opm-common/opm/material/fluidmatrixinteractions/RegularizedVanGenuchten.hpp

// -*- 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.

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  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.

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  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.
*/
/*!
 * \file
 * \copydoc Opm::RegularizedVanGenuchten
 */
#ifndef OPM_REGULARIZED_VAN_GENUCHTEN_HPP
#define OPM_REGULARIZED_VAN_GENUCHTEN_HPP

#include "VanGenuchten.hpp"
#include "RegularizedVanGenuchtenParams.hpp"

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

#include <algorithm>

namespace Opm {

/*!
 * \ingroup FluidMatrixInteractions
 * \brief 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 \f$p_c\f$ which is completely
 * unphysical. In case of very high wetting phase saturations the
 * difference between regularized and "pure" material law is not big.
 *
 * Regularizing has the additional benefit of being numerically
 * friendly: Newton's method does not like infinite gradients.
 *
 * The implementation is accomplished as follows:
 * - check whether we are in the range of regularization
 *  - yes: use the regularization
 *  - no: forward to the standard material law.
 *
 * An example of the regularization of the capillary pressure curve is
 * shown below: \image html regularizedVanGenuchten.png
 *
 * \see VanGenuchten
 */
template <class TraitsT, class ParamsT = RegularizedVanGenuchtenParams<TraitsT> >
class RegularizedVanGenuchten : public TraitsT
{
    typedef ::Opm::VanGenuchten<TraitsT, ParamsT> VanGenuchten;

public:
    typedef TraitsT Traits;
    typedef ParamsT Params;

    typedef typename Traits::Scalar Scalar;

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

    //! Specify whether this material law implements the two-phase
    //! convenience API
    static const bool implementsTwoPhaseApi = true;

    //! Specify whether this material law implements the two-phase
    //! convenience API which only depends on the phase saturations
    static const bool implementsTwoPhaseSatApi = true;

    //! Specify whether the quantities defined by this material law
    //! are saturation dependent
    static const bool isSaturationDependent = true;

    //! Specify whether the quantities defined by this material law
    //! are dependent on the absolute pressure
    static const bool isPressureDependent = false;

    //! Specify whether the quantities defined by this material law
    //! are temperature dependent
    static const bool isTemperatureDependent = false;

    //! Specify whether the quantities defined by this material law
    //! are dependent on the phase composition
    static const bool isCompositionDependent = false;

    /*!
     * \brief Calculate the pressure difference of the phases in the
     *        most generic way.
     */
    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);
    }

    /*!
     * \brief Calculate the saturations of the phases starting from
     *        their pressure differences.
     */
    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];
    }

    /*!
     * \brief Returns the relative permeabilities of the phases
     *        dependening on the phase saturations.
     */
    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);
    }

    /*!
     * \brief A regularized van Genuchten capillary pressure-saturation
     *          curve.
     *
     * regularized part:
     *    - low saturation:  extend the \f$p_c(S_w)\f$ curve with the slope at the regularization point (i.e. no kink).
     *    - high saturation: connect the high regularization point with \f$ \overline S_w =1\f$ by a straight line (yes, there is a kink :-( ).
     *
     *  For not-regularized part:
     *
     * \copydetails VanGenuchten::pC()
     */
    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation pcnw(const Params& params, const FluidState& fs)
    {
        const auto& Sw = decay<Evaluation>(fs.saturation(Traits::wettingPhaseIdx));
        return twoPhaseSatPcnw(params, Sw);
    }

    template <class Evaluation>
    static Evaluation twoPhaseSatPcnw(const Params& params, const Evaluation& Sw)
    {
        // retrieve the low and the high threshold saturations for the
        // unregularized capillary pressure curve from the parameters
        const Scalar SwThLow = params.pcnwLowSw();
        const Scalar SwThHigh = params.pcnwHighSw();

        // make sure that the capillary pressure observes a derivative
        // != 0 for 'illegal' saturations. This is favourable for the
        // newton solver (if the derivative is calculated numerically)
        // in order to get the saturation moving to the right
        // direction if it temporarily is in an 'illegal' range.
        if (Sw < SwThLow) {
            return params.pcnwLow() + params.pcnwSlopeLow()*(Sw - SwThLow);
        }
        else if (Sw > SwThHigh)
        {
            Scalar yTh = params.pcnwHigh();
            Scalar m1 = (0.0 - yTh)/(1.0 - SwThHigh)*2;

            if (Sw < 1.0) {
                // use spline between threshold Sw and 1.0
                const Spline<Scalar>& sp = params.pcnwHighSpline();

                return sp.eval(Sw);
            }
            else {
                // straight line for Sw > 1.0
                return m1*(Sw - 1.0) + 0.0;
            }
        }

        // if the effective saturation is in an 'reasonable'
        // range, we use the real van genuchten law...
        return VanGenuchten::twoPhaseSatPcnw(params, Sw);
    }

    /*!
     * \brief   A regularized van Genuchten saturation-capillary pressure curve.
     *
     * regularized part:
     *    - low saturation:  extend the \f$p_c(S_w)\f$ curve with the slope at the regularization point (i.e. no kink).
     *    - high saturation: connect the high regularization point with \f$ \overline S_w =1\f$ by a straight line (yes, there is a kink :-( ).
     *
     *  The according quantities are obtained by exploiting theorem of intersecting lines.
     *
     *  For not-regularized part:
     *
         \copydetails VanGenuchten::Sw()
     *
     */
    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation Sw(const Params& params, const FluidState& fs)
    {
        const Evaluation& pC =
            decay<Evaluation>(fs.pressure(Traits::nonWettingPhaseIdx))
            - decay<Evaluation>(fs.pressure(Traits::wettingPhaseIdx));
        return twoPhaseSatSw(params, pC);
    }

    template <class Evaluation>
    static Evaluation twoPhaseSatSw(const Params& params, const Evaluation& pC)
    {
        // retrieve the low and the high threshold saturations for the
        // unregularized capillary pressure curve from the parameters
        const Scalar SwThLow = params.pcnwLowSw();
        const Scalar SwThHigh = params.pcnwHighSw();

        // calculate the saturation which corrosponds to the
        // saturation in the non-regularized verision of van
        // Genuchten's law
        if (pC <= 0) {
            // invert straight line for Sw > 1.0
            Scalar m1 = params.pcnwSlopeHigh();
            return pC/m1 + 1.0;
        }

        Evaluation Sw = VanGenuchten::twoPhaseSatSw(params, pC);

        // invert the regularization if necessary
        if (Sw <= SwThLow) {
            // invert the low saturation regularization of pC()
            Scalar pC_SwLow = VanGenuchten::twoPhaseSatPcnw(params, SwThLow);
            return (pC - pC_SwLow)/params.pcnwSlopeLow() + SwThLow;
        }
        else if (SwThHigh < Sw /* && Sw < 1.0*/)
        {
            // invert spline between threshold saturation and 1.0
            const Spline<Scalar>& spline = params.pcnwHighSpline();

            return spline.template intersectInterval<Evaluation>(/*x0=*/SwThHigh, /*x1=*/1.0,
                                                                 /*a=*/0, /*b=*/0, /*c=*/0, /*d=*/pC);
        }

        return Sw;
    }

    /*!
     * \brief Calculate the non-wetting phase saturations depending on
     *        the phase pressures.
     */
    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); }

    /*!
     * \brief   Regularized version of the  relative permeability
     *          for the wetting phase of
     *          the medium implied by the van Genuchten
     *          parameterization.
     *
     *  regularized part:
     *    - below \f$ \overline S_w =0\f$:                  set relative permeability to zero
     *    - above \f$ \overline S_w =1\f$:                  set relative permeability to one
     *    - between \f$ 0.95 \leq \overline S_w \leq 1\f$:  use a spline as interpolation
     *
     *  For not-regularized part:
        \copydetails VanGenuchten::krw()
     */
    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation krw(const Params& params, const FluidState& fs)
    {
        const auto& Sw = decay<Evaluation>(fs.saturation(Traits::wettingPhaseIdx));
        return twoPhaseSatKrw(params, Sw);
    }

    template <class Evaluation>
    static Evaluation twoPhaseSatKrw(const Params& params, const Evaluation& Sw)
    {
        // regularize
        if (Sw <= 0)
            return 0.0;
        else if (Sw >= 1)
            return 1.0;

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

    /*!
     * \brief   Regularized version of the  relative permeability
     *          for the non-wetting phase of
     *          the medium implied by the van Genuchten
     *          parameterization.
     *
     * regularized part:
     *    - below \f$ \overline S_w =0\f$:                  set relative permeability to zero
     *    - above \f$ \overline S_w =1\f$:                  set relative permeability to one
     *    - for \f$ 0 \leq \overline S_w \leq 0.05 \f$:     use a spline as interpolation
     *
         \copydetails VanGenuchten::krn()
     *
     */
    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation krn(const Params& params, const FluidState& fs)
    {
        const Evaluation& Sw =
            1.0 - decay<Evaluation>(fs.saturation(Traits::nonWettingPhaseIdx));
        return twoPhaseSatKrn(params, Sw);
    }

    template <class Evaluation>
    static Evaluation twoPhaseSatKrn(const Params& params, const Evaluation& Sw)
    {
        // regularize
        if (Sw <= 0)
            return 1.0;
        else if (Sw >= 1)
            return 0.0;

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

} // namespace Opm

#endif