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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 brine fluid properties,. | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_BRINE_HH | ||
| 13 | #define DUMUX_BRINE_HH | ||
| 14 | |||
| 15 | #include <cmath> | ||
| 16 | |||
| 17 | #include <dune/common/math.hh> | ||
| 18 | |||
| 19 | #include <dumux/common/parameters.hh> | ||
| 20 | #include <dumux/material/components/h2o.hh> | ||
| 21 | #include <dumux/material/components/nacl.hh> | ||
| 22 | #include <dumux/material/components/tabulatedcomponent.hh> | ||
| 23 | #include <dumux/material/components/base.hh> | ||
| 24 | #include <dumux/material/components/liquid.hh> | ||
| 25 | #include <dumux/material/components/gas.hh> | ||
| 26 | |||
| 27 | namespace Dumux::Components { | ||
| 28 | |||
| 29 | /*! | ||
| 30 | * \ingroup Components | ||
| 31 | * \brief A class for the brine fluid properties. | ||
| 32 | * | ||
| 33 | * \tparam Scalar The type used for scalar values | ||
| 34 | * \tparam H2O Static polymorphism: the Brine class can access all properties of the H2O class | ||
| 35 | * \note This is an implementation of brine as a pseudo-component with a constant salinity. | ||
| 36 | * \note the salinity is read from the input file and is a mandatory parameter | ||
| 37 | */ | ||
| 38 | template <class Scalar, | ||
| 39 | class H2O_Tabulated = Components::TabulatedComponent<Components::H2O<Scalar>>> | ||
| 40 | class Brine | ||
| 41 | : public Components::Base<Scalar, Brine<Scalar, H2O_Tabulated> > | ||
| 42 | , public Components::Liquid<Scalar, Brine<Scalar, H2O_Tabulated> > | ||
| 43 | , public Components::Gas<Scalar, Brine<Scalar, H2O_Tabulated> > | ||
| 44 | { | ||
| 45 | using ThisType = Brine<Scalar, H2O_Tabulated>; | ||
| 46 | public: | ||
| 47 | using H2O = Components::TabulatedComponent<Dumux::Components::H2O<Scalar>>; | ||
| 48 | |||
| 49 | //! The ideal gas constant \f$\mathrm{[J/mol/K]}\f$ | ||
| 50 | static constexpr Scalar R = Constants<Scalar>::R; | ||
| 51 | |||
| 52 | /*! | ||
| 53 | * \brief A human readable name for the brine. | ||
| 54 | */ | ||
| 55 | static std::string name() | ||
| 56 |
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54 | { return "Brine"; } |
| 57 | |||
| 58 | /*! | ||
| 59 | * \brief Return the constant salinity | ||
| 60 | */ | ||
| 61 | 484975431 | static Scalar salinity() | |
| 62 | { | ||
| 63 |
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484975431 | static const Scalar salinity = getParam<Scalar>("Brine.Salinity"); |
| 64 | 484975431 | return salinity; | |
| 65 | } | ||
| 66 | |||
| 67 | /*! | ||
| 68 | * \brief The molar mass in \f$\mathrm{[kg/mol]}\f$ of brine. | ||
| 69 | * This assumes that the salt is pure NaCl. | ||
| 70 | */ | ||
| 71 | static Scalar molarMass() | ||
| 72 | { | ||
| 73 | 18 | const Scalar M1 = H2O::molarMass(); | |
| 74 | 18 | const Scalar M2 = Components::NaCl<Scalar>::molarMass(); // molar mass of NaCl [kg/mol] | |
| 75 |
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18 | return M1*M2/(M2 + ThisType::salinity()*(M1 - M2)); |
| 76 | }; | ||
| 77 | |||
| 78 | /*! | ||
| 79 | * \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of brine. Here, it is assumed to be equal to that of pure water. | ||
| 80 | * The critical temperature of brine is dependent on the salt concentration. | ||
| 81 | * With increasing NaCl mass fraction the critical point shifts to higher temperatures, see Bakker, 2018 (DOI: 10.1016/j.cageo.2018.03.003). | ||
| 82 | */ | ||
| 83 | static Scalar criticalTemperature() | ||
| 84 | { return H2O::criticalTemperature(); } | ||
| 85 | |||
| 86 | /*! | ||
| 87 | * \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of brine. Here, it is assumed to be equal to that of pure water. | ||
| 88 | * The critical pressure of brine is dependent on the salt concentration. | ||
| 89 | * With increasing NaCl mass fraction the critical point shifts to higher pressures, see Bakker, 2018 (DOI: 10.1016/j.cageo.2018.03.003). | ||
| 90 | */ | ||
| 91 | static Scalar criticalPressure() | ||
| 92 | { return H2O::criticalPressure(); } | ||
| 93 | |||
| 94 | /*! | ||
| 95 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at brine's triple point. Here, it is assumed to be equal to that of pure water. | ||
| 96 | * The triple temperature of brine is dependent on the salt concentration, see Bakker, 2018 (DOI: 10.1016/j.cageo.2018.03.003). | ||
| 97 | */ | ||
| 98 | static Scalar tripleTemperature() | ||
| 99 | { return H2O::tripleTemperature(); } | ||
| 100 | |||
| 101 | /*! | ||
| 102 | * \brief Returns the pressure \f$\mathrm{[Pa]}\f$ at brine's triple point. Here, it is assumed to be equal to that of pure water. | ||
| 103 | * The triple pressure of brine is dependent on the salt concentration, see Bakker, 2018 (DOI: 10.1016/j.cageo.2018.03.003). | ||
| 104 | */ | ||
| 105 | static Scalar triplePressure() | ||
| 106 | { return H2O::triplePressure(); } | ||
| 107 | |||
| 108 | /*! | ||
| 109 | * \brief The vapor pressure in \f$\mathrm{[Pa]}\f$ of pure brine | ||
| 110 | * at a given temperature. | ||
| 111 | * \note The vapor pressure of brine decreases with the mole fraction of water in the liquid phase. | ||
| 112 | * This is described by Raoult's law, see Thomas Fetzer's Dissertation Eq. 2.11. | ||
| 113 | * It is also the simplified version of the Kelvin equation, neglecting the influence of the capillary pressure here. | ||
| 114 | * | ||
| 115 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 116 | */ | ||
| 117 | static Scalar vaporPressure(Scalar temperature) | ||
| 118 | { | ||
| 119 | //calculate mole fraction | ||
| 120 | const Scalar M1 = H2O::molarMass(); | ||
| 121 | const Scalar M2 = Components::NaCl<Scalar>::molarMass(); // molar mass of NaCl [kg/mol] | ||
| 122 | const Scalar xNaClLiquid = - M1 * ThisType::salinity() / ((M2-M1) * ThisType::salinity() - M2); | ||
| 123 | |||
| 124 | // Raoult's law, see Thomas Fetzer's Dissertation Eq. 2.11. | ||
| 125 | return H2O::vaporPressure(temperature) * (1 - xNaClLiquid); | ||
| 126 | } | ||
| 127 | |||
| 128 | /*! | ||
| 129 | * \brief Specific enthalpy of gaseous brine \f$\mathrm{[J/kg]}\f$. | ||
| 130 | * Only water volatile and salt is suppose to stay in the liquid phase. | ||
| 131 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 132 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 133 | */ | ||
| 134 | static const Scalar gasEnthalpy(Scalar temperature, Scalar pressure) | ||
| 135 |
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101 | { return H2O::gasEnthalpy(temperature, pressure); } |
| 136 | |||
| 137 | /*! | ||
| 138 | * \brief Specific enthalpy of liquid brine \f$\mathrm{[J/kg]}\f$. | ||
| 139 | * | ||
| 140 | * \param T temperature of component in \f$\mathrm{[K]}\f$ | ||
| 141 | * \param p pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 142 | * | ||
| 143 | * Equations given in: | ||
| 144 | * - Palliser & McKibbin (1998) \cite palliser1998 <BR> | ||
| 145 | * - Michaelides (1981) \cite michaelides1981 <BR> | ||
| 146 | * - Daubert & Danner (1989) \cite daubert1989 | ||
| 147 | * | ||
| 148 | */ | ||
| 149 | 46343841 | static const Scalar liquidEnthalpy(Scalar T, Scalar p) | |
| 150 | { | ||
| 151 | /*Numerical coefficients from PALLISER*/ | ||
| 152 | static const Scalar f[] = { | ||
| 153 | 2.63500E-1, 7.48368E-6, 1.44611E-6, -3.80860E-10 | ||
| 154 | }; | ||
| 155 | |||
| 156 | /*Numerical coefficients from MICHAELIDES for the enthalpy of brine*/ | ||
| 157 | static const Scalar a[4][3] = { | ||
| 158 | { +9633.6, -4080.0, +286.49 }, | ||
| 159 | { +166.58, +68.577, -4.6856 }, | ||
| 160 | { -0.90963, -0.36524, +0.249667E-1 }, | ||
| 161 | { +0.17965E-2, +0.71924E-3, -0.4900E-4 } | ||
| 162 | }; | ||
| 163 | |||
| 164 | 46343841 | const Scalar theta = T - 273.15; | |
| 165 | 46343841 | const Scalar salSat = f[0] + f[1]*theta + f[2]*theta*theta + f[3]*theta*theta*theta; | |
| 166 | |||
| 167 | /*Regularization*/ | ||
| 168 | using std::min; | ||
| 169 | using std::max; | ||
| 170 |
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46343841 | const Scalar salinity = min(max(ThisType::salinity(),0.0), salSat); |
| 171 | |||
| 172 | 46343841 | const Scalar hw = H2O::liquidEnthalpy(T, p)/1E3; /* kJ/kg */ | |
| 173 | |||
| 174 | /*DAUBERT and DANNER*/ | ||
| 175 | 92687682 | /*U=*/const Scalar h_NaCl = (3.6710E4*T + 0.5*(6.2770E1)*T*T - ((6.6670E-2)/3)*T*T*T | |
| 176 | 46343841 | +((2.8000E-5)/4)*(T*T*T*T))/(58.44E3)- 2.045698e+02; /* kJ/kg */ | |
| 177 | |||
| 178 | 46343841 | const Scalar m = (1E3/58.44)*(salinity/(1-salinity)); | |
| 179 | |||
| 180 | using Dune::power; | ||
| 181 | 46343841 | Scalar d_h = 0; | |
| 182 |
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231719205 | for (int i = 0; i<=3; i++) { |
| 183 |
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741501456 | for (int j=0; j<=2; j++) { |
| 184 | 1668378276 | d_h = d_h + a[i][j] * power(theta, i) * power(m, j); | |
| 185 | } | ||
| 186 | } | ||
| 187 | |||
| 188 | /* heat of dissolution for halite according to Michaelides 1971 */ | ||
| 189 | 46343841 | const Scalar delta_h = (4.184/(1E3 + (58.44 * m)))*d_h; | |
| 190 | |||
| 191 | /* Enthalpy of brine without any dissolved gas */ | ||
| 192 | 46343841 | const Scalar h_ls1 =(1-salinity)*hw + salinity*h_NaCl + salinity*delta_h; /* kJ/kg */ | |
| 193 | 46343841 | return h_ls1*1E3; /*J/kg*/ | |
| 194 | } | ||
| 195 | |||
| 196 | /*! | ||
| 197 | * \brief Specific isobaric heat capacity of brine \f$\mathrm{[J/kg]}\f$. | ||
| 198 | * | ||
| 199 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 200 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 201 | * | ||
| 202 | * See: | ||
| 203 | * | ||
| 204 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 205 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 206 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 207 | */ | ||
| 208 | 109 | static const Scalar liquidHeatCapacity(Scalar temperature, Scalar pressure) | |
| 209 | { | ||
| 210 | 109 | const Scalar eps = temperature*1e-8; | |
| 211 | 109 | return (liquidEnthalpy(temperature + eps, pressure)- liquidEnthalpy(temperature, pressure))/eps; | |
| 212 | } | ||
| 213 | |||
| 214 | /*! | ||
| 215 | * \brief Specific isobaric heat capacity of water steam \f$\mathrm{[J/kg]}\f$. | ||
| 216 | * | ||
| 217 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 218 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 219 | * | ||
| 220 | * See: | ||
| 221 | * | ||
| 222 | * IAPWS: "Revised Release on the IAPWS Industrial Formulation | ||
| 223 | * 1997 for the Thermodynamic Properties of Water and Steam", | ||
| 224 | * http://www.iapws.org/relguide/IF97-Rev.pdf \cite IAPWS1997 | ||
| 225 | */ | ||
| 226 | static const Scalar gasHeatCapacity(Scalar temperature, | ||
| 227 | Scalar pressure) | ||
| 228 | { | ||
| 229 |
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101 | return H2O::gasHeatCapacity(temperature, pressure); |
| 230 | } | ||
| 231 | |||
| 232 | /*! | ||
| 233 | * \brief Specific internal energy of steam \f$\mathrm{[J/kg]}\f$. | ||
| 234 | * | ||
| 235 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 236 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 237 | */ | ||
| 238 | static const Scalar gasInternalEnergy(Scalar temperature, | ||
| 239 | Scalar pressure) | ||
| 240 | { | ||
| 241 | return H2O::gasInternalEnergy(temperature, pressure); | ||
| 242 | } | ||
| 243 | |||
| 244 | /*! | ||
| 245 | * \brief Specific internal energy of liquid brine \f$\mathrm{[J/kg]}\f$. | ||
| 246 | * | ||
| 247 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 248 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 249 | */ | ||
| 250 | static const Scalar liquidInternalEnergy(Scalar temperature, | ||
| 251 | Scalar pressure) | ||
| 252 | { | ||
| 253 | return liquidEnthalpy(temperature, pressure) - pressure/liquidDensity(temperature, pressure); | ||
| 254 | } | ||
| 255 | |||
| 256 | /*! | ||
| 257 | * \brief The density of steam at a given pressure and temperature \f$\mathrm{[kg/m^3]}\f$. | ||
| 258 | * | ||
| 259 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 260 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 261 | */ | ||
| 262 | static Scalar gasDensity(Scalar temperature, Scalar pressure) | ||
| 263 |
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101 | { return H2O::gasDensity(temperature, pressure); } |
| 264 | |||
| 265 | /*! | ||
| 266 | * \brief The molar density of steam in \f$\mathrm{[mol/m^3]}\f$ at a given pressure and temperature. | ||
| 267 | * We take the value of the H2O gas molar density here because salt is not in the gas phase. | ||
| 268 | * | ||
| 269 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 270 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 271 | * | ||
| 272 | */ | ||
| 273 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | ||
| 274 | { return H2O::gasMolarDensity(temperature, pressure); } | ||
| 275 | |||
| 276 | /*! | ||
| 277 | * \brief Returns true if the gas phase is assumed to be ideal | ||
| 278 | */ | ||
| 279 | static constexpr bool gasIsIdeal() | ||
| 280 | { return H2O::gasIsIdeal(); } | ||
| 281 | |||
| 282 | /*! | ||
| 283 | * \brief Returns true if the gas phase is assumed to be compressible | ||
| 284 | */ | ||
| 285 | static constexpr bool gasIsCompressible() | ||
| 286 | { return H2O::gasIsCompressible(); } | ||
| 287 | |||
| 288 | /*! | ||
| 289 | * \brief Returns true if the liquid phase is assumed to be compressible | ||
| 290 | */ | ||
| 291 | static constexpr bool liquidIsCompressible() | ||
| 292 | { return H2O::liquidIsCompressible(); } | ||
| 293 | |||
| 294 | /*! | ||
| 295 | * \brief The density of pure brine at a given pressure and temperature \f$\mathrm{[kg/m^3]}\f$. | ||
| 296 | * | ||
| 297 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 298 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 299 | * | ||
| 300 | * \note The density is computed as a function of the salt mass fraction, pressure and temperature. | ||
| 301 | * The used function is an empirical relationship fitted to experimental data. | ||
| 302 | * It is presented by Batzle and Wang, 1992 (DOI: 10.1190/1.1443207) \cite batzle1992, | ||
| 303 | * better description and comparison with other approaches in Adams and Bachu, 2002 | ||
| 304 | * (DOI: 10.1046/j.1468-8123.2002.00041.x) \cite adams2002. | ||
| 305 | */ | ||
| 306 | 145296856 | static Scalar liquidDensity(Scalar temperature, Scalar pressure) | |
| 307 | { | ||
| 308 | using std::max; | ||
| 309 | 145296856 | const Scalar TempC = temperature - 273.15; | |
| 310 | 145296856 | const Scalar pMPa = pressure/1.0E6; | |
| 311 |
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145296856 | const Scalar salinity = max(0.0, ThisType::salinity()); |
| 312 | |||
| 313 | 145296856 | const Scalar rhow = H2O::liquidDensity(temperature, pressure); | |
| 314 | |||
| 315 | 145296856 | const Scalar density = rhow + | |
| 316 | 290593712 | 1000*salinity*( | |
| 317 | 145296856 | 0.668 + | |
| 318 | 290593712 | 0.44*salinity + | |
| 319 | 145296856 | 1.0E-6*( | |
| 320 | 290593712 | 300*pMPa - | |
| 321 | 290593712 | 2400*pMPa*salinity + | |
| 322 | 145296856 | TempC*( | |
| 323 | 145296856 | 80.0 + | |
| 324 | 290593712 | 3*TempC - | |
| 325 | 290593712 | 3300*salinity - | |
| 326 | 290593712 | 13*pMPa + | |
| 327 | 145296856 | 47*pMPa*salinity))); | |
| 328 |
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145296856 | assert(density > 0.0); |
| 329 | 145296856 | return density; | |
| 330 | } | ||
| 331 | |||
| 332 | /*! | ||
| 333 | * \brief The molar density of brine in \f$\mathrm{[mol/m^3]}\f$ at a given pressure and temperature. | ||
| 334 | * | ||
| 335 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 336 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 337 | * | ||
| 338 | */ | ||
| 339 | static Scalar liquidMolarDensity(Scalar temperature, Scalar pressure) | ||
| 340 | { return liquidDensity(temperature, pressure)/molarMass(); } | ||
| 341 | |||
| 342 | /*! | ||
| 343 | * \brief The pressure of steam in \f$\mathrm{[Pa]}\f$ at a given density and temperature. | ||
| 344 | * | ||
| 345 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 346 | * \param density density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
| 347 | */ | ||
| 348 | static Scalar gasPressure(Scalar temperature, Scalar density) | ||
| 349 | { return H2O::gasPressure(temperature, density); } | ||
| 350 | |||
| 351 | /*! | ||
| 352 | * \brief The pressure of brine in \f$\mathrm{[Pa]}\f$ at a given density and | ||
| 353 | * temperature. | ||
| 354 | * | ||
| 355 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 356 | * \param density density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
| 357 | */ | ||
| 358 | static Scalar liquidPressure(Scalar temperature, Scalar density) | ||
| 359 | { | ||
| 360 | // We use the Newton method for this. For the initial value we | ||
| 361 | // assume the pressure to be 10% higher than the vapor | ||
| 362 | // pressure | ||
| 363 | Scalar pressure = 1.1*vaporPressure(temperature); | ||
| 364 | const Scalar eps = pressure*1e-7; | ||
| 365 | |||
| 366 | Scalar deltaP = pressure*2; | ||
| 367 | |||
| 368 | using std::abs; | ||
| 369 | for (int i = 0; i < 5 && abs(pressure*1e-9) < abs(deltaP); ++i) { | ||
| 370 | Scalar f = liquidDensity(temperature, pressure) - density; | ||
| 371 | |||
| 372 | Scalar df_dp; | ||
| 373 | df_dp = liquidDensity(temperature, pressure + eps); | ||
| 374 | df_dp -= liquidDensity(temperature, pressure - eps); | ||
| 375 | df_dp /= 2*eps; | ||
| 376 | |||
| 377 | deltaP = - f/df_dp; | ||
| 378 | |||
| 379 | pressure += deltaP; | ||
| 380 | } | ||
| 381 | assert(pressure > 0.0); | ||
| 382 | return pressure; | ||
| 383 | } | ||
| 384 | |||
| 385 | /*! | ||
| 386 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of steam. | ||
| 387 | * | ||
| 388 | * \param temperature temperature of component | ||
| 389 | * \param pressure pressure of component | ||
| 390 | */ | ||
| 391 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | ||
| 392 |
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101 | { return H2O::gasViscosity(temperature, pressure); }; |
| 393 | |||
| 394 | /*! | ||
| 395 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of pure brine. | ||
| 396 | * | ||
| 397 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 398 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 399 | * | ||
| 400 | * \note The viscosity is computed as a function of the salt mass fraction and temperature. | ||
| 401 | * The used function is an empirical relationship fitted to experimental data. | ||
| 402 | * It is presented by Batzle and Wang, 1992 (DOI: 10.1190/1.1443207) \cite batzle1992, | ||
| 403 | * better description and comparison with other approaches in Adams and Bachu, 2002 (DOI: 10.1046/j.1468-8123.2002.00041.x) \cite adams2002. | ||
| 404 | * However, the equation given in Adams and Bachu, 2002(DOI: 10.1046/j.1468-8123.2002.00041.x) \cite adams2002 | ||
| 405 | * is obviously wrong when compared to the original by Batzle and Wang, 1992 (DOI: 10.1190/1.1443207) \cite batzle1992. | ||
| 406 | */ | ||
| 407 | 73847610 | static Scalar liquidViscosity(Scalar temperature, Scalar pressure) | |
| 408 | { | ||
| 409 | // regularisation | ||
| 410 | using std::max; | ||
| 411 |
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73847610 | temperature = max(temperature, 275.0); |
| 412 |
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73847610 | const Scalar salinity = max(0.0, ThisType::salinity()); |
| 413 | |||
| 414 | using std::pow; | ||
| 415 | using Dune::power; | ||
| 416 | using std::exp; | ||
| 417 | 73847610 | const Scalar T_C = temperature - 273.15; | |
| 418 | 73847610 | const Scalar A = (0.42*power((pow(salinity, 0.8)-0.17), 2) + 0.045)*pow(T_C, 0.8); | |
| 419 | 73847610 | const Scalar mu_brine = 0.1 + 0.333*salinity + (1.65+91.9*salinity*salinity*salinity)*exp(-A); //[cP] | |
| 420 |
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73847610 | assert(mu_brine > 0.0); |
| 421 | 73847610 | return mu_brine/1000.0; //[Pa s] | |
| 422 | } | ||
| 423 | |||
| 424 | /*! | ||
| 425 | * \brief Thermal conductivity of a brine \f$\mathrm{[W/(m K)]}\f$. | ||
| 426 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
| 427 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
| 428 | * | ||
| 429 | * The thermal conductivity of brine is implemented based on the contribution of NaCl (\f$\lambda_{brine}\f$/\f$\lambda_{H_2O}\f$) of \cite Yusufova1975 https://link.springer.com/content/pdf/10.1007/BF00867119.pdf, also discussed in \cite Ozbek1980 https://docecity.com/thermal-conductivity-of-aqueous-sodium-chloride-acs-publicat-5f10766acba00.html | ||
| 430 | */ | ||
| 431 | 46343619 | static Scalar liquidThermalConductivity(Scalar temperature, Scalar pressure) | |
| 432 | { | ||
| 433 | 46343619 | Scalar tempC = temperature-273.15; | |
| 434 | 46343619 | Scalar xNaCl = ThisType::salinity() * H2O::molarMass() / (ThisType::salinity() * H2O::molarMass() + (1-ThisType::salinity() )*Components::NaCl<Scalar>::molarMass()); // mole fraction of NaCl | |
| 435 | 46343619 | Scalar m = xNaCl/(H2O::molarMass()*(1- xNaCl)); // molality of NaCl | |
| 436 | 46343619 | Scalar S = 5844.3 * m / (1000 + 58.443 *m); | |
| 437 | 46343619 | Scalar contribNaClFactor = 1.0 - (2.3434e-3 - 7.924e-6*tempC + 3.924e-8*tempC*tempC)*S + (1.06e-5 - 2.0e-8*tempC + 1.2e-10*tempC*tempC)*S*S; | |
| 438 | 46343619 | return contribNaClFactor * H2O::liquidThermalConductivity(temperature, pressure); | |
| 439 | } | ||
| 440 | }; | ||
| 441 | |||
| 442 | template <class Scalar, class H2O> | ||
| 443 | struct IsAqueous<Brine<Scalar, H2O>> : public std::true_type {}; | ||
| 444 | |||
| 445 | } // end namespace Dumux::Components | ||
| 446 | |||
| 447 | #endif | ||
| 448 |