Geochemical and Biogeochemical Reaction Modeling 2nd Edition by Craig Bethke ISBN 0521155703 9780521155700

1. Introduction

• 1.1 Development of Chemical Modeling

  • 1.1.1 Controversy over Free-Energy Minimization

  • 1.1.2 Application in Geochemistry

• 1.2 Scope of This Book

2. Modeling Overview

• 2.1 Conceptual Models

  • 2.1.1 Types of Equilibrium

  • 2.1.2 The Initial System

  • 2.1.3 Mass and Heat Transfer: The Reaction Path

• 2.2 Configurations of Reaction Models

  • 2.2.1 Closed-System Models

  • 2.2.2 Titration Models

  • 2.2.3 Fixed-Fugacity and Sliding-Fugacity Models

  • 2.2.4 Kinetic Reaction Models

  • 2.2.5 Local Equilibrium Models

  • 2.2.6 Reactive Transport Models

• 2.3 Uncertainty in Geochemical Modeling

Part I: Equilibrium in Natural Waters

3. The Equilibrium State

• 3.1 Thermodynamic Description of Equilibrium

  • 3.1.1 Phases and Species

  • 3.1.2 Components and the Basis

  • 3.1.3 Chemical Potentials, Activities, and Fugacities

    • 3.1.3.1 Aqueous Species

    • 3.1.3.2 Minerals

    • 3.1.3.3 Gases

  • 3.1.4 The Equilibrium Constant

• 3.2 Choice of Basis

  • 3.2.1 Convention for Choosing the Basis

  • 3.2.2 Components with Negative Masses

• 3.3 Governing Equations

  • 3.3.1 Independent Reactions

  • 3.3.2 Mass Action Equations

  • 3.3.3 Mass Balance Equations

  • 3.3.4 Substituted Equations

  • 3.3.5 Charge Balance

  • 3.3.6 Mineral Saturation States

  • 3.3.7 Gas Fugacities

  • 3.3.8 The pe and Eh

• 3.4 Number of Variables and the Phase Rule

4. Solving for the Equilibrium State

• 4.1 Governing Equations

• 4.2 Solving Nonlinear Equations

  • 4.2.1 Newton’s Method

  • 4.2.2 Newton-Raphson Iteration

• 4.3 Solving the Governing Equations

  • 4.3.1 The Reduced Problem

  • 4.3.2 Residual Functions

  • 4.3.3 Jacobian Matrix

  • 4.3.4 Newton-Raphson Iteration

  • 4.3.5 Non-Negativity

  • 4.3.6 Examples of Convergence

  • 4.3.7 Optimizing the Starting Guess

  • 4.3.8 Activity Coefficients

  • 4.3.9 Charge Balance

  • 4.3.10 Mineral Masses

  • 4.3.11 Bulk Composition

• 4.4 Finding the Stable Phase Assemblage

  • 4.4.1 Undersaturated Minerals

  • 4.4.2 Supersaturated Minerals

  • 4.4.3 Swap Procedure

  • 4.4.4 Apparent Violation of the Phase Rule

5. Changing the Basis

• 5.1 Determining the Transformation Matrix

  • 5.1.1 Example: Calculating the Transformation Matrix

  • 5.1.2 Test for a Valid Basis

• 5.2 Rewriting Reactions

• 5.3 Altering Equilibrium Constants

• 5.4 Reexpressing Bulk Composition

6. Equilibrium Models of Natural Waters

• 6.1 Chemical Model of Seawater

  • 6.1.1 Species Distribution

  • 6.1.2 Mineral Saturation

  • 6.1.3 Mass Balance and Mass Action

  • 6.1.4 Stable Phase Assemblage

  • 6.1.5 Interpreting Saturation Indices

• 6.2 Amazon River Water

• 6.3 Red Sea Brine

7. Redox Disequilibrium

• 7.1 Redox Potentials in Natural Waters

• 7.2 Redox Coupling

• 7.3 Morro do Ferro Groundwater

• 7.4 Energy Available for Microbial Respiration

8. Activity Coefficients

• 8.1 Debye–Hückel Methods

  • 8.1.1 Davies Equation

  • 8.1.2 B-dot Model

• 8.2 Virial Methods

• 8.3 Comparison of the Methods

• 8.4 Brine Deposit at Sebkhat El Melah

9. Sorption and Ion Exchange

• 9.1 Distribution Coefficient (Kd) Approach

• 9.2 Freundlich Isotherms

• 9.3 Langmuir Isotherms

• 9.4 Ion Exchange

• 9.5 Numerical Solution

• 9.6 Example Calculations

10. Surface Complexation

• 10.1 Complexation Reactions

• 10.2 Governing Equations

• 10.3 Numerical Solution

• 10.4 Example Calculation

11. Automatic Reaction Balancing

• 11.1 Calculation Procedure

  • 11.1.1 Using Species’ Stoichiometries

  • 11.1.2 Using a Reaction Database

• 11.2 Dissolution of Pyrite

• 11.3 Equilibrium Equations

  • 11.3.1 Equilibrium Activity Ratio

  • 11.3.2 Equilibrium Temperature

12. Uniqueness

• 12.1 The Question of Uniqueness

• 12.2 Examples of Nonunique Solutions

• 12.3 Coping with Nonuniqueness

Part II: Reaction Processes

13. Mass Transfer

• 13.1 Simple Reactants

• 13.2 Extracting the Overall Reaction

• 13.3 Special Configurations

14. Polythermal, Fixed, and Sliding Paths

• 14.1 Polythermal Reaction Paths

• 14.2 Fixed Activity and Fugacity Paths

• 14.3 Sliding Activity and Fugacity Paths

15. Geochemical Buffers

• 15.1 Buffers in Solution

• 15.2 Minerals as Buffers

• 15.3 Gas Buffers

16. Kinetics of Dissolution and Precipitation

• 16.1 Kinetic Rate Laws

• 16.2 From Laboratory to Application

• 16.3 Numerical Solution

• 16.4 Example Calculations

• 16.5 Modeling Strategy

17. Redox Kinetics

• 17.1 Rate Laws for Oxidation and Reduction

• 17.2 Heterogeneous Catalysis

• 17.3 Enzymes

• 17.4 Numerical Solution

• 17.5 Example Calculation

18. Microbial Kinetics

• 18.1 Microbial Respiration and Fermentation

• 18.2 Monod Equation

• 18.3 Thermodynamically Consistent Rate Laws

• 18.4 General Kinetic Model

• 18.5 Example Calculation

19. Stable Isotopes

• 19.1 Isotope Fractionation

• 19.2 Mass Balance Equations

• 19.3 Fractionation in Reacting Systems

• 19.4 Dolomitization of a Limestone

20. Transport in Flowing Groundwater

• 20.1 Groundwater Flow

• 20.2 Mass Transport

  • 20.2.1 Advection

  • 20.2.2 Hydrodynamic Dispersion

  • 20.2.3 Molecular Diffusion

• 20.3 Advection–Dispersion Equation

  • 20.3.1 Derivation

  • 20.3.2 Péclet Number

• 20.4 Numerical Solution

  • 20.4.1 Gridding

  • 20.4.2 Finite Difference Approximation

  • 20.4.3 Stability and Courant Number

  • 20.4.4 Numerical Dispersion

• 20.5 Example Calculation

21. Reactive Transport

• 21.1 Mathematical Model

  • 21.1.1 Governing Equation

  • 21.1.2 Attenuation and Retardation

  • 21.1.3 Damköhler Number

• 21.2 Numerical Solution

  • 21.2.1 Operator Splitting Method

  • 21.2.2 Mass Fluxes

  • 21.2.3 Updated Composition

• 21.3 Example Calculations

Part III: Applied Reaction Modeling

22. Hydrothermal Fluids

• 22.1 Origin of a Fluorite Deposit

• 22.2 Black Smokers

• 22.3 Energy Available to Thermophiles