mesitylene.hh

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#ifndef DUMUX_MESITYLENE_HH
#define DUMUX_MESITYLENE_HH
 
#include <dumux/material/idealgas.hh>
#include <dumux/material/constants.hh>
 
#include <dumux/material/components/base.hh>
#include <dumux/material/components/liquid.hh>
#include <dumux/material/components/gas.hh>
 
namespace Dumux {
namespace Components {

template <class Scalar>
class Mesitylene
: public Components::Base<Scalar, Mesitylene<Scalar> >
, public Components::Liquid<Scalar, Mesitylene<Scalar> >
, public Components::Gas<Scalar, Mesitylene<Scalar> >
{
    using Consts = Constants<Scalar>;
    using IdealGas = Dumux::IdealGas<Scalar>;
public:
    static std::string name()
    { return "mesitylene"; }

    constexpr static Scalar molarMass()
    { return 0.120; }

    constexpr static Scalar criticalTemperature()
    { return 637.3; }

    constexpr static Scalar criticalPressure()
    { return 31.3e5; }

    constexpr static Scalar boilingTemperature()
    { return 437.9; }

    static Scalar tripleTemperature()
    {
        DUNE_THROW(Dune::NotImplemented, "tripleTemperature for mesitylene");
    }

    static Scalar triplePressure()
    {
        DUNE_THROW(Dune::NotImplemented, "triplePressure for mesitylene");
    }

    static Scalar vaporPressure(Scalar temperature)
    {
        const Scalar A = 7.07638;
        const Scalar B = 1571.005;
        const Scalar C = 209.728;
 
        const Scalar T = temperature - 273.15;
 
        using std::pow;
        return 100 * 1.334 * pow(Scalar(10.0), Scalar(A - (B / (T + C))));
    }
 

    static Scalar liquidEnthalpy(const Scalar temperature,
                                 const Scalar 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=273.15K, b=actual temperature in Kelvin
        // \leadsto h(T) = \int_273.15^T c_p(T) dT
        //              \approx 0.5 (T-273.15) * (cp( 0.5(temperature-273.15)sqrt(1/3) ) + cp(0.5(temperature-273.15)(-1)sqrt(1/3))
 
        // Enthalpy may have arbitrary reference state, but the empirical/fitted heatCapacity function needs Kelvin as input and is
        // fit over a certain temperature range. This suggests choosing an interval of integration being in the actual fit range.
        // I.e. choosing T=273.15K  as reference point for liquid enthalpy.
        using std::sqrt;
        const Scalar sqrt1over3 = sqrt(1./3.);
        // evaluation points according to Gauss-Legendre integration
        const Scalar TEval1 = 0.5*(temperature-273.15)*        sqrt1over3 + 0.5*(273.15+temperature);
        // evaluation points according to Gauss-Legendre integration
        const Scalar TEval2 = 0.5*(temperature-273.15)* (-1)*  sqrt1over3 + 0.5*(273.15+temperature);
 
        const Scalar h_n = 0.5 * (temperature-273.15) * ( liquidHeatCapacity(TEval1, pressure) + liquidHeatCapacity(TEval2, pressure) );
 
        return h_n;
    }

    static Scalar heatVap(Scalar temperature,
                          const  Scalar pressure)
    {
        using std::min;
        using std::max;
        temperature = min(temperature, criticalTemperature()); // regularization
        temperature = max(temperature, 0.0); // regularization
 
        constexpr Scalar T_crit = criticalTemperature();
        constexpr Scalar Tr1 = boilingTemperature()/criticalTemperature();
        constexpr Scalar p_crit = criticalPressure();
 
        //        Chen method, eq. 7-11.4 (at boiling)
        using std::log;
        const Scalar DH_v_boil = Consts::R * T_crit * Tr1 * (3.978 * Tr1 - 3.958 + 1.555*log(p_crit * 1e-5 /*Pa->bar*/ ) )
                                 / (1.07 - Tr1); /* [J/mol] */
 
        /* Variation with temp according to Watson relation eq 7-12.1*/
        using std::pow;
        const Scalar Tr2 = temperature/criticalTemperature();
        const Scalar n = 0.375;
        const Scalar DH_vap = DH_v_boil * pow(((1.0 - Tr2)/(1.0 - Tr1)), n);
 
        return (DH_vap/molarMass());          // we need [J/kg]
    }
 

    static Scalar gasEnthalpy(Scalar temperature, Scalar pressure)
    {
        return liquidEnthalpy(temperature,pressure) + heatVap(temperature, pressure);
    }

    static Scalar gasDensity(Scalar temperature, Scalar pressure)
    {
        return IdealGas::density(molarMass(),
                                 temperature,
                                 pressure);
    }

    static Scalar gasMolarDensity(Scalar temperature, Scalar pressure)
    { return IdealGas::molarDensity(temperature, pressure); }

    static Scalar liquidDensity(Scalar temperature, Scalar pressure)
    {
        return liquidMolarDensity(temperature, pressure)*molarMass();
    }

    static Scalar liquidMolarDensity(Scalar temperature, Scalar pressure)
    {
        using std::min;
        using std::max;
        temperature = min(temperature, 500.0); // regularization
        temperature = max(temperature, 250.0);
 
        const Scalar Z_RA = 0.2556; // from equation
 
        using std::pow;
        const Scalar expo = 1.0 + pow(1.0 - temperature/criticalTemperature(), 2.0/7.0);
        Scalar V = Consts::R*criticalTemperature()/criticalPressure()*pow(Z_RA, expo); // liquid molar volume [cm^3/mol]
 
        return 1.0/V; // molar density [mol/m^3]
    }

    static constexpr bool gasIsCompressible()
    { return true; }

    static constexpr bool gasIsIdeal()
    { return true; }

    static constexpr bool liquidIsCompressible()
    { return false; }

    static Scalar gasViscosity(Scalar temperature, Scalar pressure, bool regularize=true)
    {
        using std::min;
        using std::max;
        temperature = min(temperature, 500.0); // regularization
        temperature = max(temperature, 250.0);
 
        // reduced temperature
        Scalar Tr = temperature/criticalTemperature();
 
        Scalar Fp0 = 1.0;
        Scalar xi = 0.00474;
 
        using std::pow;
        using std::exp;
        Scalar 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]
    }

    static Scalar liquidViscosity(Scalar temperature, Scalar pressure)
    {
        using std::min;
        using std::max;
        temperature = min(temperature, 500.0); // regularization
        temperature = max(temperature, 250.0);
 
        const Scalar A = -6.749;
        const Scalar B = 2010.0;
 
        using std::exp;
        return exp(A + B/temperature)*1e-3; // [Pa s]
    }

    static Scalar liquidHeatCapacity(const Scalar temperature,
                                     const Scalar 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)]*/
        Scalar H, CH3, C6H5;
        if(temperature<298.) {
            // extrapolation for Temperature<273 */
            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);
 
            /* take care: extrapolation for Temperature>373 */
            H = 16.7+2.1*(temperature-348.0)/25.;          /* leads probably 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)
    }

    static Scalar liquidThermalConductivity( Scalar temperature,  Scalar pressure)
    {
        return 0.1351;
    }
};
 
} // end namespace Components
 
} // end namespace Dumux
 
#endif