V.3.3.2 Proton exchange reactions V.3.3.3 Electrostatic effects V.3.4 Variations in ionic strength V.3.4.1 Empirical functions V.3.4.2 Electrostatic effects V.3.5 What is the best humic binding model? V.4 Problem solving strategies V.4.1 Models used as research tools V.4.2 Models used as assessment tools V.4.2.1 The "conservative roof" approach for performance assessment V.4.2.2 Competition of other complexes V.4.2.2.1 Competition of other cations like Ca2+ and Al3+ with toxic metal ions V.4.2.2.2 Competition of other anions like CO32- with humic binding sites V.4.2.2.3 Competition of mineral surface sites with binding sites V.4.2.3 Application of laboratory data in performance assessment VI Metal Ion Binding by Humic Substances (by James H. EPHRAIM and Bert ALLARD) VI.1 Introduction VI.2 General overview VI.2.1 Isolation and extraction of humic substances VI.2.2 Characterisation methods VI.2.3 Redox properties of humic substances VI.3 Solution chemistry of humic substances VI.3.1 Proton interactions with humic substances VI.3.1.1 Discrete ligand models VI.3.1.1.1 Tipping's model V VI.3.1.1.2 The oligoelectrolyte model VI.3.1.1.3 The Gibbs-Donnan polyelectrolyte two phase model VI.3.1.1.4 An example of the Gibbs-Donnan Approach to Humic Substance Systems VI.3.1.2 Continuous distribution models VI.3.1.3 Discrete models versus continuous distribution models VI.3.2 Models for the interaction of metals with humic/fulvic acids VI.3.2.1 Discrete ligand models VI.3.2.2 Continuous distribution models VI.3.2.3 Factors affecting the overall complex formation function VI.3.2.4 Competitive binding of various metal ions to humic substances VI.3.3 Data needs for modelling the role of humic substances VI.3.3.1 Review of studies on interactions between humic substances and metal ions VI.3.3.1.1 Anodic stripping voltammetry VI.3.3.1.2 Fluorescence spectroscopy VI.3.3.1.3 Equilibrium dialysis VI.3.3.1.4 Ion-selective electrodes VI.3.3.1.5 Ultrafiltration VI.3.3.1.6 Gel filtration chromatography VI.3.3.1.7 Solvent extraction VI.3.3.1.8 Ion exchange distribution VI.4 Modelling example: speciation of Eu3+ in the environment in presence of humic substances and Ca2+ VI.4.1 Relevance of the exercise VI.5 Summary VII Aqueous Speciation at the Interface Between Geological Solids and Groundwater (by Steven A. BANWART) VII.1 Introduction VII.2 Theoretical background VII.2.1 Intermolecular forces at the solid-solution interface VII.2.2 Mass balances for adsorbing substances: The concept of surface excess VII.2.3 Stoichiometric adsorption reactions and the thermodynamic law of mass action VII.2.4 Combining mass balances and thermodynamic mass laws: The adsorption isotherm VII.2.4.1 The Langmuir adsorption isotherm VII.2.4.2 A linear adsorption isotherm: The distribution coefficient VII.2.5 The influence of solution speciation on adsorption VII.3 Surface complexation VII.3.1 Chemisorption of water: Formation of variable charged surfaces VII.3.2 Adsorption of ligands and metals at the hydrated surface VII.3.3 The pH dependence of adsorption VII.3.4 Competitive adsorption VII.3.5 Non-ideal behaviour: Activity corrections for surface coverage VII.3.6 Charged surfaces and ion exchange VII.3.6.1 Origins of surface charge VII.3.6.2 The electrical double layer VII.3.6.3 Ion exchange reactions VII.3.7 Thermodynamic descriptions of complex adsorption systems VII.4 Surface precipitation VII.4.1 The transition from adsorption to surface precipitation VII.4.2 The conditional solubility constant for surface precipitation/co-precipitation VII.5 Implications for contaminant hydrogeology VII.5.1 Reversible partitioning of contaminants VII.5.2 Irreversible adsorption VII.5.3 Coupling geochemistry and hydrogeology VIII Systematization and Estimation of Thermochemical Data on Silicates (by Surendra K. SAXENA) VIII.1 Introduction VIII.2 A systematized data base VIII.2.1 Thermodynamics VIII.2.1.1 Temperature dependence of the Gibbs free energy VIII.2.1.2 Heat capacity at high temperature VIII.2.2 The regression technique VIII.2.3 The optimization technique VIII.2.4 Data base VIII.3 Estimation of enthalpy of silicates VIII.3.1 Principles underlying empirical correlation VIII.3.2 Tardy's method VIII.3.3 The polyhedral approach VIII.3.3.1 Chermak-Rimstidt method VIII.3.3.2 A new polyhedral method VIII.4 Estimation of entropy VIII.4.1 Example of a calculation VIII.5 Estimation of heat capacities of solids VIII.6 Conclusions IX Estimations of Medium Effects on Thermodynamic Data (by Ingmar GRENTHE, Andrey V. PLYASUNOV and Kastriot SPAHIU) IX.1 Introduction IX.2 On the estimation of activity coefficients in electrolyte systems IX.3 The Brønsted-Guggenheim-Scatchard model (SIT) IX.3.1 Determination of ion interaction coefficients IX.4 Other equations, approximately equivalent with the SIT model IX.5 On the magnitude of the specific ion interaction coefficients IX.5.1 Correlations among specific ion interaction parameters for cations IX.5.2 Correlations among specific ion interaction parameters for complexes IX.5.3 Correlations between Delta epsilon -values for chemical reactions IX.6 The Pitzer equations IX.7 Comparison of the SIT and the Pitzer models for the description of concentration-dependence of equilibrium constants of complex formation reactions in ionic media IX.7.1 The determination of the Pitzer and the SIT parameters from the log10 K data IX.8 The relationship between the SIT ε(i,j) and the Pitzer β(0)ij and β(1)ij parameters for mean-activity coefficients IX.8.1 The relationship between the delta epsilon values in the SIT model and the Δβ(0) and Δβ(1) values in the Pitzer models for complex formation reactions at "trace" concentrations of reactants/products IX.9 The use of the SIT at elevated temperatures IX.9.1 Osmotic coefficient IX.9.2 The analytical statements for partial and apparent molar properties of single electrolytes on the basis of the SIT model IX.9.3 The Debye-Hückel limiting law slopes IX.10 The concentration dependence of heats of reactions IX.10.1 The calculation of the standard enthalpy of reaction from experimental ΔrHm data using the Pitzer equation IX.10.2 The calculation of the standard enthalpy of a reaction from experimental ΔrHm data using the SIT model IX.10.3 The extrapolation equations for the determination of the standard enthalpy of reaction from the experimental ΔrHm data based on the Pitzer and the SIT models IX.11 Conclusions X Temperature Corrections to Thermodynamic Data and Enthalpy Calculations (by Ignasi PUIGDOMENECH, Joseph A. RARD, Andrey V. PLYASUNOV and Ingmar GRENTHE) X.1 Introduction X.2 Second-law extrapolations X.2.1 The hydrogen ion convention X.2.2 Approximations X.2.2.1 Constant enthalpy of reaction X.2.2.2 Constant heat capacity of reaction X.2.2.3 Isoelectric and isocoulombic reactions X.2.2.3.1 Correlation of high-temperature equilibrium constants X.2.2.3.2 Extrapolation of 298.15 K data to higher temperatures X.2.3 Calculation of ΔrHm from temperature dependence of solubility X.2.4 Alternative heat capacity expressions for aqueous species X.2.4.1 DQUANT Equation X.2.4.2 The revised Helgeson-Kirkham-Flowers model X.2.4.3 The Ryzhenko-Bryzgalin model X.2.4.3.1 Example: the mononuclear Al3+ – OH- system X.2.4.3.2 Example: the stability of acetate complexes of Fe2+ X.2.4.4 The density or "complete equilibrium constant" model X.3 Third-law method X.3.1 Evaluation from high and low-temperature calorimetric data X.3.2 Evaluation from high-temperature data X.3.3 A brief comparison of enthalpies derived from the second and third-law methods X.4 Estimation methods X.4.1 Estimation methods for heat capacities X.4.1.1 Heat capacity estimations for solid phases X.4.1.2 Heat capacity estimations for aqueous species X.4.1.2.1 Criss and Cobble's method X.4.1.2.2 Isocoulombic method X.4.1.2.3 Other correlation methods X.4.1.3 Heat capacity estimation methods for reactions in aqueous solutions X.4.2 Entropy estimation methods X.4.2.1 Entropy estimation methods for solid phases X.4.2.2 Entropy estimation methods for aqueous species X.4.3 Examples X.5 Concluding remarks X.6 Acknowledgements XI Cellular Automaton Models of Reaction-Transport Processes (by Theo KARAPIPERIS) XI.1 Introduction XI.2 Cellular automata XI.2.1 Historical development XI.2.2 Elementary examples XI.3 Cellular automata for transport with chemical reactions XI.3.1 Models XI.3.1.1 Transport XI.3.1.2 Chemical reactions XI.3.2 Applications XI.3.2.1 a + b —› c XI.3.2.2 Autocatalytic reactions XI.3.2.3 Reactions with mineral surfaces XI.4 Conclusion XI.5 Acknowledgements XII Modelling Solute Transport Using the Double Porous Medium Approach (by Andreas JAKOB) XII.1 Introduction XII.2 Classification of transport phenomena XII.3 Mass transport due to a concentration gradient XII.3.1 Fickian dispersion XII.3.2 Scale dependent dispersivity XII.3.3 The problem of local averaging XII.3.4 Sorption equations used in transport modelling XII.3.5 The double porosity medium concept XII.3.6 Effects of matrix diffusion and the effective surface sorption approximation XII.3.7 Modelling methodology and further examples XII.4 Acknowledgments XII.5 Glossary (by Jörg HADERMANN) XIII.1 Introduction XIII.2 Reduction of release rate at the source XIII.3 Retardation during transport XIII.4 Dilution (by Jordi BRUNO) XIV.1 Why are we concerned about trace metals? XIV.2 Some general aspects of (geo)chemical modelling XIV.2.1 How did all this start? XIV.3 The methodology of geochemical modelling XIV.3.1 The building blocks XIV.3.2 The system data XIV.3.3 The chemical and physical variability of subsurface environments XIV.3.3.1 Physical conditions XIV.3.3.2 Biological conditions XIV.3.3.3 Variability of chemical conditions XIV.3.4 Getting a feeling for the system. The conceptual model XIV.3.4.1 The geological setting XIV.3.4.2 The hydrogeological condition XIV.3.4.3 A quantitative description of local disequilibrium. The Peclet, Damkohler and Lichtner parameters XIV.3.4.4 The interaction of trace metals with major component solid phases XIV.4 The objective of geochemical modelling efforts. Interpretation vs. prediction XIV.4.1 An example of assessing the potential impact of an anthropogenic disturbance on a high-level nuclear waste repository. The effects of acid rain in the granitic geosphere XIV.4.2 An example of calculating the maximum release concentrations of critical radionuclides from spent fuel disposal. How information from natural system studies can be used to narrow down unrealistic predictions. XIV.5 Acknowledgments Scientific Editors: Contributors: Bert Allard, Steven A. Banwart, Jordi Bruno, James H. Ephraim, Rolf Grauer, Ingmar Grenthe, Jörg Hadermann, Wolfgang Hummel, Andreas Jakob, Theo Karapiperis, Andrey V. Plyasunov, Secretariat: OECD Nuclear Energy Agency Data Bank: M.C. Amaia Sandino and Ignasi Puigdomenech. Original text processing and layout: OECD Nuclear Energy Agency Data Bank: Cecile Lotteau |