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)
(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
(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 Irving and Williams series
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
(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)
(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
(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
(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
(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
(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
(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
(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
(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:
Ingmar Grenthe and Ignasi Puigdomenech.
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, Ignasi Puigdomenech, Joseph A. Rard, Surendra Saxena,Kastriot Spahiu.
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
Last reviewed: 27 May 2011
