262 lines
8.4 KiB
C++
262 lines
8.4 KiB
C++
// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
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// vi: set et ts=4 sw=4 sts=4:
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/*
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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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Consult the COPYING file in the top-level source directory of this
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module for the precise wording of the license and the list of
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copyright holders.
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*/
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/*!
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* \file
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* \copydoc Opm:H2
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* \brief Properties of pure molecular hydrogen \f$H_2\f$.
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*/
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#ifndef OPM_H2_HPP
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#define OPM_H2_HPP
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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/densead/Math.hpp>
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#include <cmath>
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namespace Opm {
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/*!
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* \ingroup Components
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* \brief Properties of pure molecular hydrogen \f$H_2\f$.
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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 H2 : public Component<Scalar, H2<Scalar> >
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{
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using IdealGas = Opm::IdealGas<Scalar>;
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public:
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/*!
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* \brief A human readable name for the \f$H_2\f$.
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*/
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static std::string name()
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{ return "H2"; }
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/*!
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* \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of molecular hydrogen.
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*/
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static constexpr Scalar molarMass()
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{ return 2.01588e-3; }
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/*!
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* \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of molecular hydrogen.
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*/
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static Scalar criticalTemperature()
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{ return 33.2; /* [K] */ }
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/*!
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* \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of molecular hydrogen.
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*/
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static Scalar criticalPressure()
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{ return 13.0e5; /* [N/m^2] */ }
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/*!
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* \brief Returns the critical density \f$\mathrm{[mol/cm^3]}\f$ of molecular hydrogen.
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*/
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static Scalar criticalDensity()
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{ return 15.508e-3; /* [mol/cm^3] */ }
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/*!
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* \brief Returns the temperature \f$\mathrm{[K]}\f$ at molecular hydrogen's triple point.
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*/
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static Scalar tripleTemperature()
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{ return 14.0; /* [K] */ }
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/*!
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* \brief The vapor pressure in \f$\mathrm{[Pa]}\f$ of pure molecular hydrogen
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* at a given temperature.
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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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* Taken from:
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*
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* See: R. Reid, et al. (1987, pp 208-209, 669) \cite reid1987
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*
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* \todo implement the Gomez-Thodos approach...
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*/
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template <class Evaluation>
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static Evaluation vaporPressure(Evaluation temperature)
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{
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if (temperature > criticalTemperature())
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return criticalPressure();
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if (temperature < tripleTemperature())
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return 0; // H2 is solid: We don't take sublimation into
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// account
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// antoine equation
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const Scalar A = -7.76451;
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const Scalar B = 1.45838;
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const Scalar C = -2.77580;
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return 1e5 * exp(A - B/(temperature + C));
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}
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/*!
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* \brief The density \f$\mathrm{[kg/m^3]}\f$ of \f$H_2\f$ 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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template <class Evaluation>
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static Evaluation gasDensity(Evaluation temperature, Evaluation pressure)
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{
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// Assume an ideal gas
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return IdealGas::density(Evaluation(molarMass()), temperature, pressure);
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}
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/*!
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* \brief The molar density of \f$H_2\f$ in \f$\mathrm{[mol/m^3]}\f$,
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* depending on pressure and temperature.
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* \param temperature The temperature of the gas
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* \param pressure The pressure of the gas
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*/
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template <class Evaluation>
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static Evaluation gasMolarDensity(Evaluation temperature, Evaluation pressure)
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{ return IdealGas::molarDensity(temperature, pressure); }
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/*!
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* \brief Returns true if the gas phase is assumed to be compressible
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*/
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static constexpr bool gasIsCompressible()
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{ return true; }
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/*!
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* \brief Returns true if the gas phase is assumed to be ideal
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*/
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static constexpr bool gasIsIdeal()
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{ return true; }
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/*!
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* \brief The pressure of gaseous \f$H_2\f$ 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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template <class Evaluation>
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static Evaluation gasPressure(Evaluation temperature, Evaluation 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 internal energy of H2 [J/kg].
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*/
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template <class Evaluation>
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static Evaluation gasInternalEnergy(const Evaluation& temperature,
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const Evaluation& pressure)
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{
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const Evaluation& h = gasEnthalpy(temperature, pressure);
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const Evaluation& rho = gasDensity(temperature, pressure);
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return h - (pressure / rho);
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}
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/*!
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* \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of \f$H_2\f$ 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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template <class Evaluation>
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static Evaluation gasViscosity(const Evaluation& temperature, const Evaluation& /*pressure*/)
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{
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const Scalar Tc = criticalTemperature();
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const Scalar Vc = 64.2; // critical specific volume [cm^3/mol]
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const Scalar omega = -0.217; // 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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const Evaluation& Tstar = 1.2593 * temperature/Tc;
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const Evaluation& Omega_v =
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1.16145*pow(Tstar, -0.14874) +
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0.52487*exp(- 0.77320*Tstar) +
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2.16178*exp(- 2.43787*Tstar);
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const Evaluation& mu = 40.785*Fc*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 enthalpy \f$\mathrm{[J/kg]}\f$ of pure hydrogen gas.
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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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template <class Evaluation>
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static const Evaluation gasEnthalpy(Evaluation temperature,
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Evaluation pressure)
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{
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return gasHeatCapacity(temperature, pressure) * temperature;
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}
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/*!
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* \brief Specific isobaric heat capacity \f$\mathrm{[J/(kg*K)]}\f$ of pure
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* hydrogen 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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* \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. (1987, pp 154, 657, 665) \cite reid1987
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*/
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template <class Evaluation>
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static const Evaluation gasHeatCapacity(Evaluation T,
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Evaluation pressure)
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{
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// method of Joback
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const Scalar cpVapA = 27.14;
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const Scalar cpVapB = 9.273e-3;
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const Scalar cpVapC = -1.381e-5;
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const Scalar cpVapD = 7.645e-9;
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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/2 + T*
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(cpVapC/3 + T*
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(cpVapD/4))));
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}
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};
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} // end namespace Opm
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#endif
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