Detailed Description

Hydraulic aperture equals the mechanical aperture s.t. multiplication of the permeability by the mechanical aperture yields the cubic law. The volumetric flux of incompressible fluid flow in a laminar regime within a fracture consisting of two parallel and smooth surfaces is given by the cubic law:

\[ Q = W/(u L) b^3/12 \Delta p,\]

where, \(Q\) is the volumetric flux normal to the flow direction, \(W\) is the fracture width, \(u\) is the fluid viscosity, \(L\) is the fracture length, \(p\) is the fluid pressure, and \(b\) is the fracture hydraulic aperture.

In the context of Darcy’s law, the fracture permeability becomes:

\[ k_f = b^2/12,\]

.

Ref: He, Xupeng, et al. "A corrected cubic law for single-phase laminar flow through rough-walled fractures." Advances in Water resources 154 (2021): 103984.

Definition at line 38 of file CubicLawPermeability.h.

#include <CubicLawPermeability.h>

Inheritance diagram for MaterialPropertyLib::CubicLawPermeability:

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Collaboration diagram for MaterialPropertyLib::CubicLawPermeability:

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Public Member Functions
	CubicLawPermeability (std::string name, ParameterLib::Parameter< double > const &b)

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
ParameterLib::Parameter< double > const &	_b
	fracture aperture

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

◆ CubicLawPermeability()

MaterialPropertyLib::CubicLawPermeability::CubicLawPermeability	(	std::string	name,
		ParameterLib::Parameter< double > const &	b )

inlineexplicit

Definition at line 40 of file CubicLawPermeability.h.

        : _b(b)
    {
        name_ = std::move(name);
    }

References MaterialPropertyLib::name, and MaterialPropertyLib::Property::name_.

Member Function Documentation

◆ checkScale()

void MaterialPropertyLib::CubicLawPermeability::checkScale ( ) const

inlineoverridevirtual

Reimplemented from MaterialPropertyLib::Property.

Definition at line 47 of file CubicLawPermeability.h.

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

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

◆ dValue()

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

overridevirtual

Returns: The derivative of permeability with respect to the aperture.

Reimplemented from MaterialPropertyLib::Property.

Definition at line 23 of file CubicLawPermeability.cpp.

{
    OGS_FATAL("CubicLawPermeability::dValue is not implemented.");
}

References OGS_FATAL.

◆ value()

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

overridevirtual

Returns: The permeability value.

Reimplemented from MaterialPropertyLib::Property.

Definition at line 14 of file CubicLawPermeability.cpp.

{
    double const aperture_m = _b(t, pos)[0];
    return aperture_m * aperture_m / 12;
}

References _b.

Member Data Documentation

◆ _b

ParameterLib::Parameter<double> const& MaterialPropertyLib::CubicLawPermeability::_b

private

fracture aperture

Definition at line 69 of file CubicLawPermeability.h.

Referenced by value().

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

MaterialLib/MPL/Properties/CubicLawPermeability.h
MaterialLib/MPL/Properties/CubicLawPermeability.cpp

Detailed Description

Public Member Functions

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ CubicLawPermeability()

Member Function Documentation

◆ checkScale()

◆ dValue()

◆ value()

Member Data Documentation

◆ _b