PengRobinsonMixture.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).

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  Consult the COPYING file in the top-level source directory of this
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*/
#ifndef OPM_PENG_ROBINSON_MIXTURE_HPP
#define OPM_PENG_ROBINSON_MIXTURE_HPP

#include "PengRobinson.hpp"

#include <opm/material/Constants.hpp>

namespace Opm {
template <class Scalar, class StaticParameters>
class PengRobinsonMixture
{
    enum { numComponents = StaticParameters::numComponents };

    // this class cannot be instantiated!
    PengRobinsonMixture() = default;

    // the ideal gas constant
    static const Scalar R;

    // the u and w parameters as given by the Peng-Robinson EOS
    static const Scalar u;
    static const Scalar w;

public:

    template <class FluidState, class Params, class LhsEval = typename FluidState::ValueType>
    static LhsEval computeFugacityCoefficient(const FluidState& fs,
                                              const Params& params,
                                              unsigned phaseIdx,
                                              unsigned compIdx)
    {
        // note that we normalize the component mole fractions, so
        // that their sum is 100%. This increases numerical stability
        // considerably if the fluid state is not physical.
        LhsEval Vm = params.molarVolume(phaseIdx);

        // Calculate b_i / b
        LhsEval bi_b = params.bPure(phaseIdx, compIdx) / params.b(phaseIdx);

        // Calculate the compressibility factor
        LhsEval RT = R*fs.temperature(phaseIdx);
        LhsEval p = fs.pressure(phaseIdx); // molar volume in [bar]
        LhsEval Z = p*Vm/RT; // compressibility factor

        // Calculate A^* and B^* (see: Reid, p. 42)
        LhsEval Astar = params.a(phaseIdx)*p/(RT*RT);
        LhsEval Bstar = params.b(phaseIdx)*p/(RT);

        LhsEval A_s = 0.0;
        for (unsigned compJIdx = 0; compJIdx < numComponents; ++compJIdx) {
            A_s += params.aCache(phaseIdx, compIdx, compJIdx) * fs.moleFraction(phaseIdx, compJIdx) * p / (RT * RT);
        }

        LhsEval alpha;
        LhsEval betta;
        LhsEval gamma;
        LhsEval ln_phi;
        LhsEval fugCoeff;

        Scalar m1;
        Scalar m2;

        m1 = 0.5*(u + std::sqrt(u*u - 4*w));
        m2 = 0.5*(u - std::sqrt(u*u - 4*w));

        alpha = -log(Z - Bstar) + bi_b * (Z - 1);
        betta = log((Z + m2 * Bstar) / (Z + m1 * Bstar)) * Astar / ((m1 - m2) * Bstar);
        gamma = (2 / Astar ) * A_s - bi_b;
        ln_phi = alpha + (betta * gamma);

        fugCoeff = exp(ln_phi);

        // limit the fugacity coefficient to a reasonable range:
        //
        // on one side, we want the mole fraction to be at
        // least 10^-3 if the fugacity is at the current pressure
        //
        fugCoeff = min(1e10, fugCoeff);
        //
        // on the other hand, if the mole fraction of the component is 100%, we want the
        // fugacity to be at least 10^-3 Pa
        //
        fugCoeff = max(1e-10, fugCoeff);

        return fugCoeff;
    }

};

template <class Scalar, class StaticParameters>
const Scalar PengRobinsonMixture<Scalar, StaticParameters>::R = Constants<Scalar>::R;
template<class Scalar, class StaticParameters>
const Scalar PengRobinsonMixture<Scalar, StaticParameters>::u = 2.0;
template<class Scalar, class StaticParameters>
const Scalar PengRobinsonMixture<Scalar, StaticParameters>::w = -1.0;

} // namespace Opm

#endif