SimpleHuDuanH2O.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.
 
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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.
*/
#ifndef OPM_SIMPLE_HU_DUAN_H2O_HPP
#define OPM_SIMPLE_HU_DUAN_H2O_HPP
 
#include "Component.hpp"
#include "iapws/Common.hpp"
 
 
#include <opm/material/IdealGas.hpp>
 
#include <opm/material/common/Exceptions.hpp>
#include <opm/material/common/MathToolbox.hpp>
 
#if HAVE_OPM_COMMON
#include <opm/common/OpmLog/OpmLog.hpp>
#else
#include <iostream>
#endif
 
#include <cmath>
#include <sstream>
 
namespace Opm {
 
template <class Scalar>
class SimpleHuDuanH2O : public Component<Scalar, SimpleHuDuanH2O<Scalar>>
{
    using IdealGas = ::Opm::IdealGas<Scalar>;
    using Common = IAPWS::Common<Scalar>;
 
    static constexpr Scalar R = Constants<Scalar>::R / 18e-3;  // specific gas constant of water
 
public:
    static const char* name()
    { return "H2O"; }
 
    static bool gasIsCompressible()
    { return true; }
 
    static bool liquidIsCompressible()
    { return false; }
 
    static bool gasIsIdeal()
    { return true; }
 
    static Scalar molarMass()
    { return 18e-3; }
 
    static Scalar criticalTemperature()
    { return 647.096; /* [K] */ }
 
    static Scalar criticalPressure()
    { return 22.064e6; /* [N/m^2] */ }
 
    static Scalar tripleTemperature()
    { return 273.16; /* [K] */ }
 
    static Scalar triplePressure()
    { return 611.657; /* [N/m^2] */ }
 
    template <class Evaluation>
    static Evaluation vaporPressure(const Evaluation& T)
    {
        if (T > criticalTemperature())
            return criticalPressure();
        if (T < tripleTemperature())
            return 0; // water is solid: We don't take sublimation into account
 
        static constexpr Scalar n[10] = {
            0.11670521452767e4, -0.72421316703206e6, -0.17073846940092e2,
            0.12020824702470e5, -0.32325550322333e7, 0.14915108613530e2,
            -0.48232657361591e4, 0.40511340542057e6, -0.23855557567849,
            0.65017534844798e3
        };
 
        Evaluation sigma = T + n[8]/(T - n[9]);
 
        Evaluation A = (sigma + n[0])*sigma + n[1];
        Evaluation B = (n[2]*sigma + n[3])*sigma + n[4];
        Evaluation C = (n[5]*sigma + n[6])*sigma + n[7];
 
        Evaluation tmp = 2.0*C/(sqrt(B*B - 4.0*A*C) - B);
        tmp *= tmp;
        tmp *= tmp;
 
        return 1e6*tmp;
    }
 
    template <class Evaluation>
    static Evaluation gasEnthalpy(const Evaluation& temperature,
                                  const Evaluation& /*pressure*/)
    { return 1.976e3*temperature + 40.65e3/molarMass(); }
 
 
    template <class Evaluation>
    static Evaluation gasHeatCapacity(const Evaluation&,
                                      const Evaluation&)
    { return 1.976e3; }
 
    template <class Evaluation>
    static Evaluation liquidEnthalpy(const Evaluation& temperature,
                                     const Evaluation& /*pressure*/)
    { return 4180*temperature; }
 
    template <class Evaluation>
    static Evaluation liquidHeatCapacity(const Evaluation&,
                                         const Evaluation&)
    { return 4.184e3; }
 
    template <class Evaluation>
    static Evaluation gasInternalEnergy(const Evaluation& temperature,
                                        const Evaluation& pressure)
    {
        return
            gasEnthalpy(temperature, pressure) -
            1/molarMass()* // conversion from [J/(mol K)] to [J/(kg K)]
            IdealGas::R*temperature; // = pressure *spec. volume for an ideal gas
    }
 
    template <class Evaluation>
    static Evaluation liquidInternalEnergy(const Evaluation& temperature,
                                           const Evaluation& pressure)
    {
        return
            liquidEnthalpy(temperature, pressure) -
            pressure/liquidDensity(temperature, pressure);
    }
 
    template <class Evaluation>
    static Evaluation liquidThermalConductivity(const Evaluation& /*temperature*/,
                                                const Evaluation& /*pressure*/)
    {
        return 0.578078; // conductivity of liquid water [W / (m K ) ] IAPWS evaluated at p=.1 MPa, T=8°C
    }
 
    template <class Evaluation>
    static Evaluation gasThermalConductivity(const Evaluation& /*temperature*/,
                                             const Evaluation& /*pressure*/)
    {
        return 0.028224; // conductivity of steam [W / (m K ) ] IAPWS evaluated at p=.1 MPa, T=8°C
    }
 
    template <class Evaluation>
    static Evaluation gasDensity(const Evaluation& temperature, const Evaluation& pressure)
    {
        // Assume an ideal gas
        return molarMass()*IdealGas::molarDensity(temperature, pressure);
    }
 
    template <class Evaluation>
    static Evaluation gasPressure(const Evaluation& temperature, const Evaluation& density)
    {
        // Assume an ideal gas
        return IdealGas::pressure(temperature, density/molarMass());
    }
 
    template <class Evaluation>
    static Evaluation liquidDensity(const Evaluation& temperature, const Evaluation& pressure,
                                    bool extrapolate)
    {
        return liquidDensity_(temperature, pressure, extrapolate);
    }
 
    template <class Evaluation>
    static Evaluation liquidPressure(const Evaluation& /*temperature*/, const Evaluation& /*density*/)
    {
        throw std::logic_error("The liquid pressure is undefined for incompressible fluids");
    }
 
    template <class Evaluation>
    static Evaluation gasViscosity(const Evaluation& /*temperature*/,
                                   const Evaluation& /*pressure*/)
    {
        return 1e-05;
    }
 
    template <class Evaluation>
    static Evaluation liquidViscosity(const Evaluation& temperature, const Evaluation& pressure,
                                      bool extrapolate)
    {
        if (temperature > 570) {
            std::ostringstream oss;
            oss << "Viscosity of water based on Hu et al is too different from IAPWS for T above 570K and "
                << "(T = " << temperature << ")";
            if(extrapolate)
            {
#if HAVE_OPM_COMMON
                OpmLog::warning(oss.str());
#else
                std::cerr << "warning: "<< oss.str() <<std::endl;
#endif
            }
            else
                throw NumericalIssue(oss.str());
        }
 
        const Evaluation rho = liquidDensity(temperature, pressure, extrapolate);
        return Common::viscosity(temperature, rho);
    }
 
private:
 
    template <class Evaluation>
    static Evaluation liquidDensity_(const Evaluation& T, const Evaluation& pressure, bool extrapolate) {
        // Hu, Duan, Zhu and Chou: PVTx properties of the CO2-H2O and CO2-H2O-NaCl
        // systems below 647 K: Assessment of experimental data and
        // thermodynamics models, Chemical Geology, 2007.
        if (T > 647 || pressure > 100e6) {
            std::ostringstream oss;
            oss << "Density of water is only implemented for temperatures below 647K and "
                << "pressures below 100MPa. (T = " << T << ", p=" << pressure;
            if(extrapolate)
            {
#if HAVE_OPM_COMMON
                OpmLog::warning(oss.str());
#else
                std::cerr << "warning: "<< oss.str() <<std::endl;
#endif
            }
            else
                throw NumericalIssue(oss.str());
        }
 
        Evaluation p = pressure / 1e6; // to MPa
        Scalar Mw = molarMass() * 1e3; //kg/kmol
 
        static constexpr Scalar k0[5] = { 3.27225e-07, -4.20950e-04, 2.32594e-01, -4.16920e+01, 5.71292e+03 };
        static constexpr Scalar k1[5] = { -2.32306e-10, 2.91138e-07, -1.49662e-04, 3.59860e-02, -3.55071 };
        static constexpr Scalar k2[3] = { 2.57241e-14, -1.24336e-11, 5.42707e-07 };
        static constexpr Scalar k3[3] = { -4.42028e-18, 2.10007e-15, -8.11491e-11 };
        Evaluation k0_eval = 1e-3 * (((k0[0]*T + k0[1])*T + k0[2])*T + k0[3] + k0[4]/T);
        Evaluation k1_eval = 1e-2 * (((k1[0]*T + k1[1])*T + k1[2])*T + k1[3] + k1[4]/T);
        Evaluation k2_eval = 1e-1 * ((k2[0]*T + k2[1])*T*T + k2[2]);
        Evaluation k3_eval = (k3[0]*T + k3[1])*T*T + k3[2];
 
        // molar volum (m³/kmol):
        Evaluation vw = ((k3_eval*p + k2_eval)*p + k1_eval)*p + k0_eval;
 
        // density kg/m3
        return Mw / vw;
 
    }
 
};
 
} // namespace Opm
 
#endif