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Implementation of the regularized van Genuchten's capillary pressure / relative permeability <-> saturation relation. More...
#include <RegularizedVanGenuchten.hpp>
Public Types | |
typedef TraitsT | Traits |
typedef ParamsT | Params |
typedef Traits::Scalar | Scalar |
Static Public Member Functions | |
template<class Container , class FluidState > | |
static void | capillaryPressures (Container &values, const Params ¶ms, const FluidState &fs) |
Calculate the pressure difference of the phases in the most generic way. | |
template<class Container , class FluidState > | |
static void | saturations (Container &values, const Params ¶ms, const FluidState &fs) |
Calculate the saturations of the phases starting from their pressure differences. | |
template<class Container , class FluidState > | |
static void | relativePermeabilities (Container &values, const Params ¶ms, const FluidState &fs) |
Returns the relative permeabilities of the phases dependening on the phase saturations. | |
template<class FluidState , class Evaluation = typename FluidState::Scalar> | |
static Evaluation | pcnw (const Params ¶ms, const FluidState &fs) |
A regularized van Genuchten capillary pressure-saturation curve. | |
template<class Evaluation > | |
static Evaluation | twoPhaseSatPcnw (const Params ¶ms, const Evaluation &Sw) |
template<class FluidState , class Evaluation = typename FluidState::Scalar> | |
static Evaluation | Sw (const Params ¶ms, const FluidState &fs) |
A regularized van Genuchten saturation-capillary pressure curve. | |
template<class Evaluation > | |
static Evaluation | twoPhaseSatSw (const Params ¶ms, const Evaluation &pC) |
template<class FluidState , class Evaluation = typename FluidState::Scalar> | |
static Evaluation | Sn (const Params ¶ms, const FluidState &fs) |
Calculate the non-wetting phase saturations depending on the phase pressures. | |
template<class Evaluation > | |
static Evaluation | twoPhaseSatSn (const Params ¶ms, const Evaluation &pc) |
template<class FluidState , class Evaluation = typename FluidState::Scalar> | |
static Evaluation | krw (const Params ¶ms, const FluidState &fs) |
Regularized version of the relative permeability for the wetting phase of the medium implied by the van Genuchten parameterization. | |
template<class Evaluation > | |
static Evaluation | twoPhaseSatKrw (const Params ¶ms, const Evaluation &Sw) |
template<class FluidState , class Evaluation = typename FluidState::Scalar> | |
static Evaluation | krn (const Params ¶ms, const FluidState &fs) |
Regularized version of the relative permeability for the non-wetting phase of the medium implied by the van Genuchten parameterization. | |
template<class Evaluation > | |
static Evaluation | twoPhaseSatKrn (const Params ¶ms, const Evaluation &Sw) |
Implementation of the regularized van Genuchten's capillary pressure / relative permeability <-> saturation relation.
This class bundles the "raw" curves as static members and doesn't concern itself converting absolute to effective saturations and vice 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
Regularizing has the additional benefit of being numerically friendly: Newton's method does not like infinite gradients.
The implementation is accomplished as follows:
An example of the regularization of the capillary pressure curve is shown below:
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inlinestatic |
Regularized version of the relative permeability for the non-wetting phase of the medium implied by the van Genuchten parameterization.
regularized part:
for
params | The parameter object expressing the coefficients required by the van Genuchten law. |
fs | The fluid state for which the derivative ought to be calculated |
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inlinestatic |
Regularized version of the relative permeability for the wetting phase of the medium implied by the van Genuchten parameterization.
regularized part:
For not-regularized part:
params | The parameter object expressing the coefficients required by the van Genuchten law. |
fs | The fluid state for which the relative permeability ought to be calculated |
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inlinestatic |
A regularized van Genuchten capillary pressure-saturation curve.
regularized part:
For not-regularized part:
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inlinestatic |
A regularized van Genuchten saturation-capillary pressure curve.
regularized part:
The according quantities are obtained by exploiting theorem of intersecting lines.
For not-regularized part:
This is the inverse of the capillary pressure-saturation curve:
params | The parameter object expressing the coefficients required by the van Genuchten law. |
fs | The fluid state containing valid phase pressures |