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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).
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_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::Scalar>
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
Constants.hpp
A central place for various physical constants occuring in some equations.
PengRobinson.hpp
Implements the Peng-Robinson equation of state for liquids and gases.
Opm::Constants::R
static const Scalar R
The ideal gas constant [J/(mol K)].
Definition Constants.hpp:45
Opm::PengRobinsonMixture
Implements the Peng-Robinson equation of state for a mixture.
Definition PengRobinsonMixture.hpp:41
Opm::PengRobinsonMixture::computeFugacityCoefficient
static LhsEval computeFugacityCoefficient(const FluidState &fs, const Params &params, unsigned phaseIdx, unsigned compIdx)
Returns the fugacity coefficient of an individual component in the phase.
Definition PengRobinsonMixture.hpp:74
Opm
This class implements a small container which holds the transmissibility mulitpliers for all the face...
Definition Exceptions.hpp:30