LHyGeS numerical models : a garden worth gardening

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Table of contents

Chapter 1 – General introduction
1.1 Reactive transport
1.2 Governing equations
1.3 Coupling techniques: operator splitting and global approach
1.4 A universe of reactive transport codes
1.5 LHyGeS numerical models: a garden worth gardening
1.6 Structure of the work
Chapter 2 – Implementing isotopes
2.1 Theoretical background
2.1.1 What is an isotope?
2.1.2 Notation
2.1.3 Isotopic abundance and its variations
2.1.5 Why do we care about isotopes?
2.2 Modeling isotopes
2.2.1 Modeling stable isotopes equilibrium fractionation
2.2.2 Modeling stable isotopes kinetic fractionation
2.2.3 Conclusions about modeling isotopes
Chapter 3 – Thermodynamic equilibrium
3.1 Thermodynamic equilibrium solutions through a modified Newton Raphson method
3.1.1 Abstract
3.1.2 Introduction
3.1.3 Thermodynamic equilibrium: governing equations
3.1.4 Newton Raphson algorithm
3.1.5 Condition of the linear system
3.1.6 Working on a logarithmic base
3.1.7 Preconditioning
3.1.8 Scaling procedures in this work
3.1.9 Positive continuous fraction method
3.1.10 Numerical experiments
3.1.11 Numerical simulations: discussion
3.1.12 Conclusions about the strategies to improve Newton Raphson method
3.2 Thermodynamic capabilities of the code
3.2.1 Modeling surface complexation
3.2.2 Modeling ion exchange
Chapter 4 – Mixed equilibrium and kinetics
4.1 Theoretical background and generic formulation
4.1.1 Generic formulation I
4.1.2 Generic formulation II
4.1.3 Systems of equations
4.2 Solving the systems of equations
4.2.1 Implicit and explicit, one-step or multistep methods of integration
4.2.1.1 Implicit and explicit methods
4.2.1.2 One-step and multi-step methods
4.2.1.3 Variable stepsize
4.2.2 An implemented explicit method: Richardson extrapolation of QSSA method
4.2.3 An implemented implicit method: BDF in DASPK
4.2.4 Solving systems with DASPK
4.2.4.1 Residual computation for DASPK 1
4.2.4.3 Residual computation for DASPK 2
4.2.4.3 Residual computation for DASPK 3
4.3 Numerical simulations
4.3.1 TST model, verification of results with PHREEQC and KINDIS
4.3.1.1 Description of the problem
4.3.1.2 Numerical simulations: results
4.3.2 Chilakapati test case: verification with publication
4.3.2.1 Description of the problem
4.3.2.2 Numerical simulations: results
4.3.2.3 Numerical simulations: effect of convergence criteria
4.4 Conclusions about mixed equilibrium and kinetics
Chapter 5 – Solid solutions
5.1 Introduction and theoretical background
5.1.1 The interest in solid solutions
5.1.2 Theoretical background: Thermodynamics of solid solutions
5.1.3 Modeling solid solutions and their interaction with the aqueous phase
5.1.3.1 Equilibrium models for solid solutions
5.1.3.2 Kinetic models for solid solutions
5.1.3.3 Exploiting solid solutions concept for stable kinetic isotope fractionation
5.2 Numerical simulations of solid solutions
5.2.1 Modeling solid solutions at thermodynamic equilibrium
5.2.1.1 Verification with PHREEQC
5.2.1.2 Fe-Cr redox reaction, a reactive transport example
5.3 Conclusions about solid solutions
Chapter 6 – Building SpeCTr, a reactive transport code
6.1 Coupling flow, transport and reaction
6.1.1 Governing equations
6.1.2 Global approach
6.1.3 Operator splitting
6.1.4 War of the approaches
6.1.5 Multicomponent reactive transport
6.2 TRACES
6.2.1 Code capabilities
6.2.2 Numerical schemes
6.2.3 Coupling with reaction module
6.2.4 SpeCTr
6.3 Validation: coupling and implementation of isotopes
6.3.1 Interest of validation
6.3.2 Presentation of the problem
6.3.2.1 Spatial discretization, flow characteristics and ground properties
6.3.2.2 Boundary and initial conditions, transport parameters
6.3.2.3 Reaction network
6.3.2.4 Considerations about Courant number
6.3.3 Results of numerical simulations: SpeCTr
6.3.3.1 Results: 􀀁t(CFL), 􀀂L = 0 m, no Cr fractionation
6.3.3.2 Results: 􀀁t(CFL=1), 􀀂L = 0 m, Cr fractionation
6.3.3.3 Results: reduced time step, 􀀂L = 0 m, Cr fractionation
6.3.3.2 Results: 􀀁t (CFL=1), 􀀂L = 1.0 m, Cr fractionation
6.3.3.3 Results: reduced time step, 􀀂L = 0.54 m, Cr fractionation
6.4 Conclusions about SpeCTr validation
Chapter 7 – Application of SpeCTr: modeling Calcite dissolution & precipitation
7.1 From mixed flow reactor to column experiments and modeling: upscaling of calcite dissolution rate
7.1.1 Abstract
7.1.2 Introduction
7.1.3 Materials and experimental methods
7.1.3.1 Sample preparations
7.1.3.2 Aqueous solution preparations
7.1.3.3 Mixed flow reactor experiments
7.1.3.4 Column experiment
7.1.3.5 Aqueous sample analyses and thermodynamic calculations
7.1.3.6 Determination of calcite dissolution rate
7.1.4 Mathematical modeling of flow and reactive transport for the column experiments
7.1.5 Results and discussion
7.1.5.1 Mixed-flow reactor experiments
7.1.5.1.a Etching and etch pits morphology
7.1.5.1.b R-􀀃 and R-􀀄G relationships as determined from VSI measurements
7.1.5.2 Column experiment
7.1.5.2.a Dissolution rates determined from VSI measurements
7.1.5.2.b Etch pit morphology
7.1.5.2c Comparison of the mean dissolution rates retrieved with VSI to those inferred from pit morphology
7.1.5.3 Modeled dissolution rates using 2D reactive transport simulations of the column experiment
7.1.5.4 Modeled dissolution rates: 1D versus 2D simulations.
7.1.5.5 Simulation of the Calcium breakthrough curve.
7.1.5.6 1D and 2D-reactive transport simulations of the column experiment: overview and perspectives
7.1.5.6a Mineralogical considerations
7.1.5.6.b Calcium breakthrough
7.1.5 Conclusion
7.2 Preparing Calcite dissolution rate modeling
7.2.1 Computation of reactive surface area for TST and SWM models
7.2.2 Time and spatial discretization
7.3 Mixing induced CaCO3 precipitation
7.3.1 Presentation of the test case
7.3.1.1 Spatial discretization, flow characteristics and ground properties
7.3.1.2 Boundary and initial conditions, transport parameters
7.3.1.3 Reaction network
7.3.1.4 Algorithms for porosity changes
7.3.2 Results of numerical simulations: SPeCTr
7.3.2.1 Results: constant porosity 􀀂 equilibrium and kinetic CaCO3 precipitation
7.3.2.2 Results: variable porosity – equilibrium CaCO3 precipitation
7.3.2.3 Results: variable porosity – kinetic CaCO3 precipitation
7.3.2.4 Conclusion about Calcite precipitation and porosity changes
7.4 – 3D Calcite dissolution modeling
7.4.1 Presentation of the problem
7.4.2 Results of 3D simulation
7.4.2 Conclusions about 3D simulation