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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 Properties of the component heavyoil. | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_HEAVYOIL_HH | ||
| 13 | #define DUMUX_HEAVYOIL_HH | ||
| 14 | |||
| 15 | #include <algorithm> | ||
| 16 | |||
| 17 | #include <dune/common/math.hh> | ||
| 18 | |||
| 19 | #include <dumux/material/constants.hh> | ||
| 20 | #include <dumux/material/components/base.hh> | ||
| 21 | #include <dumux/material/components/gas.hh> | ||
| 22 | #include <dumux/material/components/liquid.hh> | ||
| 23 | #include <dumux/material/idealgas.hh> | ||
| 24 | |||
| 25 | namespace Dumux::Components { | ||
| 26 | |||
| 27 | /*! | ||
| 28 | * \ingroup Components | ||
| 29 | * \brief Properties of the component heavyoil | ||
| 30 | * | ||
| 31 | * \tparam Scalar The type used for scalar values | ||
| 32 | */ | ||
| 33 | template <class Scalar> | ||
| 34 | class HeavyOil | ||
| 35 | : public Components::Base<Scalar, HeavyOil<Scalar> > | ||
| 36 | , public Components::Liquid<Scalar, HeavyOil<Scalar> > | ||
| 37 | , public Components::Gas<Scalar, HeavyOil<Scalar> > | ||
| 38 | { | ||
| 39 | using Consts = Dumux::Constants<Scalar>; | ||
| 40 | using IdealGas = Dumux::IdealGas<Scalar>; | ||
| 41 | public: | ||
| 42 | /*! | ||
| 43 | * \brief A human readable name for heavyoil | ||
| 44 | */ | ||
| 45 | static std::string name() | ||
| 46 |
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|
26 | { return "heavyoil"; } |
| 47 | |||
| 48 | /*! | ||
| 49 | * \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of heavyoil | ||
| 50 | */ | ||
| 51 | constexpr static Scalar molarMass() | ||
| 52 | { return .350; } | ||
| 53 | |||
| 54 | /*! | ||
| 55 | * \brief The MolecularWeight in \f$\mathrm{[kg/mol]}\f$ of refComponent | ||
| 56 | */ | ||
| 57 | constexpr static Scalar refComponentMolecularWeight() | ||
| 58 | { return .400; } | ||
| 59 | |||
| 60 | /*! | ||
| 61 | * \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of heavyoil | ||
| 62 | */ | ||
| 63 | |||
| 64 | constexpr static Scalar molecularWeight() | ||
| 65 | { return .350; } | ||
| 66 | |||
| 67 | /*! | ||
| 68 | * \brief The Specific Gravity \f$\mathrm{[ ]}\f$ of heavyoil | ||
| 69 | */ | ||
| 70 | constexpr static Scalar specificGravity() | ||
| 71 | { return 0.91; } | ||
| 72 | |||
| 73 | /*! | ||
| 74 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at heavyoil's triple point. | ||
| 75 | */ | ||
| 76 | static Scalar tripleTemperature() | ||
| 77 | { | ||
| 78 | DUNE_THROW(Dune::NotImplemented, "tripleTemperature for heavyoil"); | ||
| 79 | } | ||
| 80 | |||
| 81 | /*! | ||
| 82 | * \brief Returns the pressure \f$\mathrm{[Pa]}\f$ at heavyoil's triple point. | ||
| 83 | */ | ||
| 84 | static Scalar triplePressure() | ||
| 85 | { | ||
| 86 | DUNE_THROW(Dune::NotImplemented, "triplePressure for heavyoil"); | ||
| 87 | } | ||
| 88 | |||
| 89 | static Scalar refComponentSpecificGravity() | ||
| 90 | { | ||
| 91 | constexpr Scalar A = 0.83; | ||
| 92 | constexpr Scalar B = 89.9513; | ||
| 93 | constexpr Scalar C = 139.6612; | ||
| 94 | constexpr Scalar D = 3.2033; | ||
| 95 | constexpr Scalar E = 1.0564; | ||
| 96 | |||
| 97 | const Scalar mW = refComponentMolecularWeight() *1000. ; // in [g/mol]; | ||
| 98 | |||
| 99 | using std::pow; | ||
| 100 | return A+(B/mW)-(C/pow((mW+D),E)); | ||
| 101 | } | ||
| 102 | |||
| 103 | static Scalar perbutationFactorBoilingTemperature() | ||
| 104 | { | ||
| 105 | constexpr Scalar A = -7.4120e-2; //All factors for 1 atm / 101325 pascals [760 mmHg] | ||
| 106 | constexpr Scalar B = -7.5041e-3; | ||
| 107 | constexpr Scalar C = -2.6031; | ||
| 108 | constexpr Scalar D = 9.0180e-2; | ||
| 109 | constexpr Scalar E = -1.0482; | ||
| 110 | |||
| 111 | using std::log; | ||
| 112 | const Scalar deltaSpecificGravity = log(refComponentSpecificGravity()/specificGravity()); | ||
| 113 | const Scalar deltaMolecularWeight = log(refComponentMolecularWeight()/molecularWeight()); | ||
| 114 | |||
| 115 | using Dune::power; | ||
| 116 | 7710114 | return A*power(deltaSpecificGravity,2) + B*deltaSpecificGravity + C*power(deltaMolecularWeight,2) + D*deltaMolecularWeight | |
| 117 | 7710114 | + E*deltaSpecificGravity*deltaMolecularWeight; | |
| 118 | } | ||
| 119 | |||
| 120 | static Scalar perbutationFactorCriticalTemperature() | ||
| 121 | { | ||
| 122 | constexpr Scalar A = -6.1294e-2; | ||
| 123 | constexpr Scalar B = -7.0862e-2; | ||
| 124 | constexpr Scalar C = 6.1976e-1; | ||
| 125 | constexpr Scalar D = -5.7090e-2; | ||
| 126 | constexpr Scalar E = -8.4583e-2; | ||
| 127 | |||
| 128 | using std::log; | ||
| 129 | const Scalar deltaSpecificGravity = log(refComponentSpecificGravity()/specificGravity()); | ||
| 130 | const Scalar deltaMolecularWeight = log(refComponentMolecularWeight()/molecularWeight()); | ||
| 131 | |||
| 132 | using Dune::power; | ||
| 133 | 30840456 | return A*power(deltaSpecificGravity,2) + B*deltaSpecificGravity + C*power(deltaMolecularWeight,2) + D*deltaMolecularWeight | |
| 134 | 30840456 | + E*deltaSpecificGravity*deltaMolecularWeight; | |
| 135 | } | ||
| 136 | |||
| 137 | static Scalar perbutationFactorCriticalPressure() | ||
| 138 | { | ||
| 139 | constexpr Scalar A = 1.8270e-1; | ||
| 140 | constexpr Scalar B = -2.4864e-1; | ||
| 141 | constexpr Scalar C = 8.3611; | ||
| 142 | constexpr Scalar D = -2.2389e-1; | ||
| 143 | constexpr Scalar E = 2.6984; | ||
| 144 | |||
| 145 | using std::log; | ||
| 146 | const Scalar deltaSpecificGravity = log(refComponentSpecificGravity()/specificGravity()); | ||
| 147 | const Scalar deltaMolecularWeight = log(refComponentMolecularWeight()/molecularWeight()); | ||
| 148 | |||
| 149 | using Dune::power; | ||
| 150 | 7710114 | return A*power(deltaSpecificGravity,2) + B*deltaSpecificGravity + C*power(deltaMolecularWeight,2) + D*deltaMolecularWeight | |
| 151 | 7710114 | + E*deltaSpecificGravity*deltaMolecularWeight; | |
| 152 | } | ||
| 153 | |||
| 154 | static Scalar refComponentBoilingTemperature() | ||
| 155 | { | ||
| 156 | 3855057 | constexpr Scalar A = 477.63; //All factors for 1 atm / 101325 pascals [760 mmHg] | |
| 157 | 3855057 | constexpr Scalar B = 88.51; | |
| 158 | 3855057 | constexpr Scalar C = 1007; | |
| 159 | 3855057 | constexpr Scalar D = 1214.40; | |
| 160 | |||
| 161 | using std::log; | ||
| 162 | return A*log((1000.*refComponentMolecularWeight() + B)/(1000.*refComponentMolecularWeight()+C)) + D; | ||
| 163 | } | ||
| 164 | |||
| 165 | static Scalar refComponentCriticalTemperature() | ||
| 166 | { | ||
| 167 | 15420228 | constexpr Scalar A = 226.50; | |
| 168 | 15420228 | constexpr Scalar B = 6.78; | |
| 169 | 15420228 | constexpr Scalar C = 1.282e6; | |
| 170 | 15420228 | constexpr Scalar D = 2668; | |
| 171 | |||
| 172 | using std::log; | ||
| 173 | return A*log((1000.*refComponentMolecularWeight() + B)/(1000.*refComponentMolecularWeight()+C)) + D ; | ||
| 174 | } | ||
| 175 | |||
| 176 | static Scalar refComponentCriticalPressure() | ||
| 177 | { | ||
| 178 | 3855057 | constexpr Scalar A = 141.20; | |
| 179 | 3855057 | constexpr Scalar B = 45.66e-2; | |
| 180 | 3855057 | constexpr Scalar C = 16.59e-3; | |
| 181 | 3855057 | constexpr Scalar D = 2.19; | |
| 182 | |||
| 183 | using std::pow; | ||
| 184 | return (A*1000.*molecularWeight())/(pow(B + (C*1000.*molecularWeight()),D)) ; | ||
| 185 | } | ||
| 186 | |||
| 187 | /*! | ||
| 188 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at heavyoil's boiling point (1 atm) | ||
| 189 | */ | ||
| 190 | 3855057 | static Scalar boilingTemperature() | |
| 191 | { | ||
| 192 | using Dune::power; | ||
| 193 | 11565171 | return refComponentBoilingTemperature() * power((1 + 2*perbutationFactorBoilingTemperature())/(1 - 2*perbutationFactorBoilingTemperature()),2); | |
| 194 | } | ||
| 195 | |||
| 196 | /*! | ||
| 197 | * \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of heavyoil | ||
| 198 | */ | ||
| 199 | 15420228 | static Scalar criticalTemperature() | |
| 200 | { | ||
| 201 | using Dune::power; | ||
| 202 | 46260684 | return refComponentCriticalTemperature() * power((1 + 2*perbutationFactorCriticalTemperature())/(1 - 2*perbutationFactorCriticalTemperature()),2); | |
| 203 | } | ||
| 204 | |||
| 205 | /*! | ||
| 206 | * \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of heavyoil | ||
| 207 | */ | ||
| 208 | 3855057 | static Scalar criticalPressure() | |
| 209 | { | ||
| 210 | using Dune::power; | ||
| 211 | 11565171 | return refComponentCriticalPressure() * power((1 + 2*perbutationFactorCriticalPressure())/(1 - 2*perbutationFactorCriticalPressure()),2); | |
| 212 | } | ||
| 213 | |||
| 214 | /*! | ||
| 215 | * \brief The saturation vapor pressure in \f$\mathrm{[Pa]}\f$ of | ||
| 216 | * | ||
| 217 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 218 | */ | ||
| 219 | static Scalar vaporPressure(Scalar temperature) | ||
| 220 | { | ||
| 221 | 7711000 | constexpr Scalar A = 8.25990; | |
| 222 | 7711000 | constexpr Scalar B = 2830.065; | |
| 223 | 7711000 | constexpr Scalar C = 42.95101; | |
| 224 | |||
| 225 | 7711000 | const Scalar T = temperature - 273.15; | |
| 226 | |||
| 227 | using std::pow; | ||
| 228 | 7711000 | return 100*1.334*pow(10.0, (A - (B/(T + C)))); // in [Pa] | |
| 229 | } | ||
| 230 | |||
| 231 | static Scalar vaporTemperature(Scalar pressure) | ||
| 232 | { | ||
| 233 | 370 | constexpr Scalar A = 8.25990; | |
| 234 | 370 | constexpr Scalar B = 2830.065; | |
| 235 | 370 | constexpr Scalar C = 42.95101; | |
| 236 | |||
| 237 | 370 | const Scalar P = pressure; | |
| 238 | |||
| 239 | using std::log10; | ||
| 240 | 370 | return Scalar ((B/(A-log10(P/100*1.334)))-C); | |
| 241 | } | ||
| 242 | |||
| 243 | /*! | ||
| 244 | * \brief Specific enthalpy of liquid heavyoil \f$\mathrm{[J/kg]}\f$. | ||
| 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 | ✗ | static Scalar liquidEnthalpy(const Scalar temperature, | |
| 250 | const Scalar pressure) | ||
| 251 | { | ||
| 252 | // Gauss quadrature rule: | ||
| 253 | // Interval: [0K; temperature (K)] | ||
| 254 | // Gauss-Legendre-Integration with variable transformation: | ||
| 255 | // \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 ) | ||
| 256 | // with: n=2, legendre -> x_i = +/- \sqrt(1/3), \apha_i=1 | ||
| 257 | // here: a=273.15K, b=actual temperature in Kelvin | ||
| 258 | // \leadsto h(T) = \int_273.15^T c_p(T) dT | ||
| 259 | // \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)) | ||
| 260 | |||
| 261 | // Enthalpy may have arbitrary reference state, but the empirical/fitted heatCapacity function needs Kelvin as input and is | ||
| 262 | // fit over a certain temperature range. This suggests choosing an interval of integration being in the actual fit range. | ||
| 263 | // I.e. choosing T=273.15K as reference point for liquid enthalpy. | ||
| 264 | using std::sqrt; | ||
| 265 | 7710114 | const Scalar sqrt1over3 = sqrt(1./3.); | |
| 266 | 7710114 | const Scalar TEval1 = 0.5*(temperature-273.15)* sqrt1over3 + 0.5*(273.15+temperature) ; // evaluation points according to Gauss-Legendre integration | |
| 267 | 7710114 | const Scalar TEval2 = 0.5*(temperature-273.15)* (-1)* sqrt1over3 + 0.5*(273.15+temperature) ; // evaluation points according to Gauss-Legendre integration | |
| 268 | |||
| 269 | 3855057 | const Scalar h_n = 0.5 * (temperature-273.15) * ( liquidHeatCapacity(TEval1, pressure) + liquidHeatCapacity(TEval2, pressure) ) ; | |
| 270 | |||
| 271 | ✗ | return h_n; | |
| 272 | } | ||
| 273 | |||
| 274 | /*! | ||
| 275 | * \brief Latent heat of vaporization for heavyoil \f$\mathrm{[J/kg]}\f$. | ||
| 276 | * | ||
| 277 | * source : Reid et al. (fourth edition): Chen method (chap. 7-11, Delta H_v = Delta H_v (T) according to chap. 7-12) | ||
| 278 | * | ||
| 279 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 280 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 281 | */ | ||
| 282 | 3855057 | static Scalar heatVap(Scalar temperature, | |
| 283 | const Scalar pressure) | ||
| 284 | { | ||
| 285 | using std::clamp; | ||
| 286 |
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3855057 | temperature = clamp(temperature, 0.0, criticalTemperature()); // regularization |
| 287 | |||
| 288 | 3855057 | const Scalar T_crit = criticalTemperature(); | |
| 289 | 3855057 | const Scalar Tr1 = boilingTemperature()/criticalTemperature(); | |
| 290 | 3855057 | const Scalar p_crit = criticalPressure(); | |
| 291 | |||
| 292 | // Chen method, eq. 7-11.4 (at boiling) | ||
| 293 | using std::log; | ||
| 294 | 7710114 | const Scalar DH_v_boil = Consts::R * T_crit * Tr1 | |
| 295 | 3855057 | * (3.978 * Tr1 - 3.958 + 1.555*log(p_crit * 1e-5 /*Pa->bar*/ ) ) | |
| 296 | 3855057 | / (1.07 - Tr1); /* [J/mol] */ | |
| 297 | |||
| 298 | /* Variation with temp according to Watson relation eq 7-12.1*/ | ||
| 299 | using std::pow; | ||
| 300 | 3855057 | const Scalar Tr2 = temperature/criticalTemperature(); | |
| 301 | 3855057 | const Scalar n = 0.375; | |
| 302 | 3855057 | const Scalar DH_vap = DH_v_boil * pow(((1.0 - Tr2)/(1.0 - Tr1)), n); | |
| 303 | |||
| 304 | 3855057 | return (DH_vap/molarMass()); // we need [J/kg] | |
| 305 | } | ||
| 306 | |||
| 307 | |||
| 308 | /*! | ||
| 309 | * \brief Specific enthalpy of heavyoil vapor \f$\mathrm{[J/kg]}\f$. | ||
| 310 | * | ||
| 311 | * This relation is true on the vapor pressure curve, i.e. as long | ||
| 312 | * as there is a liquid phase present. | ||
| 313 | * | ||
| 314 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 315 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 316 | */ | ||
| 317 | static Scalar gasEnthalpy(Scalar temperature, Scalar pressure) | ||
| 318 | { | ||
| 319 | 3855057 | return liquidEnthalpy(temperature,pressure) + heatVap(temperature, pressure); | |
| 320 | } | ||
| 321 | |||
| 322 | /*! | ||
| 323 | * \brief The (ideal) gas density of heavyoil vapor at a given temperature and pressure \f$\mathrm{[kg/m^3]}\f$. | ||
| 324 | * | ||
| 325 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 326 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 327 | */ | ||
| 328 | static Scalar gasDensity(Scalar temperature, Scalar pressure) | ||
| 329 | { | ||
| 330 |
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7710120 | return IdealGas::density(molarMass(), temperature, pressure); |
| 331 | } | ||
| 332 | |||
| 333 | /*! | ||
| 334 | * \brief The molar density of pure heavyoil in \f$\mathrm{[mol/m^3]}\f$, | ||
| 335 | * depending on pressure and temperature. | ||
| 336 | * \param temperature The temperature of the gas | ||
| 337 | * \param pressure The pressure of the gas | ||
| 338 | */ | ||
| 339 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | ||
| 340 | 7709894 | { return IdealGas::molarDensity(temperature, pressure); } | |
| 341 | |||
| 342 | /*! | ||
| 343 | * \brief The density of pure heavyoil at a given pressure and temperature \f$\mathrm{[kg/m^3]}\f$. | ||
| 344 | * | ||
| 345 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 346 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 347 | */ | ||
| 348 | static Scalar liquidDensity(Scalar temperature, Scalar pressure) | ||
| 349 | { | ||
| 350 | |||
| 351 | /* according to Lashanizadegan et al (2008) in Chemical Engineering Communications: */ | ||
| 352 | /* Simultaneous Heat and Fluid Flow in Porous Media: Case Study: Steam Injection for Tertiary Oil Recovery */ | ||
| 353 | 7710010 | constexpr Scalar rhoReference = 906.; // [kg/m^3] at reference pressure and temperature | |
| 354 | 7710010 | constexpr Scalar compressCoeff = 1.e-8; // just a value without justification | |
| 355 | 7710010 | constexpr Scalar expansCoeff = 1.e-7; // also just a value | |
| 356 |
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3855060 | return rhoReference * (1. + (pressure - 1.e5)*compressCoeff) * (1. - (temperature - 293.)*expansCoeff); |
| 357 | } | ||
| 358 | |||
| 359 | /*! | ||
| 360 | * \brief The molar density of pure heavyoil in \f$\mathrm{[mol/m^3]}\f$ at a given pressure and temperature. | ||
| 361 | * | ||
| 362 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 363 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 364 | * | ||
| 365 | */ | ||
| 366 | static Scalar liquidMolarDensity(Scalar temperature, Scalar pressure) | ||
| 367 | 3854947 | { return liquidDensity(temperature, pressure)/molarMass(); } | |
| 368 | |||
| 369 | /*! | ||
| 370 | * \brief Returns true if the gas phase is assumed to be compressible | ||
| 371 | */ | ||
| 372 | static constexpr bool gasIsCompressible() | ||
| 373 | { return true; } | ||
| 374 | |||
| 375 | /*! | ||
| 376 | * \brief Returns true if the gas phase is assumed to be ideal | ||
| 377 | */ | ||
| 378 | static constexpr bool gasIsIdeal() | ||
| 379 | { return true; } | ||
| 380 | |||
| 381 | /*! | ||
| 382 | * \brief Returns true if the liquid phase is assumed to be compressible | ||
| 383 | */ | ||
| 384 | static constexpr bool liquidIsCompressible() | ||
| 385 | { return true; } | ||
| 386 | |||
| 387 | /*! | ||
| 388 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of heavyoil vapor | ||
| 389 | * | ||
| 390 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 391 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 392 | */ | ||
| 393 | 3855057 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | |
| 394 | { | ||
| 395 | using std::clamp; | ||
| 396 |
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3855057 | temperature = clamp(temperature, 250.0, 500.0); // regularization |
| 397 | |||
| 398 | // reduced temperature | ||
| 399 | 3855057 | const Scalar Tr = temperature/criticalTemperature(); | |
| 400 | |||
| 401 | using std::pow; | ||
| 402 | using std::exp; | ||
| 403 | 3855057 | constexpr Scalar Fp0 = 1.0; | |
| 404 | 3855057 | constexpr Scalar xi = 0.00474; | |
| 405 | 3855057 | const Scalar eta_xi = | |
| 406 | 3855057 | Fp0*(0.807*pow(Tr,0.618) | |
| 407 | 3855057 | - 0.357*exp(-0.449*Tr) | |
| 408 | 3855057 | + 0.34*exp(-4.058*Tr) | |
| 409 | + 0.018); | ||
| 410 | |||
| 411 | 3855057 | return eta_xi/xi/1e7; // [Pa s] | |
| 412 | } | ||
| 413 | |||
| 414 | /*! | ||
| 415 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of pure heavyoil. | ||
| 416 | * | ||
| 417 | * Lashanizadegan et al. (2008) \cite lashanizadegan2008 <BR> | ||
| 418 | * | ||
| 419 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 420 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 421 | */ | ||
| 422 | ✗ | static Scalar liquidViscosity(Scalar temperature, Scalar pressure) | |
| 423 | { | ||
| 424 | |||
| 425 | /* according to Lashanizadegan et al (2008) in Chemical Engineering Communications: */ | ||
| 426 | /* Simultaneous Heat and Fluid Flow in Porous Media: Case Study: Steam Injection for Tertiary Oil Recovery */ | ||
| 427 | |||
| 428 | //using std::exp; | ||
| 429 | //return 1027919.422*exp(-0.04862*temperature); // [Pa s] | ||
| 430 | |||
| 431 | //according to http://www.ecltechnology.com/subsur/reports/pvt_tgb.pdf [Page 10] | ||
| 432 | 3855057 | const Scalar temperatureFahrenheit = (9/5)*(temperature-273.15)+32; | |
| 433 | 3855057 | constexpr Scalar API = 9; | |
| 434 | |||
| 435 | using std::pow; | ||
| 436 | using Dune::power; | ||
| 437 | 3855057 | return ((pow(10,0.10231*power(API,2)-3.9464*API+46.5037))*(pow(temperatureFahrenheit,-0.04542*power(API,2)+1.70405*API-19.18)))*0.001; | |
| 438 | |||
| 439 | } | ||
| 440 | /*! | ||
| 441 | * \brief Specific heat cap of liquid heavyoil \f$\mathrm{[J/kg]}\f$. | ||
| 442 | * | ||
| 443 | * Lashanizadegan et al. (2008) \cite lashanizadegan2008 <BR> | ||
| 444 | * | ||
| 445 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 446 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 447 | * | ||
| 448 | */ | ||
| 449 | ✗ | static Scalar liquidHeatCapacity(const Scalar temperature, | |
| 450 | const Scalar pressure) | ||
| 451 | { | ||
| 452 | ✗ | return 618.; // J/(kg K) | |
| 453 | } | ||
| 454 | |||
| 455 | /*! | ||
| 456 | * \brief Thermal conductivity \f$\mathrm{[[W/(m*K)]}\f$ of heavy oil | ||
| 457 | * | ||
| 458 | * Lashanizadegan et al. (2008) \cite lashanizadegan2008 <BR> | ||
| 459 | * | ||
| 460 | * \param temperature absolute temperature in \f$\mathrm{[K]}\f$ | ||
| 461 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
| 462 | */ | ||
| 463 | ✗ | static Scalar liquidThermalConductivity( Scalar temperature, Scalar pressure) | |
| 464 | { | ||
| 465 | ✗ | return 0.127; | |
| 466 | } | ||
| 467 | }; | ||
| 468 | |||
| 469 | } // end namespace Dumux::Components | ||
| 470 | |||
| 471 | #endif | ||
| 472 |