Reaction balancing

This page follows Chapter 11 of Bethke (2007).

The geochemistry module can be used to provide balanced reactions in terms of user-defined components.

Ca-clinoptilolite

The reaction for the mineral Ca-clinoptilolite is written in the database as $var element = document.getElementById("moose-equation-1a187f19-ae35-4c81-8ca7-7b4b9af0233a");katex.render("\\mathrm{ClinoptilCa} \\rightleftharpoons 12\\mathrm{H}_{2}\\mathrm{O} + \\mathrm{Ca}^{2+} + 2\\mathrm{Al}^{3+} + 10\\mathrm{SiO}_{2}\\mathrm{(aq)} - 8\\mathrm{H}^{+} \\ ,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ with an equilibrium constant of $var element = document.getElementById("moose-equation-1d50bcdc-c615-4d1f-8f7e-34f91e87cbf4");katex.render("\\log_{10}K = -9.12", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ at 25 $var element = document.getElementById("moose-equation-889938e8-4bfa-4d59-9b92-3808d0797685");katex.render("^{\\circ}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ C. Using basis-swaps, it can be expressed in terms of muscovite (instead of Al $var element = document.getElementById("moose-equation-11736e31-8160-484b-b37d-e3c3fcceb137");katex.render("^{3+}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ ), quartz (instead of SiO $var element = document.getElementById("moose-equation-93388b00-c331-4cd1-9e07-f2614b9a9cca");katex.render("_{2}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ (aq)) and OH $var element = document.getElementById("moose-equation-8e5a0e4b-1139-476a-a505-240b46a45fbd");katex.render("{-}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ instead of H $var element = document.getElementById("moose-equation-ba1c344d-8a69-46d4-87cf-7be787d32722");katex.render("^{+}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : $var element = document.getElementById("moose-equation-5add8b34-6438-4d89-80dd-0975df9895a4");katex.render("\\mathrm{ClinoptilCa} \\rightleftharpoons -\\frac{2}{3}\\mathrm{K}^{+} + \\frac{20}{3}\\mathrm{H}_{2}\\mathrm{O} + \\mathrm{Ca}^{2+} + \\frac{2}{3}\\mathrm{muscovite} + 8\\mathrm{quartz} + \\frac{4}{3}\\mathrm{OH}^{-} \\ ,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ with $var element = document.getElementById("moose-equation-349a3393-6707-40a8-9f6d-b6d1c87d2c14");katex.render("\\log_{10}K = -5.48", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

To perform this calculation using the geochemistry module, a GeochemicalModelDefinition object must be created with the desired mineral species:

[UserObjects<<<{"href": "../../../syntax/UserObjects/index.html"}>>>]
  [definition]
    type = GeochemicalModelDefinition<<<{"description": "User object that parses a geochemical database file, and only retains information relevant to the current geochemical model", "href": "../../../source/userobjects/GeochemicalModelDefinition.html"}>>>
    database_file<<<{"description": "The name of the geochemical database file"}>>> = "../../../database/moose_geochemdb.json"
    basis_species<<<{"description": "A list of basis components relevant to the aqueous-equilibrium problem. H2O must appear first in this list.  These components must be chosen from the 'basis species' in the database, the sorbing sites (if any) and the decoupled redox states that are in disequilibrium (if any)."}>>> = "H2O Ca++ Al+++ SiO2(aq) H+ K+"
    equilibrium_minerals<<<{"description": "A list of minerals that are in equilibrium with the aqueous solution.  All members of this list must be in the 'minerals' section of the database file"}>>> = "Clinoptil-Ca Muscovite Quartz"
    piecewise_linear_interpolation<<<{"description": "If true then use a piecewise-linear interpolation of logK and Debye-Huckel parameters, regardless of the interpolation type specified in the database file.  This can be useful for comparing with results using other geochemistry software"}>>> = true # to get exact logK at 25degC with no best-fit interpolation
  []
[]

Then a GeochemicalModelInterrogator must be created which specifies the desired swaps:

[GeochemicalModelInterrogator<<<{"href": "../../../syntax/GeochemicalModelInterrogator/index.html"}>>>]
  model_definition<<<{"description": "The name of the GeochemicalModelDefinition user object"}>>> = definition
  swap_out_of_basis<<<{"description": "Species that should be removed from the model_definition's basis and be replaced with the swap_into_basis species.  There must be the same number of species in swap_out_of_basis and swap_into_basis.  If this list contains more than one species, the swapping is performed one-by-one, starting with the first pair (swap_out_of_basis[0] and swap_into_basis[0]), then the next pair, etc"}>>> = "Al+++     SiO2(aq) H+"
  swap_into_basis<<<{"description": "Species that should be removed from the model_definition's equilibrium species list and added to the basis"}>>> = "  Muscovite Quartz   OH-"
  equilibrium_species<<<{"description": "Only output results for this equilibrium species.  If not provided, results for all equilibrium species will be outputted"}>>> = "Clinoptil-Ca"
[]

The first and last lines of the output yield the desired information:


Clinoptil-Ca = 12*H2O + 1*Ca++ + 2*Al+++ + 10*SiO2(aq) - 8*H+  .  log10(K) = -9.12
Clinoptil-Ca = 8*H2O + 1*Ca++ + 0.6667*Muscovite + 8*SiO2(aq) - 1.333*H+ - 0.6667*K+  .  log10(K) = -18.83
Clinoptil-Ca = 8*H2O + 1*Ca++ + 0.6667*Muscovite + 8*Quartz - 1.333*H+ - 0.6667*K+  .  log10(K) = 13.16
Clinoptil-Ca = 6.667*H2O + 1*Ca++ + 0.6667*Muscovite + 8*Quartz + 1.333*OH- - 0.6667*K+  .  log10(K) = -5.484

Pyrite

The standard reaction for the mineral Pyrite is $var element = document.getElementById("moose-equation-3ea935bf-3fa5-48c5-a2b3-544eb8ee8901");katex.render("\\mathrm{pyrite} \\rightleftharpoons -\\mathrm{H}_{2}\\mathrm{O} + \\mathrm{Fe}^{2+} - \\frac{7}{2}\\mathrm{O}_{2}\\mathrm{(aq)} + 2\\mathrm{SO}_{4}^{2-} + 2\\mathrm{H}^{+} \\ ,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ Using basis-swaps, it can be expressed in terms Fe(OH) $var element = document.getElementById("moose-equation-1327abb6-88b8-4ac5-a3c6-5f7a370f6433");katex.render("_{3}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ (ppd) (instead of Fe $var element = document.getElementById("moose-equation-e0729db7-67f9-4891-8305-32c2b3f50817");katex.render("^{2+}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ ): $var element = document.getElementById("moose-equation-2cb92144-aae9-4d4c-ac9a-3d6d26cc30eb");katex.render("\\mathrm{pyrite} \\rightleftharpoons - \\frac{7}{2}\\mathrm{H}_{2}\\mathrm{O} - \\frac{15}{4}\\mathrm{O}_{2}\\mathrm{(aq)} + \\mathrm{Fe(OH)}_{3}\\mathrm{(ppd)} + 2\\mathrm{SO}_{4}^{2-} + 4\\mathrm{H}^{+} \\ .", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ Alternatively, it can be expressed in terms of H $var element = document.getElementById("moose-equation-92410ac1-b871-4ff2-931e-30eac197dbe3");katex.render("_{2}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ S(aq) instead of SO $var element = document.getElementById("moose-equation-b6c334a7-fe9f-499b-8008-e4cf8acb84ef");katex.render("_{4}^{-}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : $var element = document.getElementById("moose-equation-1143a624-2434-427e-8458-d263b1372862");katex.render("\\mathrm{pyrite} \\rightleftharpoons - \\mathrm{H}_{2}\\mathrm{O} + \\frac{1}{2}\\mathrm{O}_{2}\\mathrm{(aq)} + \\mathrm{Fe}^{++} + 2\\mathrm{H}_{2}\\mathrm{S(aq)} - 2\\mathrm{H}^{+} \\ .", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ Or in terms of H $var element = document.getElementById("moose-equation-7b8704f5-774a-427a-b765-c273de893ec0");katex.render("_{2}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ S(aq) and SO $var element = document.getElementById("moose-equation-1455c75c-4375-444a-9669-00a666290650");katex.render("_{4}^{-}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : $var element = document.getElementById("moose-equation-624c7d56-9683-4b21-9b51-1a97401ac38d");katex.render("\\mathrm{pyrite} \\rightleftharpoons - \\mathrm{H}_{2}\\mathrm{O} + \\frac{7}{4}\\mathrm{H}_{2}\\mathrm{S(aq)} + \\mathrm{Fe}^{++} + \\frac{1}{4}\\mathrm{SO}_{4}^{2-} - \\frac{3}{2}\\mathrm{H}^{+} \\ .", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

To perform this calculation using the geochemistry module, a GeochemicalModelDefinition object must be created with the desired mineral species:

[UserObjects<<<{"href": "../../../syntax/UserObjects/index.html"}>>>]
  [definition]
    type = GeochemicalModelDefinition<<<{"description": "User object that parses a geochemical database file, and only retains information relevant to the current geochemical model", "href": "../../../source/userobjects/GeochemicalModelDefinition.html"}>>>
    database_file<<<{"description": "The name of the geochemical database file"}>>> = "../../../database/moose_geochemdb.json"
    basis_species<<<{"description": "A list of basis components relevant to the aqueous-equilibrium problem. H2O must appear first in this list.  These components must be chosen from the 'basis species' in the database, the sorbing sites (if any) and the decoupled redox states that are in disequilibrium (if any)."}>>> = "H2O Fe++ SO4-- H+ O2(aq)"
    equilibrium_minerals<<<{"description": "A list of minerals that are in equilibrium with the aqueous solution.  All members of this list must be in the 'minerals' section of the database file"}>>> = "Pyrite Fe(OH)3(ppd)"
    piecewise_linear_interpolation<<<{"description": "If true then use a piecewise-linear interpolation of logK and Debye-Huckel parameters, regardless of the interpolation type specified in the database file.  This can be useful for comparing with results using other geochemistry software"}>>> = true # to get exact logK at 25degC with no best-fit interpolation
  []
[]

Then a GeochemicalModelInterrogator must be created which specifies the desired swaps:

[GeochemicalModelInterrogator<<<{"href": "../../../syntax/GeochemicalModelInterrogator/index.html"}>>>]
  model_definition<<<{"description": "The name of the GeochemicalModelDefinition user object"}>>> = definition
  swap_out_of_basis<<<{"description": "Species that should be removed from the model_definition's basis and be replaced with the swap_into_basis species.  There must be the same number of species in swap_out_of_basis and swap_into_basis.  If this list contains more than one species, the swapping is performed one-by-one, starting with the first pair (swap_out_of_basis[0] and swap_into_basis[0]), then the next pair, etc"}>>> = "Fe++         Fe(OH)3(ppd) SO4--   O2(aq)"
  swap_into_basis<<<{"description": "Species that should be removed from the model_definition's equilibrium species list and added to the basis"}>>> = "  Fe(OH)3(ppd) Fe++         H2S(aq) SO4--"
  equilibrium_species<<<{"description": "Only output results for this equilibrium species.  If not provided, results for all equilibrium species will be outputted"}>>> = Pyrite
[]

The output yields the desired information:


Pyrite = -1*H2O + 1*Fe++ + 2*SO4-- + 2*H+ - 3.5*O2(aq)  .  log10(K) = 217.4
Pyrite = -3.5*H2O + 1*Fe(OH)3(ppd) + 2*SO4-- + 4*H+ - 3.75*O2(aq)  .  log10(K) = 221
Pyrite = -1*H2O + 1*Fe++ + 2*SO4-- + 2*H+ - 3.5*O2(aq)  .  log10(K) = 217.4
Pyrite = -1*H2O + 1*Fe++ + 2*H2S(aq) - 2*H+ + 0.5*O2(aq)  .  log10(K) = -45.39
Pyrite = -1*H2O + 1*Fe++ + 1.75*H2S(aq) - 1.5*H+ + 0.25*SO4--  .  log10(K) = -12.54

References

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

@book{bethke_2007,
    author = "Bethke, Craig M.",
    place = "Cambridge",
    edition = "2",
    title = "Geochemical and Biogeochemical Reaction Modeling",
    DOI = "10.1017/CBO9780511619670",
    publisher = "Cambridge University Press",
    year = "2007"
}

(modules/geochemistry/test/tests/interrogate_reactions/clinoptilolite.i)

# Outputs equilibrium reactions fo Clinoptil-Ca for various different basis species, along with log10(K)
[GeochemicalModelInterrogator]
  model_definition = definition
  swap_out_of_basis = "Al+++     SiO2(aq) H+"
  swap_into_basis = "  Muscovite Quartz   OH-"
  equilibrium_species = "Clinoptil-Ca"
[]

[UserObjects]
  [definition]
    type = GeochemicalModelDefinition
    database_file = "../../../database/moose_geochemdb.json"
    basis_species = "H2O Ca++ Al+++ SiO2(aq) H+ K+"
    equilibrium_minerals = "Clinoptil-Ca Muscovite Quartz"
    piecewise_linear_interpolation = true # to get exact logK at 25degC with no best-fit interpolation
  []
[]

(modules/geochemistry/test/tests/interrogate_reactions/clinoptilolite.i)

# Outputs equilibrium reactions fo Clinoptil-Ca for various different basis species, along with log10(K)
[GeochemicalModelInterrogator]
  model_definition = definition
  swap_out_of_basis = "Al+++     SiO2(aq) H+"
  swap_into_basis = "  Muscovite Quartz   OH-"
  equilibrium_species = "Clinoptil-Ca"
[]

[UserObjects]
  [definition]
    type = GeochemicalModelDefinition
    database_file = "../../../database/moose_geochemdb.json"
    basis_species = "H2O Ca++ Al+++ SiO2(aq) H+ K+"
    equilibrium_minerals = "Clinoptil-Ca Muscovite Quartz"
    piecewise_linear_interpolation = true # to get exact logK at 25degC with no best-fit interpolation
  []
[]

(modules/geochemistry/test/tests/interrogate_reactions/pyrite.i)

# Output equilibrium reactions for pyrite using different basis components
[GeochemicalModelInterrogator]
  model_definition = definition
  swap_out_of_basis = "Fe++         Fe(OH)3(ppd) SO4--   O2(aq)"
  swap_into_basis = "  Fe(OH)3(ppd) Fe++         H2S(aq) SO4--"
  equilibrium_species = Pyrite
[]

[UserObjects]
  [definition]
    type = GeochemicalModelDefinition
    database_file = "../../../database/moose_geochemdb.json"
    basis_species = "H2O Fe++ SO4-- H+ O2(aq)"
    equilibrium_minerals = "Pyrite Fe(OH)3(ppd)"
    piecewise_linear_interpolation = true # to get exact logK at 25degC with no best-fit interpolation
  []
[]

(modules/geochemistry/test/tests/interrogate_reactions/pyrite.i)

# Output equilibrium reactions for pyrite using different basis components
[GeochemicalModelInterrogator]
  model_definition = definition
  swap_out_of_basis = "Fe++         Fe(OH)3(ppd) SO4--   O2(aq)"
  swap_into_basis = "  Fe(OH)3(ppd) Fe++         H2S(aq) SO4--"
  equilibrium_species = Pyrite
[]

[UserObjects]
  [definition]
    type = GeochemicalModelDefinition
    database_file = "../../../database/moose_geochemdb.json"
    basis_species = "H2O Fe++ SO4-- H+ O2(aq)"
    equilibrium_minerals = "Pyrite Fe(OH)3(ppd)"
    piecewise_linear_interpolation = true # to get exact logK at 25degC with no best-fit interpolation
  []
[]

Ca - clinoptilolite
Pyrite
References