Sorption onto ferric hydroxide

Definition of the sorption via surface complexation

It is assumed that there are two sorbing sites: Bethke (2007) uses the convention that a ">" indicates something to do with sorption. The sorbing reactions, written in the documentation on equilibrium reactions as are, specifically: The sorption occurs on the ferric hydroxide mineral, Fe(OH), called Fe(OH)3(ppd) in the database.

In order to complete the description of surface complexation, the surface potential must be specified. This requires the specific surface area, which is assumed to be We assume that:

• For each mol of Fe(OH)3(ppd), there is 0.005mol of >(s)FeOH

• For each mol of Fe(OH)3(ppd), there is 0.2mol of >(w)FeOH

All of the above information is contained in the MOOSE test database ferric_hydroxide_sorption.json. It is read into the MOOSE input file using a GeochemicalModelDefinition UserObject

[UserObjects]
  [definition]
    type = GeochemicalModelDefinition
    database_file = "../../database/ferric_hydroxide_sorption.json"
    basis_species = "H2O H+ Na+ Cl- Hg++ Pb++ SO4-- Fe+++ >(s)FeOH >(w)FeOH"
    equilibrium_minerals = "Fe(OH)3(ppd)"
    piecewise_linear_interpolation = true # for comparison with GWB
  []
[]

Chemical composition, mineral quantities and sorbing moles

The chemical composition of the water is shown in Table 1. In addition:

• charge balance is performed on Cl;

• two models are run: one with pH=4, and the other with pH=8.

There is 1 free gram of Fe(OH)3(ppd), which in geochemistry language means there is free mols of this mineral. Remember "free" moles means a quantity that is "floating around in the aqueous solution". This is in contrast to a "bulk composition" which consists of the free amount as well as an amount that forms equilibrium (secondary) species. This means there is

• mol of >(s)FeOH

• mol of >(w)FeOH

Note that these are bulk composition values as some of these sites will be free and some will be occupied by sorbed species.

The TimeIndependentReactionSolver defines the composition, including the pH, the free mole number of the mineral, and the bulk composition of the sorbing sites:

[TimeIndependentReactionSolver]
  model_definition = definition
  charge_balance_species = "Cl-"
  swap_out_of_basis = "Fe+++"
  swap_into_basis = "Fe(OH)3(ppd)"
  constraint_species = "H2O              H+            Na+              Cl-              Hg++             Pb++             SO4--            Fe(OH)3(ppd) >(s)FeOH         >(w)FeOH"
  constraint_value = "  1.0              1E-4          10E-3            10E-3            0.1E-3           0.1E-3           0.2E-3           9.3573E-3    4.6786E-5        1.87145E-3"
  constraint_meaning = "kg_solvent_water activity      bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition free_mineral bulk_composition bulk_composition"
  constraint_unit = "   kg               dimensionless moles            moles            moles            moles            moles            moles        moles            moles"
  ramp_max_ionic_strength_initial = 0 # not needed in this simple problem
  stoichiometric_ionic_str_using_Cl_only = true # for comparison with GWB
  mol_cutoff = 1E-10
  abs_tol = 1E-15
[]

GWB input file

The equivalent Geochemists Workbench input file is

# React script that is equivalent to ferric_hydroxide.i
surface_data = FeOH+.dat
sorbate include
data = thermo.tdat verify
conductivity = conductivity-USGS.dat
temperature = 25 C
H2O          = 1 free kg
Cl-          = 10.0E-3 mol
balance on Cl-
Na+          = 10.0E-3 mol
pH           = 4
Hg++         = 0.1E-3 mol
Pb++         = 0.1E-3 mol
SO4--        = 0.2E-3 mol
decouple Fe+++
swap Fe(OH)3(ppd) for Fe+++
Fe(OH)3(ppd) = 9.3573E-3 free mol
printout species = long
suppress all
unsuppress Fe(OH)3(ppd)
epsilon = 1e-12

Results

Bethke (2007) computes the results that are shown in Table 2, Table 3, Table 4 and Table 5. Both the geochemistry module and the GWB software give the same results. (A final note: sometimes the geochemistry results differ from the Geochemists Workbench results in the 4 significant figure. This is because of the different precision used for the permittivity of free space, the Faraday constant, etc.)

References