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opm-common/opm/material/components/Mesitylene.hpp
Andreas Lauser 27386851a2 move some basic infrastructure from opm-common to here 
all of these classes have only been used in opm-material and its
downstreams in the first place.
2018-02-07 16:44:44 +01:00

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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.
*/
/*!
* \file
* \copydoc Opm::Mesitylene
*/
#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 {
/*!
* \ingroup Components
* \brief Component for Mesitylene
*
* \tparam Scalar The type used for scalar values
*/
template <class Scalar>
class Mesitylene : public Component<Scalar, Mesitylene<Scalar> >
{
typedef Opm::Constants<Scalar> Consts;
public:
/*!
* \brief A human readable name for the mesitylene
*/
static const char* name()
{ return "mesitylene"; }
/*!
* \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of mesitylene
*/
static Scalar molarMass()
{ return 0.120; }
/*!
* \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of mesitylene
*/
static Scalar criticalTemperature()
{ return 637.3; }
/*!
* \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of mesitylene
*/
static Scalar criticalPressure()
{ return 31.3e5; }
/*!
* \brief Returns the temperature \f$\mathrm{[K]}\f$ at mesitylene's boiling point (1 atm).
*/
static Scalar boilingTemperature()
{ return 437.9; }
/*!
* \brief Returns the temperature \f$\mathrm{[K]}\f$ at mesitylene's triple point.
*/
static Scalar tripleTemperature()
{ throw std::runtime_error("Not implemented: tripleTemperature for mesitylene"); }
/*!
* \brief Returns the pressure \f$\mathrm{[Pa]}\f$ at mesitylene's triple point.
*/
static Scalar triplePressure()
{ throw std::runtime_error("Not implemented: triplePressure for mesitylene"); }
/*!
* \brief The saturation vapor pressure in \f$\mathrm{[Pa]}\f$ of
* pure mesitylene at a given temperature according to
* Antoine after Betz 1997, see Gmehling et al 1980
*
* \param temperature temperature of component in \f$\mathrm{[K]}\f$
*/
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 * Opm::pow(10.0, A - (B / (T + C)));
}
/*!
* \brief Specific enthalpy of liquid mesitylene \f$\mathrm{[J/kg]}\f$.
*
* \param temperature temperature of component in \f$\mathrm{[K]}\f$
* \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
*/
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));
}
/*!
* \brief Latent heat of vaporization for mesitylene \f$\mathrm{[J/kg]}\f$.
*
* source : Reid et al. (fourth edition): Chen method (chap. 7-11, Delta H_v = Delta H_v (T) according to chap. 7-12)
*
* \param temperature temperature of component in \f$\mathrm{[K]}\f$
* \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
*/
template <class Evaluation>
static Evaluation heatVap(const Evaluation& temperature, const Evaluation& /*pressure*/)
{
Evaluation T = Opm::min(temperature, criticalTemperature()); // regularization
T = Opm::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 * Opm::pow(((1.0 - Tr2)/(1.0 - Tr1)), n);
return (DH_vap/molarMass()); // we need [J/kg]
}
/*!
* \brief Specific enthalpy of mesitylene vapor \f$\mathrm{[J/kg]}\f$.
*
* This relation is true on the vapor pressure curve, i.e. as long
* as there is a liquid phase present.
*
* \param temperature temperature of component in \f$\mathrm{[K]}\f$
* \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
*/
template <class Evaluation>
static Evaluation gasEnthalpy(const Evaluation& temperature, const Evaluation& pressure)
{
return liquidEnthalpy(temperature,pressure) + heatVap(temperature, pressure);
}
/*!
* \brief The density of pure mesitylene vapor at a given pressure and temperature \f$\mathrm{[kg/m^3]}\f$.
*
* \param temperature temperature of component in \f$\mathrm{[K]}\f$
* \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
*/
template <class Evaluation>
static Evaluation gasDensity(const Evaluation& temperature, const Evaluation& pressure)
{ return IdealGas<Scalar>::density(Evaluation(molarMass()), temperature, pressure); }
/*!
* \brief The density of pure mesitylene at a given pressure and temperature \f$\mathrm{[kg/m^3]}\f$.
*
* \param temperature temperature of component in \f$\mathrm{[K]}\f$
* \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
*/
template <class Evaluation>
static Evaluation liquidDensity(const Evaluation& temperature, const Evaluation& /*pressure*/)
{ return molarLiquidDensity_(temperature)*molarMass(); }
/*!
* \brief Returns true iff the gas phase is assumed to be compressible
*/
static bool gasIsCompressible()
{ return true; }
/*!
* \brief Returns true iff the gas phase is assumed to be ideal
*/
static bool gasIsIdeal()
{ return true; }
/*!
* \brief Returns true iff the liquid phase is assumed to be compressible
*/
static bool liquidIsCompressible()
{ return false; }
/*!
* \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of mesitylene vapor
*
* \param temperature temperature of component in \f$\mathrm{[K]}\f$
* \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
* \param regularize defines, if the functions is regularized or not, set to true by default
*/
template <class Evaluation>
static Evaluation gasViscosity(Evaluation temperature, const Evaluation& /*pressure*/, bool /*regularize*/=true)
{
temperature = Opm::min(temperature, 500.0); // regularization
temperature = Opm::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*Opm::pow(Tr,0.618)
- 0.357*Opm::exp(-0.449*Tr)
+ 0.34*Opm::exp(-4.058*Tr)
+ 0.018);
return eta_xi/xi/1e7; // [Pa s]
}
/*!
* \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of pure mesitylene.
*
* \param temperature temperature of component in \f$\mathrm{[K]}\f$
* \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
*/
template <class Evaluation>
static Evaluation liquidViscosity(Evaluation temperature, const Evaluation& /*pressure*/)
{
temperature = Opm::min(temperature, 500.0); // regularization
temperature = Opm::max(temperature, 250.0);
const Scalar A = -6.749;
const Scalar B = 2010.0;
return Opm::exp(A + B/temperature)*1e-3; // [Pa s]
}
/*!
* \brief Specific heat cap of liquid mesitylene \f$\mathrm{[J/kg]}\f$.
*
* source : Reid et al. (fourth edition): Missenard group contrib. method (chap 5-7, Table 5-11, s. example 5-8)
*
* \param temperature temperature of component in \f$\mathrm{[K]}\f$
* \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
*
*/
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:
/*!
* \brief The molar density of pure mesitylene at a given pressure and temperature
* \f$\mathrm{[mol/m^3]}\f$.
*
* source : Reid et al. (fourth edition): Modified Racket technique (chap. 3-11, eq. 3-11.9)
*
* \param temperature temperature of component in \f$\mathrm{[K]}\f$
*/
template <class Evaluation>
static Evaluation molarLiquidDensity_(Evaluation temperature)
{
temperature = Opm::min(temperature, 500.0); // regularization
temperature = Opm::max(temperature, 250.0);
const Scalar Z_RA = 0.2556; // from equation
const Evaluation& expo = 1.0 + Opm::pow(1.0 - temperature/criticalTemperature(), 2.0/7.0);
const Evaluation& V = Consts::R*criticalTemperature()/criticalPressure()*Opm::pow(Z_RA, expo); // liquid molar volume [cm^3/mol]
return 1.0/V; // molar density [mol/m^3]
}
};
} // namespace Opm
#endif
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