RegularizedVanGenuchten.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:
/*
  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_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 {
 
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;
 
    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");
 
    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)
    {
        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);
    }
 
    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;
    }
 
    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)
    {
        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);
    }
 
    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