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| 1 | // -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- | ||
| 2 | // vi: set et ts=4 sw=4 sts=4: | ||
| 3 | // | ||
| 4 | // SPDX-FileCopyrightText: Copyright © DuMux Project contributors, see AUTHORS.md in root folder | ||
| 5 | // SPDX-License-Identifier: GPL-3.0-or-later | ||
| 6 | // | ||
| 7 | /*! | ||
| 8 | * \file | ||
| 9 | * \ingroup Components | ||
| 10 | * \brief Properties of methane \f$CH_4\f$. | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_CH4_HH | ||
| 13 | #define DUMUX_CH4_HH | ||
| 14 | |||
| 15 | #include <dumux/material/idealgas.hh> | ||
| 16 | |||
| 17 | #include <cmath> | ||
| 18 | |||
| 19 | #include <dumux/material/components/base.hh> | ||
| 20 | #include <dumux/material/components/gas.hh> | ||
| 21 | #include <dumux/material/components/shomate.hh> | ||
| 22 | |||
| 23 | namespace Dumux::Components { | ||
| 24 | |||
| 25 | /*! | ||
| 26 | * \ingroup Components | ||
| 27 | * \brief Properties of pure molecular methane \f$CH_4\f$. | ||
| 28 | * \tparam Scalar The type used for scalar values | ||
| 29 | */ | ||
| 30 | template <class Scalar> | ||
| 31 | class CH4 | ||
| 32 | : public Components::Base<Scalar, CH4<Scalar> > | ||
| 33 | , public Components::Gas<Scalar, CH4<Scalar> > | ||
| 34 | { | ||
| 35 | using IdealGas = Dumux::IdealGas<Scalar>; | ||
| 36 | using ShomateMethod = Dumux::ShomateMethod<Scalar, 3>; // three regions | ||
| 37 | |||
| 38 | public: | ||
| 39 | static const ShomateMethod shomateMethod; | ||
| 40 | |||
| 41 | /*! | ||
| 42 | * \brief A human readable name for methane. | ||
| 43 | */ | ||
| 44 |
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5 | static std::string name() |
| 45 |
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5 | { return "CH4"; } |
| 46 | |||
| 47 | /*! | ||
| 48 | * \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of molecular methane. | ||
| 49 | */ | ||
| 50 | static constexpr Scalar molarMass() | ||
| 51 | { return 16.043e-3; /* [kg/mol] */} | ||
| 52 | |||
| 53 | /*! | ||
| 54 | * \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of molecular methane | ||
| 55 | */ | ||
| 56 | static Scalar criticalTemperature() | ||
| 57 | { return 190.4; /* [K] */ } | ||
| 58 | |||
| 59 | /*! | ||
| 60 | * \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of molecular methane | ||
| 61 | */ | ||
| 62 | static Scalar criticalPressure() | ||
| 63 | { return 46e5; /* [Pa] */ } | ||
| 64 | |||
| 65 | /*! | ||
| 66 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at molecular methane's triple point. | ||
| 67 | */ | ||
| 68 | static Scalar tripleTemperature() | ||
| 69 | { return 90.7; /* [K] */ } | ||
| 70 | |||
| 71 | /*! | ||
| 72 | * \brief Returns the pressure \f$\mathrm{[Pa]}\f$ at molecular methane's triple point. | ||
| 73 | */ | ||
| 74 | static Scalar triplePressure() | ||
| 75 | { return 0; /* [Pa] */ } | ||
| 76 | |||
| 77 | /*! | ||
| 78 | * \brief The vapor pressure in \f$\mathrm{[Pa]}\f$ of pure molecular methane | ||
| 79 | * at a given temperature. | ||
| 80 | * | ||
| 81 | *\param T temperature of component in \f$\mathrm{[K]}\f$ | ||
| 82 | */ | ||
| 83 | static Scalar vaporPressure(Scalar T) | ||
| 84 | { DUNE_THROW(Dune::NotImplemented, "vaporPressure for CH4"); } | ||
| 85 | |||
| 86 | /*! | ||
| 87 | * \brief Returns true if the gas phase is assumed to be compressible | ||
| 88 | */ | ||
| 89 | static constexpr bool gasIsCompressible() | ||
| 90 | { return true; } | ||
| 91 | |||
| 92 | /*! | ||
| 93 | * \brief The density \f$\mathrm{[kg/m^3]}\f$ of \f$CH_4\f$ gas at a given pressure and temperature. | ||
| 94 | * | ||
| 95 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 96 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 97 | */ | ||
| 98 | 369622 | static Scalar gasDensity(Scalar temperature, Scalar pressure) | |
| 99 | { | ||
| 100 | // Assume an ideal gas | ||
| 101 | 369622 | return IdealGas::density(molarMass(), temperature, pressure); | |
| 102 | } | ||
| 103 | |||
| 104 | /*! | ||
| 105 | * \brief The molar density of \f$CH_4\f$ gas in \f$\mathrm{[mol/m^3]}\f$, | ||
| 106 | * depending on pressure and temperature. | ||
| 107 | * \param temperature The temperature of the gas | ||
| 108 | * \param pressure The pressure of the gas | ||
| 109 | */ | ||
| 110 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | ||
| 111 | { return IdealGas::molarDensity(temperature, pressure); } | ||
| 112 | |||
| 113 | /*! | ||
| 114 | * \brief Returns true if the gas phase is assumed to be ideal | ||
| 115 | */ | ||
| 116 | static constexpr bool gasIsIdeal() | ||
| 117 | { return true; } | ||
| 118 | |||
| 119 | /*! | ||
| 120 | * \brief The pressure of gaseous \f$CH_4\f$ in \f$\mathrm{[Pa]}\f$ at a given density and temperature. | ||
| 121 | * | ||
| 122 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 123 | * \param density density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
| 124 | */ | ||
| 125 | 9 | static Scalar gasPressure(Scalar temperature, Scalar density) | |
| 126 | { | ||
| 127 | // Assume an ideal gas | ||
| 128 | 9 | return IdealGas::pressure(temperature, density/molarMass()); | |
| 129 | } | ||
| 130 | |||
| 131 | /*! | ||
| 132 | * \brief Specific enthalpy \f$\mathrm{[J/kg]}\f$ of pure methane gas. | ||
| 133 | * Shomate Equation is used for a temperature range of 298K to 6000K. | ||
| 134 | * | ||
| 135 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 136 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 137 | */ | ||
| 138 | 110 | static const Scalar gasEnthalpy(Scalar temperature, | |
| 139 | Scalar pressure) | ||
| 140 | { | ||
| 141 |
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110 | const auto h = shomateMethod.enthalpy(temperature); // KJ/mol |
| 142 | 110 | return h * 1e3 / molarMass(); // J/kg | |
| 143 | } | ||
| 144 | |||
| 145 | /*! | ||
| 146 | * \brief Specific isobaric heat capacity \f$\mathrm{[J/(kg*K)]}\f$ of pure methane gas. | ||
| 147 | *Shomate Equation is used for a temperature range of 298K to 6000K. | ||
| 148 | */ | ||
| 149 | 110 | static Scalar gasHeatCapacity(Scalar T, | |
| 150 | Scalar pressure) | ||
| 151 | { | ||
| 152 |
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110 | const auto cp = shomateMethod.heatCapacity(T); // J/(mol K) |
| 153 | 110 | return cp / molarMass(); // J/(kg K) | |
| 154 | } | ||
| 155 | |||
| 156 | /*! | ||
| 157 | * \brief Specific enthalpy \f$\mathrm{[J/kg]}\f$ of pure methane gas. | ||
| 158 | * | ||
| 159 | * Definition of enthalpy: \f$h= u + pv = u + p / \rho\f$. | ||
| 160 | * | ||
| 161 | * Rearranging for internal energy yields: \f$u = h - pv\f$. | ||
| 162 | * | ||
| 163 | * Exploiting the Ideal Gas assumption (\f$pv = R_{\textnormal{specific}} T\f$)gives: \f$u = h - R / M T \f$. | ||
| 164 | * | ||
| 165 | * The universal gas constant can only be used in the case of molar formulations. | ||
| 166 | * | ||
| 167 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 168 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 169 | */ | ||
| 170 | static const Scalar gasInternalEnergy(Scalar temperature, | ||
| 171 | Scalar pressure) | ||
| 172 | { | ||
| 173 | |||
| 174 | return | ||
| 175 | gasEnthalpy(temperature, pressure) - | ||
| 176 | 1/molarMass()* // conversion from [J/(mol K)] to [J/(kg K)] | ||
| 177 | IdealGas::R*temperature; // = pressure * spec. volume for an ideal gas | ||
| 178 | } | ||
| 179 | |||
| 180 | /*! | ||
| 181 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of \f$CH_4\f$ at a given pressure and temperature. | ||
| 182 | * | ||
| 183 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 184 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 185 | * | ||
| 186 | * See: | ||
| 187 | * | ||
| 188 | * See: R. Reid, et al.: The Properties of Gases and Liquids, | ||
| 189 | * 4th edition (1987, pp 396-397, 670) \cite reid1987 <BR> | ||
| 190 | * 5th edition (2001, pp 9.7-9.8 (omega and V_c taken from p. A.5)) \cite poling2001 | ||
| 191 | * | ||
| 192 | */ | ||
| 193 | 369622 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | |
| 194 | { | ||
| 195 | 369622 | const Scalar Tc = criticalTemperature(); | |
| 196 | 369622 | const Scalar Vc = 98.6; // critical specific volume [cm^3/mol] | |
| 197 | 369622 | const Scalar omega = 0.011; // accentric factor | |
| 198 | 369622 | const Scalar M = molarMass() * 1e3; // molar mas [g/mol] | |
| 199 | 369622 | const Scalar dipole = 0.0; // dipole moment [debye] | |
| 200 | |||
| 201 | using std::sqrt; | ||
| 202 | Scalar mu_r4 = 131.3 * dipole / sqrt(Vc * Tc); | ||
| 203 | mu_r4 *= mu_r4; | ||
| 204 | 369622 | mu_r4 *= mu_r4; | |
| 205 | |||
| 206 | using std::exp; | ||
| 207 | using std::pow; | ||
| 208 | 369622 | Scalar Fc = 1 - 0.2756*omega + 0.059035*mu_r4; | |
| 209 | 369622 | Scalar Tstar = 1.2593 * temperature/Tc; | |
| 210 | 369622 | Scalar Omega_v = | |
| 211 | 369622 | 1.16145*pow(Tstar, -0.14874) + | |
| 212 | 369622 | 0.52487*exp(- 0.77320*Tstar) + | |
| 213 | 369622 | 2.16178*exp(- 2.43787*Tstar); | |
| 214 | 369622 | Scalar mu = 40.785*Fc*sqrt(M*temperature)/(pow(Vc, 2./3)*Omega_v); | |
| 215 | |||
| 216 | // conversion from micro poise to Pa s | ||
| 217 | 369622 | return mu/1e6 / 10; | |
| 218 | } | ||
| 219 | }; | ||
| 220 | |||
| 221 | /*! | ||
| 222 | * \brief Shomate parameters for methane published by NIST \cite NIST | ||
| 223 | * https://webbook.nist.gov/cgi/cbook.cgi?ID=C74828&Units=SI&Mask=1&Type=JANAFG&Table=on#JANAFG | ||
| 224 | * First row defines the temperature ranges, further rows give the parameters (A,B,C,D,E,F,G,H) for the respective temperature ranges. | ||
| 225 | */ | ||
| 226 | template <class Scalar> | ||
| 227 | const typename CH4<Scalar>::ShomateMethod CH4<Scalar>::shomateMethod{ | ||
| 228 | /*temperature*/{298.0, 1300.0, 6000.0}, | ||
| 229 | typename CH4<Scalar>::ShomateMethod::Coefficients{{ | ||
| 230 | {-0.703029, 108.4773, -42.52157, 5.862788, 0.678565, -76.84376, 158.7163, -74.87310}, | ||
| 231 | {85.81217, 11.26467, -2.114146, 0.138190, -26.42221, -153.5327, 224.4143, -74.87310} | ||
| 232 | }} | ||
| 233 | }; | ||
| 234 | |||
| 235 | } // end namespace Dumux::Components | ||
| 236 | |||
| 237 | #endif | ||
| 238 |