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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).

 Foreword

 

 Table of Contents

 

 I Introduction

(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 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

 

 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

 

 XIII The Pillars of Safety

(by Jörg HADERMANN)

 XIII.1 Introduction

 XIII.2 Reduction of release rate at the source

 XIII.3 Retardation during transport

 XIII.4 Dilution

 

 XIV Trace Element Modelling

(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

 

 XV Authors List

 

 XVI Reference List

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