Mesitylene.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_MESITYLENE_HPP
#define OPM_MESITYLENE_HPP
 
#include <opm/material/IdealGas.hpp>
#include <opm/material/components/Component.hpp>
#include <opm/material/Constants.hpp>
 
#include <opm/material/common/MathToolbox.hpp>
 
namespace Opm {
template <class Scalar>
class Mesitylene : public Component<Scalar, Mesitylene<Scalar> >
{
    typedef Constants<Scalar> Consts;
 
public:
    static const char* name()
    { return "mesitylene"; }
 
    static Scalar molarMass()
    { return 0.120; }
 
    static Scalar criticalTemperature()
    { return 637.3; }
 
    static Scalar criticalPressure()
    { return 31.3e5; }
 
    static Scalar boilingTemperature()
    { return 437.9; }
 
    static Scalar tripleTemperature()
    { throw std::runtime_error("Not implemented: tripleTemperature for mesitylene"); }
 
    static Scalar triplePressure()
    { throw std::runtime_error("Not implemented: triplePressure for mesitylene"); }
 
    template <class Evaluation>
    static Evaluation vaporPressure(const Evaluation& temperature)
    {
        const Scalar A = 7.07638;
        const Scalar B = 1571.005;
        const Scalar C = 209.728;
 
        const Evaluation& T = temperature - 273.15;
 
        return 100 * 1.334 * pow(10.0, A - (B / (T + C)));
    }
 
 
    template <class Evaluation>
    static Evaluation liquidEnthalpy(const Evaluation& temperature, const Evaluation& pressure)
    {
        // Gauss quadrature rule:
        // Interval: [0K; temperature (K)]
        // Gauss-Legendre-Integration with variable transformation:
        // \int_a^b f(T) dT  \approx (b-a)/2 \sum_i=1^n \alpha_i f( (b-a)/2 x_i + (a+b)/2 )
        // with: n=2, legendre -> x_i = +/- \sqrt(1/3), \apha_i=1
        // here: a=0, b=actual temperature in Kelvin
        // \leadsto h(T) = \int_0^T c_p(T) dT
        //                 \approx 0.5 T * (cp( (0.5-0.5*\sqrt(1/3)) T) + cp((0.5+0.5*\sqrt(1/3)) T))
        //                = 0.5 T * (cp(0.2113 T) + cp(0.7887 T) )
 
        // enthalpy may have arbitrary reference state, but the empirical/fitted heatCapacity function needs Kelvin as input
        return 0.5*temperature*(liquidHeatCapacity(Evaluation(0.2113*temperature), pressure)
                                + liquidHeatCapacity(Evaluation(0.7887*temperature), pressure));
    }
 
    template <class Evaluation>
    static Evaluation heatVap(const Evaluation& temperature, const Evaluation& /*pressure*/)
    {
        Evaluation T = min(temperature, criticalTemperature()); // regularization
        T = max(T, 0.0); // regularization
 
        const Scalar T_crit = criticalTemperature();
        const Scalar Tr1 = boilingTemperature()/criticalTemperature();
        const Scalar p_crit = criticalPressure();
 
        //        Chen method, eq. 7-11.4 (at boiling)
        const Scalar DH_v_boil =
            Consts::R * T_crit * Tr1
            * (3.978 * Tr1 - 3.958 + 1.555*std::log(p_crit * 1e-5 /*Pa->bar*/ ) )
            / (1.07 - Tr1); /* [J/mol] */
 
        /* Variation with temp according to Watson relation eq 7-12.1*/
        const Evaluation& Tr2 = T/criticalTemperature();
        const Scalar n = 0.375;
        const Evaluation& DH_vap = DH_v_boil * pow(((1.0 - Tr2)/(1.0 - Tr1)), n);
 
        return (DH_vap/molarMass());          // we need [J/kg]
    }
 
 
    template <class Evaluation>
    static Evaluation gasEnthalpy(const Evaluation& temperature, const Evaluation& pressure)
    {
        return liquidEnthalpy(temperature,pressure) + heatVap(temperature, pressure);
    }
 
    template <class Evaluation>
    static Evaluation gasDensity(const Evaluation& temperature, const Evaluation& pressure)
    { return IdealGas<Scalar>::density(Evaluation(molarMass()), temperature, pressure); }
 
    template <class Evaluation>
    static Evaluation liquidDensity(const Evaluation& temperature, const Evaluation& /*pressure*/)
    { return molarLiquidDensity_(temperature)*molarMass(); }
 
    static bool gasIsCompressible()
    { return true; }
 
    static bool gasIsIdeal()
    { return true; }
 
    static bool liquidIsCompressible()
    { return false; }
 
    template <class Evaluation>
    static Evaluation gasViscosity(Evaluation temperature, const Evaluation& /*pressure*/, bool /*regularize*/=true)
    {
        temperature = min(temperature, 500.0); // regularization
        temperature = max(temperature, 250.0);
 
        // reduced temperature
        const Evaluation& Tr = temperature/criticalTemperature();
 
        Scalar Fp0 = 1.0;
        Scalar xi = 0.00474;
        const Evaluation& eta_xi =
            Fp0*(0.807*pow(Tr,0.618)
                 - 0.357*exp(-0.449*Tr)
                 + 0.34*exp(-4.058*Tr)
                 + 0.018);
 
        return eta_xi/xi/1e7; // [Pa s]
    }
 
    template <class Evaluation>
    static Evaluation liquidViscosity(Evaluation temperature, const Evaluation& /*pressure*/)
    {
        temperature = min(temperature, 500.0); // regularization
        temperature = max(temperature, 250.0);
 
        const Scalar A = -6.749;
        const Scalar B = 2010.0;
 
        return exp(A + B/temperature)*1e-3; // [Pa s]
    }
 
    template <class Evaluation>
    static Evaluation liquidHeatCapacity(const Evaluation& temperature,
                                         const Evaluation& /*pressure*/)
    {
        /* according Reid et al. : Missenard group contrib. method (s. example 5-8) */
        /* Mesitylen: C9H12  : 3* CH3 ; 1* C6H5 (phenyl-ring) ; -2* H (this was to much!) */
        /* linear interpolation between table values [J/(mol K)]*/
        Evaluation H, CH3, C6H5;
        if(temperature<298.) {
            // extrapolation for temperature < 273K
            H = 13.4 + 1.2*(temperature-273.0)/25.;       // 13.4 + 1.2 = 14.6 = H(T=298K) i.e. interpolation of table values 273<T<298
            CH3 = 40.0 + 1.6*(temperature-273.0)/25.;     // 40 + 1.6 = 41.6 = CH3(T=298K)
            C6H5 = 113.0 + 4.2*(temperature-273.0)/25.;   // 113 + 4.2 =117.2 = C6H5(T=298K)
        }
        else if((temperature>=298.0)&&(temperature<323.)){ // i.e. interpolation of table values 298<T<323
            H = 14.6 + 0.9*(temperature-298.0)/25.;
            CH3 = 41.6 + 1.9*(temperature-298.0)/25.;
            C6H5 = 117.2 + 6.2*(temperature-298.0)/25.;
        }
        else if((temperature>=323.0)&&(temperature<348.)){// i.e. interpolation of table values 323<T<348
            H = 15.5 + 1.2*(temperature-323.0)/25.;
            CH3 = 43.5 + 2.3*(temperature-323.0)/25.;
            C6H5 = 123.4 + 6.3*(temperature-323.0)/25.;
        }
        else {
            assert(temperature>=348.0);
 
            // extrapolation for temperature > 373K
            H = 16.7+2.1*(temperature-348.0)/25.; // probably  leads to underestimates
            CH3 = 45.8+2.5*(temperature-348.0)/25.;
            C6H5 = 129.7+6.3*(temperature-348.0)/25.;
        }
 
        return (C6H5 + 3*CH3 - 2*H)/molarMass(); // J/(mol K) -> J/(kg K)
    }
 
protected:
    template <class Evaluation>
    static Evaluation molarLiquidDensity_(Evaluation temperature)
    {
        temperature = min(temperature, 500.0); // regularization
        temperature = max(temperature, 250.0);
 
        const Scalar Z_RA = 0.2556; // from equation
        const Evaluation& expo = 1.0 + pow(1.0 - temperature/criticalTemperature(), 2.0/7.0);
        const Evaluation& V = Consts::R*criticalTemperature()/criticalPressure()*pow(Z_RA, expo); // liquid molar volume [cm^3/mol]
 
        return 1.0/V; // molar density [mol/m^3]
    }
 
};
 
} // namespace Opm
 
#endif