PorousFlowCapillaryPressureRSC

Rogers-Stallybrass-Clements version of effective saturation for the water phase, valid for residual saturations = 0, and viscosityOil = 2 * viscosityWater. seff_water = 1 / sqrt(1 + exp((Pc - shift) / scale)), where scale = 0.25 * scale_ratio * oil_viscosity.

The Rogers-Stallybrass-Clements capillary relationship is (Rogers et al., 1983) $var element = document.getElementById("moose-equation-ea7120d2-b936-484e-990e-d4d042e00235");katex.render("S_{\\mathrm{eff}} = \\frac{1}{\\sqrt{1 + \\exp((P_{c} - A)/B)}} \\ ,", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ when the oil viscosity is exactly twice the water viscosity. This is of limited use in real simulations, and is only used in the Porous Flow module for comparison with the analytical solutions offered by the authors for multi-phase infiltration and drainage problems.

note

Only effective saturation as a function of capillary pressure is available.

Input 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
oil_viscosityViscosity of oil (gas) phase. It is assumed this is double the water-phase viscosity. (Note that this effective saturation is mostly useful for 2-phase, not single-phase.)
C++ Type:double
Options:
Description:Viscosity of oil (gas) phase. It is assumed this is double the water-phase viscosity. (Note that this effective saturation is mostly useful for 2-phase, not single-phase.)
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
scale_ratioThis is porosity / permeability / beta^2, where beta may be chosen by the user. It has dimensions [time]
C++ Type:double
Options:
Description:This is porosity / permeability / beta^2, where beta may be chosen by the user. It has dimensions [time]
shifteffective saturation is a function of (Pc - shift)
C++ Type:double
Options:
Description:effective saturation is a function of (Pc - shift)

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/infiltration_and_drainage/rsc02.i
modules/porous_flow/test/tests/jacobian/fflux09.i
modules/porous_flow/test/tests/infiltration_and_drainage/rsc01.i

modules/porous_flow/test/tests/infiltration_and_drainage/rsc02.i

# RSC test with low-res time and spatial resolution
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 200
  ny = 1
  xmin = 0
  xmax = 10 # x is the depth variable, called zeta in RSC
  ymin = 0
  ymax = 0.05
[]

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

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '3E-2 5E-1 8E-1'
    x = '0 1 5'
  [../]
[]

[UserObjects]
  [./dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pwater poil'
    number_fluid_phases = 2
    number_fluid_components = 2
  [../]
  [./pc]
    type = PorousFlowCapillaryPressureRSC
    oil_viscosity = 2E-3
    scale_ratio = 2E3
    shift = 10
  [../]
[]

[Modules]
  [./FluidProperties]
    [./water]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 10
      thermal_expansion = 0
      viscosity = 1e-3
    [../]
    [./oil]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 20
      thermal_expansion = 0
      viscosity = 2e-3
    [../]
  [../]
[]

[Materials]
  [./temperature]
    type = PorousFlowTemperature
  [../]
  [./ppss]
    type = PorousFlow2PhasePP
    phase0_porepressure = pwater
    phase1_porepressure = poil
    capillary_pressure = pc
  [../]
  [./massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  [../]
  [./water]
    type = PorousFlowSingleComponentFluid
    fp = water
    phase = 0
    compute_enthalpy = false
    compute_internal_energy = false
  [../]
  [./oil]
    type = PorousFlowSingleComponentFluid
    fp = oil
    phase = 1
    compute_enthalpy = false
    compute_internal_energy = false
  [../]
  [./relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 0
  [../]
  [./relperm_oil]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 1
  [../]
  [./porosity]
    type = PorousFlowPorosityConst
    porosity = 0.25
  [../]
  [./permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-5 0 0  0 1E-5 0  0 0 1E-5'
  [../]
[]

[Variables]
  [./pwater]
  [../]
  [./poil]
  [../]
[]

[ICs]
  [./water_init]
    type = ConstantIC
    variable = pwater
    value = 0
  [../]
  [./oil_init]
    type = ConstantIC
    variable = poil
    value = 15
  [../]
[]

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


[AuxVariables]
  [./SWater]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./SOil]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./massfrac_ph0_sp0]
    initial_condition = 1
  [../]
  [./massfrac_ph1_sp0]
    initial_condition = 0
  [../]
[]


[AuxKernels]
  [./SWater]
    type = MaterialStdVectorAux
    property = PorousFlow_saturation_qp
    index = 0
    variable = SWater
  [../]
  [./SOil]
    type = MaterialStdVectorAux
    property = PorousFlow_saturation_qp
    index = 1
    variable = SOil
  [../]
[]


[BCs]
# we are pumping water into a system that has virtually incompressible fluids, hence the pressures rise enormously.  this adversely affects convergence because of almost-overflows and precision-loss problems.  The fixed things help keep pressures low and so prevent these awful behaviours.   the movement of the saturation front is the same regardless of the fixed things.
  active = 'recharge fixedoil fixedwater'
  [./recharge]
    type = PorousFlowSink
    variable = pwater
    boundary = 'left'
    flux_function = -1.0
  [../]
  [./fixedwater]
    type = DirichletBC
    variable = pwater
    boundary = 'right'
    value = 0
  [../]
  [./fixedoil]
    type = DirichletBC
    variable = poil
    boundary = 'right'
    value = 15
  [../]
[]



[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason -ksp_diagonal_scale -ksp_diagonal_scale_fix -ksp_gmres_modifiedgramschmidt -snes_linesearch_monitor'
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2               1E-10      1E-10      10000'
  [../]
[]

[VectorPostprocessors]
  [./swater]
    type = LineValueSampler
    variable = SWater
    start_point = '0 0 0'
    end_point = '7 0 0'
    sort_by = x
    num_points = 21
    execute_on = timestep_end
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  petsc_options = '-snes_converged_reason'
  end_time = 5
  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]
[]

[Outputs]
  file_base = rsc02
  [./along_line]
    type = CSV
    execute_vector_postprocessors_on = final
  [../]
  [./exodus]
    type = Exodus
    execute_on = 'initial final'
  [../]
[]

modules/porous_flow/test/tests/jacobian/fflux09.i

# 2phase (PP), 3components (that exist in both phases), constant viscosity, constant insitu permeability
# density with constant bulk, Corey relative perm, nonzero gravity, unsaturated with RSC capillary
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  xmin = 0
  xmax = 1
  ny = 1
  ymin = 0
  ymax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [./ppwater]
  [../]
  [./ppgas]
  [../]
  [./massfrac_ph0_sp0]
  [../]
[]

[AuxVariables]
  [./massfrac_ph0_sp1]
  [../]
  [./massfrac_ph1_sp0]
  [../]
  [./massfrac_ph1_sp1]
  [../]
[]

[ICs]
  [./ppwater]
    type = RandomIC
    variable = ppwater
    min = -1
    max = 0
  [../]
  [./ppgas]
    type = RandomIC
    variable = ppgas
    min = 0
    max = 1
  [../]
  [./massfrac_ph0_sp0]
    type = RandomIC
    variable = massfrac_ph0_sp0
    min = 0
    max = 0.4
  [../]
  [./massfrac_ph0_sp1]
    type = RandomIC
    variable = massfrac_ph0_sp1
    min = 0
    max = 0.4
  [../]
  [./massfrac_ph1_sp0]
    type = RandomIC
    variable = massfrac_ph1_sp0
    min = 0
    max = 0.4
  [../]
  [./massfrac_ph1_sp1]
    type = RandomIC
    variable = massfrac_ph1_sp1
    min = 0
    max = 0.4
  [../]
[]

[Kernels]
  [./flux0]
    type = PorousFlowAdvectiveFlux
    fluid_component = 0
    variable = ppwater
    gravity = '-1 -0.1 0'
  [../]
  [./flux1]
    type = PorousFlowAdvectiveFlux
    fluid_component = 1
    variable = ppgas
    gravity = '-1 -0.1 0'
  [../]
  [./flux2]
    type = PorousFlowAdvectiveFlux
    fluid_component = 2
    variable = massfrac_ph0_sp0
    gravity = '-1 -0.1 0'
  [../]
[]

[UserObjects]
  [./dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'ppwater ppgas massfrac_ph0_sp0'
    number_fluid_phases = 2
    number_fluid_components = 3
  [../]
  [./pc]
    type = PorousFlowCapillaryPressureRSC
    shift = -0.1
    scale_ratio = 3
    oil_viscosity = 2
  [../]
[]

[Modules]
  [./FluidProperties]
    [./simple_fluid0]
      type = SimpleFluidProperties
      bulk_modulus = 1.5
      density0 = 1
      thermal_expansion = 0
      viscosity = 1
    [../]
    [./simple_fluid1]
      type = SimpleFluidProperties
      bulk_modulus = 0.5
      density0 = 0.5
      thermal_expansion = 0
      viscosity = 1
    [../]
  [../]
[]

[Materials]
  [./temperature]
    type = PorousFlowTemperature
  [../]
  [./ppss]
    type = PorousFlow2PhasePP
    phase0_porepressure = ppwater
    phase1_porepressure = ppgas
    capillary_pressure = pc
  [../]
  [./massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph0_sp1 massfrac_ph1_sp0 massfrac_ph1_sp1'
  [../]
  [./simple_fluid0]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid0
    phase = 0
  [../]
  [./simple_fluid1]
    type = PorousFlowSingleComponentFluid
    fp = simple_fluid1
    phase = 1
  [../]
  [./permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1 0 0 0 2 0 0 0 3'
  [../]
  [./relperm0]
    type = PorousFlowRelativePermeabilityCorey
    n = 2
    phase = 0
  [../]
  [./relperm1]
    type = PorousFlowRelativePermeabilityCorey
    n = 3
    phase = 1
  [../]
[]

[Preconditioning]
  active = check
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000'
  [../]
  [./check]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -snes_type'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000 test'
  [../]
[]

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

[Outputs]
  exodus = false
[]

modules/porous_flow/test/tests/infiltration_and_drainage/rsc01.i

# RSC test with high-res time and spatial resolution
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 600
  ny = 1
  xmin = 0
  xmax = 10 # x is the depth variable, called zeta in RSC
  ymin = 0
  ymax = 0.05
[]

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

[Functions]
  [./dts]
    type = PiecewiseLinear
    y = '3E-3 3E-2 0.05'
    x = '0 1 5'
  [../]
[]

[UserObjects]
  [./dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'pwater poil'
    number_fluid_phases = 2
    number_fluid_components = 2
  [../]
  [./pc]
    type = PorousFlowCapillaryPressureRSC
    oil_viscosity = 2E-3
    scale_ratio = 2E3
    shift = 10
  [../]
[]

[Modules]
  [./FluidProperties]
    [./water]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 10
      thermal_expansion = 0
      viscosity = 1e-3
    [../]
    [./oil]
      type = SimpleFluidProperties
      bulk_modulus = 2e9
      density0 = 20
      thermal_expansion = 0
      viscosity = 2e-3
    [../]
  [../]
[]

[Materials]
  [./temperature]
    type = PorousFlowTemperature
  [../]
  [./ppss]
    type = PorousFlow2PhasePP
    phase0_porepressure = pwater
    phase1_porepressure = poil
    capillary_pressure = pc
  [../]
  [./massfrac]
    type = PorousFlowMassFraction
    mass_fraction_vars = 'massfrac_ph0_sp0 massfrac_ph1_sp0'
  [../]
  [./water]
    type = PorousFlowSingleComponentFluid
    fp = water
    phase = 0
    compute_enthalpy = false
    compute_internal_energy = false
  [../]
  [./oil]
    type = PorousFlowSingleComponentFluid
    fp = oil
    phase = 1
    compute_enthalpy = false
    compute_internal_energy = false
  [../]
  [./relperm_water]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 0
  [../]
  [./relperm_oil]
    type = PorousFlowRelativePermeabilityCorey
    n = 1
    phase = 1
  [../]
  [./porosity]
    type = PorousFlowPorosityConst
    porosity = 0.25
  [../]
  [./permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-5 0 0  0 1E-5 0  0 0 1E-5'
  [../]
[]

[Variables]
  [./pwater]
  [../]
  [./poil]
  [../]
[]

[ICs]
  [./water_init]
    type = ConstantIC
    variable = pwater
    value = 0
  [../]
  [./oil_init]
    type = ConstantIC
    variable = poil
    value = 15
  [../]
[]

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

[AuxVariables]
  [./SWater]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./SOil]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./massfrac_ph0_sp0]
    initial_condition = 1
  [../]
  [./massfrac_ph1_sp0]
    initial_condition = 0
  [../]
[]

[AuxKernels]
  [./SWater]
    type = MaterialStdVectorAux
    property = PorousFlow_saturation_qp
    index = 0
    variable = SWater
  [../]
  [./SOil]
    type = MaterialStdVectorAux
    property = PorousFlow_saturation_qp
    index = 1
    variable = SOil
  [../]
[]

[BCs]
# we are pumping water into a system that has virtually incompressible fluids, hence the pressures rise enormously.  this adversely affects convergence because of almost-overflows and precision-loss problems.  The fixed things help keep pressures low and so prevent these awful behaviours.   the movement of the saturation front is the same regardless of the fixed things.
  active = 'recharge fixedoil fixedwater'
  [./recharge]
    type = PorousFlowSink
    variable = pwater
    boundary = 'left'
    flux_function = -1.0
  [../]
  [./fixedwater]
    type = DirichletBC
    variable = pwater
    boundary = 'right'
    value = 0
  [../]
  [./fixedoil]
    type = DirichletBC
    variable = poil
    boundary = 'right'
    value = 15
  [../]
[]

[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason -ksp_diagonal_scale -ksp_diagonal_scale_fix -ksp_gmres_modifiedgramschmidt -snes_linesearch_monitor'
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'gmres      asm      lu           NONZERO                   2               1E-10      1E-10      10000'
  [../]
[]

[VectorPostprocessors]
  [./swater]
    type = LineValueSampler
    variable = SWater
    start_point = '0 0 0'
    end_point = '7 0 0'
    sort_by = x
    num_points = 21
    execute_on = timestep_end
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  petsc_options = '-snes_converged_reason'
  end_time = 5
  [./TimeStepper]
    type = FunctionDT
    function = dts
  [../]
[]

[Outputs]
  file_base = rsc01
  [./along_line]
    type = CSV
    execute_vector_postprocessors_on = final
  [../]
  [./exodus]
    type = Exodus
    execute_on = 'initial final'
  [../]
[]

References

C. Rogers, M. P. Stallybrass, and D. L. Clements. On two phase filtration under gravity and with boundary infiltration: application of a Backlund transformation. Nonlinear Analysis, Theory, Methods and Applications, 7:785–799, 1983.

@article{rsc1983,
    author = "Rogers, C. and Stallybrass, M. P. and Clements, D. L.",
    title = "{On two phase filtration under gravity and with boundary infiltration: application of a Backlund transformation}",
    journal = "Nonlinear Analysis, Theory, Methods and Applications",
    volume = "7",
    pages = "785--799",
    year = "1983"
}

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Input Files
References

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