ThreePhaseParkerVanGenuchten.hpp

Go to the documentation of this file.

// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
// vi: set et ts=4 sw=4 sts=4:
/*
  This file is part of the Open Porous Media project (OPM).
 
  OPM is free software: you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation, either version 2 of the License, or
  (at your option) any later version.
 
  OPM is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.
 
  You should have received a copy of the GNU General Public License
  along with OPM.  If not, see <http://www.gnu.org/licenses/>.
 
  Consult the COPYING file in the top-level source directory of this
  module for the precise wording of the license and the list of
  copyright holders.
*/
#ifndef OPM_THREE_PHASE_PARKER_VAN_GENUCHTEN_HPP
#define OPM_THREE_PHASE_PARKER_VAN_GENUCHTEN_HPP
 
#include "ThreePhaseParkerVanGenuchtenParams.hpp"
 
#include <opm/material/common/MathToolbox.hpp>
 
#include <algorithm>
 
namespace Opm {
template <class TraitsT,
          class ParamsT = ThreePhaseParkerVanGenuchtenParams<TraitsT> >
class ThreePhaseParkerVanGenuchten
{
public:
    static_assert(TraitsT::numPhases == 3,
                  "The number of phases considered by this capillary pressure "
                  "law is always three!");
 
    typedef TraitsT Traits;
    typedef ParamsT Params;
    typedef typename Traits::Scalar Scalar;
 
    static const int numPhases = 3;
    static const int wettingPhaseIdx = Traits::wettingPhaseIdx;
    static const int nonWettingPhaseIdx = Traits::nonWettingPhaseIdx;
    static const int gasPhaseIdx = Traits::gasPhaseIdx;
 
    static const bool implementsTwoPhaseApi = false;
 
    static const bool implementsTwoPhaseSatApi = false;
 
    static const bool isSaturationDependent = true;
 
    static const bool isPressureDependent = false;
 
    static const bool isTemperatureDependent = false;
 
    static const bool isCompositionDependent = false;
 
    template <class ContainerT, class FluidState>
    static void capillaryPressures(ContainerT& values,
                                   const Params& params,
                                   const FluidState& fluidState)
    {
        typedef typename std::remove_reference<decltype(values[0])>::type Evaluation;
 
        values[gasPhaseIdx] = pcgn<FluidState, Evaluation>(params, fluidState);
        values[nonWettingPhaseIdx] = 0;
        values[wettingPhaseIdx] = - pcnw<FluidState, Evaluation>(params, fluidState);
    }
 
    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation pcgn(const Params& params, const FluidState& fluidState)
    {
        Scalar PC_VG_REG = 0.01;
 
        // sum of liquid saturations
        const auto& St =
            decay<Evaluation>(fluidState.saturation(wettingPhaseIdx))
            + decay<Evaluation>(fluidState.saturation(nonWettingPhaseIdx));
 
        Evaluation Se = (St - params.Swrx())/(1. - params.Swrx());
 
        // 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)
        {
            const Evaluation& x = pow(Se,-1/params.vgM()) - 1;
            return pow(x, 1.0 - params.vgM())/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-PC_VG_REG;
        const Evaluation& x = std::pow(Se_regu,-1/params.vgM())-1;
        const Evaluation& pc = pow(x, 1.0/params.vgN())/params.vgAlpha();
        const Evaluation& pc_prime =
            pow(x, 1/params.vgN()-1)
            * std::pow(Se_regu,-1/params.vgM()-1)
            / (-params.vgM())
            / params.vgAlpha()
            / (1 - params.Sgr() - params.Swrx())
            / params.vgN();
 
        // evaluate tangential
        return ((Se-Se_regu)*pc_prime + pc)/params.betaGN();
    }
 
    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation pcnw(const Params& params, const FluidState& fluidState)
    {
        const Evaluation& Sw =
            decay<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 = pow(Se,-1/params.vgM()) - 1.0;
            x = 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 = pow(x, 1/params.vgN())/params.vgAlpha();
        const Evaluation& pc_prime =
            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();
    }
 
    template <class ContainerT, class FluidState>
    static void saturations(ContainerT& /*values*/,
                            const Params& /*params*/,
                            const FluidState& /*fluidState*/)
    { throw std::logic_error("Not implemented: inverse capillary pressures"); }
 
    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation Sg(const Params& /*params*/, const FluidState& /*fluidState*/)
    { throw std::logic_error("Not implemented: Sg()"); }
 
    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation Sn(const Params& /*params*/, const FluidState& /*fluidState*/)
    { throw std::logic_error("Not implemented: Sn()"); }
 
    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation Sw(const Params& /*params*/, const FluidState& /*fluidState*/)
    { throw std::logic_error("Not implemented: Sw()"); }
 
    template <class ContainerT, class FluidState>
    static void relativePermeabilities(ContainerT& values,
                                       const Params& params,
                                       const FluidState& fluidState)
    {
        typedef typename std::remove_reference<decltype(values[0])>::type Evaluation;
 
        values[wettingPhaseIdx] = krw<FluidState, Evaluation>(params, fluidState);
        values[nonWettingPhaseIdx] = krn<FluidState, Evaluation>(params, fluidState);
        values[gasPhaseIdx] = krg<FluidState, Evaluation>(params, fluidState);
    }
 
    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation krw(const Params& params, const FluidState& fluidState)
    {
        const Evaluation& Sw =
            decay<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. - pow(1 - pow(Se, 1/params.vgM()), params.vgM());
        return sqrt(Se)*r*r;
    }
 
    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation krn(const Params& params, const FluidState& fluidState)
    {
        const Evaluation& Sn =
            decay<Evaluation>(fluidState.saturation(nonWettingPhaseIdx));
        const Evaluation& Sw =
            decay<Evaluation>(fluidState.saturation(wettingPhaseIdx));
        Evaluation Swe = min((Sw - params.Swr()) / (1 - params.Swr()), 1.);
        Evaluation Ste = 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_ = pow(1 - pow(Swe, 1/params.vgM()), params.vgM());
        krn_ -= pow(1 - 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 =
                max(min(Sw - params.Snr() / (1-params.Swr()), 1.0), 0.0);
            krn_ *= sqrt(resIncluded );
        }
        else
            krn_ *= sqrt(Sn / (1 - params.Swr()));
 
        return krn_;
    }
 
 
    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation krg(const Params& params, const FluidState& fluidState)
    {
        const Evaluation& Sg =
            decay<Evaluation>(fluidState.saturation(gasPhaseIdx));
        const Evaluation& Se = min(((1-Sg) - params.Sgr()) / (1 - params.Sgr()), 1.);
 
        // regularization
        if(Se > 1.0)
            return 0.0;
        if(Se < 0.0)
            return 1.0;
 
        Evaluation scaleFactor = 1.;
        if (Sg<=0.1) {
            scaleFactor = (Sg - params.Sgr())/(0.1 - params.Sgr());
            if (scaleFactor < 0.)
                return 0.0;
        }
 
        return scaleFactor
            * pow(1 - Se, 1.0/3.)
            * pow(1 - pow(Se, 1/params.vgM()), 2*params.vgM());
    }
};
} // namespace Opm
 
#endif