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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 mesitylene. | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_MESITYLENE_HH | ||
| 13 | #define DUMUX_MESITYLENE_HH | ||
| 14 | |||
| 15 | #include <dumux/material/idealgas.hh> | ||
| 16 | #include <dumux/material/constants.hh> | ||
| 17 | |||
| 18 | #include <dumux/material/components/base.hh> | ||
| 19 | #include <dumux/material/components/liquid.hh> | ||
| 20 | #include <dumux/material/components/gas.hh> | ||
| 21 | |||
| 22 | namespace Dumux::Components { | ||
| 23 | |||
| 24 | /*! | ||
| 25 | * \ingroup Components | ||
| 26 | * \brief mesitylene | ||
| 27 | * | ||
| 28 | * \tparam Scalar The type used for scalar values | ||
| 29 | */ | ||
| 30 | template <class Scalar> | ||
| 31 | class Mesitylene | ||
| 32 | : public Components::Base<Scalar, Mesitylene<Scalar> > | ||
| 33 | , public Components::Liquid<Scalar, Mesitylene<Scalar> > | ||
| 34 | , public Components::Gas<Scalar, Mesitylene<Scalar> > | ||
| 35 | { | ||
| 36 | using Consts = Constants<Scalar>; | ||
| 37 | using IdealGas = Dumux::IdealGas<Scalar>; | ||
| 38 | public: | ||
| 39 | /*! | ||
| 40 | * \brief A human readable name for the mesitylene | ||
| 41 | */ | ||
| 42 |
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22 | static std::string name() |
| 43 |
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22 | { return "mesitylene"; } |
| 44 | |||
| 45 | /*! | ||
| 46 | * \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of mesitylene | ||
| 47 | */ | ||
| 48 | constexpr static Scalar molarMass() | ||
| 49 | { return 0.120; } | ||
| 50 | |||
| 51 | /*! | ||
| 52 | * \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of mesitylene | ||
| 53 | */ | ||
| 54 | constexpr static Scalar criticalTemperature() | ||
| 55 | { return 637.3; } | ||
| 56 | |||
| 57 | /*! | ||
| 58 | * \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of mesitylene | ||
| 59 | */ | ||
| 60 | constexpr static Scalar criticalPressure() | ||
| 61 | { return 31.3e5; } | ||
| 62 | |||
| 63 | /*! | ||
| 64 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at mesitylene's boiling point (1 atm). | ||
| 65 | */ | ||
| 66 | constexpr static Scalar boilingTemperature() | ||
| 67 | { return 437.9; } | ||
| 68 | |||
| 69 | /*! | ||
| 70 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at mesitylene's triple point. | ||
| 71 | */ | ||
| 72 | static Scalar tripleTemperature() | ||
| 73 | { | ||
| 74 | DUNE_THROW(Dune::NotImplemented, "tripleTemperature for mesitylene"); | ||
| 75 | } | ||
| 76 | |||
| 77 | /*! | ||
| 78 | * \brief Returns the pressure \f$\mathrm{[Pa]}\f$ at mesitylene's triple point. | ||
| 79 | */ | ||
| 80 | static Scalar triplePressure() | ||
| 81 | { | ||
| 82 | DUNE_THROW(Dune::NotImplemented, "triplePressure for mesitylene"); | ||
| 83 | } | ||
| 84 | |||
| 85 | /*! | ||
| 86 | * \brief The saturation vapor pressure in \f$\mathrm{[Pa]}\f$ of | ||
| 87 | * pure mesitylene at a given temperature according to | ||
| 88 | * Antoine after Betz 1997, see Gmehling et al 1980 | ||
| 89 | * | ||
| 90 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 91 | */ | ||
| 92 | 7620687 | static Scalar vaporPressure(Scalar temperature) | |
| 93 | { | ||
| 94 | 7620687 | const Scalar A = 7.07638; | |
| 95 | 7620687 | const Scalar B = 1571.005; | |
| 96 | 7620687 | const Scalar C = 209.728; | |
| 97 | |||
| 98 | 7620687 | const Scalar T = temperature - 273.15; | |
| 99 | |||
| 100 | using std::pow; | ||
| 101 |
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7620687 | return 100 * 1.334 * pow(Scalar(10.0), Scalar(A - (B / (T + C)))); |
| 102 | } | ||
| 103 | |||
| 104 | |||
| 105 | /*! | ||
| 106 | * \brief Specific enthalpy of liquid mesitylene \f$\mathrm{[J/kg]}\f$. | ||
| 107 | * | ||
| 108 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 109 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 110 | */ | ||
| 111 | 3779288 | static Scalar liquidEnthalpy(const Scalar temperature, | |
| 112 | const Scalar pressure) | ||
| 113 | { | ||
| 114 | // Gauss quadrature rule: | ||
| 115 | // Interval: [0K; temperature (K)] | ||
| 116 | // Gauss-Legendre-Integration with variable transformation: | ||
| 117 | // \int_a^b f(T) dT \approx (b-a)/2 \sum_i=1^n \alpha_i f( (b-a)/2 x_i + (a+b)/2 ) | ||
| 118 | // with: n=2, legendre -> x_i = +/- \sqrt(1/3), \apha_i=1 | ||
| 119 | // here: a=273.15K, b=actual temperature in Kelvin | ||
| 120 | // \leadsto h(T) = \int_273.15^T c_p(T) dT | ||
| 121 | // \approx 0.5 (T-273.15) * (cp( 0.5(temperature-273.15)sqrt(1/3) ) + cp(0.5(temperature-273.15)(-1)sqrt(1/3)) | ||
| 122 | |||
| 123 | // Enthalpy may have arbitrary reference state, but the empirical/fitted heatCapacity function needs Kelvin as input and is | ||
| 124 | // fit over a certain temperature range. This suggests choosing an interval of integration being in the actual fit range. | ||
| 125 | // I.e. choosing T=273.15K as reference point for liquid enthalpy. | ||
| 126 | using std::sqrt; | ||
| 127 | 3779288 | const Scalar sqrt1over3 = sqrt(1./3.); | |
| 128 | // evaluation points according to Gauss-Legendre integration | ||
| 129 | 3779288 | const Scalar TEval1 = 0.5*(temperature-273.15)* sqrt1over3 + 0.5*(273.15+temperature); | |
| 130 | // evaluation points according to Gauss-Legendre integration | ||
| 131 | 3779288 | const Scalar TEval2 = 0.5*(temperature-273.15)* (-1)* sqrt1over3 + 0.5*(273.15+temperature); | |
| 132 | |||
| 133 | 3779288 | const Scalar h_n = 0.5 * (temperature-273.15) * ( liquidHeatCapacity(TEval1, pressure) + liquidHeatCapacity(TEval2, pressure) ); | |
| 134 | |||
| 135 | 3779288 | return h_n; | |
| 136 | } | ||
| 137 | |||
| 138 | /*! | ||
| 139 | * \brief Latent heat of vaporization for mesitylene \f$\mathrm{[J/kg]}\f$. | ||
| 140 | * | ||
| 141 | * source : Reid et al. (1987, Chen method (chap. 7-11, Delta H_v = Delta H_v (T) according to chap. 7-12)) \cite reid1987 | ||
| 142 | * | ||
| 143 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 144 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 145 | */ | ||
| 146 | 1889644 | static Scalar heatVap(Scalar temperature, | |
| 147 | const Scalar pressure) | ||
| 148 | { | ||
| 149 | using std::min; | ||
| 150 | using std::max; | ||
| 151 |
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1889644 | temperature = min(temperature, criticalTemperature()); // regularization |
| 152 |
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1889644 | temperature = max(temperature, 0.0); // regularization |
| 153 | |||
| 154 | 1889644 | constexpr Scalar T_crit = criticalTemperature(); | |
| 155 | 1889644 | constexpr Scalar Tr1 = boilingTemperature()/criticalTemperature(); | |
| 156 | 1889644 | constexpr Scalar p_crit = criticalPressure(); | |
| 157 | |||
| 158 | // Chen method, eq. 7-11.4 (at boiling) | ||
| 159 | using std::log; | ||
| 160 | 1889644 | const Scalar DH_v_boil = Consts::R * T_crit * Tr1 * (3.978 * Tr1 - 3.958 + 1.555*log(p_crit * 1e-5 /*Pa->bar*/ ) ) | |
| 161 | / (1.07 - Tr1); /* [J/mol] */ | ||
| 162 | |||
| 163 | /* Variation with temp according to Watson relation eq 7-12.1*/ | ||
| 164 | using std::pow; | ||
| 165 | 1889644 | const Scalar Tr2 = temperature/criticalTemperature(); | |
| 166 | 1889644 | const Scalar n = 0.375; | |
| 167 | 1889644 | const Scalar DH_vap = DH_v_boil * pow(((1.0 - Tr2)/(1.0 - Tr1)), n); | |
| 168 | |||
| 169 | 1889644 | return (DH_vap/molarMass()); // we need [J/kg] | |
| 170 | } | ||
| 171 | |||
| 172 | |||
| 173 | /*! | ||
| 174 | * \brief Specific enthalpy of mesitylene vapor \f$\mathrm{[J/kg]}\f$. | ||
| 175 | * | ||
| 176 | * This relation is true on the vapor pressure curve, i.e. as long | ||
| 177 | * as there is a liquid phase present. | ||
| 178 | * | ||
| 179 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 180 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 181 | */ | ||
| 182 | 1889644 | static Scalar gasEnthalpy(Scalar temperature, Scalar pressure) | |
| 183 | { | ||
| 184 | 1889644 | return liquidEnthalpy(temperature,pressure) + heatVap(temperature, pressure); | |
| 185 | } | ||
| 186 | |||
| 187 | /*! | ||
| 188 | * \brief The density of mesitylene at a given pressure and temperature \f$\mathrm{[kg/m^3]}\f$ . | ||
| 189 | * | ||
| 190 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 191 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 192 | */ | ||
| 193 |
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2092522 | static Scalar gasDensity(Scalar temperature, Scalar pressure) |
| 194 | { | ||
| 195 |
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2092522 | return IdealGas::density(molarMass(), |
| 196 | temperature, | ||
| 197 | pressure); | ||
| 198 | } | ||
| 199 | |||
| 200 | /*! | ||
| 201 | * \brief The molar density of mesitylene in \f$\mathrm{[mol/m^3]}\f$, | ||
| 202 | * depending on pressure and temperature. | ||
| 203 | * \param temperature The temperature of the gas | ||
| 204 | * \param pressure The pressure of the gas | ||
| 205 | */ | ||
| 206 | 1382069 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | |
| 207 | 1382069 | { return IdealGas::molarDensity(temperature, pressure); } | |
| 208 | |||
| 209 | /*! | ||
| 210 | * \brief The density of pure mesitylene at a given pressure and temperature \f$\mathrm{[kg/m^3]}\f$. | ||
| 211 | * | ||
| 212 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 213 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 214 | */ | ||
| 215 | 2345425 | static Scalar liquidDensity(Scalar temperature, Scalar pressure) | |
| 216 | { | ||
| 217 |
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2345425 | return liquidMolarDensity(temperature, pressure)*molarMass(); |
| 218 | } | ||
| 219 | |||
| 220 | /*! | ||
| 221 | * \brief The molar density of pure mesitylene at a given pressure and temperature | ||
| 222 | * \f$\mathrm{[mol/m^3]}\f$. | ||
| 223 | * | ||
| 224 | * source : Reid et al. (1987, Modified Racket technique (chap. 3-11, eq. 3-11.9)) \cite reid1987 | ||
| 225 | * | ||
| 226 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 227 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 228 | */ | ||
| 229 | 3727494 | static Scalar liquidMolarDensity(Scalar temperature, Scalar pressure) | |
| 230 | { | ||
| 231 | using std::min; | ||
| 232 | using std::max; | ||
| 233 |
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3727494 | temperature = min(temperature, 500.0); // regularization |
| 234 |
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3727494 | temperature = max(temperature, 250.0); |
| 235 | |||
| 236 | 3727494 | const Scalar Z_RA = 0.2556; // from equation | |
| 237 | |||
| 238 | using std::pow; | ||
| 239 | 3727494 | const Scalar expo = 1.0 + pow(1.0 - temperature/criticalTemperature(), 2.0/7.0); | |
| 240 | 3727494 | Scalar V = Consts::R*criticalTemperature()/criticalPressure()*pow(Z_RA, expo); // liquid molar volume [cm^3/mol] | |
| 241 | |||
| 242 | 3727494 | return 1.0/V; // molar density [mol/m^3] | |
| 243 | } | ||
| 244 | |||
| 245 | /*! | ||
| 246 | * \brief Returns true if the gas phase is assumed to be compressible | ||
| 247 | */ | ||
| 248 | static constexpr bool gasIsCompressible() | ||
| 249 | { return true; } | ||
| 250 | |||
| 251 | /*! | ||
| 252 | * \brief Returns true if the gas phase is assumed to be ideal | ||
| 253 | */ | ||
| 254 | static constexpr bool gasIsIdeal() | ||
| 255 | { return true; } | ||
| 256 | |||
| 257 | /*! | ||
| 258 | * \brief Returns true if the liquid phase is assumed to be compressible | ||
| 259 | */ | ||
| 260 | static constexpr bool liquidIsCompressible() | ||
| 261 | { return false; } | ||
| 262 | |||
| 263 | /*! | ||
| 264 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of mesitylene vapor | ||
| 265 | * | ||
| 266 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 267 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 268 | */ | ||
| 269 | 2092519 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | |
| 270 | { | ||
| 271 | using std::min; | ||
| 272 | using std::max; | ||
| 273 |
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2092519 | temperature = min(temperature, 500.0); // regularization |
| 274 |
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2092519 | temperature = max(temperature, 250.0); |
| 275 | |||
| 276 | // reduced temperature | ||
| 277 | 2092519 | Scalar Tr = temperature/criticalTemperature(); | |
| 278 | |||
| 279 | 2092519 | Scalar Fp0 = 1.0; | |
| 280 | 2092519 | Scalar xi = 0.00474; | |
| 281 | |||
| 282 | using std::pow; | ||
| 283 | using std::exp; | ||
| 284 | 2092519 | Scalar eta_xi = | |
| 285 | 2092519 | Fp0*(0.807*pow(Tr,0.618) | |
| 286 | 2092519 | - 0.357*exp(-0.449*Tr) | |
| 287 | 2092519 | + 0.34*exp(-4.058*Tr) | |
| 288 | 2092519 | + 0.018); | |
| 289 | |||
| 290 | 2092519 | return eta_xi/xi/1e7; // [Pa s] | |
| 291 | } | ||
| 292 | |||
| 293 | /*! | ||
| 294 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of pure mesitylene. | ||
| 295 | * | ||
| 296 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 297 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 298 | */ | ||
| 299 | 2345419 | static Scalar liquidViscosity(Scalar temperature, Scalar pressure) | |
| 300 | { | ||
| 301 | using std::min; | ||
| 302 | using std::max; | ||
| 303 |
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2345419 | temperature = min(temperature, 500.0); // regularization |
| 304 |
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2345419 | temperature = max(temperature, 250.0); |
| 305 | |||
| 306 | 2345419 | const Scalar A = -6.749; | |
| 307 | 2345419 | const Scalar B = 2010.0; | |
| 308 | |||
| 309 | using std::exp; | ||
| 310 | 2345419 | return exp(A + B/temperature)*1e-3; // [Pa s] | |
| 311 | } | ||
| 312 | |||
| 313 | /*! | ||
| 314 | * \brief Specific heat capacity of liquid mesitylene \f$\mathrm{[J/(kg*K)]}\f$. | ||
| 315 | * | ||
| 316 | * source : Reid et al. (1987, Missenard group contrib. method (chap 5-7, Table 5-11, s. example 5-8)) \cite reid1987 | ||
| 317 | * | ||
| 318 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 319 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 320 | * | ||
| 321 | */ | ||
| 322 | 7558686 | static Scalar liquidHeatCapacity(const Scalar temperature, | |
| 323 | const Scalar pressure) | ||
| 324 | { | ||
| 325 | /* according Reid et al. : Missenard group contrib. method (s. example 5-8) */ | ||
| 326 | /* Mesitylen: C9H12 : 3* CH3 ; 1* C6H5 (phenyl-ring) ; -2* H (this was to much!) */ | ||
| 327 | /* linear interpolation between table values [J/(mol K)]*/ | ||
| 328 | Scalar H, CH3, C6H5; | ||
| 329 |
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7558686 | if(temperature<298.) { |
| 330 | // extrapolation for Temperature<273 */ | ||
| 331 | 7371933 | H = 13.4+1.2*(temperature-273.0)/25.; // 13.4 + 1.2 = 14.6 = H(T=298K) i.e. interpolation of table values 273<T<298 | |
| 332 | 7371933 | CH3 = 40.0+1.6*(temperature-273.0)/25.; // 40 + 1.6 = 41.6 = CH3(T=298K) | |
| 333 | 7371933 | C6H5 = 113.0+4.2*(temperature-273.0)/25.; // 113 + 4.2 =117.2 = C6H5(T=298K) | |
| 334 | } | ||
| 335 |
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186753 | else if((temperature>=298.0)&&(temperature<323.)){ // i.e. interpolation of table values 298<T<323 |
| 336 | 107398 | H = 14.6+0.9*(temperature-298.0)/25.; | |
| 337 | 107398 | CH3 = 41.6+1.9*(temperature-298.0)/25.; | |
| 338 | 107398 | C6H5 = 117.2+6.2*(temperature-298.0)/25.; | |
| 339 | } | ||
| 340 |
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79355 | else if((temperature>=323.0)&&(temperature<348.)){// i.e. interpolation of table values 323<T<348 |
| 341 | 79355 | H = 15.5+1.2*(temperature-323.0)/25.; | |
| 342 | 79355 | CH3 = 43.5+2.3*(temperature-323.0)/25.; | |
| 343 | 79355 | C6H5 = 123.4+6.3*(temperature-323.0)/25.; | |
| 344 | } | ||
| 345 | else { | ||
| 346 | ✗ | assert(temperature>=348.0); | |
| 347 | |||
| 348 | /* take care: extrapolation for Temperature>373 */ | ||
| 349 | ✗ | H = 16.7+2.1*(temperature-348.0)/25.; /* leads probably to underestimates */ | |
| 350 | ✗ | CH3 = 45.8+2.5*(temperature-348.0)/25.; | |
| 351 | ✗ | C6H5 = 129.7+6.3*(temperature-348.0)/25.; | |
| 352 | } | ||
| 353 | |||
| 354 | 7558686 | return (C6H5 + 3*CH3 - 2*H)/molarMass(); // J/(mol K) -> J/(kg K) | |
| 355 | } | ||
| 356 | |||
| 357 | /*! | ||
| 358 | * \brief Thermal conductivity \f$\mathrm{[[W/(m*K)]}\f$ of mesitylene | ||
| 359 | * | ||
| 360 | * see: http://pubs.acs.org/doi/pdf/10.1021/ci000139t | ||
| 361 | * | ||
| 362 | * \param temperature absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 363 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 364 | */ | ||
| 365 | static Scalar liquidThermalConductivity( Scalar temperature, Scalar pressure) | ||
| 366 | { | ||
| 367 | return 0.1351; | ||
| 368 | } | ||
| 369 | }; | ||
| 370 | |||
| 371 | } // end namespace Dumux::Components | ||
| 372 | |||
| 373 | #endif | ||
| 374 |