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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 xylene. | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_XYLENE_HH | ||
| 13 | #define DUMUX_XYLENE_HH | ||
| 14 | |||
| 15 | #include <cmath> | ||
| 16 | #include <dumux/material/idealgas.hh> | ||
| 17 | #include <dumux/material/constants.hh> | ||
| 18 | |||
| 19 | #include <dumux/material/components/base.hh> | ||
| 20 | #include <dumux/material/components/liquid.hh> | ||
| 21 | #include <dumux/material/components/gas.hh> | ||
| 22 | |||
| 23 | namespace Dumux::Components { | ||
| 24 | |||
| 25 | /*! | ||
| 26 | * \ingroup Components | ||
| 27 | * \brief Properties of xylene. | ||
| 28 | * | ||
| 29 | * \tparam Scalar The type used for scalar values | ||
| 30 | */ | ||
| 31 | template <class Scalar> | ||
| 32 | class Xylene | ||
| 33 | : public Components::Base<Scalar, Xylene<Scalar> > | ||
| 34 | , public Components::Liquid<Scalar, Xylene<Scalar> > | ||
| 35 | , public Components::Gas<Scalar, Xylene<Scalar> > | ||
| 36 | { | ||
| 37 | using Consts = Constants<Scalar>; | ||
| 38 | using IdealGas = Dumux::IdealGas<Scalar>; | ||
| 39 | |||
| 40 | public: | ||
| 41 | /*! | ||
| 42 | * \brief A human readable name for the xylene | ||
| 43 | */ | ||
| 44 |
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16 | static std::string name() |
| 45 |
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16 | { return "xylene"; } |
| 46 | |||
| 47 | /*! | ||
| 48 | * \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of xylene | ||
| 49 | */ | ||
| 50 | constexpr static Scalar molarMass() | ||
| 51 | { return 0.106; } | ||
| 52 | |||
| 53 | /*! | ||
| 54 | * \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of xylene | ||
| 55 | */ | ||
| 56 | constexpr static Scalar criticalTemperature() | ||
| 57 | { return 617.1; } | ||
| 58 | |||
| 59 | /*! | ||
| 60 | * \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of xylene | ||
| 61 | */ | ||
| 62 | constexpr static Scalar criticalPressure() | ||
| 63 | { return 35.4e5; } | ||
| 64 | |||
| 65 | /*! | ||
| 66 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at xylene's boiling point (1 atm). | ||
| 67 | */ | ||
| 68 | constexpr static Scalar boilingTemperature() | ||
| 69 | { return 412.3; } | ||
| 70 | |||
| 71 | /*! | ||
| 72 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at xylene's triple point. | ||
| 73 | */ | ||
| 74 | static Scalar tripleTemperature() | ||
| 75 | { | ||
| 76 | DUNE_THROW(Dune::NotImplemented, "tripleTemperature for xylene"); | ||
| 77 | } | ||
| 78 | |||
| 79 | /*! | ||
| 80 | * \brief Returns the pressure \f$\mathrm{[Pa]}\f$ at xylene's triple point. | ||
| 81 | */ | ||
| 82 | static Scalar triplePressure() | ||
| 83 | { | ||
| 84 | DUNE_THROW(Dune::NotImplemented, "triplePressure for xylene"); | ||
| 85 | } | ||
| 86 | |||
| 87 | /*! | ||
| 88 | * \brief The saturation vapor pressure in \f$\mathrm{[Pa]}\f$ of pure xylene | ||
| 89 | * at a given temperature according to Antoine after Betz 1997 -> Gmehling et al 1980 \cite gmehling1980 <BR> | ||
| 90 | * | ||
| 91 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 92 | */ | ||
| 93 | 16483292 | static Scalar vaporPressure(Scalar temperature) | |
| 94 | { | ||
| 95 | 16483292 | const Scalar A = 7.00909; | |
| 96 | 16483292 | const Scalar B = 1462.266; | |
| 97 | 16483292 | const Scalar C = 215.110; | |
| 98 | |||
| 99 | 16483292 | Scalar T = temperature - 273.15; | |
| 100 | |||
| 101 | using std::pow; | ||
| 102 | 16483292 | Scalar psat = 1.334*pow(10.0, (A - (B/(T + C)))); // in [mbar] | |
| 103 |
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16483292 | psat *= 100.0; // in [Pa] (0.001*1.E5) |
| 104 | |||
| 105 | return psat; | ||
| 106 | } | ||
| 107 | |||
| 108 | /*! | ||
| 109 | * \brief Specific heat cap of liquid xylene \f$\mathrm{[J/kg]}\f$. | ||
| 110 | * | ||
| 111 | * source : Reid et al. (fourth edition): Missenard group contrib. method (chap 5-7, Table 5-11, s. example 5-8) \cite reid1987 <BR> | ||
| 112 | * | ||
| 113 | * \param temp temperature of component in \f$\mathrm{[K]}\f$ | ||
| 114 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 115 | */ | ||
| 116 | 13187182 | static Scalar liquidHeatCapacity(Scalar temp, Scalar pressure) | |
| 117 | { | ||
| 118 | Scalar CH3,C6H5,H; | ||
| 119 | // after Reid et al. : Missenard group contrib. method (s. example 5-8) \cite reid1987 <BR> | ||
| 120 | // Xylene: C9H12 : 3* CH3 ; 1* C6H5 (phenyl-ring) ; -2* H (this was too much!) | ||
| 121 | // linear interpolation between table values [J/(mol K)] | ||
| 122 | |||
| 123 |
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13187182 | if(temp < 298.0){ // take care: extrapolation for Temp<273 |
| 124 | 13113087 | H = 13.4 + 1.2*(temp - 273.0)/25.0; // 13.4 + 1.2 = 14.6 = H(T=298K) i.e. interpolation of table values 273<T<298 | |
| 125 | 13113087 | CH3 = 40.0 + 1.6*(temp - 273.0)/25.0; // 40 + 1.6 = 41.6 = CH3(T=298K) | |
| 126 | 13113087 | C6H5 = 113.0 + 4.2*(temp - 273.0)/25.0; // 113 + 4.2 = 117.2 = C6H5(T=298K) | |
| 127 | } | ||
| 128 |
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74095 | else if(temp < 323.0){ |
| 129 | 19754 | H = 14.6 + 0.9*(temp - 298.0)/25.0; // i.e. interpolation of table values 298<T<323 | |
| 130 | 19754 | CH3 = 41.6 + 1.9*(temp - 298.0)/25.0; | |
| 131 | 19754 | C6H5 = 117.2 + 6.2*(temp - 298.0)/25.0; | |
| 132 | } | ||
| 133 |
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54341 | else if(temp < 348.0){ |
| 134 | 43207 | H = 15.5 + 1.2*(temp - 323.0)/25.0; // i.e. interpolation of table values 323<T<348 | |
| 135 | 43207 | CH3 = 43.5 + 2.3*(temp - 323.0)/25.0; | |
| 136 | 43207 | C6H5 = 123.4 + 6.3*(temp - 323.0)/25.0; | |
| 137 | } | ||
| 138 | else { | ||
| 139 | 11134 | H = 16.7 + 2.1*(temp - 348.0)/25.0; // i.e. interpolation of table values 348<T<373 | |
| 140 | 11134 | CH3 = 45.8 + 2.5*(temp - 348.0)/25.0; // take care: extrapolation for Temp>373 | |
| 141 | 11134 | C6H5 = 129.7 + 6.3*(temp - 348.0)/25.0; // most likely leads to underestimation | |
| 142 | } | ||
| 143 | |||
| 144 | 13187182 | return (C6H5 + 2*CH3 - H)/molarMass();// J/(mol K) -> J/(kg K) | |
| 145 | } | ||
| 146 | |||
| 147 | |||
| 148 | /*! | ||
| 149 | * \brief Specific enthalpy of liquid xylene \f$\mathrm{[J/kg]}\f$. | ||
| 150 | * | ||
| 151 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 152 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 153 | */ | ||
| 154 | 6593536 | static Scalar liquidEnthalpy(const Scalar temperature, | |
| 155 | const Scalar pressure) | ||
| 156 | { | ||
| 157 | // Gauss quadrature rule: | ||
| 158 | // Interval: [0K; temperature (K)] | ||
| 159 | // Gauss-Legendre-Integration with variable transformation: | ||
| 160 | // \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 ) | ||
| 161 | // with: n=2, legendre -> x_i = +/- \sqrt(1/3), \apha_i=1 | ||
| 162 | // here: a=273.15K, b=actual temperature in Kelvin | ||
| 163 | // \leadsto h(T) = \int_273.15^T c_p(T) dT | ||
| 164 | // \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)) | ||
| 165 | |||
| 166 | // Enthalpy may have arbitrary reference state, but the empirical/fitted heatCapacity function needs Kelvin as input and is | ||
| 167 | // fit over a certain temperature range. This suggests choosing an interval of integration being in the actual fit range. | ||
| 168 | // I.e. choosing T=273.15K as reference point for liquid enthalpy. | ||
| 169 | using std::sqrt; | ||
| 170 | 6593536 | const Scalar sqrt1over3 = sqrt(1./3.); | |
| 171 | // evaluation points according to Gauss-Legendre integration | ||
| 172 | 6593536 | const Scalar TEval1 = 0.5*(temperature-273.15)* sqrt1over3 + 0.5*(273.15+temperature); | |
| 173 | // evaluation points according to Gauss-Legendre integration | ||
| 174 | 6593536 | const Scalar TEval2 = 0.5*(temperature-273.15)* (-1)* sqrt1over3 + 0.5*(273.15+temperature); | |
| 175 | |||
| 176 | 6593536 | const Scalar h_n = 0.5 * (temperature-273.15) * ( liquidHeatCapacity(TEval1, pressure) + liquidHeatCapacity(TEval2, pressure) ); | |
| 177 | |||
| 178 | 6593536 | return h_n; | |
| 179 | } | ||
| 180 | |||
| 181 | /*! | ||
| 182 | * \brief Latent heat of vaporization for xylene \f$\mathrm{[J/kg]}\f$. | ||
| 183 | * | ||
| 184 | * source : Reid et al. (fourth edition): Chen method (chap. 7-11, Delta H_v = Delta H_v (T) according to chap. 7-12) \cite reid1987 | ||
| 185 | * | ||
| 186 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 187 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 188 | */ | ||
| 189 | 3296768 | static Scalar heatVap(Scalar temperature, | |
| 190 | const Scalar pressure) | ||
| 191 | { | ||
| 192 | using std::min; | ||
| 193 | using std::max; | ||
| 194 |
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3296768 | temperature = min(temperature, criticalTemperature()); // regularization |
| 195 |
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3296768 | temperature = max(temperature, 0.0); // regularization |
| 196 | |||
| 197 | 3296768 | constexpr Scalar T_crit = criticalTemperature(); | |
| 198 | 3296768 | constexpr Scalar Tr1 = boilingTemperature()/criticalTemperature(); | |
| 199 | 3296768 | constexpr Scalar p_crit = criticalPressure(); | |
| 200 | |||
| 201 | // Chen method, eq. 7-11.4 (at boiling) | ||
| 202 | using std::log; | ||
| 203 | 3296768 | const Scalar DH_v_boil = Consts::R * T_crit * Tr1 | |
| 204 | * (3.978 * Tr1 - 3.958 + 1.555*log(p_crit * 1e-5 /*Pa->bar*/ ) ) | ||
| 205 | / (1.07 - Tr1); /* [J/mol] */ | ||
| 206 | |||
| 207 | /* Variation with temp according to Watson relation eq 7-12.1*/ | ||
| 208 | using std::pow; | ||
| 209 | 3296768 | const Scalar Tr2 = temperature/criticalTemperature(); | |
| 210 | 3296768 | const Scalar n = 0.375; | |
| 211 | 3296768 | const Scalar DH_vap = DH_v_boil * pow(((1.0 - Tr2)/(1.0 - Tr1)), n); | |
| 212 | |||
| 213 | 3296768 | return (DH_vap/molarMass()); // we need [J/kg] | |
| 214 | } | ||
| 215 | |||
| 216 | /*! | ||
| 217 | * \brief Specific enthalpy of xylene vapor \f$\mathrm{[J/kg]}\f$. | ||
| 218 | * | ||
| 219 | * This relation is true on the vapor pressure curve, i.e. as long | ||
| 220 | * as there is a liquid phase present. | ||
| 221 | * | ||
| 222 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 223 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 224 | */ | ||
| 225 | 3296768 | static Scalar gasEnthalpy(Scalar temperature, Scalar pressure) | |
| 226 | { | ||
| 227 | 3296768 | return liquidEnthalpy(temperature, pressure) + heatVap(temperature, pressure); | |
| 228 | } | ||
| 229 | |||
| 230 | /*! | ||
| 231 | * \brief The density \f$\mathrm{[kg/m^3]}\f$ of xylene gas at a given pressure and temperature. | ||
| 232 | * | ||
| 233 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 234 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 235 | */ | ||
| 236 |
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3296771 | static Scalar gasDensity(Scalar temperature, Scalar pressure) |
| 237 | { | ||
| 238 |
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3296771 | return IdealGas::density(molarMass(), |
| 239 | temperature, | ||
| 240 | pressure); | ||
| 241 | } | ||
| 242 | |||
| 243 | /*! | ||
| 244 | * \brief The molar gas density \f$\mathrm{[mol/m^3]}\f$ of xylene gas at a given pressure and temperature. | ||
| 245 | * | ||
| 246 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 247 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 248 | */ | ||
| 249 | 3296658 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | |
| 250 | 3296658 | { return IdealGas::molarDensity(temperature, pressure); } | |
| 251 | |||
| 252 | /*! | ||
| 253 | * \brief The molar liquid density of pure xylene at a given pressure and temperature | ||
| 254 | * \f$\mathrm{[mol/m^3]}\f$. | ||
| 255 | * | ||
| 256 | * source : Reid et al. (fourth edition): Modified Racket technique (chap. 3-11, eq. 3-11.9) \cite reid1987 <BR> | ||
| 257 | * | ||
| 258 | * \param temp temperature of component in \f$\mathrm{[K]}\f$ | ||
| 259 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 260 | */ | ||
| 261 | 6593432 | static Scalar liquidMolarDensity(Scalar temp, Scalar pressure) | |
| 262 | { | ||
| 263 | // saturated molar volume according to Lide, CRC Handbook of | ||
| 264 | // Thermophysical and Thermochemical Data, CRC Press, 1994 | ||
| 265 | // valid for 245 < Temp < 600 | ||
| 266 | using std::min; | ||
| 267 | using std::max; | ||
| 268 |
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6593432 | temp = min(temp, 500.0); // regularization |
| 269 |
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6593432 | temp = max(temp, 250.0); // regularization |
| 270 | |||
| 271 | using std::pow; | ||
| 272 | 6593432 | const Scalar A1 = 0.25919; // from table | |
| 273 | 6593432 | const Scalar A2 = 0.0014569; // from table | |
| 274 | 6593432 | const Scalar expo = 1.0 + pow((1.0 - temp/criticalTemperature()), (2.0/7.0)); | |
| 275 | 6593432 | const Scalar V = A2*pow(A1, expo); // liquid molar volume [m^3/mol] | |
| 276 | |||
| 277 | 6593432 | return 1.0/V; // molar density [mol/m^3] | |
| 278 | } | ||
| 279 | |||
| 280 | /*! | ||
| 281 | * \brief The density of pure xylene at a given pressure and temperature \f$\mathrm{[kg/m^3]}\f$. | ||
| 282 | * | ||
| 283 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 284 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 285 | */ | ||
| 286 | 3296774 | static Scalar liquidDensity(Scalar temperature, Scalar pressure) | |
| 287 | { | ||
| 288 |
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3296774 | return liquidMolarDensity(temperature, pressure)*molarMass(); |
| 289 | } | ||
| 290 | |||
| 291 | /*! | ||
| 292 | * \brief Returns true if the gas phase is assumed to be compressible | ||
| 293 | */ | ||
| 294 | static constexpr bool gasIsCompressible() | ||
| 295 | { return true; } | ||
| 296 | |||
| 297 | /*! | ||
| 298 | * \brief Returns true if the gas phase is assumed to be ideal | ||
| 299 | */ | ||
| 300 | static constexpr bool gasIsIdeal() | ||
| 301 | { return true; } | ||
| 302 | |||
| 303 | /*! | ||
| 304 | * \brief Returns true if the liquid phase is assumed to be compressible | ||
| 305 | */ | ||
| 306 | static constexpr bool liquidIsCompressible() | ||
| 307 | { return false; } | ||
| 308 | |||
| 309 | /*! | ||
| 310 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of xylene vapor | ||
| 311 | * | ||
| 312 | * \param temp temperature of component in \f$\mathrm{[K]}\f$ | ||
| 313 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 314 | */ | ||
| 315 | 3296768 | static Scalar gasViscosity(Scalar temp, Scalar pressure) | |
| 316 | { | ||
| 317 | using std::min; | ||
| 318 | using std::max; | ||
| 319 |
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3296768 | temp = min(temp, 500.0); // regularization |
| 320 |
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3296768 | temp = max(temp, 250.0); // regularization |
| 321 | |||
| 322 | using std::pow; | ||
| 323 | using std::exp; | ||
| 324 |
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3296768 | const Scalar Tr = max(temp/criticalTemperature(), 1e-10); |
| 325 | 3296768 | const Scalar Fp0 = 1.0; | |
| 326 | 3296768 | const Scalar xi = 0.004623; | |
| 327 | 3296768 | const Scalar eta_xi = Fp0*(0.807*pow(Tr, 0.618) | |
| 328 | 3296768 | - 0.357*exp(-0.449*Tr) | |
| 329 | 3296768 | + 0.34*exp(-4.058*Tr) | |
| 330 | + 0.018); | ||
| 331 | 3296768 | Scalar r = eta_xi/xi; // [1e-6 P] | |
| 332 | 3296768 | r /= 1.0e7; // [Pa s] | |
| 333 | |||
| 334 | 3296768 | return r; | |
| 335 | } | ||
| 336 | |||
| 337 | /*! | ||
| 338 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of pure xylene. | ||
| 339 | * | ||
| 340 | * \param temp temperature of component in \f$\mathrm{[K]}\f$ | ||
| 341 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 342 | */ | ||
| 343 | 3296768 | static Scalar liquidViscosity(Scalar temp, Scalar pressure) | |
| 344 | { | ||
| 345 | using std::min; | ||
| 346 | using std::max; | ||
| 347 |
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3296768 | temp = min(temp, 500.0); // regularization |
| 348 |
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3296768 | temp = max(temp, 250.0); // regularization |
| 349 | |||
| 350 | 3296768 | const Scalar A = -3.82; | |
| 351 | 3296768 | const Scalar B = 1027.0; | |
| 352 | 3296768 | const Scalar C = -6.38e-4; | |
| 353 | 3296768 | const Scalar D = 4.52e-7; | |
| 354 | |||
| 355 | using std::exp; | ||
| 356 | 3296768 | Scalar r = exp(A + B/temp + C*temp + D*temp*temp); // in [cP] | |
| 357 | 3296768 | r *= 1.0e-3; // in [Pa s] | |
| 358 | |||
| 359 | 3296768 | return r; // [Pa s] | |
| 360 | } | ||
| 361 | |||
| 362 | /*! | ||
| 363 | * \brief Thermal conductivity \f$\mathrm{[[W/(m*K)]}\f$ of xylene | ||
| 364 | * | ||
| 365 | * Thermal Conductivity of p-Xylene taken from the Dortmund Data Bank, see: | ||
| 366 | * http://www.ddbst.de/en/EED/PCP/TCN_C176.php | ||
| 367 | * | ||
| 368 | * \param temperature absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 369 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 370 | */ | ||
| 371 | static Scalar liquidThermalConductivity( Scalar temperature, Scalar pressure) | ||
| 372 | { | ||
| 373 | return 0.13; | ||
| 374 | } | ||
| 375 | }; | ||
| 376 | |||
| 377 | } // end namespace Dumux::Components | ||
| 378 | |||
| 379 | #endif | ||
| 380 |