Energy available for microbial respiration

This example closely follows Section 7.4 of Bethke (2007) in which the energy available for microbial respiration is computed using the Nernst Eh values of various redox half-reactions. Bethke (2007) has several pages of interesting explanation that are not repeated here: we are focussing primarily on the MOOSE model and validating the MOOSE results.

The following assumptions are made.

  • The following alternate oxidation states are in redox disequilibrium:

    • CH3COO-

    • CH4(aq)

    • Fe+++

    • H2(aq)

    • HS-

    • NH4+

    • NO2-

  • The pH is 6

  • The fugacity of CO(g) is fixed at 0.01, and it is used in the basis in place of the aqueous species HCO

  • There is 1 free cm of the mineral Fe(OH)(ppd) and that it is used in the basis in place of the redox aqueous species Fe.

  • The bulk composition of the other basis species are:

    • SO4– 0.3963E-3 mol (mg.kg)

    • Ca++ 0.407E-3 mol (mg.kg)

    • Cl- 0.46E-3 mol (mg.kg this is the charge-balance species)

    • Na+ 0.473E-3 mol (mg.kg)

    • Mg++ 0.0895E-3 mol (mg.kg)

    • NO3- 3.508E-5 mol (mg.kg )

    • CH4(aq) 2.712E-5 mol (mg.kg)

    • NO2- 9.456E-6 mol (mg.kg)

    • CH3COO- 5.5526E-6 mol (mg.kg)

    • Fe++ 3.895E-6 mol (mg.kg)

    • NH4+ 6.029E-6 mol (mg.kg)

    • HS- 1.6445E-6 mol (mg.kg)

      - The free composition of the remaining basis species are:

    • O2(aq) 3.399E-6 free molal (mg.kg free)

    • H2(aq) 0.004E-6 free molal (mol.kg, free (not bulk))

  • All mineralisation reactions are ignored.

MOOSE input file

The MOOSE input file that corresponding to this model description is

[TimeIndependentReactionSolver]
  model_definition = definition
  temperature = 25
  swap_out_of_basis = 'HCO3-  Fe+++'
  swap_into_basis = '  CO2(g) Fe(OH)3(ppd)'
  charge_balance_species = "Cl-"
# TDS = 80.5mg/g (roughly) = (mass_non-water) / (mass_solvent_water + mass_non-water),
# so with mass_solvent_water = 1kg, mass_non-water = 87.6mg and total_mass = 1.0876
  constraint_species = "H2O              H+          CO2(g)        Fe(OH)3(ppd) Cl-              Na+              Ca++             Mg++             SO4--            Fe++             H2(aq)             HS-              O2(aq)             CH4(aq)           NO3-              NO2-              NH4+              CH3COO-"
  constraint_value = "  1.0              1E-6        0.01          0.02914      0.46E-3          0.473E-3         0.407E-3         0.0895E-3        0.3963E-3        3.895E-6         0.004E-6           1.6445E-6        3.399E-6           2.712E-5          3.508E-5          9.456E-6          6.029E-6          5.5526E-6"
  constraint_meaning = "kg_solvent_water activity    fugacity      free_mineral bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition free_concentration bulk_composition free_concentration bulk_composition  bulk_composition  bulk_composition  bulk_composition  bulk_composition"
  constraint_unit = "   kg             dimensionless dimensionless moles        moles            moles            moles            moles            moles            moles            molal              moles            molal              moles             moles             moles             moles             moles"
  ramp_max_ionic_strength_initial = 0 # not needed in this simple problem
  max_initial_residual = 1E-2
  stoichiometric_ionic_str_using_Cl_only = true # for comparison with GWB
  mol_cutoff = 1E-5
  abs_tol = 1E-17
[]

[UserObjects]
  [definition]
    type = GeochemicalModelDefinition
    database_file = "../../../database/moose_geochemdb.json"
    basis_species = "H2O H+ Cl- Na+ Ca++ Mg++ SO4-- Fe++ H2(aq) HS- O2(aq) Fe+++ HCO3- CH3COO- CH4(aq) NH4+ NO2- NO3-"
    equilibrium_minerals = "Fe(OH)3(ppd)"
    equilibrium_gases = "CO2(g)"
    piecewise_linear_interpolation = true # for comparison with GWB
  []
[]
(modules/geochemistry/test/tests/redox_disequilibrium/microbial.i)

GWB

The Geochemists Workbench input file corresponding to this model is

# React script that is equivalent to the microbial.i MOOSE input file
data = thermo.tdat verify
conductivity = conductivity-USGS.dat
temperature = 25 C
decouple CH3COO-
decouple CH4(aq)
decouple Fe+++
decouple H2(aq)
decouple HS-
decouple NH4+
decouple NO2-
H2O          = 1 free kg
Cl-          = 0.46E-3 mol
balance on Cl-
H+           = 6 pH
swap CO2(g) for HCO3-
CO2(g)       = 0.01 fugacity
swap Fe(OH)3(ppd) for Fe+++
Fe(OH)3(ppd) = 0.02914 free mol
Na+          = 0.473E-3 mol
Ca++         = 0.407E-3 mol
Mg++         = 0.0895E-3 mol
SO4--        = 0.3963E-3 mol
Fe++         = 3.895E-6 mol
H2(aq)       = 0.004E-6 free molal
HS-          = 1.6445E-6 mol
O2(aq)       = 3.399E-6 free molal
CH4(aq)      = 2.712E-5 mol
NO3-         = 3.508E-5 mol
NO2-         = 9.456E-6 mol
NH4+         = 6.029E-6 mol
CH3COO-      = 5.5526E-6 mol
printout  species = long
suppress all
unsuppress Fe(OH)3(ppd)
epsilon = 1e-14
go
(modules/geochemistry/test/tests/redox_disequilibrium/microbial.rea)

Nernst potentials

Bethke (2007) computes the Nernst potentials for each redox couple as shown in Table 1

Table 1: Nernst potentials for redox couple

ReactionEh (mV)
e + O(aq) + H HO836
2e + 2H + NO HO + NO481
8e + 10H + NO 3HO + NH443
6e + 8H + NO 2HO + NH430
e + Fe Fe321
8e + 9H + SO 4HO + HS-126
4e + H + CHCOO HO + CH(aq)-145
8e + 9H + HCO 3HO + CH(aq)-188
2e + 2H H(aq)-199
8e + 9H + 2HCO 4HO + CHCOO-230

This output is produced by the Geochemists Workbench software. The output produced by geochemistry looks a little different:


Nernst potentials:
e- = 0.5*H2O - 1*H+ - 0.25*O2(aq);  Eh = 0.8361V
e- = 0.5*H2O - 1*H+ + 0.5*NO2- - 0.5*NO3-;  Eh = 0.4809V
e- = 0.375*H2O - 1.25*H+ + 0.125*NH4+ - 0.125*NO3-;  Eh = 0.4425V
e- = 1*Fe++ - 1*Fe+++;  Eh = 0.3206V
e- = 0.5*H2O - 1.125*H+ - 0.125*SO4-- + 0.125*HS-;  Eh = -0.1263V
e- = 0.375*H2O - 1.125*H+ - 0.125*HCO3- + 0.125*CH4(aq);  Eh = -0.1875V
e- = -1*H+ + 0.5*H2(aq);  Eh = -0.1986V
e- = 0.5*H2O - 1.125*H+ - 0.25*HCO3- + 0.125*CH3COO-;  Eh = -0.2298V

The differences are:

  • the reactions are all written with "e-" on the left-hand side

  • the values for Eh sometimes differ in their fourth significant figure (this is presumably due to geochemistry using higher precision than GWB)

  • the following reactions are missing:

    • 6e + 8H + NO 2HO + NH (Eh = 430) and

    • 4e + H + CHCOO HO + CH(aq) (Eh = -145)

The reason these reactions do not appear is that geochemistry outputs a minimal set only, from which others can be derived. For instance, the difference of the two equations produces the equation which produces the result mV when divided by 3. (Remember that Eh values quoted by GWB are normalised to the number of electrons, but when manipulating equations in the way just described, the number of electrons must be accounted for.)

References

  1. Craig M. Bethke. Geochemical and Biogeochemical Reaction Modeling. Cambridge University Press, 2 edition, 2007. doi:10.1017/CBO9780511619670.[BibTeX]