327 lines
11 KiB
C++
327 lines
11 KiB
C++
/*
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Copyright (C) 2009-2013 by Andreas Lauser
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Copyright (C) 2012 by Vishal Jambhekar
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Copyright (C) 2010 by Felix Bode
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This file is part of the Open Porous Media project (OPM).
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OPM is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 2 of the License, or
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(at your option) any later version.
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OPM is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with OPM. If not, see <http://www.gnu.org/licenses/>.
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*/
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/*!
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* \file
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* \copydoc Opm::Xylene
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*/
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#ifndef OPM_XYLENE_HPP
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#define OPM_XYLENE_HPP
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#include <cmath>
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#include <opm/material/IdealGas.hpp>
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#include <opm/material/components/Component.hpp>
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#include <opm/material/Constants.hpp>
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namespace Opm
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{
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/*!
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* \ingroup Components
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* \brief Component for Xylene
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*
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* \tparam Scalar The type used for scalar values
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*/
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template <class Scalar>
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class Xylene : public Component<Scalar, Xylene<Scalar> >
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{
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typedef Constants<Scalar> Consts;
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public:
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/*!
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* \brief A human readable name for the xylene
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*/
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static const char *name()
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{ return "xylene"; }
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/*!
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* \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of xylene
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*/
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static Scalar molarMass()
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{ return 0.106; }
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/*!
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* \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of xylene
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*/
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static Scalar criticalTemperature()
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{ return 617.1; }
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/*!
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* \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of xylene
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*/
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static Scalar criticalPressure()
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{ return 35.4e5; }
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/*!
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* \brief Returns the temperature \f$\mathrm{[K]}\f$ at xylene's triple point.
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*/
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static const Scalar tripleTemperature()
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{ OPM_THROW(std::runtime_error, "Not implemented: tripleTemperature for xylene"); }
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/*!
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* \brief Returns the pressure \f$\mathrm{[Pa]}\f$ at xylene's triple point.
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*/
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static const Scalar triplePressure()
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{ OPM_THROW(std::runtime_error, "Not implemented: triplePressure for xylene"); }
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/*!
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* \brief The saturation vapor pressure in \f$\mathrm{[Pa]}\f$ of pure xylene
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* at a given temperature according to Antoine after Betz 1997 -> Gmehling et al 1980
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*
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* \param temperature temperature of component in \f$\mathrm{[K]}\f$
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*/
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static Scalar vaporPressure(Scalar temperature)
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{
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const Scalar A = 7.00909;;
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const Scalar B = 1462.266;;
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const Scalar C = 215.110;;
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Scalar T = temperature - 273.15;
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Scalar psat = 1.334*std::pow(10.0, (A - (B/(T + C)))); // in [mbar]
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psat *= 100.0; // in [Pa] (0.001*1.E5)
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return psat;
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}
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/*!
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* \brief Specific heat cap of liquid xylene \f$\mathrm{[J/kg]}\f$.
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*
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* source : Reid et al. (fourth edition): Missenard group contrib. method (chap 5-7, Table 5-11, s. example 5-8)
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*
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* \param temp temperature of component in \f$\mathrm{[K]}\f$
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* \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
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*/
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static Scalar spHeatCapLiquidPhase(Scalar temp, Scalar pressure)
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{
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Scalar CH3,C6H5,H;
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// after Reid et al. : Missenard group contrib. method (s. example 5-8)
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// Xylene: C9H12 : 3* CH3 ; 1* C6H5 (phenyl-ring) ; -2* H (this was too much!)
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// linear interpolation between table values [J/(mol K)]
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if(temp < 298.0){ // take care: extrapolation for Temp<273
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H = 13.4 + 1.2*(temp - 273.0)/25.0; // 13.4 + 1.2 = 14.6 = H(T=298K) i.e. interpolation of table values 273<T<298
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CH3 = 40.0 + 1.6*(temp - 273.0)/25.0; // 40 + 1.6 = 41.6 = CH3(T=298K)
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C6H5 = 113.0 + 4.2*(temp - 273.0)/25.0; // 113 + 4.2 = 117.2 = C6H5(T=298K)
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}
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else if(temp < 323.0){
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H = 14.6 + 0.9*(temp - 298.0)/25.0; // i.e. interpolation of table values 298<T<323
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CH3 = 41.6 + 1.9*(temp - 298.0)/25.0;
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C6H5 = 117.2 + 6.2*(temp - 298.0)/25.0;
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}
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else if(temp < 348.0){
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H = 15.5 + 1.2*(temp - 323.0)/25.0; // i.e. interpolation of table values 323<T<348
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CH3 = 43.5 + 2.3*(temp - 323.0)/25.0;
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C6H5 = 123.4 + 6.3*(temp - 323.0)/25.0;
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}
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else {
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H = 16.7 + 2.1*(temp - 348.0)/25.0; // i.e. interpolation of table values 348<T<373
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CH3 = 45.8 + 2.5*(temp - 348.0)/25.0; // take care: extrapolation for Temp>373
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C6H5 = 129.7 + 6.3*(temp - 348.0)/25.0; // most likely leads to underestimation
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}
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return (C6H5 + 2*CH3 - H)/molarMass();// J/(mol K) -> J/(kg K)
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}
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/*!
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* \copydoc Component::liquidEnthalpy
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*/
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static Scalar liquidEnthalpy(Scalar temperature, Scalar pressure)
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{
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// Gauss quadrature rule:
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// Interval: [0K; temperature (K)]
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// Gauss-Legendre-Integration with variable transformation:
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// \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 )
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// with: n=2, legendre -> x_i = +/- \sqrt(1/3), \apha_i=1
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// here: a=0, b=actual temperature in Kelvin
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// \leadsto h(T) = \int_0^T c_p(T) dT
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// \approx 0.5 T * (cp( (0.5-0.5*\sqrt(1/3)) T) + cp((0.5+0.5*\sqrt(1/3)) T))
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// = 0.5 T * (cp(0.2113 T) + cp(0.7887 T) )
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// enthalpy may have arbitrary reference state, but the empirical/fitted heatCapacity function needs Kelvin as input
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return 0.5*temperature*(spHeatCapLiquidPhase(0.2113*temperature,pressure)
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+ spHeatCapLiquidPhase(0.7887*temperature,pressure));
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}
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/*!
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* \brief Returns the temperature \f$\mathrm{[K]}\f$ at xylene's boiling point (1 atm).
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*/
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static Scalar boilingTemperature()
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{ return 412.3; }
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/*!
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* \brief Latent heat of vaporization for xylene \f$\mathrm{[J/kg]}\f$.
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*
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* source : Reid et al. (fourth edition): Chen method (chap. 7-11, Delta H_v = Delta H_v (T) according to chap. 7-12)
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*
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* \param temperature temperature of component in \f$\mathrm{[K]}\f$
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* \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
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*/
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static Scalar heatVap(Scalar temperature,
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Scalar pressure)
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{
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temperature = std::min(temperature, criticalTemperature()); // regularization
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temperature = std::max(temperature, 0.0); // regularization
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const Scalar T_crit = criticalTemperature();
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const Scalar Tr1 = boilingTemperature()/criticalTemperature();
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const Scalar p_crit = criticalPressure();
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// Chen method, eq. 7-11.4 (at boiling)
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const Scalar DH_v_boil = Consts::R * T_crit * Tr1
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* (3.978 * Tr1 - 3.958 + 1.555*std::log(p_crit * 1e-5 /*Pa->bar*/ ) )
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/ (1.07 - Tr1); /* [J/mol] */
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/* Variation with temp according to Watson relation eq 7-12.1*/
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const Scalar Tr2 = temperature/criticalTemperature();
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const Scalar n = 0.375;
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const Scalar DH_vap = DH_v_boil * std::pow(((1.0 - Tr2)/(1.0 - Tr1)), n);
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return (DH_vap/molarMass()); // we need [J/kg]
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}
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/*!
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* \copydoc Component::gasEnthalpy
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*
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* The relation used here is true on the vapor pressure curve, i.e. as long
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* as there is a liquid phase present.
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*/
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static Scalar gasEnthalpy(Scalar temperature, Scalar pressure)
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{
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return liquidEnthalpy(temperature, pressure) + heatVap(temperature, pressure);
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}
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/*!
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* \copydoc Component::gasDensity
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*/
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static Scalar gasDensity(Scalar temperature, Scalar pressure)
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{
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return IdealGas<Scalar>::density(molarMass(),
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temperature,
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pressure);
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}
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/*!
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* \brief The density \f$\mathrm{[mol/m^3]}\f$ of xylene gas at a given pressure and temperature.
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*
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* \param temperature temperature of component in \f$\mathrm{[K]}\f$
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* \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
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*/
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static Scalar molarGasDensity(Scalar temperature, Scalar pressure)
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{
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return gasDensity(temperature, pressure) / molarMass();
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}
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/*!
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* \brief The molar density of pure xylene at a given pressure and temperature
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* \f$\mathrm{[mol/m^3]}\f$.
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*
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* source : Reid et al. (fourth edition): Modified Racket technique (chap. 3-11, eq. 3-11.9)
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*
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* \param temp temperature of component in \f$\mathrm{[K]}\f$
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* \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
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*/
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static Scalar molarLiquidDensity(Scalar temp, Scalar pressure)
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{
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// saturated molar volume according to Lide, CRC Handbook of
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// Thermophysical and Thermochemical Data, CRC Press, 1994
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// valid for 245 < Temp < 600
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temp = std::min(temp, 500.0); // regularization
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temp = std::max(temp, 250.0); // regularization
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const Scalar A1 = 0.25919; // from table
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const Scalar A2 = 0.0014569; // from table
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const Scalar expo = 1.0 + std::pow((1.0 - temp/criticalTemperature()), (2.0/7.0));
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const Scalar V = A2*std::pow(A1, expo); // liquid molar volume [m^3/mol]
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return 1.0/V; // molar density [mol/m^3]
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}
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/*!
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* \copydoc Component::liquidDensity
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*/
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static Scalar liquidDensity(Scalar temperature, Scalar pressure)
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{
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return molarLiquidDensity(temperature, pressure)*molarMass(); // [kg/m^3]
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}
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/*!
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* \copydoc Component::gasIsCompressible
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*/
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static bool gasIsCompressible()
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{ return true; }
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/*!
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* \copydoc Component::gasIsIdeal
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*/
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static bool gasIsIdeal()
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{ return true; }
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/*!
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* \copydoc Component::liquidIsCompressible
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*/
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static bool liquidIsCompressible()
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{ return false; }
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/*!
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* \copydoc Component::gasViscosity
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*/
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static Scalar gasViscosity(Scalar temperature, Scalar pressure)
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{
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temperature = std::min(temperature, 500.0); // regularization
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temperature = std::max(temperature, 250.0); // regularization
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const Scalar Tr = std::max(temperature/criticalTemperature(), 1e-10);
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const Scalar Fp0 = 1.0;
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const Scalar xi = 0.004623;
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const Scalar eta_xi = Fp0*(0.807*std::pow(Tr, 0.618)
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- 0.357*std::exp(-0.449*Tr)
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+ 0.34*std::exp(-4.058*Tr)
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+ 0.018);
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Scalar r = eta_xi/xi; // [1e-6 P]
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r /= 1.0e7; // [Pa s]
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return r;
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}
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/*!
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* \copydoc Component::liquidViscosity
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*/
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static Scalar liquidViscosity(Scalar temperature, Scalar pressure)
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{
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temperature = std::min(temperature, 500.0); // regularization
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temperature = std::max(temperature, 250.0); // regularization
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const Scalar A = -3.82;
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const Scalar B = 1027.0;
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const Scalar C = -6.38e-4;
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const Scalar D = 4.52e-7;
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Scalar r = std::exp(A + B/temperature + C*temperature + D*temperature*temperature); // in [cP]
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r *= 1.0e-3; // in [Pa s]
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return r; // [Pa s]
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}
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};
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} // namespace Opm
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#endif
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