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CHARACTERISTIC_CURVES

Specifies the relative permeability and saturation function and parameters to be associated with a material property. This card is currently only supported for GENERAL and RICHARDS modes. The SATURATION_FUNCTION card should be used in all other flow modes.

Required Blocks and Cards:

SATURATION_FUNCTION <string>

Opens a saturation function block, where <string> indicates the type of saturation function. The options include: BROOKS_COREY, LINEAR, VAN_GENUCHTEN, several BRAGFLO-related options (called KRP’s), and MODIFIED_KOSUGI. The available saturation functions are documented in the Theory Guide under Capillary Pressure - Saturation Functions.

Required cards within the SATURATION_FUNCTION block:
  • BROOKS_COREY (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • ALPHA
    • LAMBDA
    • SMOOTH (optional, but highly recommended, see Parameter Definitions)
  • LINEAR (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • ALPHA
  • VAN_GENUCHTEN (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • ALPHA
    • M
  • MODIFIED_KOSUGI (see QA plot)
    • NPARAM
    • SIGMAZ
    • MUZ
    • RMAX
    • R0
  • BRAGFLO_KRP1 (see QA plot) Note: If not running in the TWOPHASE_MODE, PCT_A and PCT_EXP should be replaced with IGNORE_PERMEABILITY and ALPHA, where \(1/\alpha = P_t = ak^v\) where ALPHA\(=\alpha\), PCT_A\(=a\), and PCT_EXP\(=v\).

    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • PCT_A
    • PCT_EXP
    • M
    • KPC
  • BRAGFLO_KRP2 (see QA plot) Note: If not running in the TWOPHASE_MODE, PCT_A and PCT_EXP should be replaced with IGNORE_PERMEABILITY and ALPHA, where \(1/\alpha = P_t = ak^v\) where ALPHA\(=\alpha\), PCT_A\(=a\), and PCT_EXP\(=v\).

    • LIQUID_RESIDUAL_SATURATION
    • PCT_A
    • PCT_EXP
    • LAMBDA
    • KPC
  • BRAGFLO_KRP3 (see QA plot) Note: If not running in the TWOPHASE_MODE, PCT_A and PCT_EXP should be replaced with IGNORE_PERMEABILITY and ALPHA, where \(1/\alpha = P_t = ak^v\) where ALPHA\(=\alpha\), PCT_A\(=a\), and PCT_EXP\(=v\).

    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • PCT_A
    • PCT_EXP
    • LAMBDA
    • KPC
  • BRAGFLO_KRP4 (see QA plot) Note: If not running in the TWOPHASE_MODE, PCT_A and PCT_EXP should be replaced with IGNORE_PERMEABILITY and ALPHA, where \(1/\alpha = P_t = ak^v\) where ALPHA\(=\alpha\), PCT_A\(=a\), and PCT_EXP\(=v\).

    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • PCT_A
    • PCT_EXP
    • LAMBDA
    • KPC
  • BRAGFLO_KRP5 (see QA plot) Note: If not running in the TWOPHASE_MODE, PCT_A and PCT_EXP should be replaced with IGNORE_PERMEABILITY and ALPHA, where \(1/\alpha = P_t = ak^v\) where ALPHA\(=\alpha\), PCT_A\(=a\), and PCT_EXP\(=v\).

    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • PCT_A
    • PCT_EXP
    • KPC
  • BRAGFLO_KRP8 (see QA plot) Note: If not running in the TWOPHASE_MODE, PCT_A and PCT_EXP should be replaced with IGNORE_PERMEABILITY and ALPHA, where \(1/\alpha = P_t = ak^v\) where ALPHA\(=\alpha\), PCT_A\(=a\), and PCT_EXP\(=v\).

    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • PCT_A
    • PCT_EXP
    • M
    • KPC
  • BRAGFLO_KRP9 (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
  • BRAGFLO_KRP11 (see QA plot)
    • [no parameters needed]
  • BRAGFLO_KRP12 (see QA plot) Note: If not running in the TWOPHASE_MODE, PCT_A and PCT_EXP should be replaced with IGNORE_PERMEABILITY and ALPHA, where \(1/\alpha = P_t = ak^v\) where ALPHA\(=\alpha\), PCT_A\(=a\), and PCT_EXP\(=v\).

    • LIQUID_RESIDUAL_SATURATION
    • PCT_A
    • PCT_EXP
    • LAMBDA
    • S_MIN
    • S_EFFMIN
    • KPC

The parameters ALPHA, LAMBDA, M, LIQUID_RESIDUAL_SATURATION, GAS_RESIDUAL_SATURATION, KPC, S_MIN, S_EFFMIN, NPARAM, SIGMAZ, MUZ, RMAX, R0, and SMOOTH are defined below under Parameter Definitions.

PERMEABILITY_FUNCTION <string>

Opens a relative permeability function block, where <string> indicates the type of liquid or gas relative permeability function. For multiphase flow, (e.g. GENERAL MODE) a relative permeability block must be included for each phase. For single phase variably saturated flow (e.g. RICHARDS MODE), only one relative permeability block for the liquid phase relative permeability should be specified.

The liquid phase options include: MUALEM_BC_LIQ, BURDINE_BC_LIQ, MUALEM_LINEAR_LIQ, BURDINE_LINEAR_LIQ, MUALEM_VG_LIQ, and BURDINE_VG_LIQ. The gas phase options include: MUALEM_BC_GAS, BURDINE_BC_GAS, MUALEM_LINEAR_GAS, BURDINE_LINEAR_GAS, MUALEM_VG_GAS, BURDINE_VG_GAS, several BRAGFLO-related options, MODIFIED_KOSUGI_LIQ, and MODIFIED_KOSUGI_GAS. The available relative permeability functions are documented in the Theory Guide under Relative Permeability Functions. (Note: BC = Brooks Corey; VG = van Genuchten)

One of the following cards are required within the liquid phase PERMEABILITY_FUNCTION block:

  • MUALEM_BC_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • LAMBDA
  • BURDINE_BC_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • LAMBDA
  • MUALEM_LINEAR_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • MAX_CAPILLARY_PRESSURE
    • ALPHA
  • BURDINE_LINEAR_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
  • MUALEM_VG_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • M
  • BURDINE_VG_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • M
  • MODIFIED_KOSUGI_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • SIGMAZ
  • BRAGFLO_KRP1_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • M
  • BRAGFLO_KRP2_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • LAMBDA
  • BRAGFLO_KRP3_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • M
  • BRAGFLO_KRP4_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • LAMBDA
  • BRAGFLO_KRP5_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
  • BRAGFLO_KRP8_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • M
  • BRAGFLO_KRP9_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
  • BRAGFLO_KRP11_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • TOLC
  • BRAGFLO_KRP12_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • LAMBDA

One of the following cards are required within the gas phase PERMEABILITY_FUNCTION block:

  • MUALEM_BC_GAS (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • LAMBDA
  • BURDINE_BC_GAS (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • LAMBDA
  • MUALEM_LINEAR_GAS (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • MAX_CAPILLARY_PRESSURE
    • ALPHA
  • BURDINE_LINEAR_LIQ (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
  • MUALEM_VG_GAS (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • M
  • BURDINE_VG_GAS (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • M
  • MODIFIED_KOSUGI_GAS (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • SIGMAZ
  • BRAGFLO_KRP1_GAS (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • M
  • BRAGFLO_KRP2_GAS (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • LAMBDA
  • BRAGFLO_KRP3_GAS (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • LAMBDA
  • BRAGFLO_KRP4_GAS (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • LAMBDA
  • BRAGFLO_KRP5_GAS (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
  • BRAGFLO_KRP8_GAS (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • M
  • BRAGFLO_KRP9_GAS (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
  • BRAGFLO_KRP11_GAS (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • TOLC
  • BRAGFLO_KRP12_GAS (see QA plot)
    • LIQUID_RESIDUAL_SATURATION
    • GAS_RESIDUAL_SATURATION
    • LAMBDA

The parameters LAMBDA, M, MAX_CAPILLARY_PRESSURE, LIQUID_RESIDUAL_SATURATION, GAS_RESIDUAL_SATURATION, TOLC, SIGMAZ, and SMOOTH are defined below under Parameter Definitions.

Parameter Definitions

ALPHA <float>
Inverse of the air entry pressure for the saturation function [Pa-1].
LAMBDA <float>
Brooks-Corey lambda parameter [-].
M <float>
van Genuchten m parameter, as in (m = 1-1/n) or (m = 1 - 2/n) [-].
GAS_RESIDUAL_SATURATION <float>
Residual saturation for gas phase [-].
LIQUID_RESIDUAL_SATURATION <float>
Residual saturation for liquid phase [-].
MAX_CAPILLARY_PRESSURE <float>
Cut off for maximum capillary pressure [Pa].
TOLC <float>
A tolerance interval over which the relative permeability changes linearly from zero to one [-].
KPC <float>
This is a flag parameter from BRAGFLO. Set KPC to 2 to activate MAX_CAPILLARY_PRESSURE. Set KPC to 1 to ignore MAX_CAPILLARY_PRESSURE.
S_MIN <float>
This is a parameter from BRAGFLO. It is a cutoff in liquid saturation that is considered numerically dry, and it is smaller than liquid residual saturation.
S_EFFMIN <float>
This is a parameter from BRAGFLO. It is the liquid saturation below S_MIN at which the Brooks Corey model becomes singular, or the capillary pressure is capped. It can also be thought of as a small tolerance which pushes the singularity in the capillary pressure to a liquid saturation slightly below S_MIN.
SMOOTH
Applies polynomial smoothing to relative permeability or saturation function. Strongly recommended for the Brooks-Corey saturation function if cells in the domain will transition from saturated to variably-saturated conditions. The smoothing operation is documented under Smoothing in the Theory Guide.
MODIFIED_KOSUGI model

This model is based on a truncated lognormal pore-size distribution. The distribution is truncated at the higher end only (3-parameter version) or higher and lower ends (4-parameter version) of the pore-size distribution. The original Kosugi model was for a 3-parameter moisture retention curve, but only developed a relative permeability function in the limit as \(\mathrm{R_{MAX}} \rightarrow \infty\) and \(\mathrm{R}_0 \rightarrow 0\) (i.e., the 2-parameter version). PFLOTRAN implements a closed-form approximation to the 3-parameter relative permeability function and an extended 4-parameter moisture retention curve and relative permeability model proposed by Malama & Kuhlman (2015). http://dx.doi.org/10.1111/gwat.12220

  • SIGMAZ <float> variance of the log pore-size distribution (in m). Essentially, this parameter is related to the slope and location of the inflection in the moisture retention and relative permeability curves.
  • MUZ <float> mean of the log pore-size distribution (in m). Essentially, this parameter is related to the position of the moisture retention curve along the capillary pressure axis (i.e., similar to the air-entry pressure).
  • NPARAM <int> number of parameters in the model. Valid values are 3 (upper-truncated pore-size distribution only) and 4 (upper- and lower-truncated pore-size distribution). When this is set to 3 the value of R0 is not used, and is not required to be set.
  • RMAX <float> maximum pore size (in m) in lognormal pore-size distribution.
  • R0 <float> minimum pore size (in m) in lognormal pore-size distribution. Only used if NPARAM=4. The user must ensure \(\mathrm{R_0}<\mathrm{R_{MAX}}\). Also, if they are too close numerical problems may arise.

Optional Cards under the CHARACTERISTIC_CURVES block:

POWER <float>
Placeholder. Currently not used.
DEFAULT
Sets up dummy saturation and permeability functions for saturated single phase flow. If DEFAULT is specified, then the SATURATION_FUNCTION and the PERMEABILITY_FUNCTION blocks need not be specified.
TEST
Including this keyword will produce output (.dat files) which provides (a) the capillary pressure for the entire range of liquid saturation, (b) the liquid saturation for the entire range of capillary pressures, and (c) the liquid and gas relative permeability values for the range of liquid saturation. See How To Test Characteristic Curves for detailed instructions on how to use this keyword.

Optional Cards under the SATURATION_FUNCTION or PERMEABILITY_FUNCTION blocks:

PHASE <string>
If this card is included under the PERMEABILITY_FUNCTION block, then PHASE indicates which phase the permeability function applies to [options include: LIQUID, GAS]. By default, relative permeability functions that end with “_LIQ” imply “PHASE LIQUID,” while relative permeability functions that end with “_GAS” imply “PHASE GAS,” and PHASE does not have to be specified. However, this card can be used to apply a phase to a relative permeability function that is not phase-specific (under development).
MAX_CAPILLARY_PRESSURE <float>
Cut off for maximum capillary pressure (default = 109) [Pa].

Examples

RICHARDS mode

! for saturated flow
CHARACTERISTIC_CURVES default
  DEFAULT
END

! note: no need to specify phase as Richards is solely water phase
CHARACTERISTIC_CURVES sf1
  SATURATION_FUNCTION VAN_GENUCHTEN
    M 0.286
    ALPHA  1.9401d-4
    LIQUID_RESIDUAL_SATURATION 0.115
  /
  PERMEABILITY_FUNCTION MUALEM_VG_LIQ
    M 0.286
    LIQUID_RESIDUAL_SATURATION 0.115
  /
END

CHARACTERISTIC_CURVES sf2
  SATURATION_FUNCTION BROOKS_COREY
    LIQUID_RESIDUAL_SATURATION 0.115d0
    LAMBDA 0.7d0
    ALPHA 1.3d-6
    MAX_CAPILLARY_PRESSURE 1.d8
    SMOOTH
  /
  PERMEABILITY_FUNCTION MUALEM_BC_LIQ
    LIQUID_RESIDUAL_SATURATION 0.115
    LAMBDA 0.7d0
    SMOOTH
  /
END

CHARACTERISTIC_CURVES hygiene_sandstone_vg
  # Table 1 of van Genuchten (1980)
  SATURATION_FUNCTION VAN_GENUCHTEN
    ALPHA 8.05D-5
    M 9.0385D-1
    LIQUID_RESIDUAL_SATURATION 1.53D-1
  END
  PERMEABILITY_FUNCTION MUALEM_VG_LIQ
    M 9.0385D-1
    LIQUID_RESIDUAL_SATURATION 1.53D-1
  END
END
CHARACTERISTIC_CURVES hygiene_sandstone_mk
  # Table 1 of Malama & Kuhlman (2015)
  SATURATION_FUNCTION MODIFIED_KOSUGI
    NPARAM 3
    SIGMAZ 3.36D-1
    MUZ -6.30D0
    RMAX 3.05D-3
    LIQUID_RESIDUAL_SATURATION 1.53D-1
  END
  PERMEABILITY_FUNCTION MODIFIED_KOSUGI_LIQ
    SIGMAZ 3.36D-1
    LIQUID_RESIDUAL_SATURATION 1.53D-1
  END
END

GENERAL mode

CHARACTERISTIC_CURVES cc1
  SATURATION_FUNCTION VAN_GENUCHTEN
    LIQUID_RESIDUAL_SATURATION 0.d0
    M 0.5d0
    ALPHA 1.d-4
    MAX_CAPILLARY_PRESSURE 1.d6
  /
  PERMEABILITY_FUNCTION MUALEM_VG_LIQ
    LIQUID_RESIDUAL_SATURATION 0.d0
    M 0.5d0
  /
  PERMEABILITY_FUNCTION MUALEM_VG_GAS
    LIQUID_RESIDUAL_SATURATION 0.d0
    GAS_RESIDUAL_SATURATION 1.d-40
    M 0.5d0
  /
/

CHARACTERISTIC_CURVES cc2
  SATURATION_FUNCTION BROOKS_COREY
    LIQUID_RESIDUAL_SATURATION 0.2d0
    LAMBDA 0.7d0
    ALPHA 9.869d-6
    MAX_CAPILLARY_PRESSURE 1.d8
    SMOOTH
  /
  PERMEABILITY_FUNCTION BURDINE_BC_LIQ
    LIQUID_RESIDUAL_SATURATION 0.2d0
    LAMBDA 0.7d0
    SMOOTH
  /
  PERMEABILITY_FUNCTION BURDINE_BC_GAS
    LIQUID_RESIDUAL_SATURATION 0.2d0
    GAS_RESIDUAL_SATURATION 1.d-5
    LAMBDA 0.7d0
    SMOOTH
  /
/

CHARACTERISTIC_CURVES cc3
  SATURATION_FUNCTION LINEAR
    LIQUID_RESIDUAL_SATURATION 0.1d0
  /
  PERMEABILITY_FUNCTION BURDINE_LINEAR_LIQ
    LIQUID_RESIDUAL_SATURATION 0.1d0
  /
  PERMEABILITY_FUNCTION BURDINE_LINEAR_GAS
    LIQUID_RESIDUAL_SATURATION 0.1d0
    GAS_RESIDUAL_SATURATION 0.15d0
  /
/