# Chemical Reactions Module

The chemical reactions module provides a set of tools for the calculation of multicomponent aqueous reactive transport in porous media, originally developed as the MOOSE application RAT (Guo et al., 2013).

## Theory

The first part of defining the chemistry of a problem is to choose a set of independent primary species from which every other species (including minerals) can be expressed in terms of. Other chemical species that can be expressed as combinations of primary species are termed secondary species.

Following Lichtner (1996), the mass conservation equation is formulated in terms of the total concentration of a primary species , , and has the form

(1) where is porosity, is the hydrodynamic dispersion tensor, is the number of minerals formed by kinetic reactions, is the stoichiometric coefficient for the species in the kinetic reaction, is the reaction rate for the mineral, and is a source (sink) of the species, and is the Darcy flux

(2) where is permeability, is fluid viscosity, is pressure, is fluid density, and is gravity.

The total concentration of the primary species, , is defined as

(3) where is the concentration of the primary species, is the concentration of the secondary species, is the total number of secondary species, and are the stoichiometric coefficients.

### Aqueous equilibrium reactions

The concentration of the secondary species, , is calculated from mass action equations corresponding to equilibrium reactions

(4) where refers to the species. This yields

(5) where is equilibrium constant, is the activity coefficient, and is the number of primary species.

### Solid kinetic reactions

Mineral precipitation/dissolution is possible via kinetic reactions of the form

(6) where refers to the mineral species.

The reaction rate is based on transition state theory, a simple form of which gives

(7) where is positive for dissolution and negative for precipitation, is the rate constant, is the specific reactive surface area, is termed the mineral saturation ratio, expressed as

(8) where is the equilibrium constant for mineral .

The rate constant is typically reported at a reference temperature (commonly 25C). Using an Arrhenius relation, the temperature dependence of is given as

(9) where is the rate constant at reference temperature , is the activation energy, is the gas constant.

The exponents and in the reaction rate equation are specific to each mineral reaction, and should be measured experimentally. For simplicity, they are set to unity in this module.

The rate of change in molar concentration, , of the mineral species is

(10)

This can be expressed in terms of the mineral volume fraction

(11) where is the molar volume of the mineral species, (12)

The total porosity, , can be defined in terms of the volume fraction of all mineral species

(13)

In this way, the change in porosity due to mineral precipitation or dissolution can be calculated, which can then be used to calculate changes in other material properties such as permeability.

## Implementation details

The physics described above is implemented in a number of Kernels and AuxKernels

### Kernels

The transport of each primary species is calculated using the following Kernels:

The transport of primary species present in a secondary species is included using:

The amount of primary species converted to an immobile mineral phase is given by

The Darcy flux is calculated using

### AuxKernels

The following AuxKernels are used to calculate secondary species and mineral concentrations, as well as total primary species concentration and solution pH.

• AqueousEquilibriumRxnAux The concentration of secondary species for the equilibrium reaction

• KineticDisPreRateAux The kinetic rate of the kinetic reaction

• KineticDisPreConcAux The concentration of mineral species

• TotalConcentrationAux The total concentration of a given primary species

• PHAux The pH of the solution

• EquilibriumConstantAux Temperature-dependent equilibrium constant

### Material properties

The Kernels above require several material properties to be defined using the following names: porosity, diffusivity and conductivity. These can be defined using one of the Materials available in the framework. For example, constant properties can be implemented using a GenericConstantMaterial with the following:

Required material properties


[Materials]
[./porous]
type = GenericConstantMaterial
prop_names = 'diffusivity conductivity porosity'
prop_values = '1e-4 1e-4 0.2'
[../]
[]
(modules/chemical_reactions/test/tests/aqueous_equilibrium/1species.i)

More complicated formulations can be added by creating new Materials as required.

### Boundary condition

A flux boundary condition, ChemicalOutFlowBC is provided to define on a boundary.

### Postprocessors

The total volume fraction of a given mineral species can be calculated using a TotalMineralVolumeFraction postprocessor.

## Reaction network parser

The chemical reactions module includes a reaction network parser in the Actions system that enables chemical reactions to be specified in a natural form in the input file. The parser then adds all required Variables, AuxVariables, Kernels and AuxKernels to represent the total geochemical model. To use the reaction network parser, a ReactionNetwork block can be added to the input file.

Equilibrium reactions can be entered in the ReactionNetwork block using an AqueousEquilibriumReactions sub-block, while kinetic reactions are entered in a SolidKineticReactions sub-block.

The input file syntax for equilibrium reactions has to following form:

(14)

Individual equilibrium reactions are provided with the primary species on the left hand side, while the equilibrium species follows the = sign, followed by the log of the equilibrium constant. A comma is used to delimit reactions, so that multiple equilibrium reactions can be entered.

The syntax for solid kinetic reactions is similar, except that no equilibrium constant is entered in the reactions block.

To demonstrate the use of the reaction network parser, consider the geochemical model used in Guo et al. (2013), which features aqueous equilibrium reactions as well as kinetic mineral dissolution and precipitation.

Equilibrium reactions:

(15)

Kinetic reaction:

with equilibrium constant , specific reactive surface area m/L, kinetic rate constant mol/m and activation energy J/mol.

Example of AqueousEquilibriumReactions action.


[ReactionNetwork]
[./AqueousEquilibriumReactions]
primary_species = 'ca2+ hco3- h+'
secondary_species = 'co2_aq co32- caco3_aq cahco3+ caoh+ oh-'
pressure = pressure
reactions = 'h+ + hco3- = co2_aq 6.341,
hco3- - h+ = co32- -10.325,
ca2+ + hco3- - h+ = caco3_aq -7.009,
ca2+ + hco3- = cahco3+ -0.653,
ca2+ - h+ = caoh+ -12.85,
- h+ = oh- -13.991'
[../]
[./SolidKineticReactions]
primary_species = 'ca2+ hco3- h+'
kin_reactions = 'ca2+ + hco3- - h+ = caco3_s'
secondary_species = caco3_s
log10_keq = 1.8487
reference_temperature = 298.15
system_temperature = 298.15
gas_constant = 8.314
specific_reactive_surface_area = 4.61e-4
kinetic_rate_constant = 6.456542e-7
activation_energy = 1.5e4
[../]
[]
(modules/chemical_reactions/examples/calcium_bicarbonate/calcium_bicarbonate.i)

The reactive transport system above can be provided in the input file without using the reaction network parser. However, this adds more than 400 lines of input in this case, due to the large number of kernels that have to be provided!

## Objects, Actions, and, Syntax

### Materialsinput

• Chemical Reactions App
• LangmuirMaterialMaterial type that holds info regarding Langmuir desorption from matrix to porespace and viceversa
• MollifiedLangmuirMaterialMaterial type that holds info regarding MollifiedLangmuir desorption from matrix to porespace and viceversa

## References

1. Luanjing Guo, Hai Huang, Derek R Gaston, Cody J Permann, David Andrs, George D Redden, Chuan Lu, Don T Fox, and Yoshiko Fujita. A parallel, fully coupled, fully implicit solution to reactive transport in porous media using the preconditioned Jacobian-Free Newton-Krylov Method. Advances in Water Resources, 53:101–108, 2013.[BibTeX]
2. Peter C Lichtner. Continuum formulation of multicomponent-multiphase reactive transport. Reviews in Mineralogy and Geochemistry, 34:1–81, 1996.[BibTeX]