Implementation of the regularized van Genuchten's capillary pressure <-> saturation relation. This class bundles the "raw" curves as static members and doesn't concern itself converting absolute to effective saturations and vince versa. More...

#include <dumux/material/fluidmatrixinteractions/3p/regularizedparkervangen3p.hh>

Description

template<class ScalarT, class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>
class Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >

Implementation of the regularized van Genuchten's capillary pressure <-> saturation relation. This class bundles the "raw" curves as static members and doesn't concern itself converting absolute to effective saturations and vince versa.

In order to avoid very steep gradients the marginal values are "regularized". This means that in stead of following the curve of the material law in these regions, some linear approximation is used. Doing this is not worse than following the material law. E.g. for very low wetting phase values the material laws predict infinite values for \(\mathrm{p_c}\) which is completely unphysical. In case of very high wetting phase saturations the difference between regularized and "pure" material law is not big.

Regularizing has the additional benefit of being numerically friendly: Newton's method does not like infinite gradients.

The implementation is accomplished as follows:

check whether we are in the range of regularization
- yes: use the regularization
- no: forward to the standard material law.
For an example figure of the regularization: RegularizedVanGenuchten

See also: BrooksCorey

Public Types
using	Params = ParamsT

using	Scalar = typename Params::Scalar

Static Public Member Functions
static Scalar	pc (const Params &params, Scalar sw)
	A regularized Parker- van Genuchten capillary pressure-saturation curve. More...

static Scalar	pcgw (const Params &params, Scalar swe)
	The capillary pressure-saturation curve for the gas and wetting phase. More...

static Scalar	pcnw (const Params &params, Scalar swe)
	The capillary pressure-saturation curve for the non-wettigng and wetting phase. More...

static Scalar	pcgn (const Params &params, Scalar ste)
	The capillary pressure-saturation curve for the gas and nonwetting phase. More...

static Scalar	pcAlpha (const Params &params, Scalar sne)
	This function ensures a continuous transition from 2 to 3 phases and vice versa. More...

static Scalar	sw (const Params &params, Scalar pc)
	The saturation-capillary pressure curve. More...

static Scalar	dpc_dswe (const Params &params, Scalar swe)
	Returns the partial derivative of the capillary pressure to the effective saturation. More...

static Scalar	dswe_dpc (const Params &params, Scalar pc)
	Returns the partial derivative of the effective saturation to the capillary pressure. More...

static Scalar	krw (const Params &params, const Scalar swe)
	The relative permeability for the wetting phase of the medium implied by van Genuchten's parameterization. More...

static Scalar	krn (const Params &params, Scalar swe, Scalar sn, Scalar ste)
	The relative permeability for the nonwetting phase after the Model of Parker et al. (1987). More...

static Scalar	krg (const Params &params, const Scalar ste)
	The relative permeability for the nonwetting phase of the medium implied by van Genuchten's parameterization. More...

static Scalar	kr (const Params &params, const int phaseIdx, const Scalar swe, const Scalar sn, const Scalar ste)
	The relative permeability for a phase. More...

static Scalar	bulkDensTimesAdsorpCoeff (const Params &params)
	the basis for calculating adsorbed NAPL in storage term More...

Member Typedef Documentation

◆ Params

template<class ScalarT , class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>

using Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >::Params = ParamsT

◆ Scalar

template<class ScalarT , class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>

using Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >::Scalar = typename Params::Scalar

Member Function Documentation

◆ bulkDensTimesAdsorpCoeff()

template<class ScalarT , class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>

static Scalar Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >::bulkDensTimesAdsorpCoeff ( const Params & params )

inlinestatic

the basis for calculating adsorbed NAPL in storage term

Parameters

params Array of parameters

◆ dpc_dswe()

template<class ScalarT , class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>

static Scalar Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >::dpc_dswe	(	const Params &	params,
		Scalar	swe
	)

inlinestatic

Returns the partial derivative of the capillary pressure to the effective saturation.

Parameters

params	Array of parameters
swe	Effective wetting liquid saturation

◆ dswe_dpc()

template<class ScalarT , class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>

static Scalar Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >::dswe_dpc	(	const Params &	params,
		Scalar	pc
	)

inlinestatic

Returns the partial derivative of the effective saturation to the capillary pressure.

Parameters

params	Array of parameters
pc	Capillary pressure in \(\mathrm{[Pa]}\)

◆ kr()

template<class ScalarT , class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>

static Scalar Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >::kr	(	const Params &	params,
		const int	phaseIdx,
		const Scalar	swe,
		const Scalar	sn,
		const Scalar	ste
	)

inlinestatic

The relative permeability for a phase.

Parameters

params	Array of parameters.
phaseIdx	Indicator, The saturation of all phases.
swe	Effective wetting phase saturation
sn	Absolute nonwetting liquid saturation
ste	Effective total liquid (wetting + nonwetting) saturation

◆ krg()

template<class ScalarT , class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>

static Scalar Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >::krg	(	const Params &	params,
		const Scalar	ste
	)

inlinestatic

The relative permeability for the nonwetting phase of the medium implied by van Genuchten's parameterization.

The permeability of gas in a 3p system equals the standard 2p description. (see p61. in "Comparison of the Three-Phase Oil Relative Permeability Models" MOJDEH DELSHAD and GARY A. POPE, Transport in Porous Media 4 (1989), 59-83.)

Parameters

params	Array of parameters.
ste	Effective total liquid (wetting + nonwetting) saturation

◆ krn()

template<class ScalarT , class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>

static Scalar Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >::krn	(	const Params &	params,
		Scalar	swe,
		Scalar	sn,
		Scalar	ste
	)

inlinestatic

The relative permeability for the nonwetting phase after the Model of Parker et al. (1987).

See model 7 in "Comparison of the Three-Phase Oil Relative Permeability Models" MOJDEH DELSHAD and GARY A. POPE, Transport in Porous Media 4 (1989), 59-83. or more comprehensive in "Estimation of primary drainage three-phase relative permeability for organic liquid transport in the vadose zone", Leonardo I. Oliveira, Avery H. Demond, Journal of Contaminant Hydrology 66 (2003), 261-285

Parameters

params	Array of parameters.
swe	Effective wetting phase saturation
sn	Absolute nonwetting liquid saturation
ste	Effective total liquid (wetting + nonwetting) saturation

◆ krw()

template<class ScalarT , class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>

static Scalar Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >::krw	(	const Params &	params,
		const Scalar	swe
	)

inlinestatic

The relative permeability for the wetting phase of the medium implied by van Genuchten's parameterization.

The permeability of water in a 3p system equals the standard 2p description. (see p61. in "Comparison of the Three-Phase Oil Relative Permeability Models" MOJDEH DELSHAD and GARY A. POPE, Transport in Porous Media 4 (1989), 59-83.)

Parameters

params	Array of parameters.
swe	Effective wetting phase saturation

◆ pc()

template<class ScalarT , class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>

static Scalar Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >::pc	(	const Params &	params,
		Scalar	sw
	)

inlinestatic

A regularized Parker- van Genuchten capillary pressure-saturation curve.

regularized part:

low saturation: extend the \(\mathrm{p_c(S_w)}\) curve with the slope at the regularization point (i.e. no kink).
high saturation: connect the high regularization point with \(\mathrm{\overline{S}_w =1}\) by a straight line (yes, there is a kink :-( ).

For the non-regularized part:

Parameters

params	Array of parameters
sw	wetting phase saturation

◆ pcAlpha()

template<class ScalarT , class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>

static Scalar Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >::pcAlpha	(	const Params &	params,
		Scalar	sne
	)

inlinestatic

This function ensures a continuous transition from 2 to 3 phases and vice versa.

Parameters

params	Array of parameters
sne	Effective nonwetting liquid saturation

◆ pcgn()

template<class ScalarT , class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>

static Scalar Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >::pcgn	(	const Params &	params,
		Scalar	ste
	)

inlinestatic

The capillary pressure-saturation curve for the gas and nonwetting phase.

Parameters

params	Array of parameters
ste	Effective total liquid (wetting + nonwetting) saturation

◆ pcgw()

template<class ScalarT , class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>

static Scalar Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >::pcgw	(	const Params &	params,
		Scalar	swe
	)

inlinestatic

The capillary pressure-saturation curve for the gas and wetting phase.

Parameters

params	Array of parameters
swe	Effective wetting phase saturation

◆ pcnw()

template<class ScalarT , class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>

static Scalar Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >::pcnw	(	const Params &	params,
		Scalar	swe
	)

inlinestatic

The capillary pressure-saturation curve for the non-wettigng and wetting phase.

Parameters

params	Array of parameters
swe	Effective wetting phase saturation

◆ sw()

template<class ScalarT , class ParamsT = RegularizedParkerVanGen3PParams<ScalarT>>

static Scalar Dumux::RegularizedParkerVanGen3P< ScalarT, ParamsT >::sw	(	const Params &	params,
		Scalar	pc
	)

inlinestatic

The saturation-capillary pressure curve.

Parameters

params	Array of parameters
pc	Capillary pressure in \(\mathrm{[Pa]}\)

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

regularizedparkervangen3p.hh

Description

Public Types

Static Public Member Functions

Member Typedef Documentation

◆ Params

◆ Scalar

Member Function Documentation

◆ bulkDensTimesAdsorpCoeff()

◆ dpc_dswe()

◆ dswe_dpc()

◆ kr()

◆ krg()

◆ krn()

◆ krw()

◆ pc()

◆ pcAlpha()

◆ pcgn()

◆ pcgw()

◆ pcnw()

◆ sw()