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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-FileCopyrightInfo: 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 A much simpler (and thus potentially less buggy) version of | ||
| 11 | * pure CO2. | ||
| 12 | */ | ||
| 13 | #ifndef DUMUX_SIMPLE_CO2_HH | ||
| 14 | #define DUMUX_SIMPLE_CO2_HH | ||
| 15 | |||
| 16 | #include <dune/common/stdstreams.hh> | ||
| 17 | |||
| 18 | #include <dumux/common/parameters.hh> | ||
| 19 | #include <dumux/material/idealgas.hh> | ||
| 20 | |||
| 21 | #include <cmath> | ||
| 22 | |||
| 23 | #include <dumux/material/components/base.hh> | ||
| 24 | #include <dumux/material/components/gas.hh> | ||
| 25 | #include <dumux/material/components/shomate.hh> | ||
| 26 | |||
| 27 | namespace Dumux::Components { | ||
| 28 | |||
| 29 | /*! | ||
| 30 | * \ingroup Components | ||
| 31 | * \brief A simple version of pure CO2 | ||
| 32 | * | ||
| 33 | * \tparam Scalar The type used for scalar values | ||
| 34 | */ | ||
| 35 | template <class Scalar> | ||
| 36 | class SimpleCO2 | ||
| 37 | : public Components::Base<Scalar, SimpleCO2<Scalar> > | ||
| 38 | , public Components::Gas<Scalar, SimpleCO2<Scalar> > | ||
| 39 | { | ||
| 40 | using IdealGas = Dumux::IdealGas<Scalar>; | ||
| 41 | using ShomateMethod = Dumux::ShomateMethod<Scalar, 2>; // two regions | ||
| 42 | |||
| 43 | public: | ||
| 44 | static const ShomateMethod shomateMethod; | ||
| 45 | |||
| 46 | /*! | ||
| 47 | * \brief A human readable name for the CO2. | ||
| 48 | */ | ||
| 49 | static std::string name() | ||
| 50 |
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10 | { return "SimpleCO2"; } |
| 51 | |||
| 52 | /*! | ||
| 53 | * \brief The mass in \f$\mathrm{[kg/mol]}\f$ of one mole of CO2. | ||
| 54 | */ | ||
| 55 | static constexpr Scalar molarMass() | ||
| 56 | { return 44.0e-3; /* [kg/mol] */ } | ||
| 57 | |||
| 58 | /*! | ||
| 59 | * \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of CO2 | ||
| 60 | */ | ||
| 61 | static Scalar criticalTemperature() | ||
| 62 | { return 273.15 + 30.95; /* [K] */ } | ||
| 63 | |||
| 64 | /*! | ||
| 65 | * \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of CO2 | ||
| 66 | */ | ||
| 67 | static Scalar criticalPressure() | ||
| 68 | { return 73.8e5; /* [Pa] */ } | ||
| 69 | |||
| 70 | /*! | ||
| 71 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at CO2's triple point. | ||
| 72 | */ | ||
| 73 | static Scalar tripleTemperature() | ||
| 74 | { return 273.15 - 56.35; /* [K] */ } | ||
| 75 | |||
| 76 | /*! | ||
| 77 | * \brief Returns the pressure \f$\mathrm{[Pa]}\f$ at CO2's triple point. | ||
| 78 | */ | ||
| 79 | static Scalar triplePressure() | ||
| 80 | { return 5.11e5; /* [N/m^2] */ } | ||
| 81 | |||
| 82 | |||
| 83 | /*! | ||
| 84 | * \brief Specific enthalpy of CO2 \f$\mathrm{[J/kg]}\f$. | ||
| 85 | * Shomate Equation is used for a temperature range of 298K to 6000K. | ||
| 86 | * | ||
| 87 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 88 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 89 | */ | ||
| 90 | ✗ | static const Scalar gasEnthalpy(Scalar temperature, | |
| 91 | Scalar pressure) | ||
| 92 | { | ||
| 93 |
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101 | const auto h = shomateMethod.enthalpy(temperature); // KJ/mol |
| 94 | 101 | return h * 1e3 / molarMass(); // J/kg | |
| 95 | } | ||
| 96 | |||
| 97 | /*! | ||
| 98 | * \brief Specific internal energy of CO2 \f$\mathrm{[J/kg]}\f$. | ||
| 99 | * | ||
| 100 | * Definition of enthalpy: \f$h= u + pv = u + p / \rho\f$. | ||
| 101 | * Rearranging for internal energy yields: \f$u = h - pv\f$. | ||
| 102 | * Exploiting the Ideal Gas assumption (\f$pv = R_{\textnormal{specific}} T\f$)gives: \f$u = h - R / M T \f$. | ||
| 103 | * | ||
| 104 | * The universal gas constant can only be used in the case of molar formulations. | ||
| 105 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 106 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 107 | */ | ||
| 108 | static const Scalar gasInternalEnergy(Scalar temperature, | ||
| 109 | Scalar pressure) | ||
| 110 | { | ||
| 111 | // 1/molarMass: conversion from [J/(mol K)] to [J/(kg K)] | ||
| 112 | // R*T/molarMass: pressure *spec. volume for an ideal gas | ||
| 113 | return gasEnthalpy(temperature, pressure) | ||
| 114 | - 1.0/molarMass()*IdealGas::R*temperature; | ||
| 115 | } | ||
| 116 | |||
| 117 | /*! | ||
| 118 | * \brief Returns true if the gas phase is assumed to be compressible | ||
| 119 | */ | ||
| 120 | static constexpr bool gasIsCompressible() | ||
| 121 | { return true; } | ||
| 122 | |||
| 123 | /*! | ||
| 124 | * \brief Returns true if the gas phase viscostiy is constant | ||
| 125 | */ | ||
| 126 | static constexpr bool gasViscosityIsConstant() | ||
| 127 | { return false; } | ||
| 128 | |||
| 129 | /*! | ||
| 130 | * \brief The density \f$\mathrm{[kg/m^3]}\f$ of CO2 at a given pressure and temperature. | ||
| 131 | * | ||
| 132 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 133 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 134 | */ | ||
| 135 | static Scalar gasDensity(Scalar temperature, Scalar pressure) | ||
| 136 | 5191746 | { return IdealGas::density(molarMass(), temperature, pressure); } | |
| 137 | |||
| 138 | /*! | ||
| 139 | * \brief The molar density of CO2 in \f$\mathrm{[mol/m^3]}\f$ at a given pressure and temperature. | ||
| 140 | * | ||
| 141 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 142 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 143 | * | ||
| 144 | */ | ||
| 145 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | ||
| 146 | 5191544 | { return IdealGas::molarDensity(temperature, pressure); } | |
| 147 | |||
| 148 | /*! | ||
| 149 | * \brief Returns true if the gas phase is assumed to be ideal | ||
| 150 | */ | ||
| 151 | static constexpr bool gasIsIdeal() | ||
| 152 | { return true; } | ||
| 153 | |||
| 154 | /*! | ||
| 155 | * \brief The pressure of CO2 in \f$\mathrm{[Pa]}\f$ at a given density and temperature. | ||
| 156 | * | ||
| 157 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 158 | * \param density density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
| 159 | */ | ||
| 160 | static Scalar gasPressure(Scalar temperature, Scalar density) | ||
| 161 | { return IdealGas::pressure(temperature, density/molarMass()); } | ||
| 162 | |||
| 163 | /*! | ||
| 164 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of CO2. | ||
| 165 | * Equations given in: - Vesovic et al., 1990 | ||
| 166 | * - Fenhour et al., 1998 | ||
| 167 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 168 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 169 | * TODO: this does not look like a really "simple" parameterization. Can this be simplified further? | ||
| 170 | */ | ||
| 171 | 5191645 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | |
| 172 | { | ||
| 173 | 5191645 | constexpr double a0 = 0.235156; | |
| 174 | 5191645 | constexpr double a1 = -0.491266; | |
| 175 | 5191645 | constexpr double a2 = 5.211155E-2; | |
| 176 | 5191645 | constexpr double a3 = 5.347906E-2; | |
| 177 | 5191645 | constexpr double a4 = -1.537102E-2; | |
| 178 | |||
| 179 | 5191645 | constexpr double d11 = 0.4071119E-2; | |
| 180 | 5191645 | constexpr double d21 = 0.7198037E-4; | |
| 181 | 5191645 | constexpr double d64 = 0.2411697E-16; | |
| 182 | 5191645 | constexpr double d81 = 0.2971072E-22; | |
| 183 | 5191645 | constexpr double d82 = -0.1627888E-22; | |
| 184 | |||
| 185 | 5191645 | constexpr double ESP = 251.196; | |
| 186 | |||
| 187 |
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5191645 | if(temperature < 275.0) // regularisation |
| 188 | { | ||
| 189 | 4 | temperature = 275.0; | |
| 190 | 4 | Dune::dgrave << "Temperature below 275K in viscosity function:" | |
| 191 | 4 | << "Regularizing temperature to 275K. " << std::endl; | |
| 192 | } | ||
| 193 | |||
| 194 | |||
| 195 | 5191645 | const double TStar = temperature/ESP; | |
| 196 | |||
| 197 | /* mu0: viscosity in zero-density limit */ | ||
| 198 | using std::exp; | ||
| 199 | using std::log; | ||
| 200 | using std::sqrt; | ||
| 201 | 5191645 | const double logTStar = log(TStar); | |
| 202 | 10383290 | const double SigmaStar = exp(a0 + a1*logTStar | |
| 203 | 5191645 | + a2*logTStar*logTStar | |
| 204 | 5191645 | + a3*logTStar*logTStar*logTStar | |
| 205 | 5191645 | + a4*logTStar*logTStar*logTStar*logTStar ); | |
| 206 | 5191645 | const double mu0 = 1.00697*sqrt(temperature) / SigmaStar; | |
| 207 | |||
| 208 | /* dmu : excess viscosity at elevated density */ | ||
| 209 | 5191645 | const double rho = gasDensity(temperature, pressure); /* CO2 mass density [kg/m^3] */ | |
| 210 | |||
| 211 | using Dune::power; | ||
| 212 | 5191645 | const double dmu = d11*rho + d21*rho*rho + d64*power(rho, 6)/(TStar*TStar*TStar) | |
| 213 | 10383290 | + d81*power(rho, 8) + d82*power(rho, 8)/TStar; | |
| 214 | |||
| 215 | 5191645 | return (mu0 + dmu)/1.0E6; /* conversion to [Pa s] */ | |
| 216 | } | ||
| 217 | |||
| 218 | |||
| 219 | /*! | ||
| 220 | * \brief Thermal conductivity \f$\mathrm{[[W/(m*K)]}\f$ of CO2. | ||
| 221 | * | ||
| 222 | * Thermal conductivity of CO2 at T=20°C, see: | ||
| 223 | * http://www.engineeringtoolbox.com/carbon-dioxide-d_1000.html | ||
| 224 | * | ||
| 225 | * \param temperature absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 226 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 227 | */ | ||
| 228 | ✗ | static Scalar gasThermalConductivity(Scalar temperature, Scalar pressure) | |
| 229 | { | ||
| 230 | ✗ | return 0.087; | |
| 231 | } | ||
| 232 | |||
| 233 | /*! | ||
| 234 | * \brief Specific isobaric heat capacity of CO2 \f$\mathrm{[J/(kg*K)]}\f$. | ||
| 235 | * Shomate Equation is used for a temperature range of 298K to 6000K. | ||
| 236 | * | ||
| 237 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 238 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 239 | */ | ||
| 240 | ✗ | static Scalar gasHeatCapacity(Scalar temperature, Scalar pressure) | |
| 241 | { | ||
| 242 |
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101 | const auto cp = shomateMethod.heatCapacity(temperature); // J/(mol K) |
| 243 | 101 | return cp / molarMass(); // J/(kg K) | |
| 244 | } | ||
| 245 | |||
| 246 | }; | ||
| 247 | |||
| 248 | /*! | ||
| 249 | * \brief Shomate parameters for carbon dioxide published by NIST \cite NIST | ||
| 250 | * https://webbook.nist.gov/cgi/cbook.cgi?ID=C124389&Units=SI&Mask=1&Type=JANAFG&Table=on#JANAFG | ||
| 251 | * First row defines the temperature ranges, further rows give the parameters (A,B,C,D,E,F,G,H) for the respective temperature ranges. | ||
| 252 | */ | ||
| 253 | template <class Scalar> | ||
| 254 | const typename SimpleCO2<Scalar>::ShomateMethod SimpleCO2<Scalar>::shomateMethod{ | ||
| 255 | /*temperature*/{298.0, 1200.0, 6000.0}, | ||
| 256 | typename SimpleCO2<Scalar>::ShomateMethod::Coefficients{{ | ||
| 257 | {24.99735, 55.18696, -33.69137, 7.948387, -0.136638, -403.6075, 228.2431, -393.5224}, | ||
| 258 | {58.16639, 2.720074, -0.492289, 0.038844, -6.447293, -425.9186, 263.6125, -393.5224} | ||
| 259 | }} | ||
| 260 | }; | ||
| 261 | |||
| 262 | |||
| 263 | } // end namespace Dumux::Components | ||
| 264 | |||
| 265 | #endif | ||
| 266 |