MaterialLib::PorousMedium::NonWettingPhaseVanGenuchten Class Reference

Detailed Description

van Genuchten model: non-wetting phase

\[k{rel}= (1 - S_e)^{1/3} (1 - S_e^{1/m})^{2m}\]

with

\[S_e=\frac{S^w-S_r}{S^w_{\mbox{max}}-S^w_r}\]

where

\begin{eqnarray*} &S^w_r& \mbox{residual saturation of wetting phase,}\\ &S^w_{\mbox{max}}& \mbox{maximum saturation of wetting phase,}\\ &m(<=1) & \mbox{ exponent.}\\ \end{eqnarray*}

Note:

\[m=1/(1-n)\]

.

Definition at line 36 of file NonWettingPhaseVanGenuchten.h.

#include <NonWettingPhaseVanGenuchten.h>

Inheritance diagram for MaterialLib::PorousMedium::NonWettingPhaseVanGenuchten:

Collaboration diagram for MaterialLib::PorousMedium::NonWettingPhaseVanGenuchten:

Public Member Functions
	NonWettingPhaseVanGenuchten (const double Snr, const double Snmax, const double m, const double krel_min)
std::string	getName () const override
	Get model name.
double	getValue (const double saturation_w) const override
double	getdValue (const double saturation_w) const override
Public Member Functions inherited from MaterialLib::PorousMedium::RelativePermeability
	RelativePermeability (const double Sr, const double Smax)
virtual	~RelativePermeability ()=default

Private Attributes
const double	_m
	Exponent m, m in [0, 1], n=1/(1-m).
const double	_krel_min
	Minimum relative permeability.

Additional Inherited Members
Protected Attributes inherited from MaterialLib::PorousMedium::RelativePermeability
const double	_minor_offset = std::numeric_limits<double>::epsilon()
const double	_saturation_r
	Residual saturation.
const double	_saturation_max
	Maximum saturation.

Constructor & Destructor Documentation

NonWettingPhaseVanGenuchten()

MaterialLib::PorousMedium::NonWettingPhaseVanGenuchten::NonWettingPhaseVanGenuchten ( const double Snr, const double Snmax, const double m, const double krel_min )

inline

Parameters

Snr	Residual saturation of the non-wetting phase, \( S^n_r \)
Snmax	Maximum saturation of the non-wetting phase, \( S^n_{\mbox{max}} \)
m	Exponent, \( m \in [0,1]\)
krel_min	Minimum relative permeability, \( k_{rel}^{\mbox{min}}\)

Definition at line 48 of file NonWettingPhaseVanGenuchten.h.

        : RelativePermeability(1. - Snmax, 1. - Snr),
          _m(m),
          _krel_min(krel_min)
    {
    }

Member Function Documentation

getdValue()

double MaterialLib::PorousMedium::NonWettingPhaseVanGenuchten::getdValue ( const double saturation_w ) const

overridevirtual

Get the derivative of relative permeability with respect to saturation.

Parameters

saturation_w

Wetting phase saturation

Implements MaterialLib::PorousMedium::RelativePermeability.

Definition at line 33 of file NonWettingPhaseVanGenuchten.cpp.

{
    const double S = std::clamp(saturation_w,
                                _saturation_r + _minor_offset,
                                _saturation_max - _minor_offset);
    const double Se = (S - _saturation_r) / (_saturation_max - _saturation_r);
    const double cbrt1_Se = std::cbrt(1.0 - Se);
    const double temp_val = 1.0 - std::pow(Se, 1.0 / _m);
    return (-std::pow(temp_val, 2. * _m) / (3. * cbrt1_Se * cbrt1_Se) -
            2. * cbrt1_Se * std::pow(temp_val, 2. * _m - 1.) *
                std::pow(Se, (1. - _m) / _m)) /
           (_saturation_max - _saturation_r);
}

References _m, MaterialLib::PorousMedium::RelativePermeability::_minor_offset, MaterialLib::PorousMedium::RelativePermeability::_saturation_max, and MaterialLib::PorousMedium::RelativePermeability::_saturation_r.

getName()

std::string MaterialLib::PorousMedium::NonWettingPhaseVanGenuchten::getName ( ) const

inlineoverridevirtual

Get model name.

Implements MaterialLib::PorousMedium::RelativePermeability.

Definition at line 57 of file NonWettingPhaseVanGenuchten.h.

    {
        return "Non-wetting phase van Genuchten relative permeability model.";
    }

getValue()

double MaterialLib::PorousMedium::NonWettingPhaseVanGenuchten::getValue ( const double saturation_w ) const

overridevirtual

Get relative permeability value.

Parameters

saturation_w

Wetting phase saturation

Implements MaterialLib::PorousMedium::RelativePermeability.

Definition at line 22 of file NonWettingPhaseVanGenuchten.cpp.

{
    const double S = std::clamp(saturation_w,
                                _saturation_r + _minor_offset,
                                _saturation_max - _minor_offset);
    const double Se = (S - _saturation_r) / (_saturation_max - _saturation_r);
    const double krel =
        std::cbrt(1.0 - Se) * std::pow(1.0 - std::pow(Se, 1.0 / _m), 2.0 * _m);
    return std::max(_krel_min, krel);
}

References _krel_min, _m, MaterialLib::PorousMedium::RelativePermeability::_minor_offset, MaterialLib::PorousMedium::RelativePermeability::_saturation_max, and MaterialLib::PorousMedium::RelativePermeability::_saturation_r.

Member Data Documentation

_krel_min

const double MaterialLib::PorousMedium::NonWettingPhaseVanGenuchten::_krel_min

private

Minimum relative permeability.

Definition at line 72 of file NonWettingPhaseVanGenuchten.h.

Referenced by getValue().

_m

const double MaterialLib::PorousMedium::NonWettingPhaseVanGenuchten::_m

private

Exponent m, m in [0, 1], n=1/(1-m).

Definition at line 71 of file NonWettingPhaseVanGenuchten.h.

Referenced by getdValue(), and getValue().

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The documentation for this class was generated from the following files:

• MaterialLib/PorousMedium/UnsaturatedProperty/RelativePermeability/NonWettingPhaseVanGenuchten.h
• MaterialLib/PorousMedium/UnsaturatedProperty/RelativePermeability/NonWettingPhaseVanGenuchten.cpp