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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 FluidSystems | ||
| 10 | * \brief A fluid system for brine, i.e. H2O with dissolved NaCl. | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_BRINE_FLUID_SYSTEM_HH | ||
| 13 | #define DUMUX_BRINE_FLUID_SYSTEM_HH | ||
| 14 | |||
| 15 | #include <dune/common/math.hh> | ||
| 16 | |||
| 17 | #include <dumux/common/exceptions.hh> | ||
| 18 | #include <dumux/io/name.hh> | ||
| 19 | #include <dumux/material/fluidsystems/base.hh> | ||
| 20 | #include <dumux/material/constants.hh> | ||
| 21 | #include <dumux/material/components/h2o.hh> | ||
| 22 | #include <dumux/material/components/nacl.hh> | ||
| 23 | #include <dumux/material/components/tabulatedcomponent.hh> | ||
| 24 | |||
| 25 | namespace Dumux::FluidSystems { | ||
| 26 | |||
| 27 | /*! | ||
| 28 | * \ingroup FluidSystems | ||
| 29 | * \brief A compositional single phase fluid system consisting of | ||
| 30 | * two components, which are H2O and NaCl. | ||
| 31 | */ | ||
| 32 | template< class Scalar, class H2OType = Components::TabulatedComponent<Dumux::Components::H2O<Scalar>> > | ||
| 33 | class Brine : public Base< Scalar, Brine<Scalar, H2OType>> | ||
| 34 | { | ||
| 35 | using ThisType = Brine<Scalar, H2OType>; | ||
| 36 | |||
| 37 | public: | ||
| 38 | //! export the involved components | ||
| 39 | using H2O = H2OType; | ||
| 40 | using NaCl = Dumux::Components::NaCl<Scalar>; | ||
| 41 | |||
| 42 | static const int numPhases = 1; //!< Number of phases in the fluid system | ||
| 43 | static const int numComponents = 2; //!< Number of components in the fluid system (H2O, NaCl) | ||
| 44 | |||
| 45 | static constexpr int phase0Idx = 0; //!< Index of the first (and only) phase | ||
| 46 | static constexpr int liquidPhaseIdx = phase0Idx; //!< The one considered phase is liquid | ||
| 47 | |||
| 48 | static constexpr int H2OIdx = 0; //!< index of the water component | ||
| 49 | static constexpr int NaClIdx = 1; //!< index of the NaCl component | ||
| 50 | static constexpr int comp0Idx = H2OIdx; //!< index of the first component | ||
| 51 | static constexpr int comp1Idx = NaClIdx; //!< index of the second component | ||
| 52 | |||
| 53 | /*! | ||
| 54 | * \brief Return the human readable name of the phase | ||
| 55 | * \param phaseIdx The index of the fluid phase to consider | ||
| 56 | */ | ||
| 57 | 39 | static const std::string phaseName(int phaseIdx = liquidPhaseIdx) | |
| 58 | { | ||
| 59 |
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39 | assert(phaseIdx == liquidPhaseIdx); |
| 60 | 39 | return IOName::liquidPhase(); | |
| 61 | } | ||
| 62 | |||
| 63 | /*! | ||
| 64 | * \brief Returns whether the fluids are miscible | ||
| 65 | * \note There is only one phase, so miscibility makes no sense here | ||
| 66 | */ | ||
| 67 | static constexpr bool isMiscible() | ||
| 68 | { | ||
| 69 | return false; | ||
| 70 | } | ||
| 71 | |||
| 72 | /*! | ||
| 73 | * \brief Return whether a phase is gaseous | ||
| 74 | * \param phaseIdx The index of the fluid phase to consider | ||
| 75 | */ | ||
| 76 | static constexpr bool isGas(int phaseIdx = liquidPhaseIdx) | ||
| 77 | { | ||
| 78 | assert(phaseIdx == liquidPhaseIdx); | ||
| 79 | return false; | ||
| 80 | } | ||
| 81 | |||
| 82 | /*! | ||
| 83 | * \brief Returns true if and only if a fluid phase is assumed to | ||
| 84 | * be an ideal mixture. | ||
| 85 | * | ||
| 86 | * We define an ideal mixture as a fluid phase where the fugacity | ||
| 87 | * coefficients of all components times the pressure of the phase | ||
| 88 | * are independent on the fluid composition. This assumption is true | ||
| 89 | * if Henry's law and Raoult's law apply. If you are unsure what | ||
| 90 | * this function should return, it is safe to return false. The | ||
| 91 | * only damage done will be (slightly) increased computation times | ||
| 92 | * in some cases. | ||
| 93 | * | ||
| 94 | * \param phaseIdx The index of the fluid phase to consider | ||
| 95 | */ | ||
| 96 | static bool isIdealMixture(int phaseIdx = liquidPhaseIdx) | ||
| 97 | { | ||
| 98 | assert(phaseIdx == liquidPhaseIdx); | ||
| 99 | return true; | ||
| 100 | } | ||
| 101 | |||
| 102 | /*! | ||
| 103 | * \brief Returns true if and only if a fluid phase is assumed to | ||
| 104 | * be compressible. | ||
| 105 | * | ||
| 106 | * Compressible means that the partial derivative of the density | ||
| 107 | * to the fluid pressure is always larger than zero. | ||
| 108 | * | ||
| 109 | * \param phaseIdx The index of the fluid phase to consider | ||
| 110 | */ | ||
| 111 | static bool isCompressible(int phaseIdx = liquidPhaseIdx) | ||
| 112 | { | ||
| 113 | assert(phaseIdx == liquidPhaseIdx); | ||
| 114 | return H2O::liquidIsCompressible(); | ||
| 115 | } | ||
| 116 | |||
| 117 | /*! | ||
| 118 | * \brief Returns true if and only if a fluid phase is assumed to | ||
| 119 | * be an ideal gas. | ||
| 120 | * | ||
| 121 | * \param phaseIdx The index of the fluid phase to consider | ||
| 122 | */ | ||
| 123 | |||
| 124 | static bool isIdealGas(int phaseIdx = liquidPhaseIdx) | ||
| 125 | { | ||
| 126 | assert(phaseIdx == liquidPhaseIdx); | ||
| 127 | return false; /*we're a liquid!*/ | ||
| 128 | } | ||
| 129 | |||
| 130 | /**************************************** | ||
| 131 | * Component related static parameters | ||
| 132 | ****************************************/ | ||
| 133 | |||
| 134 | /*! | ||
| 135 | * \brief Return the human readable name of a component | ||
| 136 | * \param compIdx The index of the component to consider | ||
| 137 | */ | ||
| 138 | 16 | static std::string componentName(int compIdx) | |
| 139 | { | ||
| 140 |
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16 | switch (compIdx) |
| 141 | { | ||
| 142 | 12 | case H2OIdx: return H2O::name(); | |
| 143 | 4 | case NaClIdx: return NaCl::name(); | |
| 144 | }; | ||
| 145 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << compIdx); | |
| 146 | } | ||
| 147 | |||
| 148 | /*! | ||
| 149 | * \brief Return the molar mass of a component in \f$\mathrm{[kg/mol]}\f$. | ||
| 150 | * \param compIdx The index of the component to consider | ||
| 151 | */ | ||
| 152 | 16231339 | static Scalar molarMass(int compIdx) | |
| 153 | { | ||
| 154 |
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16143152 | switch (compIdx) |
| 155 | { | ||
| 156 | case H2OIdx: return H2O::molarMass(); | ||
| 157 | 9023182 | case NaClIdx: return NaCl::molarMass(); | |
| 158 | }; | ||
| 159 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << compIdx); | |
| 160 | } | ||
| 161 | |||
| 162 | /**************************************** | ||
| 163 | * thermodynamic relations | ||
| 164 | ****************************************/ | ||
| 165 | /*! | ||
| 166 | * \brief Initialize the fluid system's static parameters generically | ||
| 167 | * \note If a tabulated H2O component is used, we do our best to create | ||
| 168 | * tables that always work. | ||
| 169 | */ | ||
| 170 | 1 | static void init() | |
| 171 | { | ||
| 172 |
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1 | init(/*tempMin=*/273.15, |
| 173 | /*tempMax=*/623.15, | ||
| 174 | /*numTemp=*/100, | ||
| 175 | /*pMin=*/-10., | ||
| 176 | /*pMax=*/20e6, | ||
| 177 | /*numP=*/200); | ||
| 178 | 1 | } | |
| 179 | |||
| 180 | /*! | ||
| 181 | * \brief Initialize the fluid system's static parameters using | ||
| 182 | * problem specific temperature and pressure ranges | ||
| 183 | * | ||
| 184 | * \param tempMin The minimum temperature used for tabulation of water [K] | ||
| 185 | * \param tempMax The maximum temperature used for tabulation of water [K] | ||
| 186 | * \param nTemp The number of ticks on the temperature axis of the table of water | ||
| 187 | * \param pressMin The minimum pressure used for tabulation of water [Pa] | ||
| 188 | * \param pressMax The maximum pressure used for tabulation of water [Pa] | ||
| 189 | * \param nPress The number of ticks on the pressure axis of the table of water | ||
| 190 | */ | ||
| 191 | 1 | static void init(Scalar tempMin, Scalar tempMax, unsigned nTemp, | |
| 192 | Scalar pressMin, Scalar pressMax, unsigned nPress) | ||
| 193 | { | ||
| 194 | |||
| 195 | if (H2O::isTabulated) | ||
| 196 | { | ||
| 197 | 1 | std::cout << "Initializing tables for the H2O fluid properties (" | |
| 198 | 1 | << nTemp*nPress | |
| 199 | 1 | << " entries).\n"; | |
| 200 | |||
| 201 | 1 | H2O::init(tempMin, tempMax, nTemp, pressMin, pressMax, nPress); | |
| 202 | } | ||
| 203 | 1 | } | |
| 204 | |||
| 205 | using Base<Scalar, ThisType>::density; | ||
| 206 | /*! | ||
| 207 | * \brief Return the phase density [kg/m^3]. | ||
| 208 | * \note The density is computed as a function of the salt mass fraction, pressure and temperature. | ||
| 209 | * The used function is an empirical relationship fitted to experimental data. | ||
| 210 | * It is presented by Batzle and Wang, 1992 (DOI: 10.1190/1.1443207) \cite batzle1992, | ||
| 211 | * better description and comparison with other approaches in Adams and Bachu, 2002 | ||
| 212 | * (DOI: 10.1046/j.1468-8123.2002.00041.x) \cite adams2002. | ||
| 213 | * \param fluidState An arbitrary fluid state | ||
| 214 | * \param phaseIdx The index of the phase for which to compute the density (for compatibility, should be `liquidPhaseIdx`) | ||
| 215 | */ | ||
| 216 | template <class FluidState> | ||
| 217 | 5360378 | static Scalar density(const FluidState& fluidState, int phaseIdx = liquidPhaseIdx) | |
| 218 | { | ||
| 219 |
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5360378 | assert(phaseIdx == liquidPhaseIdx); |
| 220 | 5360378 | const Scalar temperature = fluidState.temperature(phaseIdx); | |
| 221 | 5360378 | const Scalar pressure = fluidState.pressure(phaseIdx); | |
| 222 | 5360378 | const Scalar xNaCl = fluidState.massFraction(phaseIdx, NaClIdx); | |
| 223 | |||
| 224 | using std::max; | ||
| 225 | 5360378 | const Scalar TempC = temperature - 273.15; | |
| 226 | 5360378 | const Scalar pMPa = pressure/1.0E6; | |
| 227 |
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5360378 | const Scalar salinity = max(0.0, xNaCl); |
| 228 | |||
| 229 | 5360378 | const Scalar rhow = H2O::liquidDensity(temperature, pressure); | |
| 230 | 5360378 | const Scalar density = rhow + 1000*salinity*(0.668 + | |
| 231 | 5360378 | 0.44*salinity + | |
| 232 | 5360378 | 1.0E-6*(300*pMPa - | |
| 233 | 5360378 | 2400*pMPa*salinity + | |
| 234 | 5360378 | TempC*(80.0 + | |
| 235 | 5360378 | 3*TempC - | |
| 236 | 5360378 | 3300*salinity - | |
| 237 | 5360378 | 13*pMPa + | |
| 238 | 5360378 | 47*pMPa*salinity))); | |
| 239 |
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5360378 | assert(density > 0.0); |
| 240 | 5360378 | return density; | |
| 241 | } | ||
| 242 | |||
| 243 | using Base<Scalar, ThisType>::fugacityCoefficient; | ||
| 244 | //! \copydoc Base<Scalar,ThisType>::fugacityCoefficient(const FluidState&,int,int) | ||
| 245 | template <class FluidState> | ||
| 246 | 2 | static Scalar fugacityCoefficient(const FluidState &fluidState, | |
| 247 | int phaseIdx, | ||
| 248 | int compIdx) | ||
| 249 | { | ||
| 250 |
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2 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 251 |
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2 | assert(0 <= compIdx && compIdx < numComponents); |
| 252 | |||
| 253 |
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2 | if (phaseIdx == compIdx) |
| 254 | // We could calculate the real fugacity coefficient of | ||
| 255 | // the component in the fluid. Probably that's not worth | ||
| 256 | // the effort, since the fugacity coefficient of the other | ||
| 257 | // component is infinite anyway... | ||
| 258 | 1 | return 1.0; | |
| 259 | return std::numeric_limits<Scalar>::infinity(); | ||
| 260 | } | ||
| 261 | |||
| 262 | using Base<Scalar, ThisType>::viscosity; | ||
| 263 | /*! | ||
| 264 | * \brief Return the viscosity of the phase. | ||
| 265 | * \note The viscosity is computed as a function of the salt mass fraction and temperature. | ||
| 266 | * The used function is an empirical relationship fitted to experimental data. | ||
| 267 | * It is presented by Batzle and Wang, 1992 (DOI: 10.1190/1.1443207) \cite batzle1992, | ||
| 268 | * better description and comparison with other approaches in Adams and Bachu, 2002 (DOI: 10.1046/j.1468-8123.2002.00041.x) \cite adams2002. | ||
| 269 | * However, the equation given in Adams and Bachu, 2002(DOI: 10.1046/j.1468-8123.2002.00041.x) \cite adams2002 | ||
| 270 | * is obviously wrong when compared to the original by Batzle and Wang, 1992 (DOI: 10.1190/1.1443207) \cite batzle1992. | ||
| 271 | * \param fluidState An arbitrary fluid state | ||
| 272 | * \param phaseIdx The index of the phase for which to compute the viscosity (for compatibility, should be `liquidPhaseIdx`) | ||
| 273 | */ | ||
| 274 | template <class FluidState> | ||
| 275 | 2680189 | static Scalar viscosity(const FluidState& fluidState, int phaseIdx = liquidPhaseIdx) | |
| 276 | { | ||
| 277 |
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2680189 | assert(phaseIdx == liquidPhaseIdx); |
| 278 | 2680189 | const Scalar temperature = fluidState.temperature(phaseIdx); | |
| 279 | 2680189 | const Scalar xNaCl = fluidState.massFraction(phaseIdx, NaClIdx); | |
| 280 | |||
| 281 | using std::pow; | ||
| 282 | using Dune::power; | ||
| 283 | using std::exp; | ||
| 284 | using std::max; | ||
| 285 |
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2680189 | const Scalar T = max(temperature, 275.0); |
| 286 |
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2680189 | const Scalar salinity = max(0.0, xNaCl); |
| 287 | |||
| 288 | 2680189 | const Scalar T_C = T - 273.15; | |
| 289 | 2680189 | const Scalar A = ((0.42*power((pow(salinity, 0.8)-0.17), 2)) + 0.045)*pow(T_C, 0.8); | |
| 290 | 2680189 | const Scalar mu_brine = 0.1 + (0.333*salinity) + (1.65+(91.9*salinity*salinity*salinity))*exp(-A); // [cP] | |
| 291 |
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2680189 | assert(mu_brine > 0.0); |
| 292 | 2680189 | return mu_brine/1000.0; // [Pa·s] | |
| 293 | } | ||
| 294 | |||
| 295 | /*! | ||
| 296 | * \brief Vapor pressure of a component \f$\mathrm{[Pa]}\f$. | ||
| 297 | * \note The vapor pressure of brine decreases with the mole fraction of water in the liquid phase. | ||
| 298 | * This is described by Raoult's law, see Thomas Fetzer's Dissertation Eq. 2.11. | ||
| 299 | * It is also the simplified version of the Kelvin equation, without the influence of the capillary pressure | ||
| 300 | * as we have one-phase flow. | ||
| 301 | * | ||
| 302 | * \param fluidState The fluid state | ||
| 303 | * \param compIdx The index of the component to consider | ||
| 304 | */ | ||
| 305 | template <class FluidState> | ||
| 306 | static Scalar vaporPressure(const FluidState& fluidState, int compIdx) | ||
| 307 | { | ||
| 308 | if (compIdx == H2OIdx) | ||
| 309 | { | ||
| 310 | const Scalar temperature = fluidState.temperature(H2OIdx); | ||
| 311 | // Raoult's law, see Thomas Fetzer's Dissertation Eq. 2.11. | ||
| 312 | return H2O::vaporPressure(temperature)*fluidState.moleFraction(phase0Idx, H2OIdx); | ||
| 313 | } | ||
| 314 | else if (compIdx == NaClIdx) | ||
| 315 | DUNE_THROW(Dune::NotImplemented, "NaCl::vaporPressure(t)"); | ||
| 316 | else | ||
| 317 | DUNE_THROW(Dune::NotImplemented, "Invalid component index " << compIdx); | ||
| 318 | } | ||
| 319 | |||
| 320 | using Base<Scalar, ThisType>::enthalpy; | ||
| 321 | /*! | ||
| 322 | * \brief Given a phase's composition, temperature and pressure, | ||
| 323 | * return its specific enthalpy \f$\mathrm{[J/kg]}\f$. | ||
| 324 | * | ||
| 325 | * \param fluidState The fluid state | ||
| 326 | * \param phaseIdx The index of the phase to consider | ||
| 327 | * | ||
| 328 | * Equations given in: | ||
| 329 | * - Palliser & McKibbin (1998) \cite palliser1998 <BR> | ||
| 330 | * - Michaelides (1981) \cite michaelides1981 <BR> | ||
| 331 | * - Daubert & Danner (1989) \cite daubert1989 | ||
| 332 | * | ||
| 333 | */ | ||
| 334 | template <class FluidState> | ||
| 335 | 85982 | static Scalar enthalpy(const FluidState& fluidState, int phaseIdx) | |
| 336 | { | ||
| 337 | //use private enthalpy function to recycle it for the heat capacity calculation | ||
| 338 | 85982 | return enthalpy_(fluidState.pressure(phaseIdx), | |
| 339 | fluidState.temperature(phaseIdx), | ||
| 340 | 85982 | fluidState.massFraction(phase0Idx, NaClIdx)); /*J/kg*/ | |
| 341 | } | ||
| 342 | |||
| 343 | /*! | ||
| 344 | * \brief Returns the specific enthalpy \f$\mathrm{[J/kg]}\f$ of a component in a specific phase | ||
| 345 | * \param fluidState An arbitrary fluid state | ||
| 346 | * \param phaseIdx The index of the fluid phase to consider | ||
| 347 | * \param componentIdx The index of the component to consider | ||
| 348 | * | ||
| 349 | */ | ||
| 350 | template <class FluidState> | ||
| 351 | static Scalar componentEnthalpy(const FluidState &fluidState, | ||
| 352 | int phaseIdx, | ||
| 353 | int componentIdx) | ||
| 354 | { | ||
| 355 | const Scalar T = fluidState.temperature(liquidPhaseIdx); | ||
| 356 | const Scalar p = fluidState.pressure(liquidPhaseIdx); | ||
| 357 | |||
| 358 | if (phaseIdx == liquidPhaseIdx) | ||
| 359 | { | ||
| 360 | if (componentIdx == H2OIdx) | ||
| 361 | return H2O::liquidEnthalpy(T, p); | ||
| 362 | else if (componentIdx == NaClIdx) | ||
| 363 | DUNE_THROW(Dune::NotImplemented, "The component enthalpy for NaCl is not implemented."); | ||
| 364 | DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << componentIdx); | ||
| 365 | } | ||
| 366 | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx); | ||
| 367 | } | ||
| 368 | |||
| 369 | using Base<Scalar, ThisType>::molarDensity; | ||
| 370 | //! \copydoc Base<Scalar,ThisType>::molarDensity(const FluidState&,int) | ||
| 371 | template <class FluidState> | ||
| 372 | 5191558 | static Scalar molarDensity(const FluidState& fluidState, int phaseIdx = liquidPhaseIdx) | |
| 373 | { | ||
| 374 | 5191558 | return density(fluidState, phaseIdx)/fluidState.averageMolarMass(phaseIdx); | |
| 375 | } | ||
| 376 | |||
| 377 | using Base<Scalar, ThisType>::diffusionCoefficient; | ||
| 378 | //! \copydoc Base<Scalar,ThisType>::diffusionCoefficient(const FluidState&,int,int) | ||
| 379 | template <class FluidState> | ||
| 380 | 2 | static Scalar diffusionCoefficient(const FluidState& fluidState, int phaseIdx, int compIdx) | |
| 381 | { | ||
| 382 |
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8 | DUNE_THROW(Dune::NotImplemented, "FluidSystems::Brine::diffusionCoefficient()"); |
| 383 | } | ||
| 384 | |||
| 385 | using Base<Scalar, ThisType>::binaryDiffusionCoefficient; | ||
| 386 | /*! | ||
| 387 | * \brief Given a phase's composition, temperature and pressure, | ||
| 388 | * return the binary diffusion coefficient \f$\mathrm{[m^2/s]}\f$ for components | ||
| 389 | * \f$\mathrm{i}\f$ and \f$\mathrm{j}\f$ in this phase. | ||
| 390 | * \param fluidState The fluid state | ||
| 391 | * \param phaseIdx Index of the fluid phase | ||
| 392 | * \param compIIdx Index of the component i | ||
| 393 | * \param compJIdx Index of the component j | ||
| 394 | * | ||
| 395 | * The implemented value for NaCl is for a molar concentration of 2.5984 mol/l and a temperature of 25°C, | ||
| 396 | * see Rard and Miller, 1979 (DOI: 10.1007/BF00648776) \cite Rard1979. | ||
| 397 | * Dependent on the salt concentration the coefficient can vary between 1.47e-9 m^2/s and 1.6e-9 m^2/s, see Rard and Miller, 1979. | ||
| 398 | * It also depends on temperature; values for different temperatures can e.g. found here: Alanis et al., 2000 (DOI: 10.1117/1.602422) \cite Alanis2000. | ||
| 399 | */ | ||
| 400 | template <class FluidState> | ||
| 401 | 2680207 | static Scalar binaryDiffusionCoefficient(const FluidState& fluidState, | |
| 402 | int phaseIdx, | ||
| 403 | int compIIdx, | ||
| 404 | int compJIdx) | ||
| 405 | { | ||
| 406 |
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2680207 | if (phaseIdx == liquidPhaseIdx) |
| 407 | { | ||
| 408 |
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2680207 | if (compIIdx > compJIdx) |
| 409 | { | ||
| 410 | using std::swap; | ||
| 411 | 2 | swap(compIIdx, compJIdx); | |
| 412 | } | ||
| 413 | |||
| 414 |
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2680207 | if (compJIdx == NaClIdx) |
| 415 | 2680205 | return 1.54e-9; | |
| 416 | else | ||
| 417 |
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10 | DUNE_THROW(Dune::NotImplemented, "Binary diffusion coefficient of components " |
| 418 | << compIIdx << " and " << compJIdx | ||
| 419 | << " in phase " << phaseIdx); | ||
| 420 | } | ||
| 421 | |||
| 422 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index: " << phaseIdx); | |
| 423 | } | ||
| 424 | |||
| 425 | using Base<Scalar, ThisType>::thermalConductivity; | ||
| 426 | /*! | ||
| 427 | * \brief Thermal conductivity of a fluid phase \f$\mathrm{[W/(m K)]}\f$. | ||
| 428 | * \param fluidState An arbitrary fluid state | ||
| 429 | * \param phaseIdx The index of the fluid phase to consider | ||
| 430 | * | ||
| 431 | * 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 | ||
| 432 | */ | ||
| 433 | template <class FluidState> | ||
| 434 | 88194 | static Scalar thermalConductivity(const FluidState& fluidState, int phaseIdx) | |
| 435 | { | ||
| 436 |
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88194 | if (phaseIdx == liquidPhaseIdx) |
| 437 | { | ||
| 438 | 88194 | Scalar tempC = fluidState.temperature(phaseIdx)-273.15; | |
| 439 | 88194 | Scalar m = fluidState.moleFraction(phaseIdx, NaClIdx)/(molarMass(H2OIdx)*(1- fluidState.moleFraction(phaseIdx, NaClIdx))); // molality of NaCl | |
| 440 | 88194 | Scalar S = 5844.3 * m / (1000 + 58.443 *m); | |
| 441 | 88194 | 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; | |
| 442 | 88194 | return contribNaClFactor * H2O::liquidThermalConductivity(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx)); | |
| 443 | } | ||
| 444 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index: " << phaseIdx); | |
| 445 | } | ||
| 446 | |||
| 447 | using Base<Scalar, ThisType>::heatCapacity; | ||
| 448 | //! \copydoc Base<Scalar,ThisType>::heatCapacity(const FluidState&,int) | ||
| 449 | template <class FluidState> | ||
| 450 | 14 | static Scalar heatCapacity(const FluidState &fluidState, int phaseIdx) | |
| 451 | { | ||
| 452 |
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14 | if (phaseIdx == liquidPhaseIdx){ |
| 453 | 14 | const Scalar eps = fluidState.temperature(phaseIdx)*1e-8; | |
| 454 | //calculate heat capacity from the difference in enthalpy with temperature at constant pressure. | ||
| 455 | 28 | return (enthalpy_(fluidState.pressure(phaseIdx), | |
| 456 | 14 | fluidState.temperature(phaseIdx) +eps , | |
| 457 | fluidState.massFraction(phase0Idx, NaClIdx)) | ||
| 458 | 14 | - enthalpy_(fluidState.pressure(phaseIdx), | |
| 459 | fluidState.temperature(phaseIdx), | ||
| 460 | 14 | fluidState.massFraction(phase0Idx, NaClIdx)))/eps; /*J/kg*/ | |
| 461 | } | ||
| 462 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx); | |
| 463 | } | ||
| 464 | |||
| 465 | private: | ||
| 466 | /*! | ||
| 467 | * \brief Given a phase's composition, temperature and pressure, | ||
| 468 | * return its specific enthalpy \f$\mathrm{[J/kg]}\f$. | ||
| 469 | * | ||
| 470 | * Equations given in: | ||
| 471 | * - Palliser & McKibbin (1998) \cite palliser1998 <BR> | ||
| 472 | * - Michaelides (1981) \cite michaelides1981 <BR> | ||
| 473 | * - Daubert & Danner (1989) \cite daubert1989 | ||
| 474 | * | ||
| 475 | */ | ||
| 476 | 85989 | static Scalar enthalpy_(const Scalar p, const Scalar T, const Scalar xNaCl) | |
| 477 | { | ||
| 478 | /*Numerical coefficients from PALLISER*/ | ||
| 479 | static const Scalar f[] = { 2.63500E-1, 7.48368E-6, 1.44611E-6, -3.80860E-10 }; | ||
| 480 | |||
| 481 | /*Numerical coefficients from MICHAELIDES for the enthalpy of brine*/ | ||
| 482 | static const Scalar a[4][3] = { { +9633.6, -4080.0, +286.49 }, | ||
| 483 | { +166.58, +68.577, -4.6856 }, | ||
| 484 | { -0.90963, -0.36524, +0.249667E-1 }, | ||
| 485 | { +0.17965E-2, +0.71924E-3, -0.4900E-4 } }; | ||
| 486 | |||
| 487 | 85989 | const Scalar theta = T - 273.15; | |
| 488 | 85989 | const Scalar salSat = f[0] + f[1]*theta + f[2]*theta*theta + f[3]*theta*theta*theta; | |
| 489 | |||
| 490 | /*Regularization*/ | ||
| 491 | using std::min; | ||
| 492 | using std::max; | ||
| 493 |
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85989 | const Scalar salinity = min(max(xNaCl,0.0), salSat); |
| 494 | |||
| 495 | 85989 | const Scalar hw = H2O::liquidEnthalpy(T, p)/1E3; /* kJ/kg */ | |
| 496 | |||
| 497 | /*component enthalpy of soluted NaCl after DAUBERT and DANNER*/ | ||
| 498 | 85989 | const Scalar h_NaCl = (3.6710E4*T + 0.5*(6.2770E1)*T*T - ((6.6670E-2)/3)*T*T*T | |
| 499 | 85989 | + ((2.8000E-5)/4)*(T*T*T*T))/(58.44E3)- 2.045698e+02; /* U [kJ/kg] */ | |
| 500 | |||
| 501 | 85989 | const Scalar m = (1E3/58.44)*(salinity/(1-salinity)); | |
| 502 | |||
| 503 | using Dune::power; | ||
| 504 | 85989 | Scalar d_h = 0; | |
| 505 |
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429945 | for (int i = 0; i<=3; i++) |
| 506 |
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1375824 | for (int j=0; j<=2; j++) |
| 507 | 3095604 | d_h = d_h + a[i][j] * power(theta, i) * power(m, j); | |
| 508 | |||
| 509 | /* heat of dissolution for halite according to Michaelides 1981 */ | ||
| 510 | 85989 | const Scalar delta_h = (4.184/(1E3 + (58.44 * m)))*d_h; | |
| 511 | |||
| 512 | /* Enthalpy of brine without any dissolved gas */ | ||
| 513 | 85989 | const Scalar h_ls1 =(1-salinity)*hw + salinity*h_NaCl + salinity*delta_h; /* kJ/kg */ | |
| 514 | 85989 | return h_ls1*1E3; /*J/kg*/ | |
| 515 | } | ||
| 516 | }; | ||
| 517 | |||
| 518 | } // end namespace Dumux::FluidSystems | ||
| 519 | |||
| 520 | #endif | ||
| 521 |