BrineFluidProperties

Fluid properties for brine

A high-precision and consistent formulation for fluid properties for binary salt (NaCl) and water mixtures at pressures and temperatures of interest.

Density, enthalpy, internal energy and specific heat capacity are calculated using the formulations provided in Driesner and Heinrich (2007) and Driesner (2007).

Viscosity and thermal conductivity of brine are calculated using the formulation of Phillips et al. (1981).

Brine vapor pressure is calculated using the formulation presented in Haas Jr (1976).

Solubility of solid salt (halite) in water is given by Potter et al. (1977).

By default, the BrineFluidProperties UserObject uses the Water97FluidProperties and NaClFluidProperties which are constructed internally, so do not have to be supplied by the user.

The BrineFluidProperties UserObject takes an optional parameter water_fp which can be used to pass a specific water formulation. This allows the user to use a tabulated version of the water properties (using TabulatedFluidProperties), which can significantly speed up the calculation of brine properties.

Range of validity

The BrineFluidProperties UserObject is valid for:

273.15 K $var element = document.getElementById("moose-equation-251eab5b-610c-492e-8854-0d3fe53c1e78");katex.render("\\le", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ T $var element = document.getElementById("moose-equation-426da347-8f10-40f8-8273-3b8eaadaf454");katex.render("\\le", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ 1273.15 K,
0.1 MPa $var element = document.getElementById("moose-equation-b97fe37e-8c38-40ad-91bf-06f68ac6e376");katex.render("\\le", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ p $var element = document.getElementById("moose-equation-0c4c35ed-5e5a-45bb-80a2-aac347b24361");katex.render("\\le", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ 500 MPa,
0 $var element = document.getElementById("moose-equation-91983f0d-e683-4d18-b9ad-0f81fd9fb0eb");katex.render("\\le", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ x $var element = document.getElementById("moose-equation-8bc26511-c370-414b-a0fc-27a8cc226b2b");katex.render("_{\\mathrm{nacl}}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ $var element = document.getElementById("moose-equation-21132850-1559-4475-bf5f-a22923909b6b");katex.render("\\le", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ 1

Input Parameters

allow_imperfect_jacobiansFalsetrue to allow unimplemented property derivative terms to be set to zero for the AD API
Default:False
C++ Type:bool
Controllable:No
Description:true to allow unimplemented property derivative terms to be set to zero for the AD API
execute_onTIMESTEP_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, ALWAYS.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, ALWAYS
Controllable:No
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, ALWAYS.
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
water_fpThe name of the FluidProperties UserObject for water
C++ Type:UserObjectName
Controllable:No
Description:The name of the FluidProperties UserObject for water

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup
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
Controllable:No
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/porous_flow/test/tests/jacobian/brineco2_gas.i)
(modules/fluid_properties/test/tests/brine/brine.i)
(modules/porous_flow/examples/co2_intercomparison/1Dradial/1Dradial.i)
(modules/porous_flow/test/tests/jacobian/brineco2_twophase.i)
(modules/porous_flow/test/tests/fluidstate/brineco2_hightemp.i)
(modules/porous_flow/examples/lava_lamp/1phase_convection.i)
(modules/porous_flow/test/tests/fluidstate/brineco2_nonisothermal.i)
(modules/porous_flow/examples/restart/gas_injection.i)
(modules/porous_flow/test/tests/fluidstate/brineco2.i)
(modules/fluid_properties/test/tests/brine/brine_tabulated.i)
(modules/porous_flow/examples/lava_lamp/2phase_convection.i)
(modules/porous_flow/test/tests/jacobian/brineco2_twophase_nonisothermal.i)
(modules/porous_flow/test/tests/fluidstate/theis_brineco2.i)
(modules/porous_flow/test/tests/fluidstate/theis_brineco2_nonisothermal.i)
(modules/porous_flow/examples/co2_intercomparison/1Dradial/properties.i)
(modules/porous_flow/test/tests/jacobian/brineco2_liquid_2.i)
(modules/porous_flow/test/tests/jacobian/brineco2_liquid.i)
(modules/porous_flow/test/tests/fluidstate/brineco2_ic.i)
(modules/porous_flow/test/tests/fluidstate/brineco2_2.i)
(modules/porous_flow/examples/restart/gravityeq.i)
(modules/porous_flow/examples/restart/gas_injection_new_mesh.i)

References

T. Driesner. The system H$_2$O-NaCl. Part II: Correlations for molar volume, enthalpy, and isobaric heat capacity from 0 to 1000 C, 1 to 5000 bar, and 0 to 1 X$_NaCl$. Geochimica et Cosmochimica Acta, 71:4902–4919, 2007.

@article{driesner2007b,
    author = "Driesner, T.",
    title = "{The system H$\_2$O-NaCl. Part II: Correlations for molar volume, enthalpy, and isobaric heat capacity from 0 to 1000 C, 1 to 5000 bar, and 0 to 1 X$\_{NaCl}$}",
    journal = "Geochimica et Cosmochimica Acta",
    volume = "71",
    pages = "4902--4919",
    year = "2007"
}

T. Driesner and C. A. Heinrich. The system H$_2$O-NaCl. Part I: Correlation formulae for phase relations in temperature-pressure-composition space from 0 to 1000 C, 0 to 5000 bar, and 0 to 1 X$_NaCl$. Geochimica et Cosmochimica Acta, 71:4880–4901, 2007.

@article{driesner2007a,
    author = "Driesner, T. and Heinrich, C. A.",
    title = "{The system H$\_2$O-NaCl. Part I: Correlation formulae for phase relations in temperature-pressure-composition space from 0 to 1000 C, 0 to 5000 bar, and 0 to 1 X$\_{NaCl}$}",
    journal = "Geochimica et Cosmochimica Acta",
    volume = "71",
    pages = "4880--4901",
    year = "2007"
}

J. L. Haas Jr. Physical properties of the coexisting phases and thermochemical properties of the H$_2$O component in boiling NaCl solutions. Technical Report USGS Bulletin 1421-A, United States Geological Survey, 1976.

@techreport{haas1976,
    author = "Haas Jr, J. L.",
    title = "{Physical properties of the coexisting phases and thermochemical properties of the H$\_2$O component in boiling NaCl solutions}",
    institution = "United States Geological Survey",
    number = "USGS Bulletin 1421-A",
    year = "1976"
}

S. L. Phillips, A. Igbene, J. A. Fair, H. Ozbek, and M. Tavana. A technical databook for geothermal energy utilization. Technical Report LBL-12810, Lawrence Berkeley National Laboratory, Berkeley CA, USA, 1981.

@techreport{phillips1981,
    author = "Phillips, S. L. and Igbene, A. and Fair, J. A. and Ozbek, H. and Tavana, M.",
    title = "A technical databook for geothermal energy utilization",
    institution = "Lawrence Berkeley National Laboratory",
    address = "Berkeley CA, USA",
    number = "LBL-12810",
    year = "1981"
}

R. W. Potter, R. S. Babcock, and D. L. Brown. A new method for determining the solubility of salts in aqueous solutions at elevated temperatures. J. Res. US Geol. Surv., 5:389–395, 1977.

@article{potter1977,
    author = "Potter, R. W. and Babcock, R. S. and Brown, D. L.",
    title = "A new method for determining the solubility of salts in aqueous solutions at elevated temperatures",
    journal = "J. Res. US Geol. Surv.",
    volume = "5",
    pages = "389--395",
    year = "1977"
}

(modules/porous_flow/test/tests/jacobian/brineco2_gas.i)

# Tests correct calculation of properties derivatives in PorousFlowFluidState
# for conditions that give a single gas phase

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[AuxVariables]
  [xnacl]
    initial_condition = 0.05
  []
[]

[Variables]
  [pgas]
  []
  [zi]
  []
[]

[ICs]
  [pgas]
    type = RandomIC
    min = 5e4
    max = 1e5
    variable = pgas
  []
  [z]
    type = RandomIC
    min = 0.9
    max = 0.99
    variable = zi
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = pgas
    fluid_component = 0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    variable = zi
    fluid_component = 1
  []
  [adv0]
    type = PorousFlowAdvectiveFlux
    variable = pgas
    fluid_component = 0
  []
  [adv1]
    type = PorousFlowAdvectiveFlux
    variable = zi
    fluid_component = 1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas zi'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
    pc_max = 1e3
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2]
      type = CO2FluidProperties
    []
    [brine]
      type = BrineFluidProperties
    []
    [water]
      type = Water97FluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = 50
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = pgas
    z = zi
    temperature_unit = Celsius
    xnacl = xnacl
    capillary_pressure = pc
    fluid_state = fs
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-12 0 0 0 1e-12 0 0 0 1e-12'
  []
  [relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [relperm1]
    type = PorousFlowRelativePermeabilityCorey
    n = 3
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1
  end_time = 1
  nl_abs_tol = 1e-12
[]

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

[AuxVariables]
  [sgas]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [sgas]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = sgas
  []
[]

[Postprocessors]
  [sgas_min]
    type = ElementExtremeValue
    variable = sgas
    value_type = min
  []
  [sgas_max]
    type = ElementExtremeValue
    variable = sgas
    value_type = max
  []
[]

(modules/fluid_properties/test/tests/brine/brine.i)

# Test BrineFluidProperties calculations of density, viscosity and thermal
# conductivity
#
# Experimental density values from Pitzer et al, "Thermodynamic properties
# of aqueous sodium chloride solution", Journal of Physical and Chemical
# Reference Data, 13, 1-102 (1984)
#
# Experimental viscosity values from Phillips et al, "Viscosity of NaCl and
# other solutions up to 350C and 50MPa pressures", LBL-11586 (1980)
#
# Thermal conductivity values from Ozbek and Phillips, "Thermal conductivity of
# aqueous NaCl solutions from 20C to 330C", LBL-9086 (1980)
#
#  --------------------------------------------------------------
#  Pressure (Mpa)                |   20      |    20     |   40
#  Temperature (C)               |   50      |   200     |  200
#  NaCl molality (mol/kg)        |    2      |     2     |    5
#  NaCl mass fraction (kg/kg)    |  0.1047   |  0.1047   |  0.2261
#  --------------------------------------------------------------
#  Expected values
#  --------------------------------------------------------------
#  Density (kg/m^3)              |  1068.52  |  959.27   |  1065.58
#  Viscosity (1e-6Pa.s)          |  679.8    |  180.0    |  263.1
#  Thermal conductivity (W/m/K)  |  0.630    |  0.649    |  0.633
#  --------------------------------------------------------------
#  Calculated values
#  --------------------------------------------------------------
#  Density (kg/m^3)              |  1067.18  |  958.68   |  1065.46
#  Viscosity (1e-6 Pa.s)         |  681.1    |  181.98    |  266.1
#  Thermal conductivity (W/m/K)  |  0.637    |   0.662    |  0.658
#  --------------------------------------------------------------
#
# All results are within expected accuracy

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 3
  ny = 1
  xmax = 3
  # This test uses ElementalVariableValue postprocessors on specific
  # elements, so element numbering needs to stay unchanged
  allow_renumbering = false
[]

[Variables]
  [./dummy]
  [../]
[]

[AuxVariables]
  [./pressure]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./temperature]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./xnacl]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./density]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./enthalpy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./internal_energy]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[Functions]
  [./pic]
    type = ParsedFunction
    value = 'if(x<2,20e6, 40e6)'
  [../]
  [./tic]
    type = ParsedFunction
    value = 'if(x<1, 323.15, 473.15)'
  [../]
  [./xic]
    type = ParsedFunction
    value = 'if(x<2,0.1047, 0.2261)'
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    function = pic
    variable = pressure
  [../]
  [./t_ic]
    type = FunctionIC
    function = tic
    variable = temperature
  [../]
  [./x_ic]
    type = FunctionIC
    function = xic
    variable = xnacl
  [../]
[]

[AuxKernels]
  [./density]
    type = MaterialRealAux
     variable = density
     property = density
  [../]
  [./enthalpy]
    type = MaterialRealAux
     variable = enthalpy
     property = enthalpy
  [../]
  [./internal_energy]
    type = MaterialRealAux
     variable = internal_energy
     property = e
  [../]
[]

[Modules]
  [./FluidProperties]
    [./brine]
      type = BrineFluidProperties
    [../]
  [../]
[]

[Materials]
  [./fp_mat]
    type = MultiComponentFluidPropertiesMaterialPT
    pressure = pressure
    temperature = temperature
    xmass = xnacl
    fp = brine
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = dummy
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Postprocessors]
  [./density0]
    type = ElementalVariableValue
    variable = density
    elementid = 0
  [../]
  [./density1]
    type = ElementalVariableValue
    variable = density
    elementid = 1
  [../]
  [./density2]
    type = ElementalVariableValue
    variable = density
    elementid = 2
  [../]
  [./enthalpy0]
    type = ElementalVariableValue
    variable = enthalpy
    elementid = 0
  [../]
  [./enthalpy1]
    type = ElementalVariableValue
    variable = enthalpy
    elementid = 1
  [../]
  [./enthalpy2]
    type = ElementalVariableValue
    variable = enthalpy
    elementid = 2
  [../]
  [./e0]
    type = ElementalVariableValue
    variable = internal_energy
    elementid = 0
  [../]
  [./e1]
    type = ElementalVariableValue
    variable = internal_energy
    elementid = 1
  [../]
  [./e2]
    type = ElementalVariableValue
    variable = internal_energy
    elementid = 2
  [../]
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/examples/co2_intercomparison/1Dradial/1Dradial.i)

# Intercomparison problem 3: Radial flow from an injection well
#
# From Pruess et al, Code intercomparison builds confidence in
# numerical simulation models for geologic disposal of CO2, Energy 29 (2004)
#
# A variation with zero salinity can be run by changing the initial condition
# of the AuxVariable xnacl

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 500
  xmax = 10000
  bias_x = 1.01
[]

[Problem]
  type = FEProblem
  coord_type = 'RZ'
  rz_coord_axis = Y
[]

[GlobalParams]
  PorousFlowDictator = 'dictator'
  gravity = '0 0 0'
[]

[AuxVariables]
  [pressure_liquid]
    order = CONSTANT
    family = MONOMIAL
  []
  [saturation_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [x1]
    order = CONSTANT
    family = MONOMIAL
  []
  [y0]
    order = CONSTANT
    family = MONOMIAL
  []
  [xnacl]
    initial_condition = 0.15
  []
[]

[AuxKernels]
  [pressure_liquid]
    type = PorousFlowPropertyAux
    variable = pressure_liquid
    property = pressure
    phase = 0
    execute_on = 'timestep_end'
  []
  [saturation_gas]
    type = PorousFlowPropertyAux
    variable = saturation_gas
    property = saturation
    phase = 1
    execute_on = 'timestep_end'
  []
  [x1]
    type = PorousFlowPropertyAux
    variable = x1
    property = mass_fraction
    phase = 0
    fluid_component = 1
    execute_on = 'timestep_end'
  []
  [y0]
    type = PorousFlowPropertyAux
    variable = y0
    property = mass_fraction
    phase = 1
    fluid_component = 0
    execute_on = 'timestep_end'
  []
[]

[Variables]
  [pgas]
    initial_condition = 12e6
  []
  [zi]
    initial_condition = 0
    scaling = 1e4
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pgas
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pgas
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = zi
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = zi
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas zi'
    number_fluid_phases = 2
    number_fluid_components = 3
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    alpha = 5.099e-5
    m = 0.457
    sat_lr = 0.0
    pc_max = 1e7
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2sw]
      type = CO2FluidProperties
    []
    [co2]
      type = TabulatedFluidProperties
      fp = co2sw
    []
    [water]
      type = Water97FluidProperties
    []
    [watertab]
      type = TabulatedFluidProperties
      fp = water
      temperature_min = 273.15
      temperature_max = 573.15
      fluid_property_file = water_fluid_properties.csv
      save_file = false
    []
    [brine]
      type = BrineFluidProperties
      water_fp = watertab
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = '45'
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = 'pgas'
    z = 'zi'
    temperature_unit = Celsius
    xnacl = 'xnacl'
    capillary_pressure = pc
    fluid_state = fs
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = '0.12'
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-13 0 0 0 1e-13 0 0 0 1e-13'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityVG
    m = 0.457
    phase = 0
    s_res = 0.3
    sum_s_res = 0.35
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 1
    s_res = 0.05
    sum_s_res = 0.35
  []
[]

[BCs]
  [rightwater]
    type = PorousFlowPiecewiseLinearSink
    boundary = 'right'
    variable = pgas
    use_mobility = true
    PorousFlowDictator = dictator
    fluid_phase = 0
    multipliers = '0 1e9'
    PT_shift = '12e6'
    pt_vals = '0 1e9'
    mass_fraction_component = 0
    use_relperm = true
  []
  [rightco2]
    type = PorousFlowPiecewiseLinearSink
    variable = zi
    boundary = 'right'
    use_mobility = true
    PorousFlowDictator = dictator
    fluid_phase = 1
    multipliers = '0 1e9'
    PT_shift = '12e6'
    pt_vals = '0 1e9'
    mass_fraction_component = 1
    use_relperm = true
  []
[]

[DiracKernels]
  [source]
    type = PorousFlowSquarePulsePointSource
    point = '0 0 0'
    mass_flux = 1
    variable = zi
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type'
    petsc_options_value = 'gmres bjacobi lu NONZERO'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 8.64e8
  nl_max_its = 25
  l_max_its = 100
  dtmax = 5e6
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 100
  []
[]

[VectorPostprocessors]
  [vars]
    type = NodalValueSampler
    sort_by = x
    variable = 'pgas zi xnacl'
    execute_on = 'timestep_end'
    outputs = spatial
  []
  [auxvars]
    type = ElementValueSampler
    sort_by = x
    variable = 'saturation_gas x1 y0'
    execute_on = 'timestep_end'
    outputs = spatial
  []
[]

[Postprocessors]
  [pgas]
    type = PointValue
    point = '25.25 0 0'
    variable = pgas
    outputs = time
  []
  [sgas]
    type = PointValue
    point = '25.25 0 0'
    variable = saturation_gas
    outputs = time
  []
  [zi]
    type = PointValue
    point = '25.25 0 0'
    variable = zi
    outputs = time
  []
  [massgas]
    type = PorousFlowFluidMass
    fluid_component = 1
    outputs = time
  []
  [x1]
    type = PointValue
    point = '25.25 0 0'
    variable = x1
    outputs = time
  []
  [y0]
    type = PointValue
    point = '25.25 0 0'
    variable = y0
    outputs = time
  []
  [xnacl]
    type = PointValue
    point = '25.25 0 0'
    variable = xnacl
    outputs = time
  []
[]

[Outputs]
  print_linear_residuals = false
  perf_graph = true
  sync_times = '2.592e6 8.64e6 8.64e7 8.64e8'
  [time]
    type = CSV
  []
  [spatial]
    type = CSV
    sync_only = true
  []
[]

(modules/porous_flow/test/tests/jacobian/brineco2_twophase.i)

# Tests correct calculation of properties derivatives in PorousFlowFluidState
# for conditions that are appropriate for two phases

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[AuxVariables]
  [xnacl]
    initial_condition = 0.05
  []
[]

[Variables]
  [pgas]
  []
  [zi]
  []
[]

[ICs]
  [pgas]
    type = RandomIC
    min = 1e6
    max = 4e6
    variable = pgas
    seed = 1
  []
  [z]
    type = RandomIC
    min = 0.2
    max = 0.8
    variable = zi
    seed = 2
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = pgas
    fluid_component = 0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    variable = zi
    fluid_component = 1
  []
  [adv0]
    type = PorousFlowAdvectiveFlux
    variable = pgas
    fluid_component = 0
  []
  [adv1]
    type = PorousFlowAdvectiveFlux
    variable = zi
    fluid_component = 1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas zi'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1e1
    pc_max = 1e4
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2]
      type = CO2FluidProperties
    []
    [brine]
      type = BrineFluidProperties
    []
    [water]
      type = Water97FluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = 50
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = pgas
    z = zi
    temperature_unit = Celsius
    xnacl = xnacl
    capillary_pressure = pc
    fluid_state = fs
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-12 0 0 0 1e-12 0 0 0 1e-12'
  []
  [relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [relperm1]
    type = PorousFlowRelativePermeabilityCorey
    n = 3
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1
  end_time = 1
  nl_abs_tol = 1e-12
[]

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

[AuxVariables]
  [sgas]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [sgas]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = sgas
  []
[]

[Postprocessors]
  [sgas_min]
    type = ElementExtremeValue
    variable = sgas
    value_type = min
  []
  [sgas_max]
    type = ElementExtremeValue
    variable = sgas
    value_type = max
  []
[]

(modules/porous_flow/test/tests/fluidstate/brineco2_hightemp.i)

# Tests correct calculation of properties in PorousFlowBrineCO2 in the elevated
# temperature regime (T > 110C)

[Mesh]
  type = GeneratedMesh
  dim = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
  temperature = 250
[]

[Variables]
  [pgas]
    initial_condition = 20e6
  []
  [z]
     initial_condition = 0.2
  []
[]

[AuxVariables]
  [xnacl]
    initial_condition = 0.1
  []
  [pressure_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [pressure_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [saturation_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [saturation_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [density_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [density_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [viscosity_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [viscosity_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [x0_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [x0_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [x1_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [x1_gas]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [pressure_water]
    type = PorousFlowPropertyAux
    variable = pressure_water
    property = pressure
    phase = 0
    execute_on = timestep_end
  []
  [pressure_gas]
    type = PorousFlowPropertyAux
    variable = pressure_gas
    property = pressure
    phase = 1
    execute_on = timestep_end
  []
  [saturation_water]
    type = PorousFlowPropertyAux
    variable = saturation_water
    property = saturation
    phase = 0
    execute_on = timestep_end
  []
  [saturation_gas]
    type = PorousFlowPropertyAux
    variable = saturation_gas
    property = saturation
    phase = 1
    execute_on = timestep_end
  []
  [density_water]
    type = PorousFlowPropertyAux
    variable = density_water
    property = density
    phase = 0
    execute_on = timestep_end
  []
  [density_gas]
    type = PorousFlowPropertyAux
    variable = density_gas
    property = density
    phase = 1
    execute_on = timestep_end
  []
  [viscosity_water]
    type = PorousFlowPropertyAux
    variable = viscosity_water
    property = viscosity
    phase = 0
    execute_on = timestep_end
  []
  [viscosity_gas]
    type = PorousFlowPropertyAux
    variable = viscosity_gas
    property = viscosity
    phase = 1
    execute_on = timestep_end
  []
  [x1_water]
    type = PorousFlowPropertyAux
    variable = x1_water
    property = mass_fraction
    phase = 0
    fluid_component = 1
    execute_on = timestep_end
  []
  [x1_gas]
    type = PorousFlowPropertyAux
    variable = x1_gas
    property = mass_fraction
    phase = 1
    fluid_component = 1
    execute_on = timestep_end
  []
  [x0_water]
    type = PorousFlowPropertyAux
    variable = x0_water
    property = mass_fraction
    phase = 0
    fluid_component = 0
    execute_on = timestep_end
  []
  [x0_gas]
    type = PorousFlowPropertyAux
    variable = x0_gas
    property = mass_fraction
    phase = 1
    fluid_component = 0
    execute_on = timestep_end
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = pgas
    fluid_component = 0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    variable = z
    fluid_component = 1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas z'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2]
      type = CO2FluidProperties
    []
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = pgas
    z = z
    temperature_unit = Celsius
    xnacl = xnacl
    capillary_pressure = pc
    fluid_state = fs
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-12 0 0 0 1e-12 0 0 0 1e-12'
  []
  [relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [relperm1]
    type = PorousFlowRelativePermeabilityCorey
    n = 3
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1
  end_time = 1
  nl_abs_tol = 1e-12
[]

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

[Postprocessors]
  [density_water]
    type = ElementIntegralVariablePostprocessor
    variable = density_water
  []
  [density_gas]
    type = ElementIntegralVariablePostprocessor
    variable = density_gas
  []
  [viscosity_water]
    type = ElementIntegralVariablePostprocessor
    variable = viscosity_water
  []
  [viscosity_gas]
    type = ElementIntegralVariablePostprocessor
    variable = viscosity_gas
  []
  [x1_water]
    type = ElementIntegralVariablePostprocessor
    variable = x1_water
  []
  [x0_water]
    type = ElementIntegralVariablePostprocessor
    variable = x0_water
  []
  [x1_gas]
    type = ElementIntegralVariablePostprocessor
    variable = x1_gas
  []
  [x0_gas]
    type = ElementIntegralVariablePostprocessor
    variable = x0_gas
  []
  [sg]
    type = ElementIntegralVariablePostprocessor
    variable = saturation_gas
  []
  [sw]
    type = ElementIntegralVariablePostprocessor
    variable = saturation_water
  []
  [pwater]
    type = ElementIntegralVariablePostprocessor
    variable = pressure_water
  []
  [pgas]
    type = ElementIntegralVariablePostprocessor
    variable = pressure_gas
  []
  [x0mass]
    type = PorousFlowFluidMass
    fluid_component = 0
    phase = '0 1'
  []
  [x1mass]
    type = PorousFlowFluidMass
    fluid_component = 1
    phase = '0 1'
  []
[]

[Outputs]
  csv = true
  execute_on = 'TIMESTEP_END'
  perf_graph = false
[]

(modules/porous_flow/examples/lava_lamp/1phase_convection.i)

# Two phase density-driven convection of dissolved CO2 in brine
#
# The model starts with CO2 in the liquid phase only.  The CO2 diffuses into the brine.
# As the density of the CO2-saturated brine is greater
# than the unsaturated brine, a gravitational instability arises and density-driven
# convection of CO2-rich fingers descend into the unsaturated brine.
#
# The instability is seeded by a random perturbation to the porosity field.
# Mesh adaptivity is used to refine the mesh as the fingers form.
#
# Note: this model is computationally expensive, so should be run with multiple cores.

[GlobalParams]
  PorousFlowDictator = 'dictator'
  gravity = '0 -9.81 0'
[]

[Adaptivity]
  max_h_level = 2
  marker = marker
  initial_marker = initial
  initial_steps = 2
  [Indicators]
    [indicator]
      type = GradientJumpIndicator
      variable = zi
    []
  []
  [Markers]
    [marker]
      type = ErrorFractionMarker
      indicator = indicator
      refine = 0.8
    []
    [initial]
      type = BoxMarker
      bottom_left = '0 1.95 0'
      top_right = '2 2 0'
      inside = REFINE
      outside = DO_NOTHING
    []
  []
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  ymin = 1.5
  ymax = 2
  xmax = 2
  ny = 20
  nx = 40
  bias_y = 0.95
[]

[AuxVariables]
  [xnacl]
    initial_condition = 0.01
  []
  [saturation_gas]
    order = FIRST
    family = MONOMIAL
  []
  [xco2l]
    order = FIRST
    family = MONOMIAL
  []
  [density_liquid]
    order = FIRST
    family = MONOMIAL
  []
  [porosity]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [saturation_gas]
    type = PorousFlowPropertyAux
    variable = saturation_gas
    property = saturation
    phase = 1
    execute_on = 'timestep_end'
  []
  [xco2l]
    type = PorousFlowPropertyAux
    variable = xco2l
    property = mass_fraction
    phase = 0
    fluid_component = 1
    execute_on = 'timestep_end'
  []
  [density_liquid]
    type = PorousFlowPropertyAux
    variable = density_liquid
    property = density
    phase = 0
    execute_on = 'timestep_end'
  []
[]

[Variables]
  [pgas]
  []
  [zi]
    scaling = 1e4
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    function = 10e6-9.81*1000*y
    variable = pgas
  []
  [zi]
    type = ConstantIC
    value = 0
    variable = zi
  []
  [porosity]
    type = RandomIC
    variable = porosity
    min = 0.25
    max = 0.275
    seed = 0
  []
[]

[BCs]
  [top]
    type = DirichletBC
    value = 0.04
    variable = zi
    boundary = top
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pgas
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pgas
  []
  [diff0]
    type = PorousFlowDispersiveFlux
    fluid_component = 0
    variable = pgas
    disp_long = '0 0'
    disp_trans = '0 0'
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = zi
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = zi
  []
  [diff1]
    type = PorousFlowDispersiveFlux
    fluid_component = 1
    variable = zi
    disp_long = '0 0'
    disp_trans = '0 0'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas zi'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2sw]
      type = CO2FluidProperties
    []
    [co2]
      type = TabulatedFluidProperties
      fp = co2sw
    []
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = '45'
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = 'pgas'
    z = 'zi'
    temperature_unit = Celsius
    xnacl = 'xnacl'
    capillary_pressure = pc
    fluid_state = fs
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = porosity
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-11 0 0 0 1e-11 0 0 0 1e-11'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    phase = 0
    n = 2
    s_res = 0.1
    sum_s_res = 0.2
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    phase = 1
    n = 2
    s_res = 0.1
    sum_s_res = 0.2
  []
  [diffusivity]
    type = PorousFlowDiffusivityConst
    diffusion_coeff = '2e-9 2e-9 2e-9 2e-9'
    tortuosity = '1 1'
  []
[]

[Preconditioning]
  active = basic
  [mumps_is_best_for_parallel_jobs]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2             '
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 1e6
  nl_max_its = 25
  l_max_its = 100
  dtmax = 1e4
  nl_abs_tol = 1e-6
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 100
    growth_factor = 2
    cutback_factor = 0.5
  []
[]

[Functions]
  [flux]
    type = ParsedFunction
    vals = 'delta_xco2 dt'
    vars = 'dx dt'
    value = 'dx/dt'
  []
[]

[Postprocessors]
  [total_co2_in_gas]
    type = PorousFlowFluidMass
    phase = 1
    fluid_component = 1
  []
  [total_co2_in_liquid]
    type = PorousFlowFluidMass
    phase = 0
    fluid_component = 1
  []
  [numdofs]
    type = NumDOFs
  []
  [delta_xco2]
    type = ChangeOverTimePostprocessor
    postprocessor = total_co2_in_liquid
  []
  [dt]
    type = TimestepSize
  []
  [flux]
    type = FunctionValuePostprocessor
    function = flux
  []
[]

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

(modules/porous_flow/test/tests/fluidstate/brineco2_nonisothermal.i)

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [pgas]
    initial_condition = 20e6
  []
  [z]
     initial_condition = 0.2
  []
  [temperature]
    initial_condition = 70
  []
[]

[AuxVariables]
  [xnacl]
    initial_condition = 0.1
  []
  [pressure_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [pressure_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [saturation_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [saturation_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [density_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [density_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [viscosity_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [viscosity_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [enthalpy_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [enthalpy_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [internal_energy_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [internal_energy_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [x0_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [x0_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [x1_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [x1_gas]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [pressure_water]
    type = PorousFlowPropertyAux
    variable = pressure_water
    property = pressure
    phase = 0
    execute_on = timestep_end
  []
  [pressure_gas]
    type = PorousFlowPropertyAux
    variable = pressure_gas
    property = pressure
    phase = 1
    execute_on = timestep_end
  []
  [saturation_water]
    type = PorousFlowPropertyAux
    variable = saturation_water
    property = saturation
    phase = 0
    execute_on = timestep_end
  []
  [saturation_gas]
    type = PorousFlowPropertyAux
    variable = saturation_gas
    property = saturation
    phase = 1
    execute_on = timestep_end
  []
  [density_water]
    type = PorousFlowPropertyAux
    variable = density_water
    property = density
    phase = 0
    execute_on = timestep_end
  []
  [density_gas]
    type = PorousFlowPropertyAux
    variable = density_gas
    property = density
    phase = 1
    execute_on = timestep_end
  []
  [viscosity_water]
    type = PorousFlowPropertyAux
    variable = viscosity_water
    property = viscosity
    phase = 0
    execute_on = timestep_end
  []
  [viscosity_gas]
    type = PorousFlowPropertyAux
    variable = viscosity_gas
    property = viscosity
    phase = 1
    execute_on = timestep_end
  []
  [enthalpy_water]
    type = PorousFlowPropertyAux
    variable = enthalpy_water
    property = enthalpy
    phase = 0
    execute_on = timestep_end
  []
  [enthalpy_gas]
    type = PorousFlowPropertyAux
    variable = enthalpy_gas
    property = enthalpy
    phase = 1
    execute_on = timestep_end
  []
  [internal_energy_water]
    type = PorousFlowPropertyAux
    variable = internal_energy_water
    property = internal_energy
    phase = 0
    execute_on = timestep_end
  []
  [internal_energy_gas]
    type = PorousFlowPropertyAux
    variable = internal_energy_gas
    property = internal_energy
    phase = 1
    execute_on = timestep_end
  []
  [x1_water]
    type = PorousFlowPropertyAux
    variable = x1_water
    property = mass_fraction
    phase = 0
    fluid_component = 1
    execute_on = timestep_end
  []
  [x1_gas]
    type = PorousFlowPropertyAux
    variable = x1_gas
    property = mass_fraction
    phase = 1
    fluid_component = 1
    execute_on = timestep_end
  []
  [x0_water]
    type = PorousFlowPropertyAux
    variable = x0_water
    property = mass_fraction
    phase = 0
    fluid_component = 0
    execute_on = timestep_end
  []
  [x0_gas]
    type = PorousFlowPropertyAux
    variable = x0_gas
    property = mass_fraction
    phase = 1
    fluid_component = 0
    execute_on = timestep_end
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = pgas
    fluid_component = 0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    variable = z
    fluid_component = 1
  []
  [heat]
    type = TimeDerivative
    variable = temperature
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas z temperature'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2]
      type = CO2FluidProperties
    []
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = pgas
    z = z
    temperature = temperature
    temperature_unit = Celsius
    xnacl = xnacl
    capillary_pressure = pc
    fluid_state = fs
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-12 0 0 0 1e-12 0 0 0 1e-12'
  []
  [relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [relperm1]
    type = PorousFlowRelativePermeabilityCorey
    n = 3
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1
  end_time = 1
  nl_abs_tol = 1e-12
[]

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

[Postprocessors]
  [density_water]
    type = ElementIntegralVariablePostprocessor
    variable = density_water
  []
  [density_gas]
    type = ElementIntegralVariablePostprocessor
    variable = density_gas
  []
  [viscosity_water]
    type = ElementIntegralVariablePostprocessor
    variable = viscosity_water
  []
  [viscosity_gas]
    type = ElementIntegralVariablePostprocessor
    variable = viscosity_gas
  []
  [enthalpy_water]
    type = ElementIntegralVariablePostprocessor
    variable = enthalpy_water
  []
  [enthalpy_gas]
    type = ElementIntegralVariablePostprocessor
    variable = enthalpy_gas
  []
  [internal_energy_water]
    type = ElementIntegralVariablePostprocessor
    variable = internal_energy_water
  []
  [internal_energy_gas]
    type = ElementIntegralVariablePostprocessor
    variable = internal_energy_gas
  []
  [x1_water]
    type = ElementIntegralVariablePostprocessor
    variable = x1_water
  []
  [x0_water]
    type = ElementIntegralVariablePostprocessor
    variable = x0_water
  []
  [x1_gas]
    type = ElementIntegralVariablePostprocessor
    variable = x1_gas
  []
  [x0_gas]
    type = ElementIntegralVariablePostprocessor
    variable = x0_gas
  []
  [sg]
    type = ElementIntegralVariablePostprocessor
    variable = saturation_gas
  []
  [sw]
    type = ElementIntegralVariablePostprocessor
    variable = saturation_water
  []
  [pwater]
    type = ElementIntegralVariablePostprocessor
    variable = pressure_water
  []
  [pgas]
    type = ElementIntegralVariablePostprocessor
    variable = pressure_gas
  []
  [x0mass]
    type = PorousFlowFluidMass
    fluid_component = 0
    phase = '0 1'
  []
  [x1mass]
    type = PorousFlowFluidMass
    fluid_component = 1
    phase = '0 1'
  []
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

(modules/porous_flow/examples/restart/gas_injection.i)

# Using the results from the equilibrium run to provide the initial condition for
# porepressure, we now inject a gas phase into the brine-saturated reservoir. In this
# example, where the mesh used is identical to the mesh used in gravityeq.i, we can use
# the basic restart capability by simply setting the initial condition for porepressure
# using the results from gravityeq.i.
#
# Even though the gravity equilibrium is established using a 2D mesh, in this example,
# we shift the mesh 0.1 m to the right and rotate it about the Y axis to make a 2D radial
# model.
#
# Methane injection takes place over the surface of the hole created by rotating the mesh,
# and hence the injection area is 2 pi r h. We can calculate this using an AreaPostprocessor,
# and then use this in a ParsedFunction to calculate the injection rate so that 10 kg/s of
# methane is injected.
#
# Results can be improved by uniformly refining the initial mesh.
#
# Note: as this example uses the results from a previous simulation, gravityeq.i MUST be
# run before running this input file.

[Mesh]
  uniform_refine = 1
  [file]
    type = FileMeshGenerator
    file = gravityeq_out.e
  []
  [translate]
    type = TransformGenerator
    transform = TRANSLATE
    vector_value = '0.1 0 0'
    input = file
  []
[]

[Problem]
  coord_type = RZ
  rz_coord_axis = Y
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 -9.81 0'
  temperature_unit = Celsius
[]

[Variables]
  [pp_liq]
    initial_from_file_var = porepressure
  []
  [sat_gas]
    initial_condition = 0
  []
[]

[AuxVariables]
  [temperature]
    initial_condition = 50
  []
  [xnacl]
    initial_condition = 0.1
  []
  [brine_density]
    family = MONOMIAL
    order = CONSTANT
  []
  [methane_density]
    family = MONOMIAL
    order = CONSTANT
  []
  [massfrac_ph0_sp0]
    initial_condition = 1
  []
  [massfrac_ph1_sp0]
    initial_condition = 0
  []
  [pp_gas]
    family = MONOMIAL
    order = CONSTANT
  []
  [sat_liq]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = pp_liq
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    variable = pp_liq
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    variable = sat_gas
    fluid_component = 1
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    variable = sat_gas
    fluid_component = 1
  []
[]

[AuxKernels]
  [brine_density]
    type = PorousFlowPropertyAux
    property = density
    variable = brine_density
    execute_on = 'initial timestep_end'
  []
  [methane_density]
    type = PorousFlowPropertyAux
    property = density
    variable = methane_density
    phase = 1
    execute_on = 'initial timestep_end'
  []
  [pp_gas]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 1
    variable = pp_gas
    execute_on = 'initial timestep_end'
  []
  [sat_liq]
    type = PorousFlowPropertyAux
    property = saturation
    variable = sat_liq
    execute_on = 'initial timestep_end'
  []
[]

[BCs]
  [gas_injection]
    type = PorousFlowSink
    boundary = left
    variable = sat_gas
    flux_function = injection_rate
    fluid_phase = 1
  []
  [brine_out]
    type = PorousFlowPiecewiseLinearSink
    boundary = right
    variable = pp_liq
    multipliers = '0 1e9'
    pt_vals = '0 1e9'
    fluid_phase = 0
    flux_function = 1e-6
    use_mobility = true
  []
[]

[Functions]
  [injection_rate]
    type = ParsedFunction
    vals = injection_area
    vars = area
    value = '-10/area'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp_liq sat_gas'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    alpha = 1e-5
    m = 0.5
    sat_lr = 0.2
  []
[]

[Modules]
  [FluidProperties]
    [brine]
      type = BrineFluidProperties
    []
    [methane]
      type = MethaneFluidProperties
    []
    [methane_tab]
      type = TabulatedFluidProperties
      fp = methane
      save_file = false
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temperature
  []
  [ps]
    type = PorousFlow2PhasePS
    phase0_porepressure = pp_liq
    phase1_saturation = sat_gas
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [brine]
    type = PorousFlowBrine
    compute_enthalpy = false
    compute_internal_energy = false
    xnacl = xnacl
    phase = 0
  []
  [methane]
    type = PorousFlowSingleComponentFluid
    compute_enthalpy = false
    compute_internal_energy = false
    fp = methane_tab
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-13 0 0 0 1e-13 0  0 0 1e-13'
  []
  [relperm_liq]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
    s_res = 0.2
    sum_s_res = 0.3
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 1
    s_res = 0.1
    sum_s_res = 0.3
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
    petsc_options_value = ' asm      lu           NONZERO'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1e8
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-06
  nl_max_its = 20
  dtmax = 1e6
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e1
  []
[]

[Postprocessors]
  [mass_ph0]
    type = PorousFlowFluidMass
    fluid_component = 0
    execute_on = 'initial timestep_end'
  []
  [mass_ph1]
    type = PorousFlowFluidMass
    fluid_component = 1
    execute_on = 'initial timestep_end'
  []
  [injection_area]
    type = AreaPostprocessor
    boundary = left
    execute_on = initial
  []
[]

[Outputs]
  execute_on = 'initial timestep_end'
  exodus = true
  perf_graph = true
  checkpoint = true
[]

(modules/porous_flow/test/tests/fluidstate/brineco2.i)

# Tests correct calculation of properties in PorousFlowBrineCO2

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
  temperature = 30
[]

[Variables]
  [pgas]
    initial_condition = 20e6
  []
  [z]
     initial_condition = 0.2
  []
[]

[AuxVariables]
  [xnacl]
    initial_condition = 0.1
  []
  [pressure_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [pressure_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [saturation_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [saturation_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [density_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [density_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [viscosity_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [viscosity_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [enthalpy_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [enthalpy_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [internal_energy_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [internal_energy_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [x0_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [x0_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [x1_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [x1_gas]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [pressure_water]
    type = PorousFlowPropertyAux
    variable = pressure_water
    property = pressure
    phase = 0
    execute_on = timestep_end
  []
  [pressure_gas]
    type = PorousFlowPropertyAux
    variable = pressure_gas
    property = pressure
    phase = 1
    execute_on = timestep_end
  []
  [saturation_water]
    type = PorousFlowPropertyAux
    variable = saturation_water
    property = saturation
    phase = 0
    execute_on = timestep_end
  []
  [saturation_gas]
    type = PorousFlowPropertyAux
    variable = saturation_gas
    property = saturation
    phase = 1
    execute_on = timestep_end
  []
  [density_water]
    type = PorousFlowPropertyAux
    variable = density_water
    property = density
    phase = 0
    execute_on = timestep_end
  []
  [density_gas]
    type = PorousFlowPropertyAux
    variable = density_gas
    property = density
    phase = 1
    execute_on = timestep_end
  []
  [viscosity_water]
    type = PorousFlowPropertyAux
    variable = viscosity_water
    property = viscosity
    phase = 0
    execute_on = timestep_end
  []
  [viscosity_gas]
    type = PorousFlowPropertyAux
    variable = viscosity_gas
    property = viscosity
    phase = 1
    execute_on = timestep_end
  []
  [enthalpy_water]
    type = PorousFlowPropertyAux
    variable = enthalpy_water
    property = enthalpy
    phase = 0
    execute_on = timestep_end
  []
  [enthalpy_gas]
    type = PorousFlowPropertyAux
    variable = enthalpy_gas
    property = enthalpy
    phase = 1
    execute_on = timestep_end
  []
  [internal_energy_water]
    type = PorousFlowPropertyAux
    variable = internal_energy_water
    property = internal_energy
    phase = 0
    execute_on = timestep_end
  []
  [internal_energy_gas]
    type = PorousFlowPropertyAux
    variable = internal_energy_gas
    property = internal_energy
    phase = 1
    execute_on = timestep_end
  []
  [x1_water]
    type = PorousFlowPropertyAux
    variable = x1_water
    property = mass_fraction
    phase = 0
    fluid_component = 1
    execute_on = timestep_end
  []
  [x1_gas]
    type = PorousFlowPropertyAux
    variable = x1_gas
    property = mass_fraction
    phase = 1
    fluid_component = 1
    execute_on = timestep_end
  []
  [x0_water]
    type = PorousFlowPropertyAux
    variable = x0_water
    property = mass_fraction
    phase = 0
    fluid_component = 0
    execute_on = timestep_end
  []
  [x0_gas]
    type = PorousFlowPropertyAux
    variable = x0_gas
    property = mass_fraction
    phase = 1
    fluid_component = 0
    execute_on = timestep_end
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = pgas
    fluid_component = 0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    variable = z
    fluid_component = 1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas z'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2]
      type = CO2FluidProperties
    []
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = pgas
    z = z
    temperature_unit = Celsius
    xnacl = xnacl
    capillary_pressure = pc
    fluid_state = fs
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-12 0 0 0 1e-12 0 0 0 1e-12'
  []
  [relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [relperm1]
    type = PorousFlowRelativePermeabilityCorey
    n = 3
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1
  end_time = 1
  nl_abs_tol = 1e-12
[]

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

[Postprocessors]
  [density_water]
    type = ElementIntegralVariablePostprocessor
    variable = density_water
  []
  [density_gas]
    type = ElementIntegralVariablePostprocessor
    variable = density_gas
  []
  [viscosity_water]
    type = ElementIntegralVariablePostprocessor
    variable = viscosity_water
  []
  [viscosity_gas]
    type = ElementIntegralVariablePostprocessor
    variable = viscosity_gas
  []
  [enthalpy_water]
    type = ElementIntegralVariablePostprocessor
    variable = enthalpy_water
  []
  [enthalpy_gas]
    type = ElementIntegralVariablePostprocessor
    variable = enthalpy_gas
  []
  [internal_energy_water]
    type = ElementIntegralVariablePostprocessor
    variable = internal_energy_water
  []
  [internal_energy_gas]
    type = ElementIntegralVariablePostprocessor
    variable = internal_energy_gas
  []
  [x1_water]
    type = ElementIntegralVariablePostprocessor
    variable = x1_water
  []
  [x0_water]
    type = ElementIntegralVariablePostprocessor
    variable = x0_water
  []
  [x1_gas]
    type = ElementIntegralVariablePostprocessor
    variable = x1_gas
  []
  [x0_gas]
    type = ElementIntegralVariablePostprocessor
    variable = x0_gas
  []
  [sg]
    type = ElementIntegralVariablePostprocessor
    variable = saturation_gas
  []
  [sw]
    type = ElementIntegralVariablePostprocessor
    variable = saturation_water
  []
  [pwater]
    type = ElementIntegralVariablePostprocessor
    variable = pressure_water
  []
  [pgas]
    type = ElementIntegralVariablePostprocessor
    variable = pressure_gas
  []
  [x0mass]
    type = PorousFlowFluidMass
    fluid_component = 0
    phase = '0 1'
  []
  [x1mass]
    type = PorousFlowFluidMass
    fluid_component = 1
    phase = '0 1'
  []
[]

[Outputs]
  csv = true
  file_base = brineco2
  execute_on = 'TIMESTEP_END'
  perf_graph = false
[]

(modules/fluid_properties/test/tests/brine/brine_tabulated.i)

# Test BrineFluidProperties calculations of density, viscosity and thermal
# conductivity with a TabulatedFluidProperties water.
#
# Experimental density values from Pitzer et al, "Thermodynamic properties
# of aqueous sodium chloride solution", Journal of Physical and Chemical
# Reference Data, 13, 1-102 (1984)
#
# Experimental viscosity values from Phillips et al, "Viscosity of NaCl and
# other solutions up to 350C and 50MPa pressures", LBL-11586 (1980)
#
# Thermal conductivity values from Ozbek and Phillips, "Thermal conductivity of
# aqueous NaCl solutions from 20C to 330C", LBL-9086 (1980)
#
#  --------------------------------------------------------------
#  Pressure (Mpa)                |   20      |    20     |   40
#  Temperature (C)               |   50      |   200     |  200
#  NaCl molality (mol/kg)        |    2      |     2     |    5
#  NaCl mass fraction (kg/kg)    |  0.1047   |  0.1047   |  0.2261
#  --------------------------------------------------------------
#  Expected values
#  --------------------------------------------------------------
#  Density (kg/m^3)              |  1068.52  |  959.27   |  1065.58
#  Viscosity (1e-6Pa.s)          |  679.8    |  180.0    |  263.1
#  Thermal conductivity (W/m/K)  |  0.630    |  0.649    |  0.633
#  --------------------------------------------------------------
#  Calculated values
#  --------------------------------------------------------------
#  Density (kg/m^3)              |  1067.18  |  958.68   |  1065.46
#  Viscosity (1e-6 Pa.s)         |  681.1    |  181.98    |  266.1
#  Thermal conductivity (W/m/K)  |  0.637    |   0.662    |  0.658
#  --------------------------------------------------------------
#
# All results are within expected accuracy

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 3
  ny = 1
  xmax = 3
  # This test uses ElementalVariableValue postprocessors on specific
  # elements, so element numbering needs to stay unchanged
  allow_renumbering = false
[]

[Variables]
  [./dummy]
  [../]
[]

[AuxVariables]
  [./pressure]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./temperature]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./xnacl]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./density]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./enthalpy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./internal_energy]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[Functions]
  [./pic]
    type = ParsedFunction
    value = 'if(x<2,20e6, 40e6)'
  [../]
  [./tic]
    type = ParsedFunction
    value = 'if(x<1, 323.15, 473.15)'
  [../]
  [./xic]
    type = ParsedFunction
    value = 'if(x<2,0.1047, 0.2261)'
  [../]
[]

[ICs]
  [./p_ic]
    type = FunctionIC
    function = pic
    variable = pressure
  [../]
  [./t_ic]
    type = FunctionIC
    function = tic
    variable = temperature
  [../]
  [./x_ic]
    type = FunctionIC
    function = xic
    variable = xnacl
  [../]
[]

[AuxKernels]
  [./density]
    type = MaterialRealAux
     variable = density
     property = density
  [../]
  [./enthalpy]
    type = MaterialRealAux
     variable = enthalpy
     property = enthalpy
  [../]
  [./internal_energy]
    type = MaterialRealAux
     variable = internal_energy
     property = e
  [../]
[]

[Modules]
  [./FluidProperties]
    [./water]
      type = Water97FluidProperties
    [../]
    [./water_tab]
      type = TabulatedFluidProperties
      fp = water
      save_file = false
    [../]
    [./brine]
      type = BrineFluidProperties
      water_fp = water_tab
    [../]
  [../]
[]

[Materials]
  [./fp_mat]
    type = MultiComponentFluidPropertiesMaterialPT
    pressure = pressure
    temperature = temperature
    xmass = xnacl
    fp = brine
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = dummy
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Postprocessors]
  [./density0]
    type = ElementalVariableValue
    variable = density
    elementid = 0
  [../]
  [./density1]
    type = ElementalVariableValue
    variable = density
    elementid = 1
  [../]
  [./density2]
    type = ElementalVariableValue
    variable = density
    elementid = 2
  [../]
  [./enthalpy0]
    type = ElementalVariableValue
    variable = enthalpy
    elementid = 0
  [../]
  [./enthalpy1]
    type = ElementalVariableValue
    variable = enthalpy
    elementid = 1
  [../]
  [./enthalpy2]
    type = ElementalVariableValue
    variable = enthalpy
    elementid = 2
  [../]
  [./e0]
    type = ElementalVariableValue
    variable = internal_energy
    elementid = 0
  [../]
  [./e1]
    type = ElementalVariableValue
    variable = internal_energy
    elementid = 1
  [../]
  [./e2]
    type = ElementalVariableValue
    variable = internal_energy
    elementid = 2
  [../]
[]

[Outputs]
  csv = true
  file_base = brine_out
[]

(modules/porous_flow/examples/lava_lamp/2phase_convection.i)

# Two phase density-driven convection of dissolved CO2 in brine
#
# Initially, the model has a gas phase at the top with a saturation of 0.29
# (which corresponds to an initial value of zi = 0.2).
# Diffusion of the dissolved CO2
# component from the saturated liquid to the unsaturated liquid below reduces the
# amount of CO2 in the gas phase. As the density of the CO2-saturated brine is greater
# than the unsaturated brine, a gravitational instability arises and density-driven
# convection of CO2-rich fingers descend into the unsaturated brine.
#
# The instability is seeded by a random perturbation to the porosity field.
# Mesh adaptivity is used to refine the mesh as the fingers form.
#
# Note: this model is computationally expensive, so should be run with multiple cores,
# preferably on a cluster.

[GlobalParams]
  PorousFlowDictator = 'dictator'
  gravity = '0 -9.81 0'
[]

[Adaptivity]
  max_h_level = 2
  marker = marker
  initial_marker = initial
  initial_steps = 2
  [Indicators]
    [indicator]
      type = GradientJumpIndicator
      variable = zi
    []
  []
  [Markers]
    [marker]
      type = ErrorFractionMarker
      indicator = indicator
      refine = 0.8
    []
    [initial]
      type = BoxMarker
      bottom_left = '0 1.95 0'
      top_right = '2 2 0'
      inside = REFINE
      outside = DO_NOTHING
    []
  []
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  ymax = 2
  xmax = 2
  ny = 40
  nx = 40
  bias_y = 0.95
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pgas
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pgas
  []
  [diff0]
    type = PorousFlowDispersiveFlux
    fluid_component = 0
    variable = pgas
    disp_long = '0 0'
    disp_trans = '0 0'
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = zi
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = zi
  []
  [diff1]
    type = PorousFlowDispersiveFlux
    fluid_component = 1
    variable = zi
    disp_long = '0 0'
    disp_trans = '0 0'
  []
[]

[AuxVariables]
  [xnacl]
    initial_condition = 0.01
  []
  [saturation_gas]
    order = FIRST
    family = MONOMIAL
  []
  [xco2l]
    order = FIRST
    family = MONOMIAL
  []
  [density_liquid]
    order = FIRST
    family = MONOMIAL
  []
  [porosity]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [saturation_gas]
    type = PorousFlowPropertyAux
    variable = saturation_gas
    property = saturation
    phase = 1
    execute_on = 'timestep_end'
  []
  [xco2l]
    type = PorousFlowPropertyAux
    variable = xco2l
    property = mass_fraction
    phase = 0
    fluid_component = 1
    execute_on = 'timestep_end'
  []
  [density_liquid]
    type = PorousFlowPropertyAux
    variable = density_liquid
    property = density
    phase = 0
    execute_on = 'timestep_end'
  []
[]

[Variables]
  [pgas]
  []
  [zi]
    scaling = 1e4
  []
[]

[ICs]
  [pressure]
    type = FunctionIC
    function = 10e6-9.81*1000*y
    variable = pgas
  []
  [zi]
    type = BoundingBoxIC
    variable = zi
    x1 = 0
    x2 = 2
    y1 = 1.95
    y2 = 2
    inside = 0.2
    outside = 0
  []
  [porosity]
    type = RandomIC
    variable = porosity
    min = 0.25
    max = 0.275
    seed = 0
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas zi'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2sw]
      type = CO2FluidProperties
    []
    [co2]
      type = TabulatedFluidProperties
      fp = co2sw
    []
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = '45'
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = 'pgas'
    z = 'zi'
    temperature_unit = Celsius
    xnacl = 'xnacl'
    capillary_pressure = pc
    fluid_state = fs
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = porosity
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-11 0 0 0 1e-11 0 0 0 1e-11'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    phase = 0
    n = 2
    s_res = 0.1
    sum_s_res = 0.2
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    phase = 1
    n = 2
    s_res = 0.1
    sum_s_res = 0.2
  []
  [diffusivity]
    type = PorousFlowDiffusivityConst
    diffusion_coeff = '2e-9 2e-9 2e-9 2e-9'
    tortuosity = '1 1'
  []
[]

[Preconditioning]
  active = basic
  [mumps_is_best_for_parallel_jobs]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
  [basic]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2             '
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 1e6
  nl_max_its = 25
  l_max_its = 100
  dtmax = 1e4
  nl_abs_tol = 1e-6
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 10
    growth_factor = 2
    cutback_factor = 0.5
  []
[]

[Functions]
  [flux]
    type = ParsedFunction
    vals = 'delta_xco2 dt'
    vars = 'dx dt'
    value = 'dx/dt'
  []
[]

[Postprocessors]
  [total_co2_in_gas]
    type = PorousFlowFluidMass
    phase = 1
    fluid_component = 1
  []
  [total_co2_in_liquid]
    type = PorousFlowFluidMass
    phase = 0
    fluid_component = 1
  []
  [numdofs]
    type = NumDOFs
  []
  [delta_xco2]
    type = ChangeOverTimePostprocessor
    postprocessor = total_co2_in_liquid
  []
  [dt]
    type = TimestepSize
  []
  [flux]
    type = FunctionValuePostprocessor
    function = flux
  []
[]

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

(modules/porous_flow/test/tests/jacobian/brineco2_twophase_nonisothermal.i)

# Tests correct calculation of properties derivatives in PorousFlowFluidState
# for nonisothermal two phase conditions, including salt as a nonlinear variable

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
    xmax = 10
    ymax = 10
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [pgas]
  []
  [zi]
    scaling = 1e-4
  []
  [xnacl]
  []
  [temperature]
    scaling = 1e-7
  []
[]

[ICs]
  [pgas]
    type = RandomIC
    min = 1e6
    max = 4e6
    variable = pgas
    seed = 1
  []
  [z]
    type = RandomIC
    min = 0.2
    max = 0.8
    variable = zi
    seed = 1
  []
  [xnacl]
    type = RandomIC
    min = 0.01
    max = 0.15
    variable = xnacl
    seed = 1
  []
  [temperature]
    type = RandomIC
    min = 20
    max = 80
    variable = temperature
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = pgas
    fluid_component = 0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    variable = zi
    fluid_component = 1
  []
  [mass2]
    type = PorousFlowMassTimeDerivative
    variable = xnacl
    fluid_component = 2
  []
  [adv0]
    type = PorousFlowAdvectiveFlux
    variable = pgas
    fluid_component = 0
  []
  [adv1]
    type = PorousFlowAdvectiveFlux
    variable = zi
    fluid_component = 1
  []
  [adv2]
    type = PorousFlowAdvectiveFlux
    variable = xnacl
    fluid_component = 2
  []
  [energy]
    type = PorousFlowEnergyTimeDerivative
    variable = temperature
  []
  [heat]
    type = PorousFlowHeatAdvection
    variable = temperature
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas zi xnacl temperature'
    number_fluid_phases = 2
    number_fluid_components = 3
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
    pc_max = 1e3
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2]
      type = CO2FluidProperties
    []
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temperature
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = pgas
    z = zi
    temperature = temperature
    temperature_unit = Celsius
    xnacl = xnacl
    capillary_pressure = pc
    fluid_state = fs
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-12 0 0 0 1e-12 0 0 0 1e-12'
  []
  [relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [relperm1]
    type = PorousFlowRelativePermeabilityCorey
    n = 3
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [rock_heat]
    type = PorousFlowMatrixInternalEnergy
    specific_heat_capacity = 1000
    density = 2500
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1
  end_time = 1
  nl_abs_tol = 1e-12
[]

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

(modules/porous_flow/test/tests/fluidstate/theis_brineco2.i)

# Two phase Theis problem: Flow from single source.
# Constant rate injection 2 kg/s
# 1D cylindrical mesh
# Initially, system has only a liquid phase, until enough gas is injected
# to form a gas phase, in which case the system becomes two phase.
#
# This test takes a few minutes to run, so is marked heavy

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 2000
  xmax = 2000
[]

[Problem]
  type = FEProblem
  coord_type = RZ
  rz_coord_axis = Y
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[AuxVariables]
  [saturation_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [x1]
    order = CONSTANT
    family = MONOMIAL
  []
  [y0]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [saturation_gas]
    type = PorousFlowPropertyAux
    variable = saturation_gas
    property = saturation
    phase = 1
    execute_on = timestep_end
  []
  [x1]
    type = PorousFlowPropertyAux
    variable = x1
    property = mass_fraction
    phase = 0
    fluid_component = 1
    execute_on = timestep_end
  []
  [y0]
    type = PorousFlowPropertyAux
    variable = y0
    property = mass_fraction
    phase = 1
    fluid_component = 0
    execute_on = timestep_end
  []
[]

[Variables]
  [pgas]
    initial_condition = 20e6
  []
  [zi]
    initial_condition = 0
  []
  [xnacl]
    initial_condition = 0.1
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pgas
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pgas
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = zi
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = zi
  []
  [mass2]
    type = PorousFlowMassTimeDerivative
    fluid_component = 2
    variable = xnacl
  []
  [flux2]
    type = PorousFlowAdvectiveFlux
    fluid_component = 2
    variable = xnacl
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas zi xnacl'
    number_fluid_phases = 2
    number_fluid_components = 3
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2sw]
      type = CO2FluidProperties
    []
    [co2]
      type = TabulatedFluidProperties
      fp = co2sw
    []
    [water]
      type = Water97FluidProperties
    []
    [watertab]
      type = TabulatedFluidProperties
      fp = water
      temperature_min = 273.15
      temperature_max = 573.15
      fluid_property_file = water_fluid_properties.csv
      save_file = false
    []
    [brine]
      type = BrineFluidProperties
      water_fp = watertab
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = 20
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = pgas
    z = zi
    temperature_unit = Celsius
    xnacl = xnacl
    capillary_pressure = pc
    fluid_state = fs
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.2
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-12 0 0 0 1e-12 0 0 0 1e-12'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
    s_res = 0.1
    sum_s_res = 0.1
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 1
  []
[]

[BCs]
  [rightwater]
    type = DirichletBC
    boundary = right
    value = 20e6
    variable = pgas
  []
[]

[DiracKernels]
  [source]
    type = PorousFlowSquarePulsePointSource
    point = '0 0 0'
    mass_flux = 2
    variable = zi
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 1e5
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1
    growth_factor = 1.5
  []
[]

[VectorPostprocessors]
  [line]
    type = LineValueSampler
    warn_discontinuous_face_values = false
    sort_by = x
    start_point = '0 0 0'
    end_point = '2000 0 0'
    num_points = 10000
    variable = 'pgas zi xnacl x1 saturation_gas'
    execute_on = 'timestep_end'
  []
[]

[Postprocessors]
  [pgas]
    type = PointValue
    point = '4 0 0'
    variable = pgas
  []
  [sgas]
    type = PointValue
    point = '4 0 0'
    variable = saturation_gas
  []
  [zi]
    type = PointValue
    point = '4 0 0'
    variable = zi
  []
  [massgas]
    type = PorousFlowFluidMass
    fluid_component = 1
  []
  [x1]
    type = PointValue
    point = '4 0 0'
    variable = x1
  []
  [y0]
    type = PointValue
    point = '4 0 0'
    variable = y0
  []
  [xnacl]
    type = PointValue
    point = '4 0 0'
    variable = xnacl
  []
[]

[Outputs]
  print_linear_residuals = false
  perf_graph = true
  [csvout]
    type = CSV
    execute_on = timestep_end
    execute_vector_postprocessors_on = final
  []
[]

(modules/porous_flow/test/tests/fluidstate/theis_brineco2_nonisothermal.i)

# Two phase nonisothermal Theis problem: Flow from single source.
# Constant rate injection 2 kg/s of cold CO2 into warm reservoir
# 1D cylindrical mesh
# Initially, system has only a liquid phase, until enough gas is injected
# to form a gas phase, in which case the system becomes two phase.

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 40
    xmin = 0.1
    xmax = 200
    bias_x = 1.05
  []
[]

[Problem]
  type = FEProblem
  coord_type = RZ
  rz_coord_axis = Y
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[AuxVariables]
  [saturation_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [x1]
    order = CONSTANT
    family = MONOMIAL
  []
  [y0]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [saturation_gas]
    type = PorousFlowPropertyAux
    variable = saturation_gas
    property = saturation
    phase = 1
    execute_on = timestep_end
  []
  [x1]
    type = PorousFlowPropertyAux
    variable = x1
    property = mass_fraction
    phase = 0
    fluid_component = 1
    execute_on = timestep_end
  []
  [y0]
    type = PorousFlowPropertyAux
    variable = y0
    property = mass_fraction
    phase = 1
    fluid_component = 0
    execute_on = timestep_end
  []
[]

[Variables]
  [pgas]
    initial_condition = 20e6
  []
  [zi]
    initial_condition = 0
  []
  [xnacl]
    initial_condition = 0.1
  []
  [temperature]
    initial_condition = 70
    scaling = 1e-4
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = pgas
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = pgas
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = zi
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = zi
  []
  [mass2]
    type = PorousFlowMassTimeDerivative
    fluid_component = 2
    variable = xnacl
  []
  [flux2]
    type = PorousFlowAdvectiveFlux
    fluid_component = 2
    variable = xnacl
  []
  [energy]
    type = PorousFlowEnergyTimeDerivative
    variable = temperature
  []
  [heatadv]
    type = PorousFlowHeatAdvection
    variable = temperature
  []
  [conduction]
    type = PorousFlowHeatConduction
    variable = temperature
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas zi xnacl temperature'
    number_fluid_phases = 2
    number_fluid_components = 3
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2]
      type = CO2FluidProperties
    []
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temperature
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = pgas
    z = zi
    temperature = temperature
    temperature_unit = Celsius
    xnacl = xnacl
    capillary_pressure = pc
    fluid_state = fs
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.2
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-12 0 0 0 1e-12 0 0 0 1e-12'
  []
  [relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
    s_res = 0.1
    sum_s_res = 0.1
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 1
  []
  [rockheat]
    type = PorousFlowMatrixInternalEnergy
    specific_heat_capacity = 1000
    density = 2500
  []
  [rock_thermal_conductivity]
    type = PorousFlowThermalConductivityIdeal
    dry_thermal_conductivity = '50 0 0  0 50 0  0 0 50'
  []
[]

[BCs]
  [cold_gas]
    type = DirichletBC
    boundary = left
    variable = temperature
    value = 20
  []
  [gas_injecton]
    type = PorousFlowSink
    boundary = left
    variable = zi
    flux_function = -0.159155
  []
  [rightwater]
    type = DirichletBC
    boundary = right
    value = 20e6
    variable = pgas
  []
  [righttemp]
    type = DirichletBC
    boundary = right
    value = 70
    variable = temperature
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 1e4
  nl_abs_tol = 1e-7
  nl_rel_tol = 1e-5
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1
    growth_factor = 1.5
  []
[]

[Postprocessors]
  [pgas]
    type = PointValue
    point =  '2 0 0'
    variable = pgas
  []
  [sgas]
    type = PointValue
    point =  '2 0 0'
    variable = saturation_gas
  []
  [zi]
    type = PointValue
    point = '2 0 0'
    variable = zi
  []
  [temperature]
    type = PointValue
    point = '2 0 0'
    variable = temperature
  []
  [massgas]
    type = PorousFlowFluidMass
    fluid_component = 1
  []
  [x1]
    type = PointValue
    point =  '2 0 0'
    variable = x1
  []
  [y0]
    type = PointValue
    point =  '2 0 0'
    variable = y0
  []
[]

[Outputs]
  print_linear_residuals = false
  perf_graph = true
  csv = true
[]

(modules/porous_flow/examples/co2_intercomparison/1Dradial/properties.i)

# Liquid and gas properties for code intercomparison problem 3
#
# From Pruess et al, Code intercomparison builds confidence in
# numerical simulation models for geologic disposal of CO2, Energy 29 (2004)
#
# This test simply calculates density and viscosity of each phase for
# various pressures and salinities, as well as mass fractions of CO2 in the
# liquid phase and H2O in the gas phase.
#
# Four versions of this are run:
# 1) No CO2, 0 salt mass fraction (pure water)
# 2) Enough CO2 to form gas phase, 0 salt mass fraction (pure water)
# 3) No CO2, 0.15 salt mass fraction
# 4) Enough CO2 to form gas phase, 0.15 salt mass fraction
#
# These results compare well with detailed results presented in Pruess et al,
# Intercomparison of numerical simulation codes for geologic disposal of CO2,
# LBNL-51813 (2002)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 4
  xmax = 4
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[AuxVariables]
  [density_liquid]
    order = CONSTANT
    family = MONOMIAL
  []
  [density_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [viscosity_liquid]
    order = CONSTANT
    family = MONOMIAL
  []
  [viscosity_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [x1]
    order = CONSTANT
    family = MONOMIAL
  []
  [y0]
    order = CONSTANT
    family = MONOMIAL
  []
  [xnacl]
    initial_condition = 0.0
  []
[]

[AuxKernels]
  [density_liquid]
    type = PorousFlowPropertyAux
    variable = density_liquid
    property = density
    phase = 0
    execute_on = timestep_end
  []
  [density_gas]
    type = PorousFlowPropertyAux
    variable = density_gas
    property = density
    phase = 1
    execute_on = timestep_end
  []
  [viscosity_liquid]
    type = PorousFlowPropertyAux
    variable = viscosity_liquid
    property = viscosity
    phase = 0
    execute_on = timestep_end
  []
  [viscosity_gas]
    type = PorousFlowPropertyAux
    variable = viscosity_gas
    property = viscosity
    phase = 1
    execute_on = timestep_end
  []
  [x1]
    type = PorousFlowPropertyAux
    variable = x1
    property = mass_fraction
    phase = 0
    fluid_component = 1
    execute_on = timestep_end
  []
  [y0]
    type = PorousFlowPropertyAux
    variable = y0
    property = mass_fraction
    phase = 1
    fluid_component = 0
    execute_on = timestep_end
  []
[]

[Variables]
  [pgas]
    order = CONSTANT
    family = MONOMIAL
  []
  [zi]
    initial_condition = 0.0
  []
[]

[Functions]
  [pic]
    type = ParsedFunction
    value = 'if(x<1,12e6,if(x<2,16e6,if(x<3,20e6,24e6)))'
  []
[]

[ICs]
  [pic]
    type = FunctionIC
    function = pic
    variable = pgas
  []
[]

[Kernels]
  [diffusionp]
    type = NullKernel
    variable = pgas
  []
  [diffusionz]
    type = NullKernel
    variable = zi
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas zi'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2]
      type = CO2FluidProperties
    []
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = 45
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = pgas
    z = zi
    temperature_unit = Celsius
    xnacl = xnacl
    capillary_pressure = pc
    fluid_state = fs
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2             '
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Outputs]
  perf_graph = true
  csv = true
  execute_on = timestep_end
  file_base = properties_water
[]

[VectorPostprocessors]
  [vpp]
    type = ElementValueSampler
    variable = 'pgas density_liquid density_gas viscosity_liquid viscosity_gas x1 y0'
    sort_by = x
  []
[]

(modules/porous_flow/test/tests/jacobian/brineco2_liquid_2.i)

# Tests correct calculation of properties derivatives in PorousFlowFluidState
# for conditions that give a single liquid phase, including salt as a nonlinear variable

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [pgas]
  []
  [zi]
  []
  [xnacl]
  []
[]

[ICs]
  [pgas]
    type = RandomIC
    min = 5e6
    max = 8e6
    variable = pgas
  []
  [z]
    type = RandomIC
    min = 0.01
    max = 0.03
    variable = zi
  []
  [xnacl]
    type = RandomIC
    min = 0.01
    max = 0.15
    variable = xnacl
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = pgas
    fluid_component = 0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    variable = zi
    fluid_component = 1
  []
  [mass2]
    type = PorousFlowMassTimeDerivative
    variable = xnacl
    fluid_component = 2
  []
  [adv0]
    type = PorousFlowAdvectiveFlux
    variable = pgas
    fluid_component = 0
  []
  [adv1]
    type = PorousFlowAdvectiveFlux
    variable = zi
    fluid_component = 1
  []
  [adv2]
    type = PorousFlowAdvectiveFlux
    variable = xnacl
    fluid_component = 2
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas zi xnacl'
    number_fluid_phases = 2
    number_fluid_components = 3
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
    pc_max = 1e3
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2]
      type = CO2FluidProperties
    []
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = 50
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = pgas
    z = zi
    temperature_unit = Celsius
    xnacl = xnacl
    capillary_pressure = pc
    fluid_state = fs
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-12 0 0 0 1e-12 0 0 0 1e-12'
  []
  [relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [relperm1]
    type = PorousFlowRelativePermeabilityCorey
    n = 3
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1
  end_time = 1
  nl_abs_tol = 1e-12
[]

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

(modules/porous_flow/test/tests/jacobian/brineco2_liquid.i)

# Tests correct calculation of properties derivatives in PorousFlowFluidState
# for conditions that give a single liquid phase

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[AuxVariables]
  [xnacl]
    initial_condition = 0.05
  []
[]

[Variables]
  [pgas]
  []
  [zi]
  []
[]

[ICs]
  [pgas]
    type = RandomIC
    min = 5e6
    max = 8e6
    variable = pgas
  []
  [z_liquid]
    type = RandomIC
    min = 0.01
    max = 0.03
    variable = zi
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = pgas
    fluid_component = 0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    variable = zi
    fluid_component = 1
  []
  [adv0]
    type = PorousFlowAdvectiveFlux
    variable = pgas
    fluid_component = 0
  []
  [adv1]
    type = PorousFlowAdvectiveFlux
    variable = zi
    fluid_component = 1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas zi'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    m = 0.5
    alpha = 1
    pc_max = 1e4
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2]
      type = CO2FluidProperties
    []
    [brine]
      type = BrineFluidProperties
    []
    [water]
      type = Water97FluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = 50
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = pgas
    z = zi
    temperature_unit = Celsius
    xnacl = xnacl
    capillary_pressure = pc
    fluid_state = fs
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-12 0 0 0 1e-12 0 0 0 1e-12'
  []
  [relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [relperm1]
    type = PorousFlowRelativePermeabilityCorey
    n = 3
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1
  end_time = 1
  nl_abs_tol = 1e-12
[]

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

[AuxVariables]
  [sgas]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [sgas]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = sgas
  []
[]

[Postprocessors]
  [sgas_min]
    type = ElementExtremeValue
    variable = sgas
    value_type = min
  []
  [sgas_max]
    type = ElementExtremeValue
    variable = sgas
    value_type = max
  []
[]

(modules/porous_flow/test/tests/fluidstate/brineco2_ic.i)

# Tests correct calculation of z (total mass fraction of NCG summed over all
# phases) using the PorousFlowFluidStateIC initial condition. Once z is
# calculated by the initial condition, the thermophysical properties are calculated
# and the resulting gas saturation should be equal to that given in the intial condition

[Mesh]
  type = GeneratedMesh
  dim = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
  temperature_unit = Celsius
[]

[Variables]
  [pgas]
    initial_condition = 1e6
  []
  [z]
  []
[]

[ICs]
  [z]
    type = PorousFlowFluidStateIC
    saturation = 0.5
    gas_porepressure = pgas
    temperature = 50
    variable = z
    xnacl = 0.1
    fluid_state = fs
  []
[]

[AuxVariables]
  [saturation_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [saturation_water]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [saturation_water]
    type = PorousFlowPropertyAux
    variable = saturation_water
    property = saturation
    phase = 0
    execute_on = timestep_end
  []
  [saturation_gas]
    type = PorousFlowPropertyAux
    variable = saturation_gas
    property = saturation
    phase = 1
    execute_on = timestep_end
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = pgas
    fluid_component = 0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    variable = z
    fluid_component = 1
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas z'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2]
      type = CO2FluidProperties
    []
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = 50
  []
  [waterncg]
    type = PorousFlowFluidState
    gas_porepressure = pgas
    z = z
    fluid_state = fs
    capillary_pressure = pc
    xnacl = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-12 0 0 0 1e-12 0 0 0 1e-12'
  []
  [relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [relperm1]
    type = PorousFlowRelativePermeabilityCorey
    n = 3
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1
  end_time = 1
  nl_abs_tol = 1e-12
[]

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

[Postprocessors]
  [sg]
    type = ElementIntegralVariablePostprocessor
    variable = saturation_gas
    execute_on = 'initial timestep_end'
  []
  [sw]
    type = ElementIntegralVariablePostprocessor
    variable = saturation_water
    execute_on = 'initial timestep_end'
  []
  [z]
    type = ElementIntegralVariablePostprocessor
    variable = z
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
[]

(modules/porous_flow/test/tests/fluidstate/brineco2_2.i)

# Injection of supercritical CO2 into a single brine saturated cell. The CO2 initially fully
# dissolves into the brine, increasing its density slightly. After a few time steps,
# the brine is saturated with CO2, and subsequently a supercritical gas phase of CO2 saturated
# with a small amount of H2O is formed. Salt is included as a nonlinear variable.

[Mesh]
  type = GeneratedMesh
  dim = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
  temperature = 30
[]

[Variables]
  [pgas]
    initial_condition = 20e6
  []
  [z]
  []
  [xnacl]
    initial_condition = 0.1
  []
[]

[DiracKernels]
  [source]
    type = PorousFlowSquarePulsePointSource
    variable = z
    point = '0.5 0.5 0'
    mass_flux = 2
  []
[]

[BCs]
  [left]
    type = DirichletBC
    value = 20e6
    variable = pgas
    boundary = left
  []
  [right]
    type = DirichletBC
    value = 20e6
    variable = pgas
    boundary = right
  []
[]

[AuxVariables]
  [pressure_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [pressure_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [saturation_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [saturation_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [density_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [density_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [viscosity_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [viscosity_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [x0_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [x0_gas]
    order = CONSTANT
    family = MONOMIAL
  []
  [x1_water]
    order = CONSTANT
    family = MONOMIAL
  []
  [x1_gas]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [pressure_water]
    type = PorousFlowPropertyAux
    variable = pressure_water
    property = pressure
    phase = 0
    execute_on = 'initial timestep_end'
  []
  [pressure_gas]
    type = PorousFlowPropertyAux
    variable = pressure_gas
    property = pressure
    phase = 1
    execute_on = 'initial timestep_end'
  []
  [saturation_water]
    type = PorousFlowPropertyAux
    variable = saturation_water
    property = saturation
    phase = 0
    execute_on = 'initial timestep_end'
  []
  [saturation_gas]
    type = PorousFlowPropertyAux
    variable = saturation_gas
    property = saturation
    phase = 1
    execute_on = 'initial timestep_end'
  []
  [density_water]
    type = PorousFlowPropertyAux
    variable = density_water
    property = density
    phase = 0
    execute_on = 'initial timestep_end'
  []
  [density_gas]
    type = PorousFlowPropertyAux
    variable = density_gas
    property = density
    phase = 1
    execute_on = 'initial timestep_end'
  []
  [viscosity_water]
    type = PorousFlowPropertyAux
    variable = viscosity_water
    property = viscosity
    phase = 0
    execute_on = 'initial timestep_end'
  []
  [viscosity_gas]
    type = PorousFlowPropertyAux
    variable = viscosity_gas
    property = viscosity
    phase = 1
    execute_on = 'initial timestep_end'
  []
  [x1_water]
    type = PorousFlowPropertyAux
    variable = x1_water
    property = mass_fraction
    phase = 0
    fluid_component = 1
    execute_on = 'initial timestep_end'
  []
  [x1_gas]
    type = PorousFlowPropertyAux
    variable = x1_gas
    property = mass_fraction
    phase = 1
    fluid_component = 1
    execute_on = 'initial timestep_end'
  []
  [x0_water]
    type = PorousFlowPropertyAux
    variable = x0_water
    property = mass_fraction
    phase = 0
    fluid_component = 0
    execute_on = 'initial timestep_end'
  []
  [x0_gas]
    type = PorousFlowPropertyAux
    variable = x0_gas
    property = mass_fraction
    phase = 1
    fluid_component = 0
    execute_on = 'initial timestep_end'
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = pgas
    fluid_component = 0
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    variable = z
    fluid_component = 1
  []
  [mass2]
    type = PorousFlowMassTimeDerivative
    variable = xnacl
    fluid_component = 2
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pgas z xnacl'
    number_fluid_phases = 2
    number_fluid_components = 3
  []
  [pc]
    type = PorousFlowCapillaryPressureConst
    pc = 0
  []
  [fs]
    type = PorousFlowBrineCO2
    brine_fp = brine
    co2_fp = co2
    capillary_pressure = pc
  []
[]

[Modules]
  [FluidProperties]
    [co2]
      type = CO2FluidProperties
    []
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
  []
  [brineco2]
    type = PorousFlowFluidState
    gas_porepressure = pgas
    z = z
    temperature_unit = Celsius
    xnacl = xnacl
    capillary_pressure = pc
    fluid_state = fs
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-12 0 0 0 1e-12 0 0 0 1e-12'
  []
  [relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  []
  [relperm1]
    type = PorousFlowRelativePermeabilityCorey
    n = 3
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1
  end_time = 10
[]

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

[Postprocessors]
  [density_water]
    type = ElementIntegralVariablePostprocessor
    variable = density_water
    execute_on = 'initial timestep_end'
  []
  [density_gas]
    type = ElementIntegralVariablePostprocessor
    variable = density_gas
    execute_on = 'initial timestep_end'
  []
  [viscosity_water]
    type = ElementIntegralVariablePostprocessor
    variable = viscosity_water
    execute_on = 'initial timestep_end'
  []
  [viscosity_gas]
    type = ElementIntegralVariablePostprocessor
    variable = viscosity_gas
    execute_on = 'initial timestep_end'
  []
  [x1_water]
    type = ElementIntegralVariablePostprocessor
    variable = x1_water
    execute_on = 'initial timestep_end'
  []
  [x0_water]
    type = ElementIntegralVariablePostprocessor
    variable = x0_water
    execute_on = 'initial timestep_end'
  []
  [x1_gas]
    type = ElementIntegralVariablePostprocessor
    variable = x1_gas
    execute_on = 'initial timestep_end'
  []
  [x0_gas]
    type = ElementIntegralVariablePostprocessor
    variable = x0_gas
    execute_on = 'initial timestep_end'
  []
  [sg]
    type = ElementIntegralVariablePostprocessor
    variable = saturation_gas
    execute_on = 'initial timestep_end'
  []
  [sw]
    type = ElementIntegralVariablePostprocessor
    variable = saturation_water
    execute_on = 'initial timestep_end'
  []
  [pwater]
    type = ElementIntegralVariablePostprocessor
    variable = pressure_water
    execute_on = 'initial timestep_end'
  []
  [pgas]
    type = ElementIntegralVariablePostprocessor
    variable = pressure_gas
    execute_on = 'initial timestep_end'
  []
  [xnacl]
    type = ElementIntegralVariablePostprocessor
    variable = xnacl
    execute_on = 'initial timestep_end'
  []
  [x0mass]
    type = PorousFlowFluidMass
    fluid_component = 0
    phase = '0 1'
    execute_on = 'initial timestep_end'
  []
  [x1mass]
    type = PorousFlowFluidMass
    fluid_component = 1
    phase = '0 1'
    execute_on = 'initial timestep_end'
  []
  [x2mass]
    type = PorousFlowFluidMass
    fluid_component = 2
    phase = '0 1'
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
  file_base = brineco2_2
  execute_on = 'initial timestep_end'
  perf_graph = true
[]

(modules/porous_flow/examples/restart/gravityeq.i)

# Initial run to establish gravity equilibrium. As only brine is present (no gas),
# we can use the single phase equation of state and kernels, reducing the computational
# cost. An estimate of the hydrostatic pressure gradient is used as the initial condition
# using an approximate brine density of 1060 kg/m^3.
# The end time is set to a large value (~100 years) to allow the pressure to reach
# equilibrium. Steady state detection is used to halt the run when a steady state is reached.

[Mesh]
  type = GeneratedMesh
  dim = 2
  ny = 10
  nx = 10
  ymax = 100
  xmax = 5000
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 -9.81 0'
  temperature_unit = Celsius
[]

[Variables]
  [porepressure]
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    function = ppic
    variable = porepressure
  []
[]

[Functions]
  [ppic]
    type = ParsedFunction
    value = '10e6 + 1060*9.81*(100-y)'
  []
[]

[BCs]
  [top]
    type = DirichletBC
    variable = porepressure
    value = 10e6
    boundary = top
  []
[]

[AuxVariables]
  [temperature]
    initial_condition = 50
  []
  [xnacl]
    initial_condition = 0.1
  []
  [brine_density]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = porepressure
  []
  [flux0]
    type = PorousFlowFullySaturatedDarcyFlow
    variable = porepressure
  []
[]

[AuxKernels]
  [brine_density]
    type = PorousFlowPropertyAux
    property = density
    variable = brine_density
    execute_on = 'initial timestep_end'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = porepressure
    number_fluid_phases = 1
    number_fluid_components = 1
  []
[]

[Modules]
  [FluidProperties]
    [brine]
      type = BrineFluidProperties
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temperature
  []
  [ps]
    type = PorousFlow1PhaseFullySaturated
    porepressure = porepressure
  []
  [massfrac]
    type = PorousFlowMassFraction
  []
  [brine]
    type = PorousFlowBrine
    compute_enthalpy = false
    compute_internal_energy = false
    xnacl = xnacl
    phase = 0
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-13 0 0 0 1e-13 0  0 0 1e-13'
  []
[]

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

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 3e9
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-06
  steady_state_detection = true
  steady_state_tolerance = 1e-12
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e1
  []
[]

[Outputs]
  execute_on = 'initial timestep_end'
  exodus = true
  perf_graph = true
[]

(modules/porous_flow/examples/restart/gas_injection_new_mesh.i)

# Using the results from the equilibrium run to provide the initial condition for
# porepressure, we now inject a gas phase into the brine-saturated reservoir. In this
# example, the mesh is not identical to the mesh used in gravityeq.i. Rather, it is
# generated so that it is more refined near the injection boundary and at the top of
# the model, as that is where the gas plume will be present.
#
# To use the hydrostatic pressure calculated using the gravity equilibrium run as the initial
# condition for the pressure, a SolutionUserObject is used, along with a SolutionFunction to
# interpolate the pressure from the gravity equilibrium run to the initial condition for liqiud
# porepressure in this example.
#
# Even though the gravity equilibrium is established using a 2D mesh, in this example,
# we use a mesh shifted 0.1 m to the right and rotate it about the Y axis to make a 2D radial
# model.
#
# Methane injection takes place over the surface of the hole created by rotating the mesh,
# and hence the injection area is 2 pi r h. We can calculate this using an AreaPostprocessor,
# and then use this in a ParsedFunction to calculate the injection rate so that 10 kg/s of
# methane is injected.
#
# Note: as this example uses the results from a previous simulation, gravityeq.i MUST be
# run before running this input file.

[Mesh]
  type = GeneratedMesh
  dim = 2
  ny = 25
  nx = 50
  ymax = 100
  xmin = 0.1
  xmax = 5000
  bias_x = 1.05
  bias_y = 0.95
[]

[Problem]
  coord_type = RZ
  rz_coord_axis = Y
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 -9.81 0'
  temperature_unit = Celsius
[]

[Variables]
  [pp_liq]
  []
  [sat_gas]
    initial_condition = 0
  []
[]

[ICs]
  [ppliq_ic]
    type = FunctionIC
    variable = pp_liq
    function = ppliq_ic
  []
[]

[AuxVariables]
  [temperature]
    initial_condition = 50
  []
  [xnacl]
    initial_condition = 0.1
  []
  [brine_density]
    family = MONOMIAL
    order = CONSTANT
  []
  [methane_density]
    family = MONOMIAL
    order = CONSTANT
  []
  [massfrac_ph0_sp0]
    initial_condition = 1
  []
  [massfrac_ph1_sp0]
    initial_condition = 0
  []
  [pp_gas]
    family = MONOMIAL
    order = CONSTANT
  []
  [sat_liq]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[Kernels]
  [mass0]
    type = PorousFlowMassTimeDerivative
    variable = pp_liq
  []
  [flux0]
    type = PorousFlowAdvectiveFlux
    variable = pp_liq
  []
  [mass1]
    type = PorousFlowMassTimeDerivative
    variable = sat_gas
    fluid_component = 1
  []
  [flux1]
    type = PorousFlowAdvectiveFlux
    variable = sat_gas
    fluid_component = 1
  []
[]

[AuxKernels]
  [brine_density]
    type = PorousFlowPropertyAux
    property = density
    variable = brine_density
    execute_on = 'initial timestep_end'
  []
  [methane_density]
    type = PorousFlowPropertyAux
    property = density
    variable = methane_density
    phase = 1
    execute_on = 'initial timestep_end'
  []
  [pp_gas]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 1
    variable = pp_gas
    execute_on = 'initial timestep_end'
  []
  [sat_liq]
    type = PorousFlowPropertyAux
    property = saturation
    variable = sat_liq
    execute_on = 'initial timestep_end'
  []
[]

[BCs]
  [gas_injection]
    type = PorousFlowSink
    boundary = left
    variable = sat_gas
    flux_function = injection_rate
    fluid_phase = 1
  []
  [brine_out]
    type = PorousFlowPiecewiseLinearSink
    boundary = right
    variable = pp_liq
    multipliers = '0 1e9'
    pt_vals = '0 1e9'
    fluid_phase = 0
    flux_function = 1e-6
    use_mobility = true
    use_relperm = true
    mass_fraction_component = 0
  []
[]

[Functions]
  [injection_rate]
    type = ParsedFunction
    vals = injection_area
    vars = area
    value = '-1/area'
  []
  [ppliq_ic]
    type = SolutionFunction
    solution = soln
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pp_liq sat_gas'
    number_fluid_phases = 2
    number_fluid_components = 2
  []
  [pc]
    type = PorousFlowCapillaryPressureVG
    alpha = 1e-5
    m = 0.5
    sat_lr = 0.2
    pc_max = 1e7
  []
  [soln]
    type = SolutionUserObject
    mesh = gravityeq_out.e
    system_variables = porepressure
  []
[]

[Modules]
  [FluidProperties]
    [brine]
      type = BrineFluidProperties
    []
    [methane]
      type = MethaneFluidProperties
    []
    [methane_tab]
      type = TabulatedFluidProperties
      fp = methane
      save_file = false
    []
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temperature
  []
  [ps]
    type = PorousFlow2PhasePS
    phase0_porepressure = pp_liq
    phase1_saturation = sat_gas
    capillary_pressure = pc
  []
  [massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  []
  [brine]
    type = PorousFlowBrine
    compute_enthalpy = false
    compute_internal_energy = false
    xnacl = xnacl
    phase = 0
  []
  [methane]
    type = PorousFlowSingleComponentFluid
    compute_enthalpy = false
    compute_internal_energy = false
    fp = methane_tab
    phase = 1
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-13 0 0 0 5e-14 0  0 0 1e-13'
  []
  [relperm_liq]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
    s_res = 0.2
    sum_s_res = 0.3
  []
  [relperm_gas]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 1
    s_res = 0.1
    sum_s_res = 0.3
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
    petsc_options_value = ' asm      lu           NONZERO'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1e8
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-06
  nl_max_its = 20
  dtmax = 1e6
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e1
    growth_factor = 1.5
  []
[]

[Postprocessors]
  [mass_ph0]
    type = PorousFlowFluidMass
    fluid_component = 0
    execute_on = 'initial timestep_end'
  []
  [mass_ph1]
    type = PorousFlowFluidMass
    fluid_component = 1
    execute_on = 'initial timestep_end'
  []
  [injection_area]
    type = AreaPostprocessor
    boundary = left
    execute_on = initial
  []
[]

[Outputs]
  execute_on = 'initial timestep_end'
  exodus = true
  perf_graph = true
[]

Range of validity
Input Parameters
Input Files
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