VanGenuchten.hpp

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// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
// vi: set et ts=4 sw=4 sts=4:
/*
  Copyright (C) 2009-2013 by Andreas Lauser
  Copyright (C) 2010 by Bernd Flemisch

  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/>.
*/
#ifndef OPM_VAN_GENUCHTEN_HPP
#define OPM_VAN_GENUCHTEN_HPP

#include "VanGenuchtenParams.hpp"

#include <opm/material/common/MathToolbox.hpp>

#include <algorithm>
#include <cmath>
#include <cassert>

namespace Opm {
template <class TraitsT, class ParamsT = VanGenuchtenParams<TraitsT> >
class VanGenuchten : public TraitsT
{
public:
    typedef TraitsT Traits;

    typedef ParamsT Params;

    typedef typename Traits::Scalar Scalar;

    static const int numPhases = Traits::numPhases;
    static_assert(numPhases == 2,
                  "The van Genuchten capillary pressure law only "
                  "applies to the case of two fluid phases");

    static const bool implementsTwoPhaseApi = true;

    static const bool implementsTwoPhaseSatApi = true;

    static const bool isSaturationDependent = true;

    static const bool isPressureDependent = false;

    static const bool isTemperatureDependent = false;

    static const bool isCompositionDependent = false;

    template <class Container, class FluidState>
    static void capillaryPressures(Container &values, const Params &params, const FluidState &fs)
    {
        typedef typename std::remove_reference<decltype(values[0])>::type Evaluation;

        values[Traits::wettingPhaseIdx] = 0.0; // reference phase
        values[Traits::nonWettingPhaseIdx] = pcnw<FluidState, Evaluation>(params, fs);
    }

    template <class Container, class FluidState>
    static void saturations(Container &values, const Params &params, const FluidState &fs)
    {
        typedef typename std::remove_reference<decltype(values[0])>::type Evaluation;

        values[Traits::wettingPhaseIdx] = Sw<FluidState, Evaluation>(params, fs);
        values[Traits::nonWettingPhaseIdx] = 1 - values[Traits::wettingPhaseIdx];
    }

    template <class Container, class FluidState>
    static void relativePermeabilities(Container &values, const Params &params, const FluidState &fs)
    {
        typedef typename std::remove_reference<decltype(values[0])>::type Evaluation;

        values[Traits::wettingPhaseIdx] = krw<FluidState, Evaluation>(params, fs);
        values[Traits::nonWettingPhaseIdx] = krn<FluidState, Evaluation>(params, fs);
    }

    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation pcnw(const Params &params, const FluidState &fs)
    {
        typedef MathToolbox<typename FluidState::Scalar> FsToolbox;

        const Evaluation& Sw =
            FsToolbox::template toLhs<Evaluation>(fs.saturation(Traits::wettingPhaseIdx));

        assert(0 <= Sw && Sw <= 1);

        return twoPhaseSatPcnw(params, Sw);
    }

    template <class Evaluation>
    static Evaluation twoPhaseSatPcnw(const Params &params, const Evaluation& Sw)
    {
        typedef MathToolbox<Evaluation> Toolbox;

        return Toolbox::pow(Toolbox::pow(Sw, -1.0/params.vgM()) - 1, 1.0/params.vgN())/params.vgAlpha();
    }

    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation Sw(const Params &params, const FluidState &fs)
    {
        typedef MathToolbox<typename FluidState::Scalar> FsToolbox;

        Evaluation pC =
            FsToolbox::template toLhs<Evaluation>(fs.pressure(Traits::nonWettingPhaseIdx))
            - FsToolbox::template toLhs<Evaluation>(fs.pressure(Traits::wettingPhaseIdx));
        return twoPhaseSatSw(params, pC);
    }

    template <class Evaluation>
    static Evaluation twoPhaseSatSw(const Params &params, const Evaluation& pC)
    {
        typedef MathToolbox<Evaluation> Toolbox;

        assert(pC >= 0);

        return Toolbox::pow(Toolbox::pow(params.vgAlpha()*pC, params.vgN()) + 1, -params.vgM());
    }

    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation Sn(const Params &params, const FluidState &fs)
    { return 1 - Sw<FluidState, Evaluation>(params, fs); }

    template <class Evaluation>
    static Evaluation twoPhaseSatSn(const Params &params, const Evaluation& pC)
    { return 1 - twoPhaseSatSw(params, pC); }

    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation krw(const Params &params, const FluidState &fs)
    {
        typedef MathToolbox<typename FluidState::Scalar> FsToolbox;

        const Evaluation& Sw =
            FsToolbox::template toLhs<Evaluation>(fs.saturation(Traits::wettingPhaseIdx));

        return twoPhaseSatKrw(params, Sw);
    }

    template <class Evaluation>
    static Evaluation twoPhaseSatKrw(const Params &params, const Evaluation& Sw)
    {
        typedef MathToolbox<Evaluation> Toolbox;

        assert(0.0 <= Sw && Sw <= 1.0);

        Evaluation r = 1.0 - Toolbox::pow(1.0 - Toolbox::pow(Sw, 1/params.vgM()), params.vgM());
        return Toolbox::sqrt(Sw)*r*r;
    }

    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation krn(const Params &params, const FluidState &fs)
    {
        typedef MathToolbox<typename FluidState::Scalar> FsToolbox;

        const Evaluation& Sw =
            1.0 - FsToolbox::template toLhs<Evaluation>(fs.saturation(Traits::nonWettingPhaseIdx));

        return twoPhaseSatKrn(params, Sw);
    }

    template <class Evaluation>
    static Evaluation twoPhaseSatKrn(const Params &params, Evaluation Sw)
    {
        typedef MathToolbox<Evaluation> Toolbox;

        assert(0 <= Sw && Sw <= 1);

        return
            Toolbox::pow(1 - Sw, 1.0/3) *
            Toolbox::pow(1 - Toolbox::pow(Sw, 1/params.vgM()), 2*params.vgM());
    }
};
} // namespace Opm

#endif