PengRobinsonParamsMixture.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) 2011-2013 by Andreas Lauser

  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_PENG_ROBINSON_PARAMS_MIXTURE_HPP
#define OPM_PENG_ROBINSON_PARAMS_MIXTURE_HPP

#include <algorithm>
#include <opm/material/Constants.hpp>

#include "PengRobinsonParams.hpp"

namespace Opm
{

template <class Scalar, class FluidSystem, unsigned phaseIdx, bool useSpe5Relations=false>
class PengRobinsonParamsMixture
    : public PengRobinsonParams<Scalar>
{
    enum { numComponents = FluidSystem::numComponents };

    // Peng-Robinson parameters for pure substances
    typedef Opm::PengRobinsonParams<Scalar> PureParams;

    // the ideal gas constant
    static const Scalar R;

public:
    template <class FluidState>
    void updatePure(const FluidState &fluidState)
    {
        updatePure(fluidState.temperature(phaseIdx),
                   fluidState.pressure(phaseIdx));
    }

    void updatePure(Scalar temperature, Scalar pressure)
    {
        Valgrind::CheckDefined(temperature);
        Valgrind::CheckDefined(pressure);

        // Calculate the Peng-Robinson parameters of the pure
        // components
        //
        // See: R. Reid, et al.: The Properties of Gases and Liquids,
        // 4th edition, McGraw-Hill, 1987, p. 43
        for (unsigned i = 0; i < numComponents; ++i) {
            Scalar pc = FluidSystem::criticalPressure(i);
            Scalar omega = FluidSystem::acentricFactor(i);
            Scalar Tr = temperature/FluidSystem::criticalTemperature(i);
            Scalar RTc = R*FluidSystem::criticalTemperature(i);

            Scalar f_omega;

            if (useSpe5Relations) {
                if (omega < 0.49) f_omega = 0.37464  + omega*(1.54226 + omega*(-0.26992));
                else              f_omega = 0.379642 + omega*(1.48503 + omega*(-0.164423 + omega*0.016666));
            }
            else
                f_omega = 0.37464 + omega*(1.54226 - omega*0.26992);

            Valgrind::CheckDefined(f_omega);

            Scalar tmp = 1 + f_omega*(1 - std::sqrt(Tr));
            tmp = tmp*tmp;

            Scalar a = 0.4572355*RTc*RTc/pc * tmp;
            Scalar b = 0.0777961 * RTc / pc;
            assert(std::isfinite(a));
            assert(std::isfinite(b));

            this->pureParams_[i].setA(a);
            this->pureParams_[i].setB(b);
            Valgrind::CheckDefined(this->pureParams_[i].a());
            Valgrind::CheckDefined(this->pureParams_[i].b());
        }

        updateACache_();
    }

    template <class FluidState>
    void updateMix(const FluidState &fs)
    {
        Scalar sumx = 0.0;
        for (unsigned compIdx = 0; compIdx < numComponents; ++compIdx)
            sumx += fs.moleFraction(phaseIdx, compIdx);
        sumx = std::max(1e-10, sumx);

        // Calculate the Peng-Robinson parameters of the mixture
        //
        // See: R. Reid, et al.: The Properties of Gases and Liquids,
        // 4th edition, McGraw-Hill, 1987, p. 82
        Scalar a = 0;
        Scalar b = 0;
        for (unsigned compIIdx = 0; compIIdx < numComponents; ++compIIdx) {
            Scalar xi = std::max(0.0, std::min(1.0, fs.moleFraction(phaseIdx, compIIdx)));
            Valgrind::CheckDefined(xi);

            for (unsigned compJIdx = 0; compJIdx < numComponents; ++compJIdx) {
                Scalar xj = std::max(0.0, std::min(1.0, fs.moleFraction(phaseIdx, compJIdx)));
                Valgrind::CheckDefined(xj);

                // mixing rule from Reid, page 82
                a +=  xi * xj * aCache_[compIIdx][compJIdx];

                assert(std::isfinite(a));
            }

            // mixing rule from Reid, page 82
            b += std::max(0.0, xi) * this->pureParams_[compIIdx].b();
            assert(std::isfinite(b));
        }

        // assert(b > 0);
        this->setA(a);
        this->setB(b);

        Valgrind::CheckDefined(this->a());
        Valgrind::CheckDefined(this->b());

    }

    template <class FluidState>
    void updateSingleMoleFraction(const FluidState &fs,
                                  unsigned /*compIdx*/)
    {
        updateMix(fs);
    }

    const PureParams &pureParams(unsigned compIdx) const
    { return pureParams_[compIdx]; }

    const PureParams &operator[](unsigned compIdx) const
    {
        assert(0 <= compIdx && compIdx < numComponents);
        return pureParams_[compIdx];
    }

    void checkDefined() const
    {
#ifndef NDEBUG
        for (unsigned i = 0; i < numComponents; ++i)
            pureParams_[i].checkDefined();

        Valgrind::CheckDefined(this->a());
        Valgrind::CheckDefined(this->b());
#endif
    }

protected:
    PureParams pureParams_[numComponents];

private:
    void updateACache_()
    {
        for (unsigned compIIdx = 0; compIIdx < numComponents; ++ compIIdx) {
            for (unsigned compJIdx = 0; compJIdx < numComponents; ++ compJIdx) {
                // interaction coefficient as given in SPE5
                Scalar Psi = FluidSystem::interactionCoefficient(compIIdx, compJIdx);

                aCache_[compIIdx][compJIdx] =
                    std::sqrt(this->pureParams_[compIIdx].a()
                              * this->pureParams_[compJIdx].a())
                    * (1 - Psi);
            }
        }
    }

    Scalar aCache_[numComponents][numComponents];
};

template <class Scalar, class FluidSystem, unsigned phaseIdx, bool useSpe5Relations>
const Scalar PengRobinsonParamsMixture<Scalar, FluidSystem, phaseIdx, useSpe5Relations>::R = Opm::Constants<Scalar>::R;

} // namespace Opm

#endif