Detailed Description

The van Genuchten capillary pressure model.

The van Genuchten capillary pressure model ([42]) is:

\[p_c(S)=p_b (S_\text{eff}^{-1/m}-1)^{1-m}\]

with effective saturation defined as

\[S_\text{eff}=\frac{S-S_r}{S_{\text{max}}-S_r}.\]

Above, \(S_r\) and \(S_{\text{max}}\) are the residual and the maximum saturations. The exponent \(m \in (0,1)\) and the pressure scaling parameter \(p_b\) (it is equal to \(\rho g/\alpha\) in original publication) are given by the user. The scaling parameter \(p_b\) is given in same units as pressure.

In the original work another exponent \(n\) is used, but usually set to \(n = 1 / (1 - m)\), and also in this implementation.

The the capillary pressure is computed from saturation as above but is cut off at maximum capillary pressure given by user.

Definition at line 34 of file CapillaryPressureVanGenuchten.h.

#include <CapillaryPressureVanGenuchten.h>

Inheritance diagram for MaterialPropertyLib::CapillaryPressureVanGenuchten:

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Collaboration diagram for MaterialPropertyLib::CapillaryPressureVanGenuchten:

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Public Member Functions
	CapillaryPressureVanGenuchten (std::string name, double const residual_liquid_saturation, double const residual_gas_saturation, double const exponent, double const p_b, double const maximum_capillary_pressure)
void	checkScale () const override
PropertyDataType	value (VariableArray const &variable_array, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const override
PropertyDataType	dValue (VariableArray const &variable_array, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const override
Public Member Functions inherited from MaterialPropertyLib::Property
virtual	~Property ()
virtual PropertyDataType	initialValue (ParameterLib::SpatialPosition const &pos, double const t) const
virtual PropertyDataType	value () const
virtual PropertyDataType	value (VariableArray const &variable_array, VariableArray const &variable_array_prev, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const
virtual PropertyDataType	dValue (VariableArray const &variable_array, VariableArray const &variable_array_prev, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const
virtual PropertyDataType	d2Value (VariableArray const &variable_array, Variable const variable1, Variable const variable2, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const
	Default implementation: 2nd derivative of any constant property is zero.
virtual void	setProperties (std::vector< std::unique_ptr< Phase > > const &phases)
	Default implementation:
void	setScale (std::variant< Medium , Phase , Component * > scale)
template<typename T>
T	initialValue (ParameterLib::SpatialPosition const &pos, double const t) const
template<typename T>
T	value () const
template<typename T>
T	value (VariableArray const &variable_array, VariableArray const &variable_array_prev, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const
template<typename T>
T	value (VariableArray const &variable_array, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const
template<typename T>
T	dValue (VariableArray const &variable_array, VariableArray const &variable_array_prev, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const
template<typename T>
T	dValue (VariableArray const &variable_array, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const
template<typename T>
T	d2Value (VariableArray const &variable_array, Variable const &variable1, Variable const &variable2, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

Private Attributes
double const	S_L_res_
	Residual saturation of liquid phase.
double const	S_L_max_
	Maximum saturation of liquid phase.
double const	m_
	Exponent.
double const	p_b_
	Pressure scaling factor.
double const	p_cap_max_
	Maximum capillary pressure.

Additional Inherited Members
Protected Attributes inherited from MaterialPropertyLib::Property
std::string	name_
PropertyDataType	value_
	The single value of a property.
PropertyDataType	dvalue_
std::variant< Medium , Phase , Component * >	scale_

Constructor & Destructor Documentation

◆ CapillaryPressureVanGenuchten()

MaterialPropertyLib::CapillaryPressureVanGenuchten::CapillaryPressureVanGenuchten	(	std::string	name,
		double const	residual_liquid_saturation,
		double const	residual_gas_saturation,
		double const	exponent,
		double const	p_b,
		double const	maximum_capillary_pressure )

Definition at line 13 of file CapillaryPressureVanGenuchten.cpp.

    : S_L_res_(residual_liquid_saturation),
      S_L_max_(1. - residual_gas_saturation),
      m_(exponent),
      p_b_(p_b),
      p_cap_max_(maximum_capillary_pressure)
{
    name_ = std::move(name);
 
    if (S_L_res_ < 0 || S_L_res_ > 1)
    {
        OGS_FATAL(
            "Van Genuchten capillary pressure model: The residual liquid "
            "saturation value S_L_res = {:g} is out of admissible range [0, "
            "1].",
            S_L_res_);
    }
    if (S_L_max_ < 0 || S_L_max_ > 1)
    {
        OGS_FATAL(
            "Van Genuchten capillary pressure model: The maximum liquid "
            "saturation value S_L_max = {:g} is out of admissible range [0, "
            "1].",
            S_L_max_);
    }
    if (S_L_res_ >= S_L_max_)
    {
        OGS_FATAL(
            "Van Genuchten capillary pressure model: The maximum liquid "
            "saturation S_L_max = {:g} must not be less or equal to the "
            "residual liquid saturion S_L_res = {:g}.",
            S_L_max_, S_L_res_);
    }
    if (!(m_ > 0 && m_ < 1))
    {
        OGS_FATAL(
            "Van Genuchten capillary pressure model: The exponent value m = "
            "{:g} is out of of admissible range (0, 1).",
            m_);
    }
    if (p_b_ <= 0)
    {
        OGS_FATAL(
            "Van Genuchten capillary pressure model: The pressure scaling "
            "value p_b = {:g} must be positive.",
            p_b_);
    }
    if (p_cap_max_ < 0)
    {
        OGS_FATAL(
            "Van Genuchten capillary pressure model: The maximum capillary "
            "pressure value p_cap_max = {:g} must be non-negative.",
            p_cap_max_);
    }
}

References m_, MaterialPropertyLib::name, MaterialPropertyLib::Property::name_, OGS_FATAL, p_b_, p_cap_max_, MaterialPropertyLib::residual_gas_saturation, MaterialPropertyLib::residual_liquid_saturation, S_L_max_, and S_L_res_.

Member Function Documentation

◆ checkScale()

void MaterialPropertyLib::CapillaryPressureVanGenuchten::checkScale ( ) const

inlineoverridevirtual

Reimplemented from MaterialPropertyLib::Property.

Definition at line 44 of file CapillaryPressureVanGenuchten.h.

    {
        if (!std::holds_alternative<Medium*>(scale_))
        {
            OGS_FATAL(
                "The property 'CapillaryPressureVanGenuchten' is implemented "
                "on the 'media' scale only.");
        }
    }

References OGS_FATAL, and MaterialPropertyLib::Property::scale_.

◆ dValue()

PropertyDataType MaterialPropertyLib::CapillaryPressureVanGenuchten::dValue	(	VariableArray const &	variable_array,
		Variable const	variable,
		ParameterLib::SpatialPosition const &	pos,
		double const	t,
		double const	dt ) const

overridevirtual

Returns: \( \frac{\partial p_c(S)}{\partial S} \)

Reimplemented from MaterialPropertyLib::Property.

Definition at line 101 of file CapillaryPressureVanGenuchten.cpp.

{
    if (variable != Variable::liquid_saturation)
    {
        OGS_FATAL(
            "CapillaryPressureVanGenuchten::dValue is implemented for "
            "derivatives with respect to liquid saturation only.");
    }
 
    double const S_L = variable_array.liquid_saturation;
 
    if (S_L <= S_L_res_)
    {
        return 0.;
    }
 
    if (S_L >= S_L_max_)
    {
        return 0.;
    }
 
    double const S_eff = (S_L - S_L_res_) / (S_L_max_ - S_L_res_);
 
    assert(0 < S_eff && S_eff < 1.0);
 
    double const val1 = std::pow(S_eff, -1.0 / m_);
    double const p_cap = p_b_ * std::pow(val1 - 1.0, 1.0 - m_);
    if (p_cap >= p_cap_max_)
    {
        return 0.;
    }
 
    double const val2 = std::pow(val1 - 1.0, -m_);
    return p_b_ * (m_ - 1.0) * val1 * val2 / (m_ * (S_L - S_L_res_));
}

References MaterialPropertyLib::liquid_saturation, MaterialPropertyLib::VariableArray::liquid_saturation, m_, OGS_FATAL, p_b_, p_cap_max_, S_L_max_, and S_L_res_.

◆ value()

PropertyDataType MaterialPropertyLib::CapillaryPressureVanGenuchten::value	(	VariableArray const &	variable_array,
		ParameterLib::SpatialPosition const &	pos,
		double const	t,
		double const	dt ) const

overridevirtual

Returns: \( p_c(S) \).

Reimplemented from MaterialPropertyLib::Property.

Definition at line 75 of file CapillaryPressureVanGenuchten.cpp.

{
    double const S_L = variable_array.liquid_saturation;
 
    if (S_L <= S_L_res_)
    {
        return p_cap_max_;
    }
 
    if (S_L >= S_L_max_)
    {
        return 0.;
    }
 
    double const S_eff = (S_L - S_L_res_) / (S_L_max_ - S_L_res_);
    assert(0 <= S_eff && S_eff <= 1);
 
    double const p_cap =
        p_b_ * std::pow(std::pow(S_eff, -1.0 / m_) - 1.0, 1.0 - m_);
    assert(p_cap > 0);
    return std::min(p_cap, p_cap_max_);
}