static Evaluation krw(const Params ¶ms, const FluidState &fluidState)
{
typedef MathToolbox<typename FluidState::Scalar> FsToolbox;
typedef MathToolbox<Evaluation> Toolbox;
const Evaluation& Sw =
FsToolbox::template toLhs<Evaluation>(fluidState.saturation(wettingPhaseIdx));
// transformation to effective saturation
const Evaluation& Se = (Sw - params.Swr()) / (1-params.Swr());
// regularization
if(Se > 1.0) return 1.;
if(Se < 0.0) return 0.;
const Evaluation& r = 1. - Toolbox::pow(1 - Toolbox::pow(Se, 1/params.vgM()), params.vgM());
return Toolbox::sqrt(Se)*r*r;
}
static Evaluation pcnw(const Params ¶ms, const FluidState &fluidState)
{
typedef MathToolbox<typename FluidState::Scalar> FsToolbox;
typedef MathToolbox<Evaluation> Toolbox;
const Evaluation& Sw =
FsToolbox::template toLhs<Evaluation>(fluidState.saturation(wettingPhaseIdx));
Evaluation Se = (Sw-params.Swr())/(1.-params.Snr());
Scalar PC_VG_REG = 0.01;
// regularization
if (Se<0.0)
Se=0.0;
if (Se>1.0)
Se=1.0;
if (Se>PC_VG_REG && Se<1-PC_VG_REG) {
Evaluation x = Toolbox::pow(Se,-1/params.vgM()) - 1.0;
x = Toolbox::pow(x, 1 - params.vgM());
return x/params.vgAlpha();
}
// value and derivative at regularization point
Scalar Se_regu;
if (Se<=PC_VG_REG)
Se_regu = PC_VG_REG;
else
Se_regu = 1.0 - PC_VG_REG;
const Evaluation& x = std::pow(Se_regu,-1/params.vgM())-1;
const Evaluation& pc = Toolbox::pow(x, 1/params.vgN())/params.vgAlpha();
const Evaluation& pc_prime =
Toolbox::pow(x,1/params.vgN()-1)
* std::pow(Se_regu, -1.0/params.vgM() - 1)
/ (-params.vgM())
/ params.vgAlpha()
/ (1-params.Snr()-params.Swr())
/ params.vgN();
// evaluate tangential
return ((Se-Se_regu)*pc_prime + pc)/params.betaNW();
}
static Evaluation krn(const Params ¶ms, const FluidState &fluidState)
{
typedef MathToolbox<typename FluidState::Scalar> FsToolbox;
typedef MathToolbox<Evaluation> Toolbox;
const Evaluation& Sn =
FsToolbox::template toLhs<Evaluation>(fluidState.saturation(nonWettingPhaseIdx));
const Evaluation& Sw =
FsToolbox::template toLhs<Evaluation>(fluidState.saturation(wettingPhaseIdx));
Evaluation Swe = Toolbox::min((Sw - params.Swr()) / (1 - params.Swr()), 1.);
Evaluation Ste = Toolbox::min((Sw + Sn - params.Swr()) / (1 - params.Swr()), 1.);
// regularization
if(Swe <= 0.0) Swe = 0.;
if(Ste <= 0.0) Ste = 0.;
if(Ste - Swe <= 0.0) return 0.;
Evaluation krn_;
krn_ = Toolbox::pow(1 - Toolbox::pow(Swe, 1/params.vgM()), params.vgM());
krn_ -= Toolbox::pow(1 - Toolbox::pow(Ste, 1/params.vgM()), params.vgM());
krn_ *= krn_;
if (params.krRegardsSnr())
{
// regard Snr in the permeability of the non-wetting
// phase, see Helmig1997
const Evaluation& resIncluded =
Toolbox::max(Toolbox::min(Sw - params.Snr() / (1-params.Swr()), 1.0), 0.0);
krn_ *= Toolbox::sqrt(resIncluded );
}
else
krn_ *= Toolbox::sqrt(Sn / (1 - params.Swr()));
return krn_;
}
