Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Preface to Second Edition
- Preface to First Edition
- A Note About Software
- 1 Introduction
- 2 Modeling Overview
- PART I EQUILIBRIUM IN NATURAL WATERS
- 3 The Equilibrium State
- 4 Solving for the Equilibrium State
- 5 Changing the Basis
- 6 Equilibrium Models of NaturalWaters
- 7 Redox Disequilibrium
- 8 Activity Coefficients
- 9 Sorption and Ion Exchange
- 10 Surface Complexation
- 11 Three-Layer Complexation
- 12 Automatic Reaction Balancing
- 13 Uniqueness
- PART II REACTION PROCESSES
- PART III APPLIED REACTION MODELING
- Appendix A Sources of Modeling Software
- Appendix B Evaluating the HMW Activity Model
- Appendix C Minerals in the LLNL Database
- Appendix D Nonlinear Rate Laws
- References
- Index
13 - Uniqueness
from PART I - EQUILIBRIUM IN NATURAL WATERS
Published online by Cambridge University Press: 09 December 2021
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Preface to Second Edition
- Preface to First Edition
- A Note About Software
- 1 Introduction
- 2 Modeling Overview
- PART I EQUILIBRIUM IN NATURAL WATERS
- 3 The Equilibrium State
- 4 Solving for the Equilibrium State
- 5 Changing the Basis
- 6 Equilibrium Models of NaturalWaters
- 7 Redox Disequilibrium
- 8 Activity Coefficients
- 9 Sorption and Ion Exchange
- 10 Surface Complexation
- 11 Three-Layer Complexation
- 12 Automatic Reaction Balancing
- 13 Uniqueness
- PART II REACTION PROCESSES
- PART III APPLIED REACTION MODELING
- Appendix A Sources of Modeling Software
- Appendix B Evaluating the HMW Activity Model
- Appendix C Minerals in the LLNL Database
- Appendix D Nonlinear Rate Laws
- References
- Index
Summary
Valid solutions to the multicomponent equilibrium problem are commonly but not invariably unique roots of the governing equations. Modelers for this reason need to consider the possibility of the existence of more than one mathematically correct root to the equations describing chemical equilibrium in multicomponent systems. This chapter demonstrates the origin of nonunique roots to the equilibrium problem, provides several worked examples of how such roots may arise, and gives advice about coping with the possibility of nonuniqueness.
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- Geochemical and Biogeochemical Reaction Modeling , pp. 167 - 174Publisher: Cambridge University PressPrint publication year: 2022