300 lines
9.6 KiB
C++
300 lines
9.6 KiB
C++
/*
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Copyright (C) 2009-2013 by Andreas Lauser
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Copyright (C) 2011 by Benjamin Faigle
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Copyright (C) 2010 by Katherina Baber
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Copyright (C) 2011-2012 by Philipp Nuske
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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::N2
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*/
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#ifndef OPM_N2_HPP
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#define OPM_N2_HPP
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#include <opm/material/IdealGas.hpp>
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#include "Component.hpp"
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#include <cmath>
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namespace Opm
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{
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/*!
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* \ingroup Components
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*
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* \brief Properties of pure molecular nitrogen \f$N_2\f$.
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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 N2 : public Component<Scalar, N2<Scalar> >
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{
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typedef Opm::IdealGas<Scalar> IdealGas;
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public:
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/*!
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* \brief A human readable name for nitrogen.
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*/
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static const char *name()
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{ return "N2"; }
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/*!
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* \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of molecular nitrogen.
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*/
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static Scalar molarMass()
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{ return 28.0134e-3;}
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/*!
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* \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of molecular nitrogen
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*/
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static Scalar criticalTemperature()
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{ return 126.192; /* [K] */ }
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/*!
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* \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of molecular nitrogen.
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*/
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static Scalar criticalPressure()
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{ return 3.39858e6; /* [N/m^2] */ }
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/*!
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* \brief Returns the temperature \f$\mathrm{[K]}\f$ at molecular nitrogen's triple point.
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*/
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static Scalar tripleTemperature()
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{ return 63.151; /* [K] */ }
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/*!
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* \brief Returns the pressure \f$\mathrm{[Pa]}\f$ at molecular nitrogen's triple point.
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*/
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static Scalar triplePressure()
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{ return 12.523e3; /* [N/m^2] */ }
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/*!
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* \brief The vapor pressure in \f$\mathrm{[Pa]}\f$ of pure molecular nitrogen
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* at a given temperature.
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*
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*\param T temperature of component in \f$\mathrm{[K]}\f$
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*
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* Taken from:
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*
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* R. Span, E.W. Lemmon, et al.: "A Reference Equation of State
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* for the Thermodynamic Properties of Nitrogen for Temperatures
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* from 63.151 to 1000 K and Pressures to 2200 MPa", Journal of
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* Physical and Chemical Refefence Data, Vol. 29, No. 6,
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* pp. 1361-1433
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*/
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static Scalar vaporPressure(Scalar T)
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{
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if (T > criticalTemperature())
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return criticalPressure();
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if (T < tripleTemperature())
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return 0; // N2 is solid: We don't take sublimation into
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// account
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// note: this is the ancillary equation given on page 1368
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Scalar sigma = Scalar(1.0) - T/criticalTemperature();
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Scalar sqrtSigma = std::sqrt(sigma);
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const Scalar N1 = -6.12445284;
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const Scalar N2 = 1.26327220;
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const Scalar N3 = -0.765910082;
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const Scalar N4 = -1.77570564;
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return
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criticalPressure() *
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std::exp(criticalTemperature()/T*
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(sigma*(N1 +
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sqrtSigma*N2 +
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sigma*(sqrtSigma*N3 +
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sigma*sigma*sigma*N4))));
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}
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/*!
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* \brief The density \f$\mathrm{[kg/m^3]}\f$ of \f$N_2\f$ 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 gasDensity(Scalar temperature, Scalar pressure)
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{
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// Assume an ideal gas
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return IdealGas::density(molarMass(), temperature, pressure);
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}
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/*!
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* \brief Returns true iff the gas phase is assumed to be compressible
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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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* \brief Returns true iff the gas phase is assumed to be ideal
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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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* \brief The pressure of gaseous \f$N_2\f$ in \f$\mathrm{[Pa]}\f$ at a given density 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 density density of component in \f$\mathrm{[kg/m^3]}\f$
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*/
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static Scalar gasPressure(Scalar temperature, Scalar density)
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{
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// Assume an ideal gas
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return IdealGas::pressure(temperature, density/molarMass());
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}
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/*!
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* \brief Specific enthalpy \f$\mathrm{[J/kg]}\f$ of pure nitrogen gas.
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*
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* \param T 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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* See: R. Reid, et al.: The Properties of Gases and Liquids, 4th
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* edition, McGraw-Hill, 1987, pp 154, 657, 665
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*/
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static const Scalar gasEnthalpy(Scalar T,
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Scalar pressure)
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{
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// method of Joback
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const Scalar cpVapA = 31.15;
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const Scalar cpVapB = -0.01357;
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const Scalar cpVapC = 2.680e-5;
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const Scalar cpVapD = -1.168e-8;
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// calculate: \int_0^T c_p dT
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return
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1/molarMass()* // conversion from [J/(mol K)] to [J/(kg K)]
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T*(cpVapA + T*
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(cpVapB/2 + T*
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(cpVapC/3 + T*
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(cpVapD/4))));
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//#warning NIST DATA STUPID INTERPOLATION
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// Scalar T2 = 300.;
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// Scalar T1 = 285.;
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// Scalar h2 = 311200.;
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// Scalar h1 = 295580.;
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// Scalar h = h1+ (h2-h1) / (T2-T1) * (T-T1);
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// return h ;
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}
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/*!
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* \brief Specific enthalpy \f$\mathrm{[J/kg]}\f$ of pure nitrogen gas.
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*
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* Definition of enthalpy: \f$h= u + pv = u + p / \rho\f$.
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*
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* Rearranging for internal energy yields: \f$u = h - pv\f$.
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*
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* Exploiting the Ideal Gas assumption (\f$pv = R_{\textnormal{specific}} T\f$)gives: \f$u = h - R / M T \f$.
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*
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* The universal gas constant can only be used in the case of molar formulations.
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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 const Scalar gasInternalEnergy(Scalar temperature,
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Scalar pressure)
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{
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return
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gasEnthalpy(temperature, pressure) -
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1/molarMass()* // conversion from [J/(mol K)] to [J/(kg K)]
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IdealGas::R*temperature; // = pressure * spec. volume for an ideal gas
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}
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/*!
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* \brief Specific isobaric heat capacity \f$[J/(kg K)]\f$ of pure
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* nitrogen gas.
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*
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* This is equivalent to the partial derivative of the specific
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* enthalpy to the temperature.
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*/
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static const Scalar gasHeatCapacity(Scalar T,
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Scalar pressure)
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{
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// method of Joback
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const Scalar cpVapA = 31.15;
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const Scalar cpVapB = -0.01357;
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const Scalar cpVapC = 2.680e-5;
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const Scalar cpVapD = -1.168e-8;
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return
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1/molarMass()* // conversion from [J/(mol K)] to [J/(kg K)]
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cpVapA + T*
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(cpVapB + T*
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(cpVapC + T*
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(cpVapD)));
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}
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/*!
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* \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of \f$N_2\f$ 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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* See:
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*
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* See: R. Reid, et al.: The Properties of Gases and Liquids,
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* 4th edition, McGraw-Hill, 1987, pp 396-397,
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* 5th edition, McGraw-Hill, 2001 pp 9.7-9.8 (omega and V_c taken from p. A.19)
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*
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*/
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static Scalar gasViscosity(Scalar temperature, Scalar pressure)
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{
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const Scalar Tc = criticalTemperature();
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const Scalar Vc = 90.1; // critical specific volume [cm^3/mol]
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const Scalar omega = 0.037; // accentric factor
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const Scalar M = molarMass() * 1e3; // molar mas [g/mol]
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const Scalar dipole = 0.0; // dipole moment [debye]
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Scalar mu_r4 = 131.3 * dipole / std::sqrt(Vc * Tc);
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mu_r4 *= mu_r4;
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mu_r4 *= mu_r4;
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Scalar Fc = 1 - 0.2756*omega + 0.059035*mu_r4;
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Scalar Tstar = 1.2593 * temperature/Tc;
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Scalar Omega_v =
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1.16145*std::pow(Tstar, -0.14874) +
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0.52487*std::exp(- 0.77320*Tstar) +
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2.16178*std::exp(- 2.43787*Tstar);
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Scalar mu = 40.785*Fc*std::sqrt(M*temperature)/(std::pow(Vc, 2./3)*Omega_v);
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// convertion from micro poise to Pa s
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return mu/1e6 / 10;
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}
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/*!
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* \brief Specific heat conductivity of steam \f$\mathrm{[W/(m K)]}\f$.
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*
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* Isobaric Properties for Nitrogen in: NIST Standard Reference
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* Database Number 69, Eds. P.J. Linstrom and W.G. Mallard
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* evaluated at p=.1 MPa, T=8°C, does not change dramatically with
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* p,T
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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 const Scalar gasThermalConductivity(Scalar temperature,
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Scalar pressure)
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{ return 0.024572; }
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};
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} // namespace Opm
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#endif
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