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).


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. Competition of other cations like Ca2+ and Al3+ with toxic metal ions

V. Competition of other anions like CO32- with humic binding sites

V. 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. Tipping's model V

VI. The oligoelectrolyte model

VI. The Gibbs-Donnan polyelectrolyte two phase model

VI. 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. Anodic stripping voltammetry

VI. Fluorescence spectroscopy

VI. Equilibrium dialysis

VI. Ion-selective electrodes

VI. Ultrafiltration

VI. Gel filtration chromatography

VI. Solvent extraction

VI. 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. Correlation of high-temperature equilibrium constants

X. 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. Example: the mononuclear Al3+ OH- system

X. 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. Criss and Cobble's method

X. Isocoulombic method

X. 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


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


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.


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.


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