PorousFlowCapillaryPressureBC

Brooks-Corey capillary pressure

The Brooks-Corey capillary-pressure relationship is (Brooks and Corey, 1966)

$var element = document.getElementById("moose-equation-6b348df6-acf2-42f9-8344-c1e6325d4af3");katex.render("S_{\\mathrm{eff}} = \\left( \\frac{P_c}{P_e} \\right)^{-\\lambda},", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ or $var element = document.getElementById("moose-equation-2605189e-2dd4-4fc2-8e7f-916e2f179d7c");katex.render("P_c = P_e S_{\\mathrm{eff}}^{-1/\\lambda},", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-edd3dfed-1dd7-4f00-ad60-3f6c3594b5ed");katex.render("P_e", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , the threshold entry pressure, and $var element = document.getElementById("moose-equation-4e27500e-3195-4f4a-af00-8aa9176942c3");katex.render("\\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , the exponent, are required parameters.

Input Parameters

lambdaBrooks-Corey exponent lambda
C++ Type:double
Options:
Description:Brooks-Corey exponent lambda
peBrooks-Corey entry pressure. Must be positive
C++ Type:double
Options:
Description:Brooks-Corey entry pressure. Must be positive

Required Parameters

blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
log_extensionTrueUse a logarithmic extension for low saturation to avoid capillary pressure going to infinity. Default is true. Set to false if your capillary pressure depends on spatially-dependent variables other than saturation, as the log-extension C++ code for this case has yet to be implemented
Default:True
C++ Type:bool
Options:
Description:Use a logarithmic extension for low saturation to avoid capillary pressure going to infinity. Default is true. Set to false if your capillary pressure depends on spatially-dependent variables other than saturation, as the log-extension C++ code for this case has yet to be implemented
pc_max1e+09Maximum capillary pressure (Pa). Must be > 0. Default is 1e9
Default:1e+09
C++ Type:double
Options:
Description:Maximum capillary pressure (Pa). Must be > 0. Default is 1e9
sat_lr0Liquid residual saturation. Must be between 0 and 1. Default is 0
Default:0
C++ Type:double
Options:
Description:Liquid residual saturation. Must be between 0 and 1. Default is 0

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

Advanced Parameters

Input Files

modules/porous_flow/test/tests/capillary_pressure/brooks_corey2.i
modules/porous_flow/test/tests/gravity/grav02g.i
modules/porous_flow/test/tests/fluidstate/water_vapor.i
modules/porous_flow/test/tests/fluidstate/water_vapor_phasechange.i
modules/porous_flow/test/tests/capillary_pressure/brooks_corey1.i

modules/porous_flow/test/tests/capillary_pressure/brooks_corey2.i

# Test Brooks-Corey capillary pressure curve by varying saturation over the mesh
# lambda = 2, sat_lr = 0.1, log_extension = true

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 500
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [./p0]
    initial_condition = 1e6
  [../]
  [./s1]
  [../]
[]

[AuxVariables]
  [./s0aux]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./s1aux]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./p0aux]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./p1aux]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[AuxKernels]
  [./s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  [../]
  [./s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  [../]
  [./p0]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 0
    variable = p0aux
  [../]
  [./p1]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 1
    variable = p1aux
  [../]
[]

[Functions]
  [./s1]
    type = ParsedFunction
    value = x
  [../]
[]

[ICs]
  [./s1]
    type = FunctionIC
    variable = s1
    function = s1
  [../]
[]

[Kernels]
  [./p0]
    type = Diffusion
    variable = p0
  [../]
  [./s1]
    type = Diffusion
    variable = s1
  [../]
[]

[UserObjects]
  [./dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  [../]
  [./pc]
    type = PorousFlowCapillaryPressureBC
    lambda = 2
    log_extension = true
    pe = 1e5
    sat_lr = 0.1
  [../]
[]

[Materials]
  [./temperature]
    type = PorousFlowTemperature
  [../]
  [./ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  [../]
  [./kr0]
    type = PorousFlowRelativePermeabilityVG
    phase = 0
    m = 0.5
  [../]
  [./kr1]
    type = PorousFlowRelativePermeabilityCorey
    phase = 1
    n = 2
  [../]
[]

[VectorPostprocessors]
  [./vpp]
    type = LineValueSampler
    variable = 's0aux s1aux p0aux p1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 500
    sort_by = id
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-6
[]

[BCs]
  [./sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  [../]
  [./sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  [../]
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

modules/porous_flow/test/tests/gravity/grav02g.i

# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PS), 2components, Brooks-Corey capillary pressure, constant fluid bulk-moduli for each phase, constant viscosity,
# constant permeability, Brooks-Corey relative permeabilities with residual saturation

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

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 -10 0'
[]

[Variables]
  [./ppwater]
    initial_condition = 1.5e6
  [../]
  [./sgas]
    initial_condition = 0.3
  [../]
[]

[AuxVariables]
  [./massfrac_ph0_sp0]
    initial_condition = 1
  [../]
  [./massfrac_ph1_sp0]
    initial_condition = 0
  [../]
  [./ppgas]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./swater]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./relpermwater]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./relpermgas]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[Kernels]
  [./mass0]
    type = PorousFlowMassTimeDerivative
    fluid_component = 0
    variable = ppwater
  [../]
  [./flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = ppwater
  [../]
  [./mass1]
    type = PorousFlowMassTimeDerivative
    fluid_component = 1
    variable = sgas
  [../]
  [./flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = sgas
  [../]
[]

[AuxKernels]
  [./ppgas]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 1
    variable = ppgas
  [../]
  [./swater]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = swater
  [../]
  [./relpermwater]
    type = MaterialStdVectorAux
    property = PorousFlow_relative_permeability_qp
    index = 0
    variable = relpermwater
  [../]
  [./relpermgas]
    type = PorousFlowPropertyAux
    property = relperm
    phase = 1
    variable = relpermgas
  [../]
[]

[UserObjects]
  [./dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'ppwater sgas'
    number_fluid_phases = 2
    number_fluid_components = 2
  [../]
  [./pc]
    type = PorousFlowCapillaryPressureBC
    lambda = 2
    pe = 1e4
  [../]
[]

[Modules]
  [./FluidProperties]
    [./simple_fluid0]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 1000
      viscosity = 1e-3
      thermal_expansion = 0
    [../]
    [./simple_fluid1]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 10
      viscosity = 1e-5
      thermal_expansion = 0
    [../]
  [../]
[]

[Materials]
  [./temperature]
    type = PorousFlowTemperature
  [../]
  [./ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = ppwater
    phase1_saturation = sgas
    capillary_pressure = pc
  [../]
  [./massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  [../]
  [./simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  [../]
  [./simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  [../]
  [./porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  [../]
  [./permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-11 0 0 0 1e-11 0  0 0 1e-11'
  [../]
  [./relperm_water]
    type = PorousFlowRelativePermeabilityBC
    lambda = 2
    phase = 0
    s_res = 0.25
    sum_s_res = 0.35
  [../]
  [./relperm_gas]
    type = PorousFlowRelativePermeabilityBC
    lambda = 2
    phase = 1
    s_res = 0.1
    sum_s_res = 0.35
    nw_phase = true
  [../]
[]

[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'
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_stol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-13 15'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 1e5
  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 5e3
  [../]
[]

[Outputs]
  execute_on = 'initial timestep_end'
  file_base = grav02g
  exodus = true
  perf_graph = true
  csv = false
[]

modules/porous_flow/test/tests/fluidstate/water_vapor.i

# Tests correct calculation of properties in PorousFlowWaterVapor in the two-phase region

[Mesh]
  type = GeneratedMesh
  dim = 2
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [./pliq]
    initial_condition = 1e6
  [../]
  [./h]
    initial_condition = 8e5
    scaling = 1e-3
  [../]
[]

[AuxVariables]
  [./pressure_gas]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./pressure_water]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./enthalpy_gas]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./enthalpy_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
  [../]
  [./temperature]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./enthalpy_water]
    type = PorousFlowPropertyAux
    variable = enthalpy_water
    property = enthalpy
    phase = 0
    execute_on = 'initial timestep_end'
  [../]
  [./enthalpy_gas]
    type = PorousFlowPropertyAux
    variable = enthalpy_gas
    property = enthalpy
    phase = 1
    execute_on = 'initial timestep_end'
  [../]
  [./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'
  [../]
  [./temperature]
    type = PorousFlowPropertyAux
    variable = temperature
    property = temperature
    execute_on = 'initial timestep_end'
  [../]
[]

[Kernels]
  [./mass]
    type = PorousFlowMassTimeDerivative
    variable = pliq
  [../]
  [./heat]
    type = PorousFlowEnergyTimeDerivative
    variable = h
  [../]
[]

[UserObjects]
  [./dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pliq h'
    number_fluid_phases = 2
    number_fluid_components = 1
  [../]
  [./pc]
    type = PorousFlowCapillaryPressureBC
    pe = 1e5
    lambda = 2
    pc_max = 1e6
  [../]
  [./fs]
    type = PorousFlowWaterVapor
    water_fp = water
    capillary_pressure = pc
  [../]
[]

[Modules]
  [./FluidProperties]
    [./water]
      type = Water97FluidProperties
    [../]
  [../]
[]

[Materials]
  [./watervapor]
    type = PorousFlowFluidStateSingleComponent
    porepressure = pliq
    enthalpy = h
    temperature_unit = Celsius
    capillary_pressure = pc
    fluid_state = fs
  [../]
  [./permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-13 0 0 0 1e-13 0 0 0 1e-13'
  [../]
  [./relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  [../]
  [./relperm1]
    type = PorousFlowRelativePermeabilityCorey
    n = 3
    phase = 1
  [../]
  [./porosity]
    type = PorousFlowPorosityConst
    porosity = 0.1
  [../]
  [./internal_energy]
    type = PorousFlowMatrixInternalEnergy
    density = 2500
    specific_heat_capacity = 1200
  [../]
[]

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

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

[Postprocessors]
  [./density_water]
    type = ElementAverageValue
    variable = density_water
    execute_on = 'initial timestep_end'
  [../]
  [./density_gas]
    type = ElementAverageValue
    variable = density_gas
    execute_on = 'initial timestep_end'
  [../]
  [./viscosity_water]
    type = ElementAverageValue
    variable = viscosity_water
    execute_on = 'initial timestep_end'
  [../]
  [./viscosity_gas]
    type = ElementAverageValue
    variable = viscosity_gas
    execute_on = 'initial timestep_end'
  [../]
  [./enthalpy_water]
    type = ElementAverageValue
    variable = enthalpy_water
    execute_on = 'initial timestep_end'
  [../]
  [./enthalpy_gas]
    type = ElementAverageValue
    variable = enthalpy_gas
    execute_on = 'initial timestep_end'
  [../]
  [./sg]
    type = ElementAverageValue
    variable = saturation_gas
    execute_on = 'initial timestep_end'
  [../]
  [./sw]
    type = ElementAverageValue
    variable = saturation_water
    execute_on = 'initial timestep_end'
  [../]
  [./pwater]
    type = ElementAverageValue
    variable = pressure_water
    execute_on = 'initial timestep_end'
  [../]
  [./pgas]
    type = ElementAverageValue
    variable = pressure_gas
    execute_on = 'initial timestep_end'
  [../]
  [./temperature]
    type = ElementAverageValue
    variable = temperature
    execute_on = 'initial timestep_end'
  [../]
  [./enthalpy]
    type = ElementAverageValue
    variable = h
    execute_on = 'initial timestep_end'
  [../]
  [./liquid_mass]
    type = PorousFlowFluidMass
    phase = 0
    execute_on = 'initial timestep_end'
  [../]
  [./vapor_mass]
    type = PorousFlowFluidMass
    phase = 1
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  file_base = water_vapor_twophase
  csv = true
[]

modules/porous_flow/test/tests/fluidstate/water_vapor_phasechange.i

# Tests correct calculation of properties in PorousFlowWaterVapor as a phase change
# from liquid to a two-phase model occurs due to a pressure drop.
# A single 10 m^3 element is used, with constant mass and heat production using
# a Dirac kernel. Initial conditions correspond to just outside the two-phase region in
# the liquid state.
#
# An identical problem can be run using TOUGH2, with the following outputs after 1,000s
# Pressure: 8.58 Mpa
# Temperature: 299.92 K
# Vapor saturation: 0.00637

[Mesh]
  type = GeneratedMesh
  dim = 3
  xmax = 10
  ymax = 10
  zmax = 10
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [./pliq]
    initial_condition = 9e6
  [../]
  [./h]
    scaling = 1e-3
  [../]
[]

[ICs]
  [./hic]
    type = PorousFlowFluidPropertyIC
    variable = h
    porepressure = pliq
    property = enthalpy
    temperature = 300
    temperature_unit = Celsius
    fp = water
  [../]
[]

[DiracKernels]
  [./mass]
    type = ConstantPointSource
    point = '5 5 5'
    variable = pliq
    value = -1
  [../]
  [./heat]
    type = ConstantPointSource
    point = '5 5 5'
    variable = h
    value = -1.344269e6
  [../]
[]

[AuxVariables]
  [./pressure_gas]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./pressure_water]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./enthalpy_gas]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./enthalpy_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
  [../]
  [./temperature]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e_gas]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e_water]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./enthalpy_water]
    type = PorousFlowPropertyAux
    variable = enthalpy_water
    property = enthalpy
    phase = 0
    execute_on = 'initial timestep_end'
  [../]
  [./enthalpy_gas]
    type = PorousFlowPropertyAux
    variable = enthalpy_gas
    property = enthalpy
    phase = 1
    execute_on = 'initial timestep_end'
  [../]
  [./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'
  [../]
  [./temperature]
    type = PorousFlowPropertyAux
    variable = temperature
    property = temperature
    execute_on = 'initial timestep_end'
  [../]
  [./e_water]
    type = PorousFlowPropertyAux
    variable = e_water
    property = internal_energy
    phase = 0
    execute_on = 'initial timestep_end'
  [../]
  [./egas]
    type = PorousFlowPropertyAux
    variable = e_gas
    property = internal_energy
    phase = 1
    execute_on = 'initial timestep_end'
  [../]
[]

[Kernels]
  [./mass]
    type = PorousFlowMassTimeDerivative
    variable = pliq
  [../]
  [./heat]
    type = PorousFlowEnergyTimeDerivative
    variable = h
  [../]
[]

[UserObjects]
  [./dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pliq h'
    number_fluid_phases = 2
    number_fluid_components = 1
  [../]
  [./pc]
    type = PorousFlowCapillaryPressureBC
    pe = 1e5
    lambda = 2
    pc_max = 1e6
  [../]
  [./fs]
    type = PorousFlowWaterVapor
    water_fp = water
    capillary_pressure = pc
  [../]
[]

[Modules]
  [./FluidProperties]
    [./water]
      type = Water97FluidProperties
    [../]
  [../]
[]

[Materials]
  [./watervapor]
    type = PorousFlowFluidStateSingleComponent
    porepressure = pliq
    enthalpy = h
    temperature_unit = Celsius
    capillary_pressure = pc
    fluid_state = fs
  [../]
  [./permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1e-14 0 0 0 1e-14 0 0 0 1e-14'
  [../]
  [./relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  [../]
  [./relperm1]
    type = PorousFlowRelativePermeabilityCorey
    n = 3
    phase = 1
  [../]
  [./porosity]
    type = PorousFlowPorosityConst
    porosity = 0.2
  [../]
  [./internal_energy]
    type = PorousFlowMatrixInternalEnergy
    density = 2650
    specific_heat_capacity = 1000
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 1e3
  nl_abs_tol = 1e-12
  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 10
  [../]
[]

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

[Postprocessors]
  [./density_water]
    type = ElementAverageValue
    variable = density_water
    execute_on = 'initial timestep_end'
  [../]
  [./density_gas]
    type = ElementAverageValue
    variable = density_gas
    execute_on = 'initial timestep_end'
  [../]
  [./viscosity_water]
    type = ElementAverageValue
    variable = viscosity_water
    execute_on = 'initial timestep_end'
  [../]
  [./viscosity_gas]
    type = ElementAverageValue
    variable = viscosity_gas
    execute_on = 'initial timestep_end'
  [../]
  [./enthalpy_water]
    type = ElementAverageValue
    variable = enthalpy_water
    execute_on = 'initial timestep_end'
  [../]
  [./enthalpy_gas]
    type = ElementAverageValue
    variable = enthalpy_gas
    execute_on = 'initial timestep_end'
  [../]
  [./sg]
    type = ElementAverageValue
    variable = saturation_gas
    execute_on = 'initial timestep_end'
  [../]
  [./sw]
    type = ElementAverageValue
    variable = saturation_water
    execute_on = 'initial timestep_end'
  [../]
  [./pwater]
    type = ElementAverageValue
    variable = pressure_water
    execute_on = 'initial timestep_end'
  [../]
  [./pgas]
    type = ElementAverageValue
    variable = pressure_gas
    execute_on = 'initial timestep_end'
  [../]
  [./temperature]
    type = ElementAverageValue
    variable = temperature
    execute_on = 'initial timestep_end'
  [../]
  [./enthalpy]
    type = ElementAverageValue
    variable = h
    execute_on = 'initial timestep_end'
  [../]
  [./pliq]
    type = ElementAverageValue
    variable = pliq
    execute_on = 'initial timestep_end'
  [../]
  [./liquid_mass]
    type = PorousFlowFluidMass
    phase = 0
    execute_on = 'initial timestep_end'
  [../]
  [./vapor_mass]
    type = PorousFlowFluidMass
    phase = 1
    execute_on = 'initial timestep_end'
  [../]
  [./liquid_heat]
    type = PorousFlowHeatEnergy
    phase = 0
    execute_on = 'initial timestep_end'
  [../]
  [./vapor_heat]
    type = PorousFlowHeatEnergy
    phase = 1
    execute_on = 'initial timestep_end'
  [../]
  [./e_water]
    type = ElementAverageValue
    variable = e_water
    execute_on = 'initial timestep_end'
  [../]
  [./e_gas]
    type = ElementAverageValue
    variable = e_gas
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  csv = true
  perf_graph = false
[]

modules/porous_flow/test/tests/capillary_pressure/brooks_corey1.i

# Test Brooks-Corey capillary pressure curve by varying saturation over the mesh
# lambda = 2, sat_lr = 0.1, log_extension = false

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 500
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [./p0]
    initial_condition = 1e6
  [../]
  [./s1]
  [../]
[]

[AuxVariables]
  [./s0aux]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./s1aux]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./p0aux]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./p1aux]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[AuxKernels]
  [./s0]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 0
    variable = s0aux
  [../]
  [./s1]
    type = PorousFlowPropertyAux
    property = saturation
    phase = 1
    variable = s1aux
  [../]
  [./p0]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 0
    variable = p0aux
  [../]
  [./p1]
    type = PorousFlowPropertyAux
    property = pressure
    phase = 1
    variable = p1aux
  [../]
[]

[Functions]
  [./s1]
    type = ParsedFunction
    value = x
  [../]
[]

[ICs]
  [./s1]
    type = FunctionIC
    variable = s1
    function = s1
  [../]
[]

[Kernels]
  [./p0]
    type = Diffusion
    variable = p0
  [../]
  [./s1]
    type = Diffusion
    variable = s1
  [../]
[]

[UserObjects]
  [./dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'p0 s1'
    number_fluid_phases = 2
    number_fluid_components = 2
  [../]
  [./pc]
    type = PorousFlowCapillaryPressureBC
    lambda = 2
    log_extension = false
    pe = 1e5
    sat_lr = 0.1
  [../]
[]

[Materials]
  [./temperature]
    type = PorousFlowTemperature
  [../]
  [./ppss]
    type = PorousFlow2PhasePS
    phase0_porepressure = p0
    phase1_saturation = s1
    capillary_pressure = pc
  [../]
  [./kr0]
    type = PorousFlowRelativePermeabilityVG
    phase = 0
    m = 0.5
  [../]
  [./kr1]
    type = PorousFlowRelativePermeabilityCorey
    phase = 1
    n = 2
  [../]
[]

[VectorPostprocessors]
  [./vpp]
    type = LineValueSampler
    variable = 's0aux s1aux p0aux p1aux'
    start_point = '0 0 0'
    end_point = '1 0 0'
    num_points = 500
    sort_by = id
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-6
[]

[BCs]
  [./sleft]
    type = DirichletBC
    variable = s1
    value = 0
    boundary = left
  [../]
  [./sright]
    type = DirichletBC
    variable = s1
    value = 1
    boundary = right
  [../]
[]

[Outputs]
  csv = true
  execute_on = timestep_end
[]

References

R. H. Brooks and A. T. Corey. Properties of porous media affecting fluid flow. J. Irrig. Drain. Div., 92:61–88, 1966.

@article{brookscorey1966,
    author = "Brooks, R. H. and Corey, A. T.",
    title = "Properties of porous media affecting fluid flow",
    journal = "J. Irrig. Drain. Div.",
    volume = "92",
    pages = "61--88",
    year = "1966"
}

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