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docs: readmes for dolo & barite
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Marco De Lucia
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@ -128,6 +128,7 @@ transported species: H, O, Charge, Ba, Cl, S(6), Sr.
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- Tranter, Wetzel, De Lucia and Kühn (2021): Reactive transport model
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of kinetically controlled celestite to barite replacement, Advances
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in Geosciences, 1, 1–9, https://doi.org/10.5194/adgeo-1-1-2021
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in Geosciences, 56, 57-–65, 2021.
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https://doi.org/10.5194/adgeo-56-57-20211
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176
bench/dolo/README.org
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176
bench/dolo/README.org
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#+TITLE: Description of =barite= benchmark
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#+AUTHOR: MDL <delucia@gfz-potsdam.de>
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#+DATE: 2023-08-26
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#+STARTUP: inlineimages
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#+LATEX_CLASS_OPTIONS: [a4paper,9pt]
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#+LATEX_HEADER: \usepackage{fullpage}
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#+LATEX_HEADER: \usepackage{amsmath, systeme}
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#+LATEX_HEADER: \usepackage{graphicx}
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#+LATEX_HEADER: \usepackage{charter}
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#+OPTIONS: toc:nil
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* Quick start
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#+begin_src sh :language sh :frame single
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mpirun -np 4 ./poet dolomite.R dolomite_results
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mpirun -np 4 ./poet --interp dolomite_interp_eval.R dolomite_results
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#+end_src
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* List of Files
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- =dolo.R=: POET input script for a 20x20 simulation grid
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- =dolo_diffu_inner.R=: POET input script for a 400x200 simulation
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grid
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- =dolo_diffu_inner_large.R=: POET input script for a 400x200
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simulation grid
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- =dolo_interp_long.R=: POET input script for a 400x200 simulation
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grid
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- =phreeqc_kin.dat=: PHREEQC database containing the kinetic expressions
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for dolomite and celestite, stripped down from =phreeqc.dat=
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- =dol.pqi=: PHREEQC input script for the chemical system
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* Chemical system
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This model describes a simplified version of /dolomitization/ of
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calcite, itself a complex and not yet fully understood natural process
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which is observed naturally at higher temperatures (Möller and De
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Lucia, 2020). Variants of such model have been widely used in many
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instances especially for the purpose of benchmarking numerical codes
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(De Lucia et al., 2021 and references therein).
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We consider an isotherm porous system at *25 °C* in which pure water
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is initially at equilibrium with *calcite* (calcium carbonate; brute
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formula: CaCO_{3}). An MgCl_{2} solution enters the system causing
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calcite dissolution. The released excess concentration of dissolved
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calcium Ca^{2+} and carbonate (CO_{3}^{2-}) induces after a while
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supersaturation and hence precipitation of *dolomite*
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(calcium-magnesium carbonate; brute formula: CaMg(CO_{3})_{2}). The
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overall /dolomitization/ reaction can be written:
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Mg^{2+} + 2 \cdot calcite \rightarrow dolomite + 2 \cdot Ca^{2+}
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The precipitation of dolomite continues until enough Ca^{2+} is
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present in solution. Further injection of MgCl_{2} changes its
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saturation state causing its dissolution too. After enough time, the
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whole system has depleted all minerals and the injected MgCl_{2}
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solution fills up the domain.
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Both calcite dissolution and dolomite precipitation/dissolution follow
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a kinetics rate law based on transition state theory (Palandri and
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Karhaka, 2004; De Lucia et al., 2021).
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rate = -S_{m} k_{m} (1-SR_{m})
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where the reaction rate has units mol/s, S_{m} (m^{2}) is the reactive
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surface area, k_{m} (mol/m^{2}/s) is the kinetic coefficient, and SR
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is the saturation ratio, i.e., the ratio of the ion activity product
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of the reacting species and the solubility constant, calculated
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internally by PHREEQC from the speciated solution.
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For dolomite, the kinetic coefficient results from the sum of two
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mechanisms, r_{/acid/} and r_{/neutral/}:
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rate_{dolomite} = S_{dolomite} (k_{/acid/} + k_{/neutral/}) * (1 - SR_{dolomite})
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where:
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k_{/acid/} = 10^{-3.19} e^{-36100 / R} \cdot act(H^{+})^{0.5}
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k_{/neutral/} = 10^{-7.53} e^{-52200 / R}
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R (8.314462 J K^{-1} mol^{-1}) is the gas constant.
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Similarly, the kinetic law for calcite reads:
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k_{/acid/} = 10^{-0.3} e^{-14400 / R} \cdot act(H^{+})^{0.5}
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k_{/neutral/} = 10^{-5.81} e^{-23500 / R}
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The kinetic laws as implemented in the =phreeqc_kin.dat= file accepts
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one parameter which represents reactive surface area in m^{2}. For the
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benchmarks the surface areas are set to
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- S_{dolomite}: 0.005 m^{2}
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- S_{calcite}: 0.05 m^{2}
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The initial content of calcite in the domain is of 0.0002 mol per kg
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of water. A constant partial pressure of 10^{-1675} atm of O_{2(g)} is
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maintained at any time in the domain in order to fix the redox
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potential of the solution to an oxidizing state (pe around 9).
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Note that Cl is unreactive in this system and only effects the
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computation of the activities in solution.
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* POET simulations
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Several benchmarks based on the same chemical system are defined here
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with different grid sizes, resolution and boundary conditions. The
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transported elemental concentrations are 7: C(4), Ca, Cl, Mg and the
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implicit total H, total O and Charge as required by PHREEQC_RM.
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** =dolo_diffu_inner.R=
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- Grid discretization: square domain of 1 \cdot 1 m^{2} discretized in
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100x100 cells
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- Boundary conditions: All sides of the domain are closed. *Fixed
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concentration* of 0.001 molal of MgCl_{2} is defined in the domain
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cell (20, 20) and of 0.002 molal MgCl_{2} at cells (60, 60) and
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(80, 80)
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- Diffusion coefficients: isotropic homogeneous \alpha = 1E-06
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- Time steps & iterations: 10 iterations with \Delta t of 200 s
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- *DHT* parameters:
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| H | 10 |
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| O | 10 |
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| Charge | 3 |
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| C(4) | 5 |
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| Ca | 5 |
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| Cl | 5 |
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| Mg | 5 |
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| Calcite | 5 |
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| Dolomite | 5 |
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- Hooks: the following hooks are defined:
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1. =dht_fill=:
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2. =dht_fuzz=:
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3. =interp_pre_func=:
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4. =interp_post_func=:
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** =dolo_interp_long.R=
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- Grid discretization: rectangular domain of 5 \cdot 2.5 m^{2}
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discretized in 400 \times 200 cells
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- Boundary conditions: *Fixed concentrations* equal to the initial
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state are imposed at all four sides of the domain. *Fixed
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concentration* of 0.001 molal of MgCl_{2} is defined in the domain
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center at cell (100, 50)
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- Diffusion coefficients: isotropic homogeneous \alpha = 1E-06
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- Time steps & iterations: 20000 iterations with \Delta t of 200 s
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- *DHT* parameters:
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| H | 10 |
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| O | 10 |
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| Charge | 3 |
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| C(4) | 5 |
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| Ca | 5 |
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| Cl | 5 |
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| Mg | 5 |
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| Calcite | 5 |
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| Dolomite | 5 |
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- Hooks: the following hooks are defined:
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1. =dht_fill=:
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2. =dht_fuzz=:
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3. =interp_pre_func=:
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4. =interp_post_func=:
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* References
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- De Lucia, Kühn, Lindemann, Lübke, Schnor: POET (v0.1): speedup of
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many-core parallel reactive transport simulations with fast DHT
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lookups, Geosci. Model Dev., 14, 7391–7409, 2021.
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https://doi.org/10.5194/gmd-14-7391-2021
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- Möller, Marco De Lucia: The impact of Mg^{2+} ions on equilibration
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of Mg-Ca carbonates in groundwater and brines, Geochemistry
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80, 2020. https://doi.org/10.1016/j.chemer.2020.125611
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- Palandri, Kharaka: A Compilation of Rate Parameters of Water-Mineral
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Interaction Kinetics for Application to Geochemical Modeling, Report
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2004-1068, USGS, 2004.
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