Establishment of gravitational head in 1D
These tests concern the steady-state pressure distribution obtained either by running a transient model for a long time, or by running a steady-state analysis, both of which should lead to the same result.
Without fluxes, the steadystate pressure distribution is just if the fluid bulk modulus, , is large enough compared with . Here is the porepressure at . For smaller bulk modulus (1) Here it is assumed that the density is given by with constant bulk modulus, is the magnitude acceleration due to gravity (a vector assumed to be pointing in the negative direction), and is position. The tests described below are simple tests and are part of the automatic test suite.
Single-phase, single-component
Two single-phase simulations with 100 1D elements are run: one with fully-saturated conditions, and the other with unsaturated conditions using the van Genuchten capillary pressure (this should not, and does not, make any difference to the results). The porepressure is held fixed at one boundary (). The parameters are tabulated in Table 1.
Parameter | Value |
---|---|
x | m |
Bulk modulus (B) | 1.2 Pa |
Reference density | 1 kg.m |
gravitational acceleration | -1 m.s |
The steady-state input file with full saturation:
# Checking that gravity head is established
# 1phase, vanGenuchten, constant fluid-bulk, constant viscosity, constant permeability, Corey relative perm
# fully saturated
# For better agreement with the analytical solution (ana_pp), just increase nx
[Mesh]
type = GeneratedMesh
dim = 1
nx = 100
xmin = -1
xmax = 0
[]
[GlobalParams]
PorousFlowDictator = dictator
[]
[Variables]
[pp]
[InitialCondition]
type = RandomIC
min = 0
max = 1
[]
[]
[]
[Kernels]
[flux0]
type = PorousFlowAdvectiveFlux
fluid_component = 0
variable = pp
gravity = '-1 0 0'
[]
[]
[Functions]
[ana_pp]
type = ParsedFunction
symbol_names = 'g B p0 rho0'
symbol_values = '1 1.2 0 1'
expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
[]
[]
[BCs]
[z]
type = DirichletBC
variable = pp
boundary = right
value = 0
[]
[]
[UserObjects]
[dictator]
type = PorousFlowDictator
porous_flow_vars = 'pp'
number_fluid_phases = 1
number_fluid_components = 1
[]
[pc]
type = PorousFlowCapillaryPressureVG
m = 0.5
alpha = 1
[]
[]
[FluidProperties]
[simple_fluid]
type = SimpleFluidProperties
bulk_modulus = 1.2
density0 = 1
viscosity = 1
thermal_expansion = 0
[]
[]
[Materials]
[temperature]
type = PorousFlowTemperature
[]
[ppss]
type = PorousFlow1PhaseP
porepressure = pp
capillary_pressure = pc
[]
[massfrac]
type = PorousFlowMassFraction
[]
[simple_fluid]
type = PorousFlowSingleComponentFluid
fp = simple_fluid
phase = 0
[]
[permeability]
type = PorousFlowPermeabilityConst
permeability = '1 0 0 0 2 0 0 0 3'
[]
[relperm]
type = PorousFlowRelativePermeabilityCorey
n = 1
phase = 0
[]
[]
[Postprocessors]
[pp_base]
type = PointValue
variable = pp
point = '-1 0 0'
[]
[pp_analytical]
type = FunctionValuePostprocessor
function = ana_pp
point = '-1 0 0'
[]
[pp_00]
type = PointValue
variable = pp
point = '0 0 0'
[]
[pp_01]
type = PointValue
variable = pp
point = '-0.1 0 0'
[]
[pp_02]
type = PointValue
variable = pp
point = '-0.2 0 0'
[]
[pp_03]
type = PointValue
variable = pp
point = '-0.3 0 0'
[]
[pp_04]
type = PointValue
variable = pp
point = '-0.4 0 0'
[]
[pp_05]
type = PointValue
variable = pp
point = '-0.5 0 0'
[]
[pp_06]
type = PointValue
variable = pp
point = '-0.6 0 0'
[]
[pp_07]
type = PointValue
variable = pp
point = '-0.7 0 0'
[]
[pp_08]
type = PointValue
variable = pp
point = '-0.8 0 0'
[]
[pp_09]
type = PointValue
variable = pp
point = '-0.9 0 0'
[]
[pp_10]
type = PointValue
variable = pp
point = '-1 0 0'
[]
[]
[Preconditioning]
[andy]
type = SMP
full = true
[]
[]
[Executioner]
type = Steady
solve_type = Newton
[]
[Outputs]
execute_on = 'timestep_end'
file_base = grav01a
[csv]
type = CSV
[]
[]
(modules/porous_flow/test/tests/gravity/grav01a.i)The steady-state input file with partial saturation
# Checking that gravity head is established
# 1phase, vanGenuchten, constant fluid-bulk, constant viscosity, constant permeability, Corey relative perm
# unsaturated
# For better agreement with the analytical solution (ana_pp), just increase nx
[Mesh]
type = GeneratedMesh
dim = 1
nx = 100
xmin = -1
xmax = 0
[]
[GlobalParams]
PorousFlowDictator = dictator
[]
[Variables]
[pp]
[InitialCondition]
type = RandomIC
min = -1
max = 1
[]
[]
[]
[Kernels]
[flux0]
type = PorousFlowAdvectiveFlux
fluid_component = 0
variable = pp
gravity = '-1 0 0'
[]
[]
[Functions]
[ana_pp]
type = ParsedFunction
symbol_names = 'g B p0 rho0'
symbol_values = '1 2 -1 1'
expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
[]
[]
[BCs]
[z]
type = DirichletBC
variable = pp
boundary = right
value = -1
[]
[]
[UserObjects]
[dictator]
type = PorousFlowDictator
porous_flow_vars = 'pp'
number_fluid_phases = 1
number_fluid_components = 1
[]
[pc]
type = PorousFlowCapillaryPressureVG
m = 0.5
alpha = 1
[]
[]
[FluidProperties]
[simple_fluid]
type = SimpleFluidProperties
bulk_modulus = 2
density0 = 1
viscosity = 1
thermal_expansion = 0
[]
[]
[Materials]
[temperature]
type = PorousFlowTemperature
[]
[ppss]
type = PorousFlow1PhaseP
porepressure = pp
capillary_pressure = pc
[]
[massfrac]
type = PorousFlowMassFraction
[]
[simple_fluid]
type = PorousFlowSingleComponentFluid
fp = simple_fluid
phase = 0
[]
[permeability]
type = PorousFlowPermeabilityConst
permeability = '1 0 0 0 2 0 0 0 3'
[]
[relperm]
type = PorousFlowRelativePermeabilityCorey
n = 1
phase = 0
[]
[]
[Postprocessors]
[pp_base]
type = PointValue
variable = pp
point = '-1 0 0'
[]
[pp_analytical]
type = FunctionValuePostprocessor
function = ana_pp
point = '-1 0 0'
[]
[]
[Preconditioning]
[andy]
type = SMP
full = true
[]
[]
[Executioner]
type = Steady
solve_type = Newton
[]
[Outputs]
execute_on = 'timestep_end'
file_base = grav01c
exodus = true
[csv]
type = CSV
[]
[]
(modules/porous_flow/test/tests/gravity/grav01c.i)An example verification is shown in Figure 1, which also shows results from a 2-phase simulation (see next section)
Two-phase, two-component
Two-phase, two-component simulations may also be checked against Eq. (1). A number of simulations are performed with parameters tabulated in Table 2.
Parameter | Value |
---|---|
x | m |
Bulk modulus of heavy phase | 1.2 Pa |
Bulk modulus of light phase | 1 Pa |
Reference density of heavy phase | 1 kg.m |
Reference density of light phase | 0.1 kg.m |
gravitational acceleration | -1 m.s |
One steady-state simulation is performed. Steady-state simulations are more difficult to perform in two-phase situations because of the inherently stronger nonlinearities, but mostly because simulations can easily enter unphysical domains (negative saturation, for instance) without the stabilising presence of the mass time-derivative. The steady-state input file:
# Checking that gravity head is established in the steady-state situation when 0<saturation<1 (note the strictly less-than).
# 2phase (PP), 2components, vanGenuchten, constant fluid bulk-moduli for each phase, constant viscosity, constant permeability, Corey relative perm
# For better agreement with the analytical solution (ana_pp), just increase nx
[Mesh]
type = GeneratedMesh
dim = 1
nx = 10
xmin = -1
xmax = 0
[]
[GlobalParams]
PorousFlowDictator = dictator
[]
[Variables]
[ppwater]
initial_condition = -1.0
[]
[ppgas]
initial_condition = 0
[]
[]
[AuxVariables]
[massfrac_ph0_sp0]
initial_condition = 1
[]
[massfrac_ph1_sp0]
initial_condition = 0
[]
[]
[Kernels]
[flux0]
type = PorousFlowAdvectiveFlux
fluid_component = 0
variable = ppwater
gravity = '-1 0 0'
[]
[flux1]
type = PorousFlowAdvectiveFlux
fluid_component = 1
variable = ppgas
gravity = '-1 0 0'
[]
[]
[BCs]
[ppwater]
type = DirichletBC
boundary = right
variable = ppwater
value = -1
[]
[ppgas]
type = DirichletBC
boundary = right
variable = ppgas
value = 0
[]
[]
[Functions]
[ana_ppwater]
type = ParsedFunction
symbol_names = 'g B p0 rho0'
symbol_values = '1 2 pp_water_top 1'
expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
[]
[ana_ppgas]
type = ParsedFunction
symbol_names = 'g B p0 rho0'
symbol_values = '1 1 pp_gas_top 0.1'
expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
[]
[]
[UserObjects]
[dictator]
type = PorousFlowDictator
porous_flow_vars = 'ppwater ppgas'
number_fluid_phases = 2
number_fluid_components = 2
[]
[pc]
type = PorousFlowCapillaryPressureVG
m = 0.5
alpha = 1
[]
[]
[FluidProperties]
[simple_fluid0]
type = SimpleFluidProperties
bulk_modulus = 2
density0 = 1
viscosity = 1
thermal_expansion = 0
[]
[simple_fluid1]
type = SimpleFluidProperties
bulk_modulus = 1
density0 = 0.1
viscosity = 0.5
thermal_expansion = 0
[]
[]
[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_ph1_sp0'
[]
[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'
[]
[relperm_water]
type = PorousFlowRelativePermeabilityCorey
n = 1
phase = 0
[]
[relperm_gas]
type = PorousFlowRelativePermeabilityCorey
n = 1
phase = 1
[]
[]
[Postprocessors]
[pp_water_top]
type = PointValue
variable = ppwater
point = '0 0 0'
[]
[pp_water_base]
type = PointValue
variable = ppwater
point = '-1 0 0'
[]
[pp_water_analytical]
type = FunctionValuePostprocessor
function = ana_ppwater
point = '-1 0 0'
[]
[pp_gas_top]
type = PointValue
variable = ppgas
point = '0 0 0'
[]
[pp_gas_base]
type = PointValue
variable = ppgas
point = '-1 0 0'
[]
[pp_gas_analytical]
type = FunctionValuePostprocessor
function = ana_ppgas
point = '-1 0 0'
[]
[]
[Preconditioning]
[andy]
type = SMP
full = true
[]
[]
[Executioner]
type = Steady
solve_type = Newton
[]
[Outputs]
file_base = grav02b
[csv]
type = CSV
[]
exodus = false
[]
(modules/porous_flow/test/tests/gravity/grav02b.i)A variety of transient simulations are performed. In the transient simulations, conservation of mass can be checked, and the tests demonstrate MOOSE conserves mass. Depending on the initial and boundary conditions, the "heavy" phase (with greatest mass) can completely displace the "light" phase, which is forced to move to the top of the simulation. Eq. (1) only governs the light phase in the unsaturated zone, since in the saturated zone (where there is zero light phase) the pressure must follow the heavy-phase version of Eq. (1). An example is shown in Figure 1.
Using the PP formulation with unsaturated fluids:
# Checking that gravity head is established in the transient situation when 0<saturation<1 (note the strictly less-than).
# 2phase (PP), 2components, vanGenuchten, constant fluid bulk-moduli for each phase, constant viscosity, constant permeability, Corey relative perm
# For better agreement with the analytical solution (ana_pp), just increase nx
[Mesh]
type = GeneratedMesh
dim = 1
nx = 10
xmin = -1
xmax = 0
[]
[GlobalParams]
PorousFlowDictator = dictator
[]
[Variables]
[ppwater]
initial_condition = -1.0
[]
[ppgas]
initial_condition = 0
[]
[]
[AuxVariables]
[massfrac_ph0_sp0]
initial_condition = 1
[]
[massfrac_ph1_sp0]
initial_condition = 0
[]
[]
[Kernels]
[mass0]
type = PorousFlowMassTimeDerivative
fluid_component = 0
variable = ppwater
[]
[flux0]
type = PorousFlowAdvectiveFlux
fluid_component = 0
variable = ppwater
gravity = '-1 0 0'
[]
[mass1]
type = PorousFlowMassTimeDerivative
fluid_component = 1
variable = ppgas
[]
[flux1]
type = PorousFlowAdvectiveFlux
fluid_component = 1
variable = ppgas
gravity = '-1 0 0'
[]
[]
[Functions]
[ana_ppwater]
type = ParsedFunction
symbol_names = 'g B p0 rho0'
symbol_values = '1 2 pp_water_top 1'
expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
[]
[ana_ppgas]
type = ParsedFunction
symbol_names = 'g B p0 rho0'
symbol_values = '1 1 pp_gas_top 0.1'
expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
[]
[]
[UserObjects]
[dictator]
type = PorousFlowDictator
porous_flow_vars = 'ppwater ppgas'
number_fluid_phases = 2
number_fluid_components = 2
[]
[pc]
type = PorousFlowCapillaryPressureVG
m = 0.5
alpha = 1
[]
[]
[FluidProperties]
[simple_fluid0]
type = SimpleFluidProperties
bulk_modulus = 2
density0 = 1
viscosity = 1
thermal_expansion = 0
[]
[simple_fluid1]
type = SimpleFluidProperties
bulk_modulus = 1
density0 = 0.1
viscosity = 0.5
thermal_expansion = 0
[]
[]
[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_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 = '1 0 0 0 2 0 0 0 3'
[]
[relperm_water]
type = PorousFlowRelativePermeabilityCorey
n = 1
phase = 0
[]
[relperm_gas]
type = PorousFlowRelativePermeabilityCorey
n = 1
phase = 1
[]
[]
[Postprocessors]
[pp_water_top]
type = PointValue
variable = ppwater
point = '0 0 0'
[]
[pp_water_base]
type = PointValue
variable = ppwater
point = '-1 0 0'
[]
[pp_water_analytical]
type = FunctionValuePostprocessor
function = ana_ppwater
point = '-1 0 0'
[]
[pp_gas_top]
type = PointValue
variable = ppgas
point = '0 0 0'
[]
[pp_gas_base]
type = PointValue
variable = ppgas
point = '-1 0 0'
[]
[pp_gas_analytical]
type = FunctionValuePostprocessor
function = ana_ppgas
point = '-1 0 0'
[]
[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]
[andy]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = Newton
dt = 0.1
end_time = 1.0
nl_rel_tol = 1E-10
nl_abs_tol = 1E-12
[]
[Outputs]
[csv]
type = CSV
file_base = grav02a
execute_on = 'initial final'
[]
[]
(modules/porous_flow/test/tests/gravity/grav02a.i)Using the PP formulation with saturated and unsaturated fluids::
# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PP), 2components, vanGenuchten, constant fluid bulk-moduli for each phase, constant viscosity, constant permeability, Corey relative perm
# For better agreement with the analytical solution (ana_pp), just increase nx
[Mesh]
type = GeneratedMesh
dim = 1
nx = 10
xmin = -1
xmax = 0
[]
[GlobalParams]
PorousFlowDictator = dictator
[]
[Functions]
[dts]
type = PiecewiseLinear
y = '1E-3 1E-2 1E-1'
x = '1E-3 1E-2 1E-1'
[]
[]
[Variables]
[ppwater]
initial_condition = -0.1
[]
[ppgas]
initial_condition = 0
[]
[]
[AuxVariables]
[massfrac_ph0_sp0]
initial_condition = 1
[]
[massfrac_ph1_sp0]
initial_condition = 0
[]
[]
[Kernels]
[mass0]
type = PorousFlowMassTimeDerivative
fluid_component = 0
variable = ppwater
[]
[flux0]
type = PorousFlowAdvectiveFlux
fluid_component = 0
variable = ppwater
gravity = '-1 0 0'
[]
[mass1]
type = PorousFlowMassTimeDerivative
fluid_component = 1
variable = ppgas
[]
[flux1]
type = PorousFlowAdvectiveFlux
fluid_component = 1
variable = ppgas
gravity = '-1 0 0'
[]
[]
[Functions]
[ana_ppwater]
type = ParsedFunction
symbol_names = 'g B p0 rho0'
symbol_values = '1 2 pp_water_top 1'
expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
[]
[]
[UserObjects]
[dictator]
type = PorousFlowDictator
porous_flow_vars = 'ppwater ppgas'
number_fluid_phases = 2
number_fluid_components = 2
[]
[pc]
type = PorousFlowCapillaryPressureVG
m = 0.5
alpha = 1
[]
[]
[FluidProperties]
[simple_fluid0]
type = SimpleFluidProperties
bulk_modulus = 2
density0 = 1
viscosity = 1
thermal_expansion = 0
[]
[simple_fluid1]
type = SimpleFluidProperties
bulk_modulus = 1
density0 = 0.1
viscosity = 0.5
thermal_expansion = 0
[]
[]
[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_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 = '1 0 0 0 2 0 0 0 3'
[]
[relperm_water]
type = PorousFlowRelativePermeabilityCorey
n = 1
phase = 0
[]
[relperm_gas]
type = PorousFlowRelativePermeabilityCorey
n = 1
phase = 1
[]
[]
[Postprocessors]
[pp_water_top]
type = PointValue
variable = ppwater
point = '0 0 0'
[]
[pp_water_base]
type = PointValue
variable = ppwater
point = '-1 0 0'
[]
[pp_water_analytical]
type = FunctionValuePostprocessor
function = ana_ppwater
point = '-1 0 0'
[]
[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]
active = andy
[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-12 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-12 1E-10 10000 test'
[]
[]
[Executioner]
type = Transient
solve_type = Newton
[TimeStepper]
type = FunctionDT
function = dts
[]
end_time = 1.0
[]
[Outputs]
execute_on = 'initial timestep_end'
file_base = grav02c
[csv]
type = CSV
[]
exodus = true
[]
(modules/porous_flow/test/tests/gravity/grav02c.i)Using the PP formulation with a boundary condition fixing porepressures:
# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PP), 2components, vanGenuchten, constant fluid bulk-moduli for each phase, constant viscosity, constant permeability, Corey relative perm.
# A boundary condition enforces porepressures at the right boundary
# For better agreement with the analytical solution (ana_pp), just increase nx
[Mesh]
type = GeneratedMesh
dim = 1
nx = 10
xmin = -1
xmax = 0
[]
[GlobalParams]
PorousFlowDictator = dictator
[]
[Functions]
[dts]
type = PiecewiseLinear
x = '1E-3 1E-2 1E-1 2E-1'
y = '1E-3 1E-2 0.2E-1 1E-1'
[]
[]
[Variables]
[ppwater]
initial_condition = 0
[]
[ppgas]
initial_condition = 0.5
[]
[]
[AuxVariables]
[massfrac_ph0_sp0]
initial_condition = 1
[]
[massfrac_ph1_sp0]
initial_condition = 0
[]
[]
[BCs]
[ppwater]
type = DirichletBC
boundary = right
variable = ppwater
value = 0
[]
[ppgas]
type = DirichletBC
boundary = right
variable = ppgas
value = 0.5
[]
[]
[Kernels]
[mass0]
type = PorousFlowMassTimeDerivative
fluid_component = 0
variable = ppwater
[]
[flux0]
type = PorousFlowAdvectiveFlux
fluid_component = 0
variable = ppwater
gravity = '-1 0 0'
[]
[mass1]
type = PorousFlowMassTimeDerivative
fluid_component = 1
variable = ppgas
[]
[flux1]
type = PorousFlowAdvectiveFlux
fluid_component = 1
variable = ppgas
gravity = '-1 0 0'
[]
[]
[Functions]
[ana_ppwater]
type = ParsedFunction
symbol_names = 'g B p0 rho0'
symbol_values = '1 2 pp_water_top 1'
expression = '-B*log(exp(-p0/B)+g*rho0*x/B)' # expected pp at base
[]
[]
[UserObjects]
[dictator]
type = PorousFlowDictator
porous_flow_vars = 'ppwater ppgas'
number_fluid_phases = 2
number_fluid_components = 2
[]
[pc]
type = PorousFlowCapillaryPressureVG
m = 0.5
alpha = 1
[]
[]
[FluidProperties]
[simple_fluid0]
type = SimpleFluidProperties
bulk_modulus = 1.2
density0 = 1
viscosity = 1
thermal_expansion = 0
[]
[simple_fluid1]
type = SimpleFluidProperties
bulk_modulus = 1
density0 = 0.1
viscosity = 0.5
thermal_expansion = 0
[]
[]
[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_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 = '1 0 0 0 2 0 0 0 3'
[]
[relperm_water]
type = PorousFlowRelativePermeabilityCorey
n = 1
phase = 0
[]
[relperm_gas]
type = PorousFlowRelativePermeabilityCorey
n = 1
phase = 1
[]
[]
[Postprocessors]
[pp_water_top]
type = PointValue
variable = ppwater
point = '0 0 0'
[]
[pp_water_base]
type = PointValue
variable = ppwater
point = '-1 0 0'
[]
[pp_water_analytical]
type = FunctionValuePostprocessor
function = ana_ppwater
point = '-1 0 0'
[]
[ppwater_00]
type = PointValue
variable = ppwater
point = '0 0 0'
[]
[ppwater_01]
type = PointValue
variable = ppwater
point = '-0.1 0 0'
[]
[ppwater_02]
type = PointValue
variable = ppwater
point = '-0.2 0 0'
[]
[ppwater_03]
type = PointValue
variable = ppwater
point = '-0.3 0 0'
[]
[ppwater_04]
type = PointValue
variable = ppwater
point = '-0.4 0 0'
[]
[ppwater_05]
type = PointValue
variable = ppwater
point = '-0.5 0 0'
[]
[ppwater_06]
type = PointValue
variable = ppwater
point = '-0.6 0 0'
[]
[ppwater_07]
type = PointValue
variable = ppwater
point = '-0.7 0 0'
[]
[ppwater_08]
type = PointValue
variable = ppwater
point = '-0.8 0 0'
[]
[ppwater_09]
type = PointValue
variable = ppwater
point = '-0.9 0 0'
[]
[ppwater_10]
type = PointValue
variable = ppwater
point = '-1 0 0'
[]
[ppgas_00]
type = PointValue
variable = ppgas
point = '0 0 0'
[]
[ppgas_01]
type = PointValue
variable = ppgas
point = '-0.1 0 0'
[]
[ppgas_02]
type = PointValue
variable = ppgas
point = '-0.2 0 0'
[]
[ppgas_03]
type = PointValue
variable = ppgas
point = '-0.3 0 0'
[]
[ppgas_04]
type = PointValue
variable = ppgas
point = '-0.4 0 0'
[]
[ppgas_05]
type = PointValue
variable = ppgas
point = '-0.5 0 0'
[]
[ppgas_06]
type = PointValue
variable = ppgas
point = '-0.6 0 0'
[]
[ppgas_07]
type = PointValue
variable = ppgas
point = '-0.7 0 0'
[]
[ppgas_08]
type = PointValue
variable = ppgas
point = '-0.8 0 0'
[]
[ppgas_09]
type = PointValue
variable = ppgas
point = '-0.9 0 0'
[]
[ppgas_10]
type = PointValue
variable = ppgas
point = '-1 0 0'
[]
[]
[Preconditioning]
active = andy
[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-12 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-12 1E-10 10000 test'
[]
[]
[Executioner]
type = Transient
solve_type = Newton
[TimeStepper]
type = FunctionDT
function = dts
[]
end_time = 1.0
[]
[Outputs]
[csv]
type = CSV
execute_on = 'initial final'
file_base = grav02d
[]
[]
(modules/porous_flow/test/tests/gravity/grav02d.i)Using the PS formulation with no residual saturation
# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PS), 2components, constant capillary pressure, constant fluid bulk-moduli for each phase, constant viscosity,
# constant permeability, Corey relative permeabilities with no 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 = FIRST
[]
[swater]
family = MONOMIAL
order = FIRST
[]
[relpermwater]
family = MONOMIAL
order = FIRST
[]
[relpermgas]
family = MONOMIAL
order = FIRST
[]
[]
[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 = PorousFlowPropertyAux
property = relperm
phase = 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 = PorousFlowCapillaryPressureConst
pc = 1e5
[]
[]
[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 = PorousFlowRelativePermeabilityCorey
n = 2
phase = 0
[]
[relperm_gas]
type = PorousFlowRelativePermeabilityCorey
n = 2
phase = 1
[]
[]
[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_atol -snes_rtol'
petsc_options_value = 'bcgs bjacobi 1E-12 1E-10'
[]
[]
[Executioner]
type = Transient
solve_type = Newton
end_time = 1e5
[TimeStepper]
type = IterationAdaptiveDT
dt = 1e4
[]
[]
[Outputs]
execute_on = 'initial timestep_end'
file_base = grav02e
exodus = true
perf_graph = true
csv = false
[]
(modules/porous_flow/test/tests/gravity/grav02e.i)Using the PS formulation with residual saturation
# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PS), 2components, van Genuchten capillary pressure, constant fluid bulk-moduli for each phase, constant viscosity,
# constant permeability, 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 = PorousFlowCapillaryPressureVG
m = 0.5
alpha = 1e-4
pc_max = 2e5
[]
[]
[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 = PorousFlowRelativePermeabilityCorey
n = 2
phase = 0
s_res = 0.25
sum_s_res = 0.35
[]
[relperm_gas]
type = PorousFlowRelativePermeabilityCorey
n = 2
phase = 1
s_res = 0.1
sum_s_res = 0.35
[]
[]
[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 = 1e4
[]
[]
[Outputs]
execute_on = 'initial timestep_end'
file_base = grav02f
exodus = true
perf_graph = true
csv = false
[]
(modules/porous_flow/test/tests/gravity/grav02f.i)Using the PS formulation with Brooks-Corey capillarity and residual saturation
# Checking that gravity head is established in the transient situation when 0<=saturation<=1 (note the less-than-or-equal-to).
# 2phase (PS), 2components, van Genuchten capillary pressure, constant fluid bulk-moduli for each phase, constant viscosity,
# constant permeability, 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 = PorousFlowCapillaryPressureVG
m = 0.5
alpha = 1e-4
pc_max = 2e5
[]
[]
[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 = PorousFlowRelativePermeabilityCorey
n = 2
phase = 0
s_res = 0.25
sum_s_res = 0.35
[]
[relperm_gas]
type = PorousFlowRelativePermeabilityCorey
n = 2
phase = 1
s_res = 0.1
sum_s_res = 0.35
[]
[]
[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 = 1e4
[]
[]
[Outputs]
execute_on = 'initial timestep_end'
file_base = grav02f
exodus = true
perf_graph = true
csv = false
[]
(modules/porous_flow/test/tests/gravity/grav02f.i)