KineticDisPreRateAux

Kinetic rate of secondary kinetic species

Calculates the kinetic reaction rate based on transition state theory

$var element = document.getElementById("moose-equation-f941172b-29b6-4e17-bf66-17f0e20236f3");katex.render("I_m = \\pm k_m a_m \\left|1 - \\Omega_m^{\\theta}\\right|^{\\eta},", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-56cdb194-24a4-4f72-ba7d-157a2bf0d1d9");katex.render("I_m", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is positive for dissolution and negative for precipitation, $var element = document.getElementById("moose-equation-98c13dfb-e77e-4027-82f7-1e1e9a670cb3");katex.render("k_m", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the rate constant, $var element = document.getElementById("moose-equation-2dbce3c0-dac9-4cef-85ae-5cfc318ed3a3");katex.render("a_m", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the specific reactive surface area, $var element = document.getElementById("moose-equation-b0e64be6-3bbc-40e8-9979-4155db66cbac");katex.render("\\Omega_m", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is termed the mineral saturation ratio, expressed as

$var element = document.getElementById("moose-equation-c64953b7-2407-49b6-be78-14b471c2d745");katex.render("\\Omega_m = \\frac{1}{K_m} \\prod_{j}(\\gamma_j C_j)^{\\nu_{jm}},", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-e024eedd-71db-4bb9-aac7-c9e010ce9e38");katex.render("K_m", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the equilibrium constant for mineral $var element = document.getElementById("moose-equation-65dd2509-9c1a-45df-b721-8e5cc2a2fdd6");katex.render("m", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , $var element = document.getElementById("moose-equation-4e845573-09c9-401e-998d-96401558d41e");katex.render("\\gamma_j", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the activity coefficient, $var element = document.getElementById("moose-equation-991e9ec9-40b9-4025-9b6e-190d6c36cccc");katex.render("C_j", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the concentration of the $var element = document.getElementById("moose-equation-51cdde05-d727-429f-9228-541702170e81");katex.render("j^{\\mathrm{th}}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ primary species and $var element = document.getElementById("moose-equation-ec52b143-879a-46fa-b0ba-d09a31a175cc");katex.render("\\nu_{jm}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the stoichiometric coefficient.

The rate constant $var element = document.getElementById("moose-equation-b1cc24a7-24ed-4925-bb22-9519fe18ccc1");katex.render("k_m", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is typically reported at a reference temperature (commonly 25 $var element = document.getElementById("moose-equation-fca97b69-485a-468b-bd26-1d9bf08d38ea");katex.render("^{\\circ}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ C). Using an Arrhenius relation, the temperature dependence of $var element = document.getElementById("moose-equation-e0a67f8b-0dd6-4736-b7d3-631136556179");katex.render("k_m", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is given as

$var element = document.getElementById("moose-equation-58612cce-b488-4a49-8dc7-4a9423ded333");katex.render("k_m(T) = k_{m,0} \\exp\\left[\\frac{E_a}{R} \\left(\\frac{1}{T_0} - \\frac{1}{T}\\right)\\right],", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-92e17e26-4a79-40b1-8816-99020a42ffbc");katex.render("k_{m,0}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the rate constant at reference temperature $var element = document.getElementById("moose-equation-b8fc3f49-3d54-480f-b255-b2ce0e47a271");katex.render("T_0", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , $var element = document.getElementById("moose-equation-d56e9041-463d-4181-9ccc-3980c765afee");katex.render("E_a", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the activation energy, $var element = document.getElementById("moose-equation-1e35f247-efc7-43a0-bd25-248e9f8d278d");katex.render("R", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the gas constant.

The exponents $var element = document.getElementById("moose-equation-69084546-94e6-4684-b9b7-920e8cc0be07");katex.render("\\theta", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-4366bd17-961c-4810-bcc8-082c887a588d");katex.render("\\eta", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ 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.

Input Parameters

sto_vThe stoichiometric coefficients of reactant species
C++ Type:std::vector
Options:
Description:The stoichiometric coefficients of reactant species
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Options:
Description:The name of the variable that this object applies to

Required Parameters

blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
e_act29100Activation energy, J/mol
Default:29100
C++ Type:double
Options:
Description:Activation energy, J/mol
execute_onLINEAR TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.
Default:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE INITIAL LINEAR NONLINEAR TIMESTEP_END TIMESTEP_BEGIN FINAL CUSTOM PRE_DISPLACE
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.
gas_const8.31434Gas constant, in J/mol K
Default:8.31434
C++ Type:double
Options:
Description:Gas constant, in J/mol K
log_kThe equilibrium constant of the dissolution reaction
C++ Type:std::vector
Options:
Description:The equilibrium constant of the dissolution reaction
r_area0.1Specific reactive surface area in m^2/L solution
Default:0.1
C++ Type:double
Options:
Description:Specific reactive surface area in m^2/L solution
ref_kconst6.45654e-08Kinetic rate constant in mol/m^2 s
Default:6.45654e-08
C++ Type:double
Options:
Description:Kinetic rate constant in mol/m^2 s
ref_temp298.15Reference temperature, K
Default:298.15
C++ Type:double
Options:
Description:Reference temperature, K
sys_temp298.15System temperature, K
Default:298.15
C++ Type:std::vector
Options:
Description:System temperature, K
vThe list of reactant species
C++ Type:std::vector
Options:
Description:The list of reactant species

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

Input Files

modules/chemical_reactions/test/tests/kinetic_rate/arrhenius.i

modules/chemical_reactions/test/tests/kinetic_rate/arrhenius.i

# Check the correct temperature dependence of the kinetic rate constant using
# the Arrhenius equation. Two kinetic reactions take place at different system
# temperatures. The Arrhenius equation states that the kinetic rate increases
# with temperature, so more mineral should be precipitated for the higher system
# temperature. In this case, the AuxVariables kinetic_rate1 and mineral1 should
# be larger than kinetic_rate0 and mineral0.

[Mesh]
  type = GeneratedMesh
  dim = 2
[]

[Variables]
  [./a0]
    initial_condition = 0.1
  [../]
  [./b0]
    initial_condition = 0.1
  [../]
  [./a1]
    initial_condition = 0.1
  [../]
  [./b1]
    initial_condition = 0.1
  [../]
[]

[AuxVariables]
  [./mineral0]
  [../]
  [./mineral1]
  [../]
  [./kinetic_rate0]
  [../]
  [./kinetic_rate1]
  [../]
[]

[AuxKernels]
  [./kinetic_rate0]
    type = KineticDisPreRateAux
    variable = kinetic_rate0
    e_act = 1.5e4
    r_area = 1
    log_k = -6
    ref_kconst = 1e-8
    gas_const = 8.31434
    ref_temp = 298.15
    sys_temp = 298.15
    sto_v = '1 1'
    v = 'a0 b0'
  [../]
  [./kinetic_rate1]
    type = KineticDisPreRateAux
    variable = kinetic_rate1
    e_act = 1.5e4
    r_area = 1
    log_k = -6
    ref_kconst = 1e-8
    gas_const = 8.31434
    ref_temp = 298.15
    sys_temp = 323.15
    sto_v = '1 1'
    v = 'a1 b1'
  [../]
  [./mineral0_conc]
    type = KineticDisPreConcAux
    variable = mineral0
    e_act = 1.5e4
    r_area = 1
    log_k = -6
    ref_kconst = 1e-8
    gas_const = 8.31434
    ref_temp = 298.15
    sys_temp = 298.15
    sto_v = '1 1'
    v = 'a0 b0'
  [../]
  [./mineral1_conc]
    type = KineticDisPreConcAux
    variable = mineral1
    e_act = 1.5e4
    r_area = 1
    log_k = -6
    ref_kconst = 1e-8
    gas_const = 8.31434
    ref_temp = 298.15
    sys_temp = 323.15
    sto_v = '1 1'
    v = 'a1 b1'
  [../]
[]

[Kernels]
  [./a0_ie]
    type = PrimaryTimeDerivative
    variable = a0
  [../]
  [./b0_ie]
    type = PrimaryTimeDerivative
    variable = b0
  [../]
  [./a0_r]
    type = CoupledBEKinetic
    variable = a0
    v = mineral0
    weight = 1
  [../]
  [./b0_r]
    type = CoupledBEKinetic
    variable = b0
    v = mineral0
    weight = 1
  [../]
  [./a1_ie]
    type = PrimaryTimeDerivative
    variable = a1
  [../]
  [./b1_ie]
    type = PrimaryTimeDerivative
    variable = b1
  [../]
  [./a1_r]
    type = CoupledBEKinetic
    variable = a1
    v = mineral1
    weight = 1
  [../]
  [./b1_r]
    type = CoupledBEKinetic
    variable = b1
    v = mineral1
    weight = 1
  [../]
[]

[Materials]
  [./porous]
    type = GenericConstantMaterial
    prop_names = porosity
    prop_values = 0.2
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  end_time = 1
  dt = 1
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Outputs]
  exodus = true
  perf_graph = true
  print_linear_residuals = true
[]

Child Objects

modules/chemical_reactions/include/auxkernels/KineticDisPreConcAux.h

modules/chemical_reactions/include/auxkernels/KineticDisPreConcAux.h

// This file is part of the MOOSE framework
// https://www.mooseframework.org
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#pragma once

#include "KineticDisPreRateAux.h"

class KineticDisPreConcAux;

template <>
InputParameters validParams<KineticDisPreConcAux>();

/**
 * Calculate the kinetic mineral species concentrations according to
 * transient state theory rate law.
 */
class KineticDisPreConcAux : public KineticDisPreRateAux
{
public:
  KineticDisPreConcAux(const InputParameters & parameters);

  virtual ~KineticDisPreConcAux() {}

protected:
  virtual Real computeValue() override;
};

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Input Files
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