Porous Flow Tutorial Page 13. More elaborate chemistry
A very simple chemical system was built in Page 07. The reader is encouraged to consult that page before moving to the more elaborate situation described here. This page:
does not use an
Actionto describe the Kernels, Materials, etc. This makes the input file quite long, but perhaps more easy to extend to multi-phase situations, different boundary conditions, etc. AnActioncould easily be used instead, by copying the chemistry from this tutorial to that on Page 07.builds a fully-saturated aqueous chemical system that could be used to describe dolomite precipitation and dissolution.
The equilibrium system
The equilibrium system has:
5 primary species, which are H, HCO, Ca, Mg, Fe.
5 secondary species, which are CO(aq), CO, CaHCO, MgHCO, FeHCO.
The equations are Some of these equilibrium constants have been chosen rather arbitrarily.
The primary species are represented as PorousFlow variables:
[Variables]
[./h+]
[../]
[./hco3-]
[../]
[./ca2+]
[../]
[./mg2+]
[../]
[./fe2+]
[../]
[]
The equilibrium reactions are encoded into this Material:
# Example of reactive transport model with dissolution of dolomite
#
# The equilibrium system has 5 primary species (Variables) and
# 5 secondary species (PorousFlowMassFractionAqueousEquilibrium).
# Some of the equilibrium constants have been chosen rather arbitrarily.
#
# Equilibrium reactions
# H+ + HCO3- = CO2(aq)
# -H+ + HCO3- = CO32-
# HCO3- + Ca2+ = CaHCO3+
# HCO3- + Mg2+ = MgHCO3+
# HCO3- + Fe2+ = FeHCO3+
#
# The kinetic reaction that dissolves dolomite involves all 5 primary species.
#
# -2H+ + 2HCO3- + Ca2+ + 0.8Mg2+ + 0.2Fe2+ = CaMg0.8Fe0.2(CO3)2
#
# The initial concentration of precipitated dolomite is high, so it starts
# to dissolve immediately, increasing the concentrations of the primary species.
#
# Only single-phase, fully saturated physics is used.
# The pressure gradient is fixed, so that the Darcy velocity is 0.1m/s.
#
# Primary species are injected from the left side, and they flow to the right.
# Less dolomite dissolution therefore occurs on the left side (where
# the primary species have higher concentration).
#
# This test is more fully documented in tutorial_13
[Mesh]
type = GeneratedMesh
dim = 1
nx = 100
xmax = 1
[]
[Variables]
[./h+]
[../]
[./hco3-]
[../]
[./ca2+]
[../]
[./mg2+]
[../]
[./fe2+]
[../]
[]
[AuxVariables]
[./eqm_k0]
initial_condition = 2.19E6
[../]
[./eqm_k1]
initial_condition = 4.73E-11
[../]
[./eqm_k2]
initial_condition = 0.222
[../]
[./eqm_k3]
initial_condition = 1E-2
[../]
[./eqm_k4]
initial_condition = 1E-3
[../]
[./kinetic_k]
initial_condition = 326.2
[../]
[./pressure]
[../]
[./dolomite]
family = MONOMIAL
order = CONSTANT
[../]
[./dolomite_initial]
initial_condition = 1E-7
[../]
[]
[AuxKernels]
[./dolomite]
type = PorousFlowPropertyAux
property = mineral_concentration
mineral_species = 0
variable = dolomite
[../]
[]
[GlobalParams]
PorousFlowDictator = dictator
gravity = '0 0 0'
[]
[ICs]
[./pressure_ic]
type = FunctionIC
variable = pressure
function = '(1 - x) * 1E6'
[../]
[./h+_ic]
type = BoundingBoxIC
variable = h+
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
[./hco3_ic]
type = BoundingBoxIC
variable = hco3-
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
[./ca2_ic]
type = BoundingBoxIC
variable = ca2+
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
[./mg2_ic]
type = BoundingBoxIC
variable = mg2+
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
[./fe2_ic]
type = BoundingBoxIC
variable = fe2+
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
[]
[Kernels]
[./h+_ie]
type = PorousFlowMassTimeDerivative
fluid_component = 0
variable = h+
[../]
[./h+_conv]
type = PorousFlowAdvectiveFlux
fluid_component = 0
variable = h+
[../]
[./predis_h+]
type = PorousFlowPreDis
variable = h+
mineral_density = 2875.0
stoichiometry = -2
[../]
[./hco3-_ie]
type = PorousFlowMassTimeDerivative
fluid_component = 1
variable = hco3-
[../]
[./hco3-_conv]
type = PorousFlowAdvectiveFlux
fluid_component = 1
variable = hco3-
[../]
[./predis_hco3-]
type = PorousFlowPreDis
variable = hco3-
mineral_density = 2875.0
stoichiometry = 2
[../]
[./ca2+_ie]
type = PorousFlowMassTimeDerivative
fluid_component = 2
variable = ca2+
[../]
[./ca2+_conv]
type = PorousFlowAdvectiveFlux
fluid_component = 2
variable = ca2+
[../]
[./predis_ca2+]
type = PorousFlowPreDis
variable = ca2+
mineral_density = 2875.0
stoichiometry = 1
[../]
[./mg2+_ie]
type = PorousFlowMassTimeDerivative
fluid_component = 3
variable = mg2+
[../]
[./mg2+_conv]
type = PorousFlowAdvectiveFlux
fluid_component = 3
variable = mg2+
[../]
[./predis_mg2+]
type = PorousFlowPreDis
variable = mg2+
mineral_density = 2875.0
stoichiometry = 0.8
[../]
[./fe2+_ie]
type = PorousFlowMassTimeDerivative
fluid_component = 4
variable = fe2+
[../]
[./fe2+_conv]
type = PorousFlowAdvectiveFlux
fluid_component = 4
variable = fe2+
[../]
[./predis_fe2+]
type = PorousFlowPreDis
variable = fe2+
mineral_density = 2875.0
stoichiometry = 0.2
[../]
[]
[UserObjects]
[./dictator]
type = PorousFlowDictator
porous_flow_vars = 'h+ hco3- ca2+ mg2+ fe2+'
number_fluid_phases = 1
number_fluid_components = 6
number_aqueous_equilibrium = 5
number_aqueous_kinetic = 1
[../]
[]
[Modules]
[./FluidProperties]
[./simple_fluid]
type = SimpleFluidProperties
viscosity = 1E-3
[../]
[../]
[]
[BCs]
[./hco3-_left]
type = DirichletBC
variable = hco3-
boundary = left
value = 5E-2
[../]
[./h+_left]
type = DirichletBC
variable = h+
boundary = left
value = 5E-2
[../]
[./ca2+_left]
type = DirichletBC
variable = ca2+
boundary = left
value = 5E-2
[../]
[./mg2+_left]
type = DirichletBC
variable = mg2+
boundary = left
value = 5E-2
[../]
[./fe2+_left]
type = DirichletBC
variable = fe2+
boundary = left
value = 5E-2
[../]
[./hco3-_right]
type = DirichletBC
variable = hco3-
boundary = right
value = 1E-6
[../]
[./h+_right]
type = DirichletBC
variable = h+
boundary = right
value = 1e-6
[../]
[./ca2+_right]
type = DirichletBC
variable = ca2+
boundary = right
value = 1E-6
[../]
[./mg2+_right]
type = DirichletBC
variable = mg2+
boundary = right
value = 1E-6
[../]
[./fe2+_right]
type = DirichletBC
variable = fe2+
boundary = right
value = 1E-6
[../]
[]
[Materials]
[./temperature]
type = PorousFlowTemperature
temperature = 298.15
[../]
[./ppss]
type = PorousFlow1PhaseFullySaturated
porepressure = pressure
[../]
[./equilibrium_massfrac]
type = PorousFlowMassFractionAqueousEquilibriumChemistry
mass_fraction_vars = 'h+ hco3- ca2+ mg2+ fe2+'
num_reactions = 5
equilibrium_constants = 'eqm_k0 eqm_k1 eqm_k2 eqm_k3 eqm_k4'
primary_activity_coefficients = '1 1 1 1 1'
secondary_activity_coefficients = '1 1 1 1 1'
reactions = '1 1 0 0 0
-1 1 0 0 0
0 1 1 0 0
0 1 0 1 0
0 1 0 0 1'
[../]
[./kinetic]
type = PorousFlowAqueousPreDisChemistry
primary_concentrations = 'h+ hco3- ca2+ mg2+ fe2+'
num_reactions = 1
equilibrium_constants = kinetic_k
primary_activity_coefficients = '1 1 1 1 1'
reactions = '-2 2 1 0.8 0.2'
specific_reactive_surface_area = '1.2E-8'
kinetic_rate_constant = '3E-4'
activation_energy = '1.5e4'
molar_volume = 64365.0
gas_constant = 8.314
reference_temperature = 298.15
[../]
[./dolomite_conc]
type = PorousFlowAqueousPreDisMineral
initial_concentrations = dolomite_initial
[../]
[./simple_fluid]
type = PorousFlowSingleComponentFluid
fp = simple_fluid
phase = 0
[../]
[./porosity]
type = PorousFlowPorosityConst
porosity = 0.2
[../]
[./permeability]
type = PorousFlowPermeabilityConst
permeability = '1E-10 0 0 0 1E-10 0 0 0 1E-10'
[../]
[./relp]
type = PorousFlowRelativePermeabilityConst
phase = 0
[../]
[]
[Executioner]
type = Transient
solve_type = Newton
end_time = 1
[./TimeStepper]
type = IterationAdaptiveDT
dt = 0.1
[../]
[]
[Preconditioning]
active = basic
[./basic]
type = SMP
full = true
petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
petsc_options_value = ' asm lu NONZERO 2'
[../]
[./preferred_but_might_not_be_installed]
type = SMP
full = true
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = ' lu mumps'
[../]
[]
[Outputs]
print_linear_residuals = false
perf_graph = true
exodus = true
[]
The kinetic system
This is with the following parameters:
molar volume 64365.0L(solution)/mol,
mineral density 2875.0kg(precipitate)/m(precipitate)
equilibrium constant ,
specific reactive surface area m/L,
kinetic rate constant mol/m/s,
activation energy J/mol,
the primary activity coefficients are all unity,
and the and exponents are also unity.
Some of these quantities have been chosen rather arbitrarily. This kinetic system is encoded in the input file as:
# Example of reactive transport model with dissolution of dolomite
#
# The equilibrium system has 5 primary species (Variables) and
# 5 secondary species (PorousFlowMassFractionAqueousEquilibrium).
# Some of the equilibrium constants have been chosen rather arbitrarily.
#
# Equilibrium reactions
# H+ + HCO3- = CO2(aq)
# -H+ + HCO3- = CO32-
# HCO3- + Ca2+ = CaHCO3+
# HCO3- + Mg2+ = MgHCO3+
# HCO3- + Fe2+ = FeHCO3+
#
# The kinetic reaction that dissolves dolomite involves all 5 primary species.
#
# -2H+ + 2HCO3- + Ca2+ + 0.8Mg2+ + 0.2Fe2+ = CaMg0.8Fe0.2(CO3)2
#
# The initial concentration of precipitated dolomite is high, so it starts
# to dissolve immediately, increasing the concentrations of the primary species.
#
# Only single-phase, fully saturated physics is used.
# The pressure gradient is fixed, so that the Darcy velocity is 0.1m/s.
#
# Primary species are injected from the left side, and they flow to the right.
# Less dolomite dissolution therefore occurs on the left side (where
# the primary species have higher concentration).
#
# This test is more fully documented in tutorial_13
[Mesh]
type = GeneratedMesh
dim = 1
nx = 100
xmax = 1
[]
[Variables]
[./h+]
[../]
[./hco3-]
[../]
[./ca2+]
[../]
[./mg2+]
[../]
[./fe2+]
[../]
[]
[AuxVariables]
[./eqm_k0]
initial_condition = 2.19E6
[../]
[./eqm_k1]
initial_condition = 4.73E-11
[../]
[./eqm_k2]
initial_condition = 0.222
[../]
[./eqm_k3]
initial_condition = 1E-2
[../]
[./eqm_k4]
initial_condition = 1E-3
[../]
[./kinetic_k]
initial_condition = 326.2
[../]
[./pressure]
[../]
[./dolomite]
family = MONOMIAL
order = CONSTANT
[../]
[./dolomite_initial]
initial_condition = 1E-7
[../]
[]
[AuxKernels]
[./dolomite]
type = PorousFlowPropertyAux
property = mineral_concentration
mineral_species = 0
variable = dolomite
[../]
[]
[GlobalParams]
PorousFlowDictator = dictator
gravity = '0 0 0'
[]
[ICs]
[./pressure_ic]
type = FunctionIC
variable = pressure
function = '(1 - x) * 1E6'
[../]
[./h+_ic]
type = BoundingBoxIC
variable = h+
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
[./hco3_ic]
type = BoundingBoxIC
variable = hco3-
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
[./ca2_ic]
type = BoundingBoxIC
variable = ca2+
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
[./mg2_ic]
type = BoundingBoxIC
variable = mg2+
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
[./fe2_ic]
type = BoundingBoxIC
variable = fe2+
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
[]
[Kernels]
[./h+_ie]
type = PorousFlowMassTimeDerivative
fluid_component = 0
variable = h+
[../]
[./h+_conv]
type = PorousFlowAdvectiveFlux
fluid_component = 0
variable = h+
[../]
[./predis_h+]
type = PorousFlowPreDis
variable = h+
mineral_density = 2875.0
stoichiometry = -2
[../]
[./hco3-_ie]
type = PorousFlowMassTimeDerivative
fluid_component = 1
variable = hco3-
[../]
[./hco3-_conv]
type = PorousFlowAdvectiveFlux
fluid_component = 1
variable = hco3-
[../]
[./predis_hco3-]
type = PorousFlowPreDis
variable = hco3-
mineral_density = 2875.0
stoichiometry = 2
[../]
[./ca2+_ie]
type = PorousFlowMassTimeDerivative
fluid_component = 2
variable = ca2+
[../]
[./ca2+_conv]
type = PorousFlowAdvectiveFlux
fluid_component = 2
variable = ca2+
[../]
[./predis_ca2+]
type = PorousFlowPreDis
variable = ca2+
mineral_density = 2875.0
stoichiometry = 1
[../]
[./mg2+_ie]
type = PorousFlowMassTimeDerivative
fluid_component = 3
variable = mg2+
[../]
[./mg2+_conv]
type = PorousFlowAdvectiveFlux
fluid_component = 3
variable = mg2+
[../]
[./predis_mg2+]
type = PorousFlowPreDis
variable = mg2+
mineral_density = 2875.0
stoichiometry = 0.8
[../]
[./fe2+_ie]
type = PorousFlowMassTimeDerivative
fluid_component = 4
variable = fe2+
[../]
[./fe2+_conv]
type = PorousFlowAdvectiveFlux
fluid_component = 4
variable = fe2+
[../]
[./predis_fe2+]
type = PorousFlowPreDis
variable = fe2+
mineral_density = 2875.0
stoichiometry = 0.2
[../]
[]
[UserObjects]
[./dictator]
type = PorousFlowDictator
porous_flow_vars = 'h+ hco3- ca2+ mg2+ fe2+'
number_fluid_phases = 1
number_fluid_components = 6
number_aqueous_equilibrium = 5
number_aqueous_kinetic = 1
[../]
[]
[Modules]
[./FluidProperties]
[./simple_fluid]
type = SimpleFluidProperties
viscosity = 1E-3
[../]
[../]
[]
[BCs]
[./hco3-_left]
type = DirichletBC
variable = hco3-
boundary = left
value = 5E-2
[../]
[./h+_left]
type = DirichletBC
variable = h+
boundary = left
value = 5E-2
[../]
[./ca2+_left]
type = DirichletBC
variable = ca2+
boundary = left
value = 5E-2
[../]
[./mg2+_left]
type = DirichletBC
variable = mg2+
boundary = left
value = 5E-2
[../]
[./fe2+_left]
type = DirichletBC
variable = fe2+
boundary = left
value = 5E-2
[../]
[./hco3-_right]
type = DirichletBC
variable = hco3-
boundary = right
value = 1E-6
[../]
[./h+_right]
type = DirichletBC
variable = h+
boundary = right
value = 1e-6
[../]
[./ca2+_right]
type = DirichletBC
variable = ca2+
boundary = right
value = 1E-6
[../]
[./mg2+_right]
type = DirichletBC
variable = mg2+
boundary = right
value = 1E-6
[../]
[./fe2+_right]
type = DirichletBC
variable = fe2+
boundary = right
value = 1E-6
[../]
[]
[Materials]
[./temperature]
type = PorousFlowTemperature
temperature = 298.15
[../]
[./ppss]
type = PorousFlow1PhaseFullySaturated
porepressure = pressure
[../]
[./equilibrium_massfrac]
type = PorousFlowMassFractionAqueousEquilibriumChemistry
mass_fraction_vars = 'h+ hco3- ca2+ mg2+ fe2+'
num_reactions = 5
equilibrium_constants = 'eqm_k0 eqm_k1 eqm_k2 eqm_k3 eqm_k4'
primary_activity_coefficients = '1 1 1 1 1'
secondary_activity_coefficients = '1 1 1 1 1'
reactions = '1 1 0 0 0
-1 1 0 0 0
0 1 1 0 0
0 1 0 1 0
0 1 0 0 1'
[../]
[./kinetic]
type = PorousFlowAqueousPreDisChemistry
primary_concentrations = 'h+ hco3- ca2+ mg2+ fe2+'
num_reactions = 1
equilibrium_constants = kinetic_k
primary_activity_coefficients = '1 1 1 1 1'
reactions = '-2 2 1 0.8 0.2'
specific_reactive_surface_area = '1.2E-8'
kinetic_rate_constant = '3E-4'
activation_energy = '1.5e4'
molar_volume = 64365.0
gas_constant = 8.314
reference_temperature = 298.15
[../]
Geometry
The model is just a 1D line, extending between and .
[Mesh]
type = GeneratedMesh
dim = 1
nx = 100
xmax = 1
[]
The initial and boundary conditions
Primary variables
Each of the primary variables are initialised to have concentration m(species)/m(solution) everywhere in the domain except for at the left-hand side () where they have concentration . The boundary conditions are to fix these values at the left and right sides of the domain. For instance:
[./h+_ic]
type = BoundingBoxIC
variable = h+
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
and
[./h+_left]
type = DirichletBC
variable = h+
boundary = left
value = 5E-2
[../]
[./h+_right]
type = DirichletBC
variable = h+
boundary = right
value = 1e-6
[../]
Please remember that boundary conditions in PorousFlow are usually more complicated than setting Dirichlet or Preset boundary conditions: see boundary conditions. Looking at the results below you can clearly see the effect of the naive boundary conditions placed on the right-hand side.
Dolomite
The initial condition for dolomite is m(precipitate)/m(porous material). This is implemented in the Auxillary system by
[AuxVariables]
[./eqm_k0]
initial_condition = 2.19E6
[../]
[./eqm_k1]
initial_condition = 4.73E-11
[../]
[./eqm_k2]
initial_condition = 0.222
[../]
[./eqm_k3]
initial_condition = 1E-2
[../]
[./eqm_k4]
initial_condition = 1E-3
[../]
[./kinetic_k]
initial_condition = 326.2
[../]
[./pressure]
[../]
[./dolomite]
family = MONOMIAL
order = CONSTANT
[../]
[./dolomite_initial]
initial_condition = 1E-7
[../]
[]
[AuxKernels]
[./dolomite]
type = PorousFlowPropertyAux
property = mineral_concentration
mineral_species = 0
variable = dolomite
[../]
[]
and the Material:
# Example of reactive transport model with dissolution of dolomite
#
# The equilibrium system has 5 primary species (Variables) and
# 5 secondary species (PorousFlowMassFractionAqueousEquilibrium).
# Some of the equilibrium constants have been chosen rather arbitrarily.
#
# Equilibrium reactions
# H+ + HCO3- = CO2(aq)
# -H+ + HCO3- = CO32-
# HCO3- + Ca2+ = CaHCO3+
# HCO3- + Mg2+ = MgHCO3+
# HCO3- + Fe2+ = FeHCO3+
#
# The kinetic reaction that dissolves dolomite involves all 5 primary species.
#
# -2H+ + 2HCO3- + Ca2+ + 0.8Mg2+ + 0.2Fe2+ = CaMg0.8Fe0.2(CO3)2
#
# The initial concentration of precipitated dolomite is high, so it starts
# to dissolve immediately, increasing the concentrations of the primary species.
#
# Only single-phase, fully saturated physics is used.
# The pressure gradient is fixed, so that the Darcy velocity is 0.1m/s.
#
# Primary species are injected from the left side, and they flow to the right.
# Less dolomite dissolution therefore occurs on the left side (where
# the primary species have higher concentration).
#
# This test is more fully documented in tutorial_13
[Mesh]
type = GeneratedMesh
dim = 1
nx = 100
xmax = 1
[]
[Variables]
[./h+]
[../]
[./hco3-]
[../]
[./ca2+]
[../]
[./mg2+]
[../]
[./fe2+]
[../]
[]
[AuxVariables]
[./eqm_k0]
initial_condition = 2.19E6
[../]
[./eqm_k1]
initial_condition = 4.73E-11
[../]
[./eqm_k2]
initial_condition = 0.222
[../]
[./eqm_k3]
initial_condition = 1E-2
[../]
[./eqm_k4]
initial_condition = 1E-3
[../]
[./kinetic_k]
initial_condition = 326.2
[../]
[./pressure]
[../]
[./dolomite]
family = MONOMIAL
order = CONSTANT
[../]
[./dolomite_initial]
initial_condition = 1E-7
[../]
[]
[AuxKernels]
[./dolomite]
type = PorousFlowPropertyAux
property = mineral_concentration
mineral_species = 0
variable = dolomite
[../]
[]
[GlobalParams]
PorousFlowDictator = dictator
gravity = '0 0 0'
[]
[ICs]
[./pressure_ic]
type = FunctionIC
variable = pressure
function = '(1 - x) * 1E6'
[../]
[./h+_ic]
type = BoundingBoxIC
variable = h+
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
[./hco3_ic]
type = BoundingBoxIC
variable = hco3-
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
[./ca2_ic]
type = BoundingBoxIC
variable = ca2+
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
[./mg2_ic]
type = BoundingBoxIC
variable = mg2+
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
[./fe2_ic]
type = BoundingBoxIC
variable = fe2+
x1 = 0.0
y1 = 0.0
x2 = 1.0e-10
y2 = 0.25
inside = 5.0e-2
outside = 1.0e-6
[../]
[]
[Kernels]
[./h+_ie]
type = PorousFlowMassTimeDerivative
fluid_component = 0
variable = h+
[../]
[./h+_conv]
type = PorousFlowAdvectiveFlux
fluid_component = 0
variable = h+
[../]
[./predis_h+]
type = PorousFlowPreDis
variable = h+
mineral_density = 2875.0
stoichiometry = -2
[../]
[./hco3-_ie]
type = PorousFlowMassTimeDerivative
fluid_component = 1
variable = hco3-
[../]
[./hco3-_conv]
type = PorousFlowAdvectiveFlux
fluid_component = 1
variable = hco3-
[../]
[./predis_hco3-]
type = PorousFlowPreDis
variable = hco3-
mineral_density = 2875.0
stoichiometry = 2
[../]
[./ca2+_ie]
type = PorousFlowMassTimeDerivative
fluid_component = 2
variable = ca2+
[../]
[./ca2+_conv]
type = PorousFlowAdvectiveFlux
fluid_component = 2
variable = ca2+
[../]
[./predis_ca2+]
type = PorousFlowPreDis
variable = ca2+
mineral_density = 2875.0
stoichiometry = 1
[../]
[./mg2+_ie]
type = PorousFlowMassTimeDerivative
fluid_component = 3
variable = mg2+
[../]
[./mg2+_conv]
type = PorousFlowAdvectiveFlux
fluid_component = 3
variable = mg2+
[../]
[./predis_mg2+]
type = PorousFlowPreDis
variable = mg2+
mineral_density = 2875.0
stoichiometry = 0.8
[../]
[./fe2+_ie]
type = PorousFlowMassTimeDerivative
fluid_component = 4
variable = fe2+
[../]
[./fe2+_conv]
type = PorousFlowAdvectiveFlux
fluid_component = 4
variable = fe2+
[../]
[./predis_fe2+]
type = PorousFlowPreDis
variable = fe2+
mineral_density = 2875.0
stoichiometry = 0.2
[../]
[]
[UserObjects]
[./dictator]
type = PorousFlowDictator
porous_flow_vars = 'h+ hco3- ca2+ mg2+ fe2+'
number_fluid_phases = 1
number_fluid_components = 6
number_aqueous_equilibrium = 5
number_aqueous_kinetic = 1
[../]
[]
[Modules]
[./FluidProperties]
Given the above equilibrium constant and concentrations of the primary species, the dolomite immediately begins to dissolve into solution.
Porepressure
The porepressure is fixed to have gradient Pa/m.
[./pressure_ic]
type = FunctionIC
variable = pressure
function = '(1 - x) * 1E6'
[../]
With a permeability of m and a fluid viscosity of Pa.s, the Darcy velocity is m/s. The porosity is held fixed at 0.2.
Results
Figure 1: Two of the primary species concentrations at the end of the simulation.
Figure 2: The precipitated dolomite concentration at the end of the simulation.