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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 class for the CO2 fluid properties | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_CO2_HH | ||
| 13 | #define DUMUX_CO2_HH | ||
| 14 | |||
| 15 | #include <cmath> | ||
| 16 | #include <iostream> | ||
| 17 | |||
| 18 | #include <dune/common/stdstreams.hh> | ||
| 19 | #include <dune/common/math.hh> | ||
| 20 | |||
| 21 | #include <dumux/common/exceptions.hh> | ||
| 22 | |||
| 23 | #include <dumux/material/constants.hh> | ||
| 24 | #include <dumux/material/components/base.hh> | ||
| 25 | #include <dumux/material/components/liquid.hh> | ||
| 26 | #include <dumux/material/components/gas.hh> | ||
| 27 | |||
| 28 | namespace Dumux { | ||
| 29 | namespace Components { | ||
| 30 | |||
| 31 | /*! | ||
| 32 | * \ingroup Components | ||
| 33 | * \brief A class for the CO2 fluid properties | ||
| 34 | * | ||
| 35 | * Under reservoir conditions, CO2 is typically in supercritical state. These | ||
| 36 | * properties can be provided in tabulated form, which is necessary for this | ||
| 37 | * component implementation. The template is passed through the fluidsystem | ||
| 38 | * brineco2fluidsystem.hh. | ||
| 39 | * Depending on the used tabulation, the fluidsystem can also be used for gaseous CO2 | ||
| 40 | */ | ||
| 41 | |||
| 42 | template <class Scalar, class CO2Tables> | ||
| 43 | class CO2 | ||
| 44 | : public Components::Base<Scalar, CO2<Scalar, CO2Tables> > | ||
| 45 | , public Components::Liquid<Scalar, CO2<Scalar, CO2Tables> > | ||
| 46 | , public Components::Gas<Scalar, CO2<Scalar, CO2Tables> > | ||
| 47 | { | ||
| 48 | static const Scalar R; | ||
| 49 | |||
| 50 | static bool warningThrown; | ||
| 51 | |||
| 52 | public: | ||
| 53 | /*! | ||
| 54 | * \brief A human readable name for the CO2. | ||
| 55 | */ | ||
| 56 | static std::string name() | ||
| 57 |
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44 | { return "CO2"; } |
| 58 | |||
| 59 | /*! | ||
| 60 | * \brief The mass in \f$\mathrm{[kg/mol]}\f$ of one mole of CO2. | ||
| 61 | */ | ||
| 62 | static constexpr Scalar molarMass() | ||
| 63 | { return 44e-3; /* [kg/mol] */ } | ||
| 64 | |||
| 65 | /*! | ||
| 66 | * \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of CO2 | ||
| 67 | */ | ||
| 68 | static Scalar criticalTemperature() | ||
| 69 | { return 273.15 + 30.95; /* [K] */ } | ||
| 70 | |||
| 71 | /*! | ||
| 72 | * \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of CO2 | ||
| 73 | */ | ||
| 74 | static Scalar criticalPressure() | ||
| 75 | { return 73.8e5; /* [Pa] */ } | ||
| 76 | |||
| 77 | /*! | ||
| 78 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at CO2's triple point. | ||
| 79 | */ | ||
| 80 | static Scalar tripleTemperature() | ||
| 81 | { return 273.15 - 56.35; /* [K] */ } | ||
| 82 | |||
| 83 | /*! | ||
| 84 | * \brief Returns the pressure \f$\mathrm{[Pa]}\f$ at CO2's triple point. | ||
| 85 | */ | ||
| 86 | static Scalar triplePressure() | ||
| 87 | { return 5.11e5; /* [N/m^2] */ } | ||
| 88 | |||
| 89 | /*! | ||
| 90 | * \brief Returns the minimal tabulated pressure \f$\mathrm{[Pa]}\f$ of the used table | ||
| 91 | */ | ||
| 92 | static Scalar minTabulatedPressure() | ||
| 93 | { return CO2Tables::tabulatedEnthalpy.minPress(); /* [Pa] */ } | ||
| 94 | |||
| 95 | /*! | ||
| 96 | * \brief Returns the maximal tabulated pressure \f$\mathrm{[Pa]}\f$ of the used table | ||
| 97 | */ | ||
| 98 | static Scalar maxTabulatedPressure() | ||
| 99 | { return CO2Tables::tabulatedEnthalpy.maxPress(); /* [Pa] */ } | ||
| 100 | |||
| 101 | /*! | ||
| 102 | * \brief Returns the minimal tabulated temperature \f$\mathrm{[K]}\f$ of the used table | ||
| 103 | */ | ||
| 104 | static Scalar minTabulatedTemperature() | ||
| 105 | { return CO2Tables::tabulatedEnthalpy.minTemp(); /* [K] */ } | ||
| 106 | |||
| 107 | /*! | ||
| 108 | * \brief Returns the maximal tabulated temperature \f$\mathrm{[K]}\f$ of the used table | ||
| 109 | */ | ||
| 110 | static Scalar maxTabulatedTemperature() | ||
| 111 | { return CO2Tables::tabulatedEnthalpy.maxTemp(); /* [K] */ } | ||
| 112 | |||
| 113 | /*! | ||
| 114 | * \brief Returns true if the gas phase is assumed to be ideal | ||
| 115 | */ | ||
| 116 | static constexpr bool gasIsIdeal() | ||
| 117 | { return false; } | ||
| 118 | |||
| 119 | /*! | ||
| 120 | * \brief The vapor pressure in \f$\mathrm{[Pa]}\f$ of pure CO2 | ||
| 121 | * at a given temperature. | ||
| 122 | * \param T the temperature \f$\mathrm{[K]}\f$ | ||
| 123 | * See: | ||
| 124 | * | ||
| 125 | * R. Span and W. Wagner (1996, pp. 1509-1596) \cite span1996 | ||
| 126 | */ | ||
| 127 | static Scalar vaporPressure(Scalar T) | ||
| 128 | { | ||
| 129 | static const Scalar a[4] = | ||
| 130 | { -7.0602087, 1.9391218, -1.6463597, -3.2995634 }; | ||
| 131 | static const Scalar t[4] = | ||
| 132 | { 1.0, 1.5, 2.0, 4.0 }; | ||
| 133 | |||
| 134 | // this is on page 1524 of the reference | ||
| 135 | Scalar exponent = 0; | ||
| 136 | Scalar Tred = T/criticalTemperature(); | ||
| 137 | |||
| 138 | using std::pow; | ||
| 139 | for (int i = 0; i < 4; ++i) | ||
| 140 | exponent += a[i]*pow(1 - Tred, t[i]); | ||
| 141 | exponent *= 1.0/Tred; | ||
| 142 | |||
| 143 | using std::exp; | ||
| 144 | return exp(exponent)*criticalPressure(); | ||
| 145 | } | ||
| 146 | |||
| 147 | /*! | ||
| 148 | * \brief Specific enthalpy of gaseous CO2 \f$\mathrm{[J/kg]}\f$. | ||
| 149 | * \param temperature the temperature \f$\mathrm{[K]}\f$ | ||
| 150 | * \param pressure the pressure \f$\mathrm{[Pa]}\f$ | ||
| 151 | */ | ||
| 152 | 93487316 | static Scalar gasEnthalpy(Scalar temperature, | |
| 153 | Scalar pressure) | ||
| 154 | { | ||
| 155 |
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93487316 | if ((temperature < criticalTemperature() || pressure < criticalPressure()) && !warningThrown) |
| 156 | { | ||
| 157 | ✗ | Dune::dwarn << "Subcritical values: Be aware to use " | |
| 158 | ✗ | <<"Tables with sufficient resolution!"<< std::endl; | |
| 159 | ✗ | warningThrown=true; | |
| 160 | } | ||
| 161 | return | ||
| 162 | 93487316 | CO2Tables::tabulatedEnthalpy.at(temperature, pressure); | |
| 163 | } | ||
| 164 | |||
| 165 | /*! | ||
| 166 | * \brief Specific enthalpy of liquid CO2 \f$\mathrm{[J/kg]}\f$. | ||
| 167 | * \param temperature the temperature \f$\mathrm{[K]}\f$ | ||
| 168 | * \param pressure the pressure \f$\mathrm{[Pa]}\f$ | ||
| 169 | */ | ||
| 170 | 46661842 | static Scalar liquidEnthalpy(Scalar temperature, | |
| 171 | Scalar pressure) | ||
| 172 | { | ||
| 173 |
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46661842 | if ((temperature < criticalTemperature() || pressure < criticalPressure()) && !warningThrown) |
| 174 | { | ||
| 175 | 1 | Dune::dwarn << "Subcritical values: Be aware to use " | |
| 176 | 1 | <<"Tables with sufficient resolution!"<< std::endl; | |
| 177 | 1 | warningThrown=true; | |
| 178 | } | ||
| 179 | |||
| 180 | 46661842 | return gasEnthalpy(temperature, pressure); | |
| 181 | } | ||
| 182 | |||
| 183 | /*! | ||
| 184 | * \brief Specific internal energy of CO2 \f$\mathrm{[J/kg]}\f$. | ||
| 185 | * \param temperature the temperature \f$\mathrm{[K]}\f$ | ||
| 186 | * \param pressure the pressure \f$\mathrm{[Pa]}\f$ | ||
| 187 | */ | ||
| 188 | static Scalar gasInternalEnergy(Scalar temperature, | ||
| 189 | Scalar pressure) | ||
| 190 | { | ||
| 191 | Scalar h = gasEnthalpy(temperature, pressure); | ||
| 192 | Scalar rho = gasDensity(temperature, pressure); | ||
| 193 | |||
| 194 | return h - (pressure / rho); | ||
| 195 | } | ||
| 196 | |||
| 197 | /*! | ||
| 198 | * \brief Specific internal energy of liquid CO2 \f$\mathrm{[J/kg]}\f$. | ||
| 199 | * \param temperature the temperature \f$\mathrm{[K]}\f$ | ||
| 200 | * \param pressure the pressure \f$\mathrm{[Pa]}\f$ | ||
| 201 | */ | ||
| 202 | static Scalar liquidInternalEnergy(Scalar temperature, | ||
| 203 | Scalar pressure) | ||
| 204 | { | ||
| 205 | Scalar h = liquidEnthalpy(temperature, pressure); | ||
| 206 | Scalar rho = liquidDensity(temperature, pressure); | ||
| 207 | |||
| 208 | return h - (pressure / rho); | ||
| 209 | } | ||
| 210 | |||
| 211 | /*! | ||
| 212 | * \brief The density of CO2 at a given pressure and temperature \f$\mathrm{[kg/m^3]}\f$. | ||
| 213 | * \param temperature the temperature \f$\mathrm{[K]}\f$ | ||
| 214 | * \param pressure the pressure \f$\mathrm{[Pa]}\f$ | ||
| 215 | */ | ||
| 216 | 533787595 | static Scalar gasDensity(Scalar temperature, Scalar pressure) | |
| 217 | { | ||
| 218 |
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533787595 | if ((temperature < criticalTemperature() || pressure < criticalPressure()) && !warningThrown) |
| 219 | { | ||
| 220 | 3 | Dune::dwarn << "Subcritical values: Be aware to use " | |
| 221 | 3 | <<"Tables with sufficient resolution!"<< std::endl; | |
| 222 | 3 | warningThrown=true; | |
| 223 | } | ||
| 224 | 533787595 | return CO2Tables::tabulatedDensity.at(temperature, pressure); | |
| 225 | } | ||
| 226 | |||
| 227 | /*! | ||
| 228 | * \brief The molar density of CO2 gas in \f$\mathrm{[mol/m^3]}\f$ at a given pressure and temperature. | ||
| 229 | * | ||
| 230 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 231 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 232 | * | ||
| 233 | */ | ||
| 234 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | ||
| 235 | 71506773 | { return gasDensity(temperature, pressure)/molarMass(); } | |
| 236 | |||
| 237 | /*! | ||
| 238 | * \brief The density of pure CO2 at a given pressure and temperature \f$\mathrm{[kg/m^3]}\f$. | ||
| 239 | * \param temperature the temperature \f$\mathrm{[K]}\f$ | ||
| 240 | * \param pressure the pressure \f$\mathrm{[Pa]}\f$ | ||
| 241 | */ | ||
| 242 | static Scalar liquidDensity(Scalar temperature, Scalar pressure) | ||
| 243 | { | ||
| 244 | if ((temperature < criticalTemperature() || pressure < criticalPressure()) && !warningThrown) | ||
| 245 | { | ||
| 246 | Dune::dwarn << "Subcritical values: Be aware to use " | ||
| 247 | <<"Tables with sufficient resolution!"<< std::endl; | ||
| 248 | warningThrown=true; | ||
| 249 | } | ||
| 250 | return CO2Tables::tabulatedDensity.at(temperature, pressure); | ||
| 251 | } | ||
| 252 | |||
| 253 | /*! | ||
| 254 | * \brief The molar density of CO2 in \f$\mathrm{[mol/m^3]}\f$ at a given pressure and temperature. | ||
| 255 | * | ||
| 256 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 257 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 258 | * | ||
| 259 | */ | ||
| 260 | static Scalar liquidMolarDensity(Scalar temperature, Scalar pressure) | ||
| 261 | { return liquidDensity(temperature, pressure)/molarMass(); } | ||
| 262 | |||
| 263 | /*! | ||
| 264 | * \brief The pressure of steam in \f$\mathrm{[Pa]}\f$ at a given density and temperature. | ||
| 265 | * | ||
| 266 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 267 | * \param density density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
| 268 | */ | ||
| 269 | static Scalar gasPressure(Scalar temperature, Scalar density) | ||
| 270 | { | ||
| 271 | DUNE_THROW(NumericalProblem, "CO2::gasPressure()"); | ||
| 272 | } | ||
| 273 | |||
| 274 | /*! | ||
| 275 | * \brief The pressure of liquid water in \f$\mathrm{[Pa]}\f$ at a given density and | ||
| 276 | * temperature. | ||
| 277 | * | ||
| 278 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 279 | * \param density density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
| 280 | */ | ||
| 281 | static Scalar liquidPressure(Scalar temperature, Scalar density) | ||
| 282 | { | ||
| 283 | DUNE_THROW(NumericalProblem, "CO2::liquidPressure()"); | ||
| 284 | } | ||
| 285 | |||
| 286 | /*! | ||
| 287 | * \brief Specific isobaric heat capacity of the component \f$\mathrm{[J/(kg*K)]}\f$ as a liquid. | ||
| 288 | * USE WITH CAUTION! Exploits enthalpy function with artificial increment | ||
| 289 | * of the temperature! | ||
| 290 | * Equation with which the specific heat capacity is calculated : \f$ c_p = \frac{dh}{dT}\f$ | ||
| 291 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 292 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 293 | */ | ||
| 294 | 8 | static Scalar liquidHeatCapacity(Scalar temperature, Scalar pressure) | |
| 295 | { | ||
| 296 | //temperature difference : | ||
| 297 | 8 | Scalar dT = 1.; // 1K temperature increment | |
| 298 | 8 | Scalar temperature2 = temperature+dT; | |
| 299 | |||
| 300 | // enthalpy difference | ||
| 301 | 8 | Scalar hold = liquidEnthalpy(temperature, pressure); | |
| 302 | 8 | Scalar hnew = liquidEnthalpy(temperature2, pressure); | |
| 303 | 8 | Scalar dh = hold-hnew; | |
| 304 | |||
| 305 | //specific heat capacity | ||
| 306 | 8 | return dh/dT ; | |
| 307 | } | ||
| 308 | |||
| 309 | |||
| 310 | /*! | ||
| 311 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of CO2. | ||
| 312 | * Equations given in: - Vesovic et al., 1990 | ||
| 313 | * - Fenhour et al., 1998 | ||
| 314 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 315 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 316 | */ | ||
| 317 | 145672595 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | |
| 318 | { | ||
| 319 | static const double a0 = 0.235156; | ||
| 320 | static const double a1 = -0.491266; | ||
| 321 | static const double a2 = 5.211155E-2; | ||
| 322 | static const double a3 = 5.347906E-2; | ||
| 323 | static const double a4 = -1.537102E-2; | ||
| 324 | |||
| 325 | static const double d11 = 0.4071119E-2; | ||
| 326 | static const double d21 = 0.7198037E-4; | ||
| 327 | static const double d64 = 0.2411697E-16; | ||
| 328 | static const double d81 = 0.2971072E-22; | ||
| 329 | static const double d82 = -0.1627888E-22; | ||
| 330 | |||
| 331 | static const double ESP = 251.196; | ||
| 332 | |||
| 333 | double mu0, SigmaStar, TStar; | ||
| 334 | double dmu, rho; | ||
| 335 | double visco_CO2; | ||
| 336 | |||
| 337 |
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145672595 | if(temperature < 275.) // regularisation |
| 338 | { | ||
| 339 | ✗ | temperature = 275; | |
| 340 | ✗ | Dune::dgrave << "Temperature below 275K in viscosity function:" | |
| 341 | ✗ | << "Regularizing temperature to 275K. " << std::endl; | |
| 342 | } | ||
| 343 | |||
| 344 | |||
| 345 | 145672595 | TStar = temperature/ESP; | |
| 346 | |||
| 347 | /* mu0: viscosity in zero-density limit */ | ||
| 348 | using std::exp; | ||
| 349 | using std::log; | ||
| 350 | using std::sqrt; | ||
| 351 | 291345190 | SigmaStar = exp(a0 + a1*log(TStar) | |
| 352 | 145672595 | + a2*log(TStar)*log(TStar) | |
| 353 | 145672595 | + a3*log(TStar)*log(TStar)*log(TStar) | |
| 354 | 145672595 | + a4*log(TStar)*log(TStar)*log(TStar)*log(TStar) ); | |
| 355 | 145672595 | mu0 = 1.00697*sqrt(temperature) / SigmaStar; | |
| 356 | |||
| 357 | /* dmu : excess viscosity at elevated density */ | ||
| 358 | 145672595 | rho = gasDensity(temperature, pressure); /* CO2 mass density [kg/m^3] */ | |
| 359 | |||
| 360 | using Dune::power; | ||
| 361 | 145672595 | dmu = d11*rho + d21*rho*rho + d64*power(rho,6)/(TStar*TStar*TStar) | |
| 362 | 291345190 | + d81*power(rho,8) + d82*power(rho,8)/TStar; | |
| 363 | |||
| 364 | 145672595 | visco_CO2 = (mu0 + dmu)/1.0E6; /* conversion to [Pa s] */ | |
| 365 | |||
| 366 | 145672595 | return visco_CO2; | |
| 367 | } | ||
| 368 | |||
| 369 | /*! | ||
| 370 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of pure CO2. | ||
| 371 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 372 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 373 | */ | ||
| 374 | static Scalar liquidViscosity(Scalar temperature, Scalar pressure) | ||
| 375 | { | ||
| 376 | // no difference for supercritical CO2 | ||
| 377 | return gasViscosity(temperature, pressure); | ||
| 378 | } | ||
| 379 | |||
| 380 | /*! | ||
| 381 | * \brief Thermal conductivity \f$\mathrm{[[W/(m*K)]}\f$ of CO2. | ||
| 382 | * | ||
| 383 | * Thermal conductivity of CO2 at T=20°C, see: | ||
| 384 | * http://www.engineeringtoolbox.com/carbon-dioxide-d_1000.html | ||
| 385 | * | ||
| 386 | * \param temperature absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 387 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 388 | */ | ||
| 389 | ✗ | static Scalar gasThermalConductivity(Scalar temperature, Scalar pressure) | |
| 390 | { | ||
| 391 | ✗ | return 0.087; | |
| 392 | } | ||
| 393 | }; | ||
| 394 | |||
| 395 | template <class Scalar, class CO2Tables> | ||
| 396 | const Scalar CO2<Scalar, CO2Tables>::R = Constants<Scalar>::R; | ||
| 397 | |||
| 398 | template <class Scalar, class CO2Tables> | ||
| 399 | bool CO2<Scalar, CO2Tables>::warningThrown = false; | ||
| 400 | |||
| 401 | } // end namespace Components | ||
| 402 | |||
| 403 | } // end namespace Dumux | ||
| 404 | |||
| 405 | #endif | ||
| 406 |