Detailed Description

van Genuchten water retention model

\[p_c=p_b (S_e^{-1/m}-1)^{1-m}\]

with

\[S_e=\frac{S-S_r}{S_{\mbox{max}}-S_r}\]

where

\begin{eqnarray*} &p_b& \mbox{ entry pressure,}\\ &S_r& \mbox{ residual saturation,}\\ &S_{\mbox{max}}& \mbox{ maximum saturation,}\\ &m(<=1) & \mbox{ exponent.}\\ \end{eqnarray*}

Note:

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

.

If \(\alpha\) instead of \(p_b\) is available, \(p_b\) can be calculated as

\[p_b=\rho g/\alpha\]

The regularized van Genuchten model, please ref to Marchand E, Mueller T, Knabner P. Fully coupled generalized hybrid-mixed finite element approximation of two-phase two-component flow in porous media. Part I: formulation and properties of the mathematical model. Comput Geosci 2013;17(2):431-442.

Definition at line 53 of file VanGenuchtenCapillaryPressureSaturation.h.

#include <VanGenuchtenCapillaryPressureSaturation.h>

Inheritance diagram for MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation:

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Collaboration diagram for MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation:

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Public Member Functions
	VanGenuchtenCapillaryPressureSaturation (const double pb, const double Sr, const double Sg_r, const double Smax, const double m, const double Pc_max, const bool has_regularized)

std::string	getName () const override
	Get model name.

double	getCapillaryPressure (const double saturation) const override
	Get capillary pressure.

double	getSaturation (const double capillary_pressure) const override
	Get saturation.

double	getdPcdS (const double saturation) const override
	Get the derivative of the capillary pressure with respect to saturation.

double	getd2PcdS2 (const double saturation) const override

Public Member Functions inherited from MaterialLib::PorousMedium::CapillaryPressureSaturation
	CapillaryPressureSaturation (const double Sr, const double Sg_r, const double Smax, const double Pc_max)

virtual	~CapillaryPressureSaturation ()=default

Private Member Functions
double	getPcBarvGSg (double Sg) const
	parameter in regularized van Genuchten model

double	getSBar (double Sg) const
	Regularized van Genuchten capillary pressure-saturation Model.

double	getPcvGSg (double Sg) const
	van Genuchten capillary pressure-saturation Model

double	getdPcdSvGBar (double Sg) const

double	getdPcdSvG (const double Sg) const

Private Attributes
const double	_pb
	Entry pressure.

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

const bool	_has_regularized

const double	_xi = 1e-5
	using regularized van Genuchten model

Additional Inherited Members
Protected Attributes inherited from MaterialLib::PorousMedium::CapillaryPressureSaturation
const double	_saturation_r
	Residual saturation.

const double	_saturation_nonwet_r

const double	_saturation_max
	Maximum saturation.

const double	_pc_max
	Maximum capillary pressure.

const double	_minor_offset = std::numeric_limits<double>::epsilon()

Constructor & Destructor Documentation

◆ VanGenuchtenCapillaryPressureSaturation()

MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation::VanGenuchtenCapillaryPressureSaturation	(	const double	pb,
		const double	Sr,
		const double	Sg_r,
		const double	Smax,
		const double	m,
		const double	Pc_max,
		const bool	has_regularized )

inline

Parameters

pb	Entry pressure, \( p_b \)
Sr	Residual saturation, \( S_r \)
Sg_r	Residual saturation, \( S_g^{\mbox{r}} \)
Smax	Maximum saturation, \( S_{\mbox{max}} \)
m	Exponent, \( m \)
Pc_max	Maximum capillary pressure, \( P_c^{\mbox{max}}\)
has_regularized	whether use the regularized van Genuchten model, \( m \)

Definition at line 67 of file VanGenuchtenCapillaryPressureSaturation.h.

        : CapillaryPressureSaturation(Sr, Sg_r, Smax, Pc_max),
          _pb(pb),
          _m(m),
          _has_regularized(has_regularized)
    {
    }

Member Function Documentation

◆ getCapillaryPressure()

double MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation::getCapillaryPressure ( const double saturation ) const

overridevirtual

Get capillary pressure.

Implements MaterialLib::PorousMedium::CapillaryPressureSaturation.

Definition at line 24 of file VanGenuchtenCapillaryPressureSaturation.cpp.

{
    if (_has_regularized)
    {
        double Sg = 1 - saturation;
        if (Sg <= 1 - _saturation_r && Sg >= _saturation_nonwet_r)
        {
            return getPcBarvGSg(Sg);
        }
        if (Sg < _saturation_nonwet_r)
        {
            return getPcBarvGSg(_saturation_nonwet_r) +
                   getdPcdSvGBar(_saturation_nonwet_r) *
                       (Sg - _saturation_nonwet_r);
        }
 
        return getPcBarvGSg(1 - _saturation_r) +
               getdPcdSvGBar(1 - _saturation_r) * (Sg - 1 + _saturation_r);
    }
    const double S = std::clamp(saturation, _saturation_r + _minor_offset,
                                _saturation_max - _minor_offset);
    const double Se = (S - _saturation_r) / (_saturation_max - _saturation_r);
    const double pc = _pb * std::pow(std::pow(Se, (-1.0 / _m)) - 1.0, 1.0 - _m);
    return std::clamp(pc, _minor_offset, _pc_max);
}

References _has_regularized, _m, MaterialLib::PorousMedium::CapillaryPressureSaturation::_minor_offset, _pb, MaterialLib::PorousMedium::CapillaryPressureSaturation::_pc_max, MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_max, MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_nonwet_r, MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_r, getdPcdSvGBar(), and getPcBarvGSg().

◆ getd2PcdS2()

double MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation::getd2PcdS2 ( const double saturation ) const

overridevirtual

Get the second derivative of the capillary pressure with respect to saturation

Implements MaterialLib::PorousMedium::CapillaryPressureSaturation.

Definition at line 95 of file VanGenuchtenCapillaryPressureSaturation.cpp.

{
    if (_has_regularized)
    {
        OGS_FATAL(
            "Second derivative of regularized van-Genuchten saturation "
            "pressure relation is not implemented.");
    }
    if (saturation < _saturation_r)
    {
        return 0;
    }
    if (saturation > _saturation_max)
    {
        return 0;
    }
 
    const double S = std::clamp(saturation, _saturation_r + _minor_offset,
                                _saturation_max - _minor_offset);
    const double val1 = std::pow(
        ((S - _saturation_r) / (_saturation_max - _saturation_r)), 1.0 / _m);
    return -_pb / (_m * _m * (S - _saturation_r) * (S - _saturation_r)) *
           std::pow(1 - val1, -_m - 1) * std::pow(val1, _m - 1) *
           ((1 - _m * _m) * val1 + _m - 1);
}

References _has_regularized, _m, MaterialLib::PorousMedium::CapillaryPressureSaturation::_minor_offset, _pb, MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_max, MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_r, and OGS_FATAL.

◆ getdPcdS()

double MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation::getdPcdS ( const double saturation ) const

overridevirtual

Get the derivative of the capillary pressure with respect to saturation.

Implements MaterialLib::PorousMedium::CapillaryPressureSaturation.

Definition at line 61 of file VanGenuchtenCapillaryPressureSaturation.cpp.

{
    if (_has_regularized)
    {
        double const Sg = 1 - saturation;
        if (Sg >= _saturation_nonwet_r && Sg <= 1 - _saturation_r)
        {
            return -getdPcdSvGBar(Sg);
        }
        if (Sg < _saturation_nonwet_r)
        {
            return -getdPcdSvGBar(_saturation_nonwet_r);
        }
 
        return -getdPcdSvGBar(1 - _saturation_r);
    }
    if (saturation < _saturation_r)
    {
        return 0;
    }
    if (saturation > _saturation_max)
    {
        return 0;
    }
 
    const double S = std::clamp(saturation, _saturation_r + _minor_offset,
                                _saturation_max - _minor_offset);
    const double val1 = std::pow(
        ((S - _saturation_r) / (_saturation_max - _saturation_r)), -1.0 / _m);
    const double val2 = std::pow(val1 - 1.0, -_m);
    return _pb * (_m - 1.0) * val1 * val2 / (_m * (S - _saturation_r));
}

References _has_regularized, _m, MaterialLib::PorousMedium::CapillaryPressureSaturation::_minor_offset, _pb, MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_max, MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_nonwet_r, MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_r, and getdPcdSvGBar().

◆ getdPcdSvG()

double MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation::getdPcdSvG ( const double Sg ) const

private

derivative dPCdS based on standard van Genuchten capillary pressure-saturation Model

Definition at line 154 of file VanGenuchtenCapillaryPressureSaturation.cpp.

{
    double const Sg_r = CapillaryPressureSaturation::_saturation_nonwet_r;
    double const S_lr = CapillaryPressureSaturation::_saturation_r;
    double const nn = 1 / (1 - _m);
    double const S_le = (1 - Sg - S_lr) / (1 - Sg_r - S_lr);
    return _pb * (1 / (_m * nn)) * (1 / (1 - S_lr - Sg_r)) *
           std::pow(std::pow(S_le, (-1 / _m)) - 1, (1 / nn) - 1) *
           std::pow(S_le, (-1 / _m)) / S_le;
}

References _m, _pb, MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_nonwet_r, and MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_r.

Referenced by getdPcdSvGBar().

◆ getdPcdSvGBar()

double MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation::getdPcdSvGBar ( double Sg ) const

private

derivative dPCdS based on regularized van Genuchten capillary pressure-saturation Model

Definition at line 147 of file VanGenuchtenCapillaryPressureSaturation.cpp.

{
    double S_bar = getSBar(Sg);
    return getdPcdSvG(S_bar) * (1 - _xi);
}

References _xi, getdPcdSvG(), and getSBar().

Referenced by getCapillaryPressure(), and getdPcdS().

◆ getName()

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

inlineoverridevirtual

Get model name.

Implements MaterialLib::PorousMedium::CapillaryPressureSaturation.

Definition at line 80 of file VanGenuchtenCapillaryPressureSaturation.h.

    {
        return "van Genuchten water retention model.";
    }

◆ getPcBarvGSg()

double MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation::getPcBarvGSg ( double Sg ) const

private

parameter in regularized van Genuchten model

Regularized van Genuchten capillary pressure-saturation Model.

Regularized van Genuchten capillary pressure-saturation Model

Definition at line 122 of file VanGenuchtenCapillaryPressureSaturation.cpp.

{
    double const Sg_r = CapillaryPressureSaturation::_saturation_nonwet_r;
    double const S_lr = CapillaryPressureSaturation::_saturation_r;
    double const S_bar = getSBar(Sg);
    return getPcvGSg(S_bar) - getPcvGSg(Sg_r + (1 - Sg_r - S_lr) * _xi / 2);
}

References MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_nonwet_r, MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_r, _xi, getPcvGSg(), and getSBar().

Referenced by getCapillaryPressure().

◆ getPcvGSg()

double MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation::getPcvGSg ( double Sg ) const

private

van Genuchten capillary pressure-saturation Model

Definition at line 137 of file VanGenuchtenCapillaryPressureSaturation.cpp.

{
    double const Sg_r = CapillaryPressureSaturation::_saturation_nonwet_r;
    double const S_lr = CapillaryPressureSaturation::_saturation_r;
    double const S_le = (1 - Sg - S_lr) /
                        (1 - Sg_r - CapillaryPressureSaturation::_saturation_r);
    return _pb * std::pow(std::pow(S_le, (-1.0 / _m)) - 1.0, 1.0 - _m);
}

References _m, _pb, MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_nonwet_r, and MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_r.

Referenced by getPcBarvGSg().

◆ getSaturation()

double MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation::getSaturation ( const double capillary_pressure ) const

overridevirtual

Get saturation.

Implements MaterialLib::PorousMedium::CapillaryPressureSaturation.

Definition at line 51 of file VanGenuchtenCapillaryPressureSaturation.cpp.

{
    const double pc = std::max(_minor_offset, capillary_pressure);
    const double Se = std::pow(std::pow(pc / _pb, 1.0 / (1.0 - _m)) + 1.0, -_m);
    const double S = Se * (_saturation_max - _saturation_r) + _saturation_r;
    return std::clamp(S, _saturation_r + _minor_offset,
                      _saturation_max - _minor_offset);
}

References _m, MaterialLib::PorousMedium::CapillaryPressureSaturation::_minor_offset, _pb, MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_max, and MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_r.

◆ getSBar()

double MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation::getSBar ( double Sg ) const

private

Regularized van Genuchten capillary pressure-saturation Model.

Definition at line 130 of file VanGenuchtenCapillaryPressureSaturation.cpp.

{
    double const Sg_r = CapillaryPressureSaturation::_saturation_nonwet_r;
    double const S_lr = CapillaryPressureSaturation::_saturation_r;
    return Sg_r + (1 - _xi) * (Sg - Sg_r) + 0.5 * _xi * (1 - Sg_r - S_lr);
}

References MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_nonwet_r, MaterialLib::PorousMedium::CapillaryPressureSaturation::_saturation_r, and _xi.

Referenced by getdPcdSvGBar(), and getPcBarvGSg().

Member Data Documentation

◆ _has_regularized

const bool MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation::_has_regularized

private

Definition at line 99 of file VanGenuchtenCapillaryPressureSaturation.h.

Referenced by getCapillaryPressure(), getd2PcdS2(), and getdPcdS().

◆ _m

const double MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation::_m

private

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

Definition at line 98 of file VanGenuchtenCapillaryPressureSaturation.h.

Referenced by getCapillaryPressure(), getd2PcdS2(), getdPcdS(), getdPcdSvG(), getPcvGSg(), and getSaturation().

◆ _pb

const double MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation::_pb

private

Entry pressure.

Definition at line 97 of file VanGenuchtenCapillaryPressureSaturation.h.

Referenced by getCapillaryPressure(), getd2PcdS2(), getdPcdS(), getdPcdSvG(), getPcvGSg(), and getSaturation().

◆ _xi

const double MaterialLib::PorousMedium::VanGenuchtenCapillaryPressureSaturation::_xi = 1e-5

private

using regularized van Genuchten model

Definition at line 100 of file VanGenuchtenCapillaryPressureSaturation.h.

Referenced by getdPcdSvGBar(), getPcBarvGSg(), and getSBar().

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

MaterialLib/PorousMedium/UnsaturatedProperty/CapillaryPressure/VanGenuchtenCapillaryPressureSaturation.h
MaterialLib/PorousMedium/UnsaturatedProperty/CapillaryPressure/VanGenuchtenCapillaryPressureSaturation.cpp

Detailed Description

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ VanGenuchtenCapillaryPressureSaturation()

Member Function Documentation

◆ getCapillaryPressure()

◆ getd2PcdS2()

◆ getdPcdS()

◆ getdPcdSvG()

◆ getdPcdSvGBar()

◆ getName()

◆ getPcBarvGSg()

◆ getPcvGSg()

◆ getSaturation()

◆ getSBar()

Member Data Documentation

◆ _has_regularized

◆ _m

◆ _pb

◆ _xi