mirror of
https://git.gfz-potsdam.de/naaice/poet.git
synced 2025-12-16 12:54:50 +01:00
125 lines
4.1 KiB
Org Mode
125 lines
4.1 KiB
Org Mode
#+TITLE: Description of =barite= benchmark
|
||
#+AUTHOR: MDL <delucia@gfz-potsdam.de>
|
||
#+DATE: 2023-08-26
|
||
#+STARTUP: inlineimages
|
||
#+LATEX_CLASS_OPTIONS: [a4paper,9pt]
|
||
#+LATEX_HEADER: \usepackage{fullpage}
|
||
#+LATEX_HEADER: \usepackage{amsmath, systeme}
|
||
#+LATEX_HEADER: \usepackage{graphicx}
|
||
#+LATEX_HEADER: \usepackage{charter}
|
||
#+OPTIONS: toc:nil
|
||
|
||
* Quick start
|
||
|
||
#+begin_src sh :language sh :frame single
|
||
mpirun -np 4 ./poet barite.R barite_results
|
||
mpirun -np 4 ./poet --interp barite_interp_eval.R barite_results
|
||
#+end_src
|
||
|
||
* List of Files
|
||
|
||
- =barite.R=: POET input script for a 20x20 simulation grid
|
||
- =barite_interp_eval.R=: POET input script for a 400x200 simulation
|
||
grid
|
||
- =db_barite.dat=: PHREEQC database containing the kinetic expressions
|
||
for barite and celestite, stripped down from =phreeqc.dat=
|
||
- =barite.pqi=: PHREEQC input script defining the chemical system
|
||
|
||
* Chemical system
|
||
|
||
The benchmark depicts an isotherm porous system at *25 °C* where pure
|
||
water is initially at equilibrium with *celestite* (strontium sulfate;
|
||
brute formula: SrSO_{4}). A solution containing only dissolved Ba^{2+}
|
||
and Cl^- diffuses into the system causing celestite dissolution. The
|
||
increased concentration of dissolved sulfate SO_{4}^{2-} induces
|
||
precipitation of *barite* (barium sulfate; brute formula:
|
||
BaSO_{4}^{2-}). The overall reaction can be written:
|
||
|
||
Ba^{2+} + celestite \rightarrow barite + Sr^{2+}
|
||
|
||
Both celestite dissolution and barite precipitation are calculated
|
||
using a kinetics rate law based on transition state theory:
|
||
|
||
rate = -S_{m} k_{barite} (1-SR_{m})
|
||
|
||
where the reaction rate has units mol/s, S_{m} (m^{2}) is the reactive
|
||
surface area, k (mol/m^{2}/s) is the kinetic coefficient, and SR is
|
||
the saturation ratio, i.e., the ratio of the ion activity product of
|
||
the reacting species and the solubility constant, calculated
|
||
internally by PHREEQC from the speciated solution.
|
||
|
||
For barite, the reaction rate is computed as sum of two mechanisms,
|
||
r_{/acid/} and r_{/neutral/}:
|
||
|
||
rate_{barite} = S_{barite} (k_{/acid/} + k_{/neutral/}) * (1 - SR_{barite})
|
||
|
||
where:
|
||
|
||
k_{/acid/} = 10^{-6.9} e^{-30800 / R} \cdot act(H^{+})^{0.22}
|
||
|
||
k_{/neutral/} = 10^{-7.9} e^{-30800 / R}
|
||
|
||
R (8.314462 J K^{-1} mol^{-1}) is the gas constant.
|
||
|
||
For celestite the kinetic law considers only the acidic mechanism and
|
||
reads:
|
||
|
||
rate_{celestite} = S_{celestite} 10^{-5.66} e^{-23800 / R} \cdot
|
||
act(H^{+})^{0.109} \cdot (1 - SR_{celestite})
|
||
|
||
The kinetic rates as implemented in the =db_barite.dat= file accepts
|
||
one parameter which represents reactive surface area in m^{2}. For the
|
||
benchmarks the surface areas are set to
|
||
|
||
- S_{barite}: 50 m^{2}
|
||
- S_{celestite}: 10 m^{2}
|
||
|
||
A starting seed for barite is given at 0.001 mol in each domain
|
||
element.
|
||
|
||
* Nucleation (TODO)
|
||
|
||
Geochemical benchmark inspired by Tranter et al. (2021) without
|
||
nucleation.
|
||
|
||
* POET simulations
|
||
|
||
Currently these benchmarks are pure diffusion simulations. There are 7
|
||
transported species: H, O, Charge, Ba, Cl, S(6), Sr.
|
||
|
||
** =barite.R=
|
||
|
||
- Grid discretization: square domain of 1 \cdot 1 m^{2} discretized in
|
||
20x20 cells
|
||
- Boundary conditions: E, S and W sides of the domain are closed; the
|
||
N boundary has a *fixed concentration* (Dirichlet) of 0.1 molal
|
||
BaCl_{2}
|
||
- Diffusion coefficients: isotropic homogeneous \alpha = 1E-06
|
||
- Time steps & iterations: 20 iteration with \Delta t = 250 s
|
||
- *DHT* parameters:
|
||
| H | O | Charge | Ba | Cl | S(6) | Sr |
|
||
| 10 | 10 | 3 | 5 | 5 | 5 | 5 |
|
||
|
||
|
||
|
||
** =barite_interp_eval.R=
|
||
- Grid discretization: rectangular domain of 40 \cdot 20 m^{2}
|
||
discretized in 400 \cdot 200 cells
|
||
- Boundary conditions: all boundaries are closed. The center of the
|
||
domain at indeces (200, 100) has fixed concentration of 0.1 molal of
|
||
BaCl_{2}
|
||
- Diffusion coefficients: isotropic homogeneous \alpha = 1E-06
|
||
- Time steps & iterations: 200 iterations with \Delta t = 250 s
|
||
- *DHT* parameters:
|
||
| H | O | Charge | Ba | Cl | S(6) | Sr |
|
||
| 10 | 10 | 3 | 5 | 5 | 5 | 5 |
|
||
|
||
* References
|
||
|
||
- Tranter, Wetzel, De Lucia and Kühn (2021): Reactive transport model
|
||
of kinetically controlled celestite to barite replacement, Advances
|
||
in Geosciences, 56, 57-–65, 2021.
|
||
https://doi.org/10.5194/adgeo-56-57-20211
|
||
|
||
|