#+TITLE: Description of =surfex= 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 ex.R ex_res
mpirun -np 4 ./poet surfex.R surfex_res
#+end_src

* List of Files
- =ex.R=: POET input script for a 100x100 simulation grid, only
  exchange
- =ExBase.pqi=: PHREEQC input script for the =ex.R= model
- =surfex.R=: POET input script for a 1000x1000 simulation grid
  considering both cation exchange and surface complexation
- =SurfExBase.pqi=: PHREEQC input script for the =surfex.R= model
- =SMILE_2021_11_01_TH.dat=: PHREEQC database containing the
  parametrized data for Surface and Exchange, based on the SMILE
  Thermodynamic Database (Version 01-November-2021)

* Chemical system

This model describes migration of Uranium radionuclide in Opalinus
clay subject to surface complexation and cation exchange on the
surface of clay minerals. These two processes account for the binding
of aqueous complexes to the surfaces of minerals, which may have a
significant impact on safety of underground nuclear waste repository.
Namely, they can act as retardation buffer for uranium complexes
entering into a natural system. The system is kindly provided by Dr.
T. Hennig and is inspired to the sandy facies BWS-A3 sample from the
Mont Terri underground lab (Hennig and Kühn, 2021).

This chemical system is highly redox-sensitive, and several elements
are defined in significant amounts in different valence states. In
total, 20 elemental concentrations and valences are transported:
C(-4), C(4), Ca, Cl, Fe(2), Fe(3), K, Mg, Na, S(-2), S(2), S(4), S(6),
Sr , U(4), U(5), U(6); plus the total H, total O and Charge implicitly
required by PHREEQC_RM.

** Exchange

The SMILE database defines thermodynamical data for exchange of all
major cations and uranyl-ions on Illite and Montmorillonite. In
PHREEQC terms:
- *Y* for Montmorillonite, with a total amount of 1.2585
  milliequivalents and
- *Z* for Illite, with a total amount of 0.9418 meq

** Surface

Here we consider a Donnan diffuse double layer of 0.49 nm. Six
distinct sorption sites are defined:
- Kln_aOH (aluminol site) and Kln_siOH (silanol) for Kaolinite
- For Illite, strong and weak sites Ill_sOH and Ill_wOH respectively
- For Montmorillonite, strong and weak sites Mll_sOH and Mll_wOH
  respectively
  
Refer to the =SurfExBase.pqi= script for the actual numerical values
of the parameters.

* POET simulations

** =ex.R=

This benchmark only considers EXCHANGE, no mineral or SURFACE
complexation is involved.

- Grid discretization: square domain of 1 \cdot 1 m^{2} discretized in
  100x100 cells
- Boundary conditions: E, S and W sides of the domain are closed.
  *Fixed concentrations* are fixed at the N boundary.
- Diffusion coefficients: isotropic homogeneous \alpha = 1E-06
- Time steps & iterations: 10 iterations with \Delta t of 200 s
- *DHT* is not implemented as of yet for models including SURFACE and
  EXCHANGE geochemical processes *TODO*
- Hooks: no hooks defined *TODO*

** =surfex.R=

- Grid discretization: rectangular domain of 1 \cdot 1 m^{2}
  discretized in 10 \times 10 cells
- Boundary conditions: E, S and W sides of the domain are closed.
  *Fixed concentrations* are fixed at the N boundary.
- Diffusion coefficients: isotropic homogeneous \alpha = 1E-06
- Time steps & iterations: 10 iterations with \Delta t of 200 s
     
* References

- Hennig, T.; Kühn, M.Surrogate Model for Multi-Component Diffusion of
  Uranium through Opalinus Clay on the Host Rock Scale. Appl. Sci.
  2021, 11, 786. https://doi.org/10.3390/app11020786