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78 lines
2.5 KiB
Org Mode
78 lines
2.5 KiB
Org Mode
#+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 barite.R barite_results
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mpirun -np 4 ./poet --interp barite_interp_eval.R barite_results
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#+end_src
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* List of Files
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- =barite.R=: POET input script for a 20x20 simulation grid
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- =barite_interp_eval.R=: POET input script for a 400x200 simulation
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grid
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- =db_barite.dat=: PHREEQC database containing the kinetic expressions
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for barite and celestite, stripped down from =phreeqc.dat=
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- =barite.pqi=: PHREEQC input script defining the chemical system
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* Chemical system
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The benchmark depicts a porous system where pure water is initially at
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equilibrium with *celestite* (strontium sulfate; brute formula:
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SrSO_4).
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A solution containing only dissolved Ba^{2+} and Cl^- diffuses into
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the system causing celestite dissolution. The increased concentration
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of dissolved sulfate SO_{4}^{2-} induces precipitation of *barite*
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(barium sulfate; brute formula: BaSO_{4}^{2-}). The overall reaction
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can be written:
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Ba^{2+} + celestite \rightarrow barite + Sr^{2+}
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Both celestite dissolution and barite precipitation are calculated
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using a kinetics rate law based on transition state theory:
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rate = -S_{m} K (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 (mol/m^{2}/s) is the rate constant, and SR is the
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saturation ratio, i.e., the ratio of the ion activity product of the
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reacting species and the solubility constant.
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For barite, the reaction rate is computed as sum of two mechanisms,
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/acid/ and /neutral/:
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rate_{barite} = S_{m} (acid + neutral) * (1 - SR_{barite})
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where
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acid = 10^{-6.9} \exp(\frac {-30800 \cdot T'} R) * act(H^{+})^{0.22}
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and
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neutral = 10^{-7.9} \exp( \frac {-30800 * T'} R)
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R is the gas constant (8.314462 J / K / mol) and T' (K^{-1}) accounts
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for temperature dependence of the kinetic coefficients which are
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experimentally determined at 25 °C or 298.15 K
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T' = (1 / K) - (1 / 298.15)
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The kinetic rate law as implemented in the =db_barite.dat= file
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accepts one parameter which represents reactive surface area in m^{2}.
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For this benchmarks the surface areas are set to
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- S_{barite}: 50 m^{2}
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- S_{celestite}: 10 m^{2}
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