MaterialPropertyLib::CubicLawPermeability Struct Reference

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 42 of file CubicLawPermeability.h.

#include <CubicLawPermeability.h>

Inheritance diagram for MaterialPropertyLib::CubicLawPermeability:

Collaboration diagram for MaterialPropertyLib::CubicLawPermeability:

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 = nullptr
	Predefined 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 )

Definition at line 14 of file CubicLawPermeability.cpp.

    : _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' scale only.");
        }
    }

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 32 of file CubicLawPermeability.cpp.

{
    if (variable != Variable::fracture_aperture || _b)
    {
        return 0.0;
    }
 
    return variable_array.fracture_aperture / 6.0;
}

References _b, MaterialPropertyLib::fracture_aperture, and MaterialPropertyLib::VariableArray::fracture_aperture.

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 21 of file CubicLawPermeability.cpp.

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

References _b, and MaterialPropertyLib::VariableArray::fracture_aperture.

Member Data Documentation

_b

ParameterLib::Parameter<double> const* MaterialPropertyLib::CubicLawPermeability::_b = nullptr

private

Predefined fracture aperture.

Definition at line 69 of file CubicLawPermeability.h.

Referenced by dValue(), and value().

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

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