RegularizedBrooksCorey.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) 2008-2013 by Andreas Lauser
  Copyright (C) 2010 by Philipp Nuske

  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 REGULARIZED_BROOKS_COREY_HPP
#define REGULARIZED_BROOKS_COREY_HPP

#include "BrooksCorey.hpp"
#include "RegularizedBrooksCoreyParams.hpp"

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

namespace Opm {
template <class TraitsT, class ParamsT = RegularizedBrooksCoreyParams<TraitsT> >
class RegularizedBrooksCorey : public TraitsT
{
    typedef Opm::BrooksCorey<TraitsT, ParamsT> BrooksCorey;

public:
    typedef TraitsT Traits;
    typedef ParamsT Params;
    typedef typename Traits::Scalar Scalar;

    static const int numPhases = Traits::numPhases;
    static_assert(numPhases == 2,
                  "The regularized Brooks-Corey 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;

    static_assert(Traits::numPhases == 2,
                  "The number of fluid phases must be two if you want to use "
                  "this material law!");

    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 auto& Sw = FsToolbox::template toLhs<Evaluation>(fs.saturation(Traits::wettingPhaseIdx));
        return twoPhaseSatPcnw(params, Sw);
    }

    template <class Evaluation>
    static Evaluation twoPhaseSatPcnw(const Params &params, const Evaluation& Sw)
    {
        const Scalar Sthres = params.pcnwLowSw();

        if (Sw <= Sthres) {
            Scalar m = params.pcnwSlopeLow();
            Scalar pcnw_SwLow = params.pcnwLow();
            return pcnw_SwLow + m*(Sw - Sthres);
        }
        else if (Sw >= 1.0) {
            Scalar m = params.pcnwSlopeHigh();
            Scalar pcnw_SwHigh = params.pcnwHigh();
            return pcnw_SwHigh + m*(Sw - 1.0);
        }

        // if the effective saturation is in an 'reasonable'
        // range, we use the real Brooks-Corey law...
        return BrooksCorey::twoPhaseSatPcnw(params, Sw);
    }

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

        const 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& pcnw)
    {
        const Scalar Sthres = params.pcnwLowSw();

        // calculate the saturation which corrosponds to the
        // saturation in the non-regularized version of the
        // Brooks-Corey law. If the input capillary pressure is
        // smaller than the entry pressure, make sure that we will
        // regularize.
        Evaluation Sw = 1.5;
        if (pcnw >= params.entryPressure())
            Sw = BrooksCorey::twoPhaseSatSw(params, pcnw);

        // make sure that the capilary pressure observes a
        // derivative != 0 for 'illegal' saturations. This is
        // required for example by newton solvers (if the
        // derivative calculated numerically) in order to get the
        // saturation moving to the right direction if it
        // temporarily is in an 'illegal' range.
        if (Sw <= Sthres) {
            // invert the low saturation regularization of pcnw()
            Scalar m = params.pcnwSlopeLow();
            Scalar pcnw_SwLow = params.pcnwLow();
            return Sthres + (pcnw - pcnw_SwLow)/m;
        }
        else if (Sw > 1.0) {
            Scalar m = params.pcnwSlopeHigh();
            Scalar pcnw_SwHigh = params.pcnwHigh();
            return 1.0 + (pcnw - pcnw_SwHigh)/m;;
        }

        return BrooksCorey::twoPhaseSatSw(params, pcnw);
    }

    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& pcnw)
    { return 1 - twoPhaseSatSw(params, pcnw); }

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

        const auto& 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;

        if (Sw <= 0.0)
            return Toolbox::createConstant(0.0);
        else if (Sw >= 1.0)
            return Toolbox::createConstant(1.0);

        return BrooksCorey::twoPhaseSatKrw(params, Sw);
    }

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

        if (krw <= 0.0)
            return Toolbox::createConstant(0.0);
        else if (krw >= 1.0)
            return Toolbox::createConstant(1.0);

        return BrooksCorey::twoPhaseSatKrwInv(params, krw);
    }

    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, const Evaluation& Sw)
    {
        typedef MathToolbox<Evaluation> Toolbox;

        if (Sw >= 1.0)
            return Toolbox::createConstant(0.0);
        else if (Sw <= 0.0)
            return Toolbox::createConstant(1.0);

        return BrooksCorey::twoPhaseSatKrn(params, Sw);
    }

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

        if (krn <= 0.0)
            return Toolbox::createConstant(1.0);
        else if (krn >= 1.0)
            return Toolbox::createConstant(0.0);

        return BrooksCorey::twoPhaseSatKrnInv(params, krn);
    }
};
} // namespace Opm

#endif