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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 FluidSystems | ||
| 10 | * \copybrief Dumux::FluidSystems::BrineAir | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_BRINE_AIR_FLUID_SYSTEM_HH | ||
| 13 | #define DUMUX_BRINE_AIR_FLUID_SYSTEM_HH | ||
| 14 | |||
| 15 | #include <array> | ||
| 16 | #include <cassert> | ||
| 17 | #include <iomanip> | ||
| 18 | |||
| 19 | #include <dumux/material/idealgas.hh> | ||
| 20 | #include <dumux/material/fluidstates/adapter.hh> | ||
| 21 | #include <dumux/material/fluidsystems/base.hh> | ||
| 22 | #include <dumux/material/fluidsystems/brine.hh> | ||
| 23 | #include <dumux/material/components/air.hh> | ||
| 24 | #include <dumux/material/components/h2o.hh> | ||
| 25 | #include <dumux/material/components/nacl.hh> | ||
| 26 | #include <dumux/material/binarycoefficients/h2o_air.hh> | ||
| 27 | #include <dumux/material/components/tabulatedcomponent.hh> | ||
| 28 | |||
| 29 | #include <dumux/common/exceptions.hh> | ||
| 30 | |||
| 31 | #include <dumux/io/name.hh> | ||
| 32 | |||
| 33 | #include "brine.hh" | ||
| 34 | |||
| 35 | namespace Dumux { | ||
| 36 | namespace FluidSystems { | ||
| 37 | |||
| 38 | /*! | ||
| 39 | * \ingroup FluidSystems | ||
| 40 | * \brief Policy for the brine-air fluid system | ||
| 41 | */ | ||
| 42 | template<bool fastButSimplifiedRelations = false> | ||
| 43 | struct BrineAirDefaultPolicy | ||
| 44 | { | ||
| 45 | static constexpr bool useBrineDensityAsLiquidMixtureDensity() { return fastButSimplifiedRelations;} | ||
| 46 | static constexpr bool useIdealGasDensity() { return fastButSimplifiedRelations; } | ||
| 47 | static constexpr bool useKelvinVaporPressure() { return false; } | ||
| 48 | }; | ||
| 49 | |||
| 50 | /*! | ||
| 51 | * \ingroup FluidSystems | ||
| 52 | * \brief A compositional two-phase fluid system with a liquid and a gaseous phase | ||
| 53 | * and \f$H_2O\f$, \f$Air\f$ and \f$S\f$ (dissolved minerals) as components. | ||
| 54 | * | ||
| 55 | * \note This fluidsystem is applied by default with the tabulated version of | ||
| 56 | * water of the IAPWS-formulation. | ||
| 57 | */ | ||
| 58 | template <class Scalar, | ||
| 59 | class H2Otype = Components::TabulatedComponent<Components::H2O<Scalar>>, | ||
| 60 | class Policy = BrineAirDefaultPolicy<>> | ||
| 61 | class BrineAir | ||
| 62 | : public Base<Scalar, BrineAir<Scalar, H2Otype, Policy>> | ||
| 63 | { | ||
| 64 | using ThisType = BrineAir<Scalar, H2Otype, Policy>; | ||
| 65 | using IdealGas = Dumux::IdealGas<Scalar>; | ||
| 66 | |||
| 67 | public: | ||
| 68 | //! export the involved components | ||
| 69 | using H2O = H2Otype; | ||
| 70 | using Air = Components::Air<Scalar>; | ||
| 71 | using NaCl = Components::NaCl<Scalar>; | ||
| 72 | |||
| 73 | //! export the underlying brine fluid system for the liquid phase | ||
| 74 | using Brine = Dumux::FluidSystems::Brine<Scalar, H2Otype>; | ||
| 75 | |||
| 76 | //! export the binary coefficients between air and water | ||
| 77 | using H2O_Air = BinaryCoeff::H2O_Air; | ||
| 78 | |||
| 79 | //! the type of parameter cache objects | ||
| 80 | using ParameterCache = NullParameterCache; | ||
| 81 | |||
| 82 | /**************************************** | ||
| 83 | * Fluid phase related static parameters | ||
| 84 | ****************************************/ | ||
| 85 | static constexpr int numPhases = 2; // one liquid and one gas phase | ||
| 86 | static constexpr int numComponents = 3; // H2O, Air, NaCl | ||
| 87 | |||
| 88 | static constexpr int liquidPhaseIdx = 0; // index of the liquid phase | ||
| 89 | static constexpr int gasPhaseIdx = 1; // index of the gas phase | ||
| 90 | |||
| 91 | static constexpr int phase0Idx = liquidPhaseIdx; // index of the first phase | ||
| 92 | static constexpr int phase1Idx = gasPhaseIdx; // index of the second phase | ||
| 93 | |||
| 94 | // export component indices to indicate the main component | ||
| 95 | // of the corresponding phase at atmospheric pressure 1 bar | ||
| 96 | // and room temperature 20°C: | ||
| 97 | static constexpr int H2OIdx = 0; | ||
| 98 | static constexpr int AirIdx = 1; | ||
| 99 | static constexpr int NaClIdx = 2; | ||
| 100 | static constexpr int comp0Idx = H2OIdx; | ||
| 101 | static constexpr int comp1Idx = AirIdx; | ||
| 102 | static constexpr int comp2Idx = NaClIdx; | ||
| 103 | |||
| 104 | private: | ||
| 105 | struct BrineAdapterPolicy | ||
| 106 | { | ||
| 107 | using FluidSystem = Brine; | ||
| 108 | |||
| 109 | ✗ | static constexpr int phaseIdx(int brinePhaseIdx) { return liquidPhaseIdx; } | |
| 110 | static constexpr int compIdx(int brineCompIdx) | ||
| 111 | { | ||
| 112 |
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21335685 | switch (brineCompIdx) |
| 113 | { | ||
| 114 | case Brine::H2OIdx: return H2OIdx; | ||
| 115 | 14166246 | case Brine::NaClIdx: return NaClIdx; | |
| 116 | default: return 0; // this will never be reached, only needed to suppress compiler warning | ||
| 117 | } | ||
| 118 | } | ||
| 119 | }; | ||
| 120 | |||
| 121 | template<class FluidState> | ||
| 122 | using BrineAdapter = FluidStateAdapter<FluidState, BrineAdapterPolicy>; | ||
| 123 | |||
| 124 | public: | ||
| 125 | |||
| 126 | /**************************************** | ||
| 127 | * phase related static parameters | ||
| 128 | ****************************************/ | ||
| 129 | |||
| 130 | /*! | ||
| 131 | * \brief Return the human readable name of a fluid phase | ||
| 132 | * \param phaseIdx index of the phase | ||
| 133 | */ | ||
| 134 | 418 | static std::string phaseName(int phaseIdx) | |
| 135 | { | ||
| 136 |
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418 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 137 |
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418 | switch (phaseIdx) |
| 138 | { | ||
| 139 | 209 | case liquidPhaseIdx: return IOName::liquidPhase(); | |
| 140 | 209 | case gasPhaseIdx: return IOName::gaseousPhase(); | |
| 141 | } | ||
| 142 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx); | |
| 143 | } | ||
| 144 | |||
| 145 | /*! | ||
| 146 | * \brief Returns whether the fluids are miscible | ||
| 147 | */ | ||
| 148 | static constexpr bool isMiscible() | ||
| 149 | { return true; } | ||
| 150 | |||
| 151 | /*! | ||
| 152 | * \brief Return whether a phase is gaseous | ||
| 153 | * \param phaseIdx The index of the fluid phase to consider | ||
| 154 | */ | ||
| 155 | static constexpr bool isGas(int phaseIdx) | ||
| 156 | { | ||
| 157 |
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4 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 158 | return phaseIdx == gasPhaseIdx; | ||
| 159 | } | ||
| 160 | |||
| 161 | /*! | ||
| 162 | * \brief Returns true if and only if a fluid phase is assumed to | ||
| 163 | * be an ideal mixture. | ||
| 164 | * | ||
| 165 | * We define an ideal mixture as a fluid phase where the fugacity | ||
| 166 | * coefficients of all components times the pressure of the phase | ||
| 167 | * are independent on the fluid composition. This assumption is true | ||
| 168 | * if Henry's law and Raoult's law apply. If you are unsure what | ||
| 169 | * this function should return, it is safe to return false. The | ||
| 170 | * only damage done will be (slightly) increased computation times | ||
| 171 | * in some cases. | ||
| 172 | * | ||
| 173 | * \param phaseIdx The index of the fluid phase to consider | ||
| 174 | */ | ||
| 175 | static bool isIdealMixture(int phaseIdx) | ||
| 176 | { | ||
| 177 |
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904846 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 178 | // we assume Henry's and Raoult's laws for the water phase and | ||
| 179 | // and no interaction between gas molecules of different | ||
| 180 | // components, so all phases are ideal mixtures! | ||
| 181 | return true; | ||
| 182 | } | ||
| 183 | |||
| 184 | /*! | ||
| 185 | * \brief Returns true if and only if a fluid phase is assumed to | ||
| 186 | * be compressible. | ||
| 187 | * | ||
| 188 | * Compressible means that the partial derivative of the density | ||
| 189 | * to the fluid pressure is always larger than zero. | ||
| 190 | * | ||
| 191 | * \param phaseIdx The index of the fluid phase to consider | ||
| 192 | */ | ||
| 193 | static constexpr bool isCompressible(int phaseIdx) | ||
| 194 | { | ||
| 195 | assert(0 <= phaseIdx && phaseIdx < numPhases); | ||
| 196 | // ideal gases are always compressible | ||
| 197 |
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4 | if (phaseIdx == gasPhaseIdx) |
| 198 | return true; | ||
| 199 | // let brine decide for the liquid phase... | ||
| 200 | return Brine::isCompressible(Brine::liquidPhaseIdx); | ||
| 201 | } | ||
| 202 | |||
| 203 | /*! | ||
| 204 | * \brief Returns true if and only if a fluid phase is assumed to | ||
| 205 | * be an ideal gas. | ||
| 206 | * \param phaseIdx The index of the fluid phase to consider | ||
| 207 | */ | ||
| 208 | static bool isIdealGas(int phaseIdx) | ||
| 209 | { | ||
| 210 | assert(0 <= phaseIdx && phaseIdx < numPhases); | ||
| 211 | // let the fluids decide | ||
| 212 | if (phaseIdx == gasPhaseIdx) | ||
| 213 | return H2O::gasIsIdeal() && Air::gasIsIdeal(); | ||
| 214 | return false; // not a gas | ||
| 215 | } | ||
| 216 | |||
| 217 | /*! | ||
| 218 | * \brief Get the main component of a given phase if possible | ||
| 219 | * \param phaseIdx The index of the fluid phase to consider | ||
| 220 | */ | ||
| 221 | static constexpr int getMainComponent(int phaseIdx) | ||
| 222 | { | ||
| 223 |
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78612728 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 224 |
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90618524 | if (phaseIdx == liquidPhaseIdx) |
| 225 | return H2OIdx; | ||
| 226 | else | ||
| 227 | return AirIdx; | ||
| 228 | } | ||
| 229 | |||
| 230 | /**************************************** | ||
| 231 | * Component related static parameters | ||
| 232 | ****************************************/ | ||
| 233 | /*! | ||
| 234 | * \brief Return the human readable name of a component | ||
| 235 | * \param compIdx The index of the component to consider | ||
| 236 | */ | ||
| 237 | 36 | static std::string componentName(int compIdx) | |
| 238 | { | ||
| 239 |
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36 | assert(0 <= compIdx && compIdx < numComponents); |
| 240 |
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36 | switch (compIdx) |
| 241 | { | ||
| 242 | 12 | case H2OIdx: return H2O::name(); | |
| 243 | 12 | case AirIdx: return Air::name(); | |
| 244 | 12 | case NaClIdx: return NaCl::name(); | |
| 245 | } | ||
| 246 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << compIdx); | |
| 247 | } | ||
| 248 | |||
| 249 | /*! | ||
| 250 | * \brief Return the molar mass of a component in \f$\mathrm{[kg/mol]}\f$. | ||
| 251 | * \param compIdx The index of the component to consider | ||
| 252 | */ | ||
| 253 | 206124543 | static Scalar molarMass(int compIdx) | |
| 254 | { | ||
| 255 |
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206124543 | assert(0 <= compIdx && compIdx < numComponents); |
| 256 | switch (compIdx) | ||
| 257 | { | ||
| 258 | case H2OIdx: return H2O::molarMass(); | ||
| 259 | case AirIdx: return Air::molarMass(); | ||
| 260 | case NaClIdx: return NaCl::molarMass(); | ||
| 261 | } | ||
| 262 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << compIdx); | |
| 263 | } | ||
| 264 | |||
| 265 | /*! | ||
| 266 | * \brief Vapor pressure of a component \f$\mathrm{[Pa]}\f$. | ||
| 267 | * | ||
| 268 | * \param fluidState The fluid state | ||
| 269 | * \param compIdx The index of the component to consider | ||
| 270 | */ | ||
| 271 | template <class FluidState> | ||
| 272 | static Scalar vaporPressure(const FluidState& fluidState, int compIdx) | ||
| 273 | { | ||
| 274 | // The vapor pressure of the water is affected by the | ||
| 275 | // salinity, thus, we forward to the interface of Brine here | ||
| 276 | if (compIdx == H2OIdx) | ||
| 277 | { | ||
| 278 | if (!Policy::useKelvinVaporPressure()) | ||
| 279 | return Brine::vaporPressure(BrineAdapter<FluidState>(fluidState), Brine::H2OIdx); | ||
| 280 | else | ||
| 281 | { | ||
| 282 | //additionally taking the influence of the capillary pressure on the vapor pressure, described by Kelvin's equation, into account. | ||
| 283 | const auto t = fluidState.temperature(liquidPhaseIdx); | ||
| 284 | const auto pc = (fluidState.wettingPhase() == (int) liquidPhaseIdx) | ||
| 285 | ? fluidState.pressure(gasPhaseIdx)-fluidState.pressure(liquidPhaseIdx) | ||
| 286 | : fluidState.pressure(liquidPhaseIdx)-fluidState.pressure(gasPhaseIdx); | ||
| 287 | //influence of the capillary pressure on the vapor pressure, the influence of the salt concentration is already taken into account in the brine vapour pressure | ||
| 288 | return Brine::vaporPressure(BrineAdapter<FluidState>(fluidState), Brine::H2OIdx) | ||
| 289 | *exp( -pc / (Brine::molarDensity(fluidState, liquidPhaseIdx) * (Dumux::Constants<Scalar>::R*t))); | ||
| 290 | } | ||
| 291 | } | ||
| 292 | else if (compIdx == NaClIdx) | ||
| 293 | DUNE_THROW(Dune::NotImplemented, "NaCl::vaporPressure(t)"); | ||
| 294 | else | ||
| 295 | DUNE_THROW(Dune::NotImplemented, "Invalid component index " << compIdx); | ||
| 296 | } | ||
| 297 | |||
| 298 | /**************************************** | ||
| 299 | * thermodynamic relations | ||
| 300 | ****************************************/ | ||
| 301 | /*! | ||
| 302 | * \brief Initialize the fluid system's static parameters generically | ||
| 303 | * | ||
| 304 | * If a tabulated H2O component is used, we do our best to create | ||
| 305 | * tables that always work. | ||
| 306 | */ | ||
| 307 | static void init() | ||
| 308 | { | ||
| 309 | 2 | init(/*tempMin=*/273.15, | |
| 310 | /*tempMax=*/800.0, | ||
| 311 | /*numTemptempSteps=*/200, | ||
| 312 | /*startPressure=*/-10, | ||
| 313 | /*endPressure=*/20e6, | ||
| 314 | /*pressureSteps=*/200); | ||
| 315 | } | ||
| 316 | |||
| 317 | /*! | ||
| 318 | * \brief Initialize the fluid system's static parameters using | ||
| 319 | * problem specific temperature and pressure ranges | ||
| 320 | * | ||
| 321 | * \param tempMin The minimum temperature used for tabulation of water \f$\mathrm{[K]}\f$ | ||
| 322 | * \param tempMax The maximum temperature used for tabulation of water \f$\mathrm{[K]}\f$ | ||
| 323 | * \param nTemp The number of ticks on the temperature axis of the table of water | ||
| 324 | * \param pressMin The minimum pressure used for tabulation of water \f$\mathrm{[Pa]}\f$ | ||
| 325 | * \param pressMax The maximum pressure used for tabulation of water \f$\mathrm{[Pa]}\f$ | ||
| 326 | * \param nPress The number of ticks on the pressure axis of the table of water | ||
| 327 | */ | ||
| 328 | 8 | static void init(Scalar tempMin, Scalar tempMax, unsigned nTemp, | |
| 329 | Scalar pressMin, Scalar pressMax, unsigned nPress) | ||
| 330 | { | ||
| 331 | 8 | std::cout << "The brine-air fluid system was configured with the following policy:\n"; | |
| 332 | 16 | std::cout << " - use brine density as liquid mixture density: " << std::boolalpha << Policy::useBrineDensityAsLiquidMixtureDensity() << "\n"; | |
| 333 | 16 | std::cout << " - use ideal gas density: " << std::boolalpha << Policy::useIdealGasDensity() << std::endl; | |
| 334 | |||
| 335 | if (H2O::isTabulated) | ||
| 336 | H2O::init(tempMin, tempMax, nTemp, pressMin, pressMax, nPress); | ||
| 337 | 8 | } | |
| 338 | |||
| 339 | using Base<Scalar, ThisType>::density; | ||
| 340 | /*! | ||
| 341 | * \brief Given a phase's composition, temperature, pressure, and | ||
| 342 | * the partial pressures of all components, return its | ||
| 343 | * density \f$\mathrm{[kg/m^3]}\f$. | ||
| 344 | * | ||
| 345 | * \param fluidState the fluid state | ||
| 346 | * \param phaseIdx index of the phase | ||
| 347 | * | ||
| 348 | * Equation given in: | ||
| 349 | * - Batzle & Wang (1992) \cite batzle1992 | ||
| 350 | * - cited by: Bachu & Adams (2002) | ||
| 351 | * "Equations of State for basin geofluids" \cite adams2002 | ||
| 352 | */ | ||
| 353 | template <class FluidState> | ||
| 354 | 4607002 | static Scalar density(const FluidState &fluidState, int phaseIdx) | |
| 355 | { | ||
| 356 |
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4607002 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 357 | |||
| 358 |
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4607002 | const auto T = fluidState.temperature(phaseIdx); |
| 359 |
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4607002 | const auto p = fluidState.pressure(phaseIdx); |
| 360 | |||
| 361 |
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4607002 | if (phaseIdx == liquidPhaseIdx) |
| 362 | { | ||
| 363 | // assume pure brine | ||
| 364 | if (Policy::useBrineDensityAsLiquidMixtureDensity()) | ||
| 365 | 4 | return Brine::density(BrineAdapter<FluidState>(fluidState), Brine::liquidPhaseIdx); | |
| 366 | |||
| 367 | // assume one molecule of gas replaces one "brine" molecule | ||
| 368 | else | ||
| 369 | 4606998 | return Brine::molarDensity(BrineAdapter<FluidState>(fluidState), Brine::liquidPhaseIdx) | |
| 370 | 2303499 | *(H2O::molarMass()*fluidState.moleFraction(liquidPhaseIdx, H2OIdx) | |
| 371 | 2303499 | + NaCl::molarMass()*fluidState.moleFraction(liquidPhaseIdx, NaClIdx) | |
| 372 | 4606996 | + Air::molarMass()*fluidState.moleFraction(liquidPhaseIdx, AirIdx)); | |
| 373 | } | ||
| 374 | else if (phaseIdx == phase1Idx) | ||
| 375 | { | ||
| 376 | // for the gas phase assume an ideal gas | ||
| 377 | if (Policy::useIdealGasDensity()) | ||
| 378 | 2 | return IdealGas::density(fluidState.averageMolarMass(phase1Idx), T, p); | |
| 379 | |||
| 380 | // if useComplexRelations = true, compute density. NaCl is assumed | ||
| 381 | // not to be present in gas phase, NaCl has only solid interfaces implemented | ||
| 382 | 4606996 | return H2O::gasDensity(T, fluidState.partialPressure(phase1Idx, H2OIdx)) | |
| 383 | 6910493 | + Air::gasDensity(T, fluidState.partialPressure(phase1Idx, AirIdx)); | |
| 384 | } | ||
| 385 | else | ||
| 386 | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx); | ||
| 387 | } | ||
| 388 | |||
| 389 | using Base<Scalar, ThisType>::molarDensity; | ||
| 390 | //! \copydoc Base<Scalar,ThisType>::molarDensity(const FluidState&,int) | ||
| 391 | template <class FluidState> | ||
| 392 | 4607002 | static Scalar molarDensity(const FluidState& fluidState, int phaseIdx) | |
| 393 | { | ||
| 394 |
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4607002 | if (phaseIdx == liquidPhaseIdx) |
| 395 | 6910503 | return Brine::molarDensity(BrineAdapter<FluidState>(fluidState), Brine::liquidPhaseIdx); | |
| 396 |
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2303501 | else if (phaseIdx == phase1Idx) |
| 397 | { | ||
| 398 | 2303501 | const Scalar T = fluidState.temperature(phaseIdx); | |
| 399 | |||
| 400 | // for the gas phase assume an ideal gas | ||
| 401 | if (Policy::useIdealGasDensity()) | ||
| 402 | 2 | return IdealGas::molarDensity(T, fluidState.pressure(phaseIdx)); | |
| 403 | |||
| 404 | // if useComplexRelations = true, compute density. NaCl is assumed | ||
| 405 | // not to be present in gas phase, NaCl has only solid interfaces implemented | ||
| 406 | 4606996 | return H2O::gasMolarDensity(T, fluidState.partialPressure(phase1Idx, H2OIdx)) | |
| 407 | 6910493 | + Air::gasMolarDensity(T, fluidState.partialPressure(phase1Idx, AirIdx)); | |
| 408 | } | ||
| 409 | else | ||
| 410 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx); | |
| 411 | } | ||
| 412 | |||
| 413 | using Base<Scalar, ThisType>::viscosity; | ||
| 414 | /*! | ||
| 415 | * \brief Calculate the dynamic viscosity of a fluid phase \f$\mathrm{[Pa*s]}\f$ | ||
| 416 | * | ||
| 417 | * \param fluidState An arbitrary fluid state | ||
| 418 | * \param phaseIdx The index of the fluid phase to consider | ||
| 419 | * | ||
| 420 | * \note For the viscosity of the phases the contribution of the minor | ||
| 421 | * component is neglected. This contribution is probably not big, but somebody | ||
| 422 | * would have to find out its influence. | ||
| 423 | */ | ||
| 424 | template <class FluidState> | ||
| 425 | 4607002 | static Scalar viscosity(const FluidState& fluidState, int phaseIdx) | |
| 426 | { | ||
| 427 |
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4607002 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 428 | |||
| 429 |
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4607002 | if (phaseIdx == liquidPhaseIdx) |
| 430 | 4607002 | return Brine::viscosity(BrineAdapter<FluidState>(fluidState), Brine::liquidPhaseIdx); | |
| 431 | else | ||
| 432 | 6910495 | return Air::gasViscosity(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx)); | |
| 433 | } | ||
| 434 | |||
| 435 | using Base<Scalar, ThisType>::fugacityCoefficient; | ||
| 436 | /*! | ||
| 437 | * \brief Returns the fugacity coefficient \f$\mathrm{[-]}\f$ of a component in a | ||
| 438 | * phase. | ||
| 439 | * \param fluidState The fluid state | ||
| 440 | * \param phaseIdx Index of the phase | ||
| 441 | * \param compIdx Index of the component | ||
| 442 | * | ||
| 443 | * The fugacity coefficient \f$\mathrm{\phi^\kappa_\alpha}\f$ of | ||
| 444 | * component \f$\mathrm{\kappa}\f$ in phase \f$\mathrm{\alpha}\f$ is connected to | ||
| 445 | * the fugacity \f$\mathrm{f^\kappa_\alpha}\f$ and the component's mole | ||
| 446 | * fraction \f$\mathrm{x^\kappa_\alpha}\f$ by means of the relation | ||
| 447 | * | ||
| 448 | * \f[ | ||
| 449 | f^\kappa_\alpha = \phi^\kappa_\alpha\;x^\kappa_\alpha\;p_\alpha | ||
| 450 | \f] | ||
| 451 | * where \f$\mathrm{p_\alpha}\f$ is the pressure of the fluid phase. | ||
| 452 | * | ||
| 453 | * For liquids with very low miscibility this boils down to the | ||
| 454 | * Henry constant for the solutes and the saturated vapor pressure | ||
| 455 | * both divided by phase pressure. | ||
| 456 | */ | ||
| 457 | template <class FluidState> | ||
| 458 | 13821006 | static Scalar fugacityCoefficient(const FluidState& fluidState, int phaseIdx, int compIdx) | |
| 459 | { | ||
| 460 |
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13821006 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 461 |
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13821006 | assert(0 <= compIdx && compIdx < numComponents); |
| 462 | |||
| 463 |
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13821006 | Scalar T = fluidState.temperature(phaseIdx); |
| 464 |
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13821006 | Scalar p = fluidState.pressure(phaseIdx); |
| 465 | |||
| 466 |
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13821006 | if (phaseIdx == gasPhaseIdx) |
| 467 | return 1.0; | ||
| 468 | |||
| 469 | else if (phaseIdx == liquidPhaseIdx) | ||
| 470 | { | ||
| 471 | // TODO: Should we use the vapor pressure of the mixture (brine) here? | ||
| 472 | // The presence of NaCl lowers the vapor pressure, thus, we would | ||
| 473 | // expect the fugacity coefficient to be lower as well. However, | ||
| 474 | // with the fugacity coefficient being dependent on the salinity, | ||
| 475 | // the equation system for the phase equilibria becomes non-linear | ||
| 476 | // and our constraint solvers assume linear system of equations. | ||
| 477 |
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6910503 | if (compIdx == H2OIdx) |
| 478 | 2303501 | return H2O::vaporPressure(T)/p; | |
| 479 | |||
| 480 |
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4607002 | else if (compIdx == AirIdx) |
| 481 | 4607002 | return BinaryCoeff::H2O_Air::henry(T)/p; | |
| 482 | |||
| 483 | // we assume nacl always stays in the liquid phase | ||
| 484 | else | ||
| 485 | return 0.0; | ||
| 486 | } | ||
| 487 | |||
| 488 | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx); | ||
| 489 | } | ||
| 490 | |||
| 491 | using Base<Scalar, ThisType>::diffusionCoefficient; | ||
| 492 | //! \copydoc Base<Scalar,ThisType>::diffusionCoefficient(const FluidState&,int,int) | ||
| 493 | template <class FluidState> | ||
| 494 | 24 | static Scalar diffusionCoefficient(const FluidState &fluidState, | |
| 495 | int phaseIdx, | ||
| 496 | int compIdx) | ||
| 497 | { | ||
| 498 |
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264 | DUNE_THROW(Dune::NotImplemented, "Diffusion coefficients"); |
| 499 | } | ||
| 500 | |||
| 501 | using Base<Scalar, ThisType>::binaryDiffusionCoefficient; | ||
| 502 | //! \copydoc Base<Scalar,ThisType>::binaryDiffusionCoefficient(const FluidState&,int,int,int) | ||
| 503 | template <class FluidState> | ||
| 504 | 9231008 | static Scalar binaryDiffusionCoefficient(const FluidState& fluidState, | |
| 505 | int phaseIdx, | ||
| 506 | int compIIdx, | ||
| 507 | int compJIdx) | ||
| 508 | { | ||
| 509 |
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9231008 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 510 |
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9231008 | assert(0 <= compIIdx && compIIdx < numComponents); |
| 511 |
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9231008 | assert(0 <= compJIdx && compJIdx < numComponents); |
| 512 | |||
| 513 |
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9231008 | const auto T = fluidState.temperature(phaseIdx); |
| 514 |
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9231008 | const auto p = fluidState.pressure(phaseIdx); |
| 515 | |||
| 516 |
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9231008 | if (compIIdx > compJIdx) |
| 517 | 2320469 | std::swap(compIIdx, compJIdx); | |
| 518 | |||
| 519 |
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9231008 | if (phaseIdx == liquidPhaseIdx) |
| 520 | { | ||
| 521 |
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4607030 | if(compIIdx == H2OIdx && compJIdx == AirIdx) |
| 522 | 4607010 | return H2O_Air::liquidDiffCoeff(T, p); | |
| 523 |
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2303525 | else if (compIIdx == H2OIdx && compJIdx == NaClIdx) |
| 524 | 4607010 | return Brine::binaryDiffusionCoefficient(BrineAdapter<FluidState>(fluidState), Brine::liquidPhaseIdx, Brine::H2OIdx, Brine::NaClIdx); | |
| 525 | else | ||
| 526 |
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280 | DUNE_THROW(Dune::NotImplemented, "Binary diffusion coefficient of components " |
| 527 | << compIIdx << " and " << compJIdx | ||
| 528 | << " in phase " << phaseIdx); | ||
| 529 | } | ||
| 530 | else if (phaseIdx == gasPhaseIdx) | ||
| 531 | { | ||
| 532 |
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4623978 | if (compIIdx == H2OIdx && compJIdx == AirIdx) |
| 533 | 4640906 | return H2O_Air::gasDiffCoeff(T, p); | |
| 534 | |||
| 535 | // NaCl is expected to never be present in the gas phase. we need to | ||
| 536 | // return a diffusion coefficient that does not case numerical problems. | ||
| 537 | // We choose a very small value here. | ||
| 538 |
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2303525 | else if (compIIdx == AirIdx && compJIdx == NaClIdx) |
| 539 | return 1e-12; | ||
| 540 | |||
| 541 | else | ||
| 542 |
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280 | DUNE_THROW(Dune::NotImplemented, "Binary diffusion coefficient of components " |
| 543 | << compIIdx << " and " << compJIdx | ||
| 544 | << " in phase " << phaseIdx); | ||
| 545 | } | ||
| 546 | |||
| 547 | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx); | ||
| 548 | } | ||
| 549 | |||
| 550 | using Base<Scalar, ThisType>::enthalpy; | ||
| 551 | /*! | ||
| 552 | * \brief Given a phase's composition, temperature and pressure, | ||
| 553 | * return its specific enthalpy \f$\mathrm{[J/kg]}\f$. | ||
| 554 | * \param fluidState The fluid state | ||
| 555 | * \param phaseIdx The index of the phase | ||
| 556 | * | ||
| 557 | * See: | ||
| 558 | * Class 2000 | ||
| 559 | * Theorie und numerische Modellierung nichtisothermer Mehrphasenprozesse in NAPL-kontaminierten porösen Medien | ||
| 560 | * Chapter 2.1.13 Innere Energie, Wäremekapazität, Enthalpie \cite A3:class:2001 | ||
| 561 | * | ||
| 562 | * Formula (2.42): | ||
| 563 | * the specific enthalpy of a gas phase result from the sum of (enthalpies*mass fraction) of the components | ||
| 564 | * For the calculation of enthalpy of brine we refer to (Michaelides 1981) | ||
| 565 | * | ||
| 566 | * \note For the phase enthalpy the contribution of gas-molecules in the liquid phase | ||
| 567 | * is neglected. This contribution is probably not big. Somebody would have to | ||
| 568 | * find out the enthalpy of solution for this system. ... | ||
| 569 | */ | ||
| 570 | template <class FluidState> | ||
| 571 | 172640 | static Scalar enthalpy(const FluidState& fluidState, int phaseIdx) | |
| 572 | { | ||
| 573 |
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172640 | assert(0 <= phaseIdx && phaseIdx < numPhases); |
| 574 | |||
| 575 |
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172640 | const Scalar T = fluidState.temperature(phaseIdx); |
| 576 |
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172640 | const Scalar p = fluidState.pressure(phaseIdx); |
| 577 | |||
| 578 |
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172640 | if (phaseIdx == liquidPhaseIdx) |
| 579 | 172640 | return Brine::enthalpy(BrineAdapter<FluidState>(fluidState), Brine::liquidPhaseIdx); | |
| 580 | else if (phaseIdx == gasPhaseIdx) | ||
| 581 | { | ||
| 582 | // This assumes NaCl not to be present in the gas phase | ||
| 583 | 86320 | const Scalar XAir = fluidState.massFraction(gasPhaseIdx, AirIdx); | |
| 584 | 86320 | const Scalar XH2O = fluidState.massFraction(gasPhaseIdx, H2OIdx); | |
| 585 | 86320 | return XH2O*H2O::gasEnthalpy(T, p) + XAir*Air::gasEnthalpy(T, p); | |
| 586 | } | ||
| 587 | |||
| 588 | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx); | ||
| 589 | } | ||
| 590 | |||
| 591 | /*! | ||
| 592 | * \brief Returns the specific enthalpy \f$\mathrm{[J/kg]}\f$ of a component in a specific phase | ||
| 593 | * \param fluidState The fluid state | ||
| 594 | * \param phaseIdx The index of the phase | ||
| 595 | * \param componentIdx The index of the component | ||
| 596 | */ | ||
| 597 | template <class FluidState> | ||
| 598 | 33896 | static Scalar componentEnthalpy(const FluidState& fluidState, int phaseIdx, int componentIdx) | |
| 599 | { | ||
| 600 |
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33896 | const Scalar T = fluidState.temperature(gasPhaseIdx); |
| 601 |
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33896 | const Scalar p = fluidState.pressure(gasPhaseIdx); |
| 602 | |||
| 603 |
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33896 | if (phaseIdx == liquidPhaseIdx) |
| 604 | ✗ | DUNE_THROW(Dune::NotImplemented, "The component enthalpies in the liquid phase are not implemented."); | |
| 605 | |||
| 606 |
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33896 | else if (phaseIdx == gasPhaseIdx) |
| 607 | { | ||
| 608 |
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33896 | if (componentIdx == H2OIdx) |
| 609 | 16948 | return H2O::gasEnthalpy(T, p); | |
| 610 |
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16948 | else if (componentIdx == AirIdx) |
| 611 | 33896 | return Air::gasEnthalpy(T, p); | |
| 612 | ✗ | else if (componentIdx == NaClIdx) | |
| 613 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Implementation assumes NaCl not to be present in gas phase"); | |
| 614 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << componentIdx); | |
| 615 | } | ||
| 616 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx); | |
| 617 | } | ||
| 618 | |||
| 619 | using Base<Scalar, ThisType>::thermalConductivity; | ||
| 620 | /*! | ||
| 621 | * \brief Thermal conductivity of a fluid phase \f$\mathrm{[W/(m K)]}\f$. | ||
| 622 | * \param fluidState An arbitrary fluid state | ||
| 623 | * \param phaseIdx The index of the fluid phase to consider | ||
| 624 | * | ||
| 625 | * \note We assume an ideal mixture for the gas-phase thermal conductivity, as a first approximation. | ||
| 626 | * In porous media, gas-phase thermal conductivities are negligible, as they are | ||
| 627 | * orders of magnitude lower than the thermal conductivity in solid and liquids (gas: 0.0x compared to solid: x.). | ||
| 628 | * However, moisture can have a significant influce on the thermal conductivity of moist air, see e.g. \cite Beirao2012, | ||
| 629 | * which could be relevant for free-flow systems. | ||
| 630 | */ | ||
| 631 | template <class FluidState> | ||
| 632 | 189588 | static Scalar thermalConductivity(const FluidState& fluidState, int phaseIdx) | |
| 633 | { | ||
| 634 |
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189588 | if (phaseIdx == liquidPhaseIdx) |
| 635 | 172640 | return Brine::thermalConductivity(BrineAdapter<FluidState>(fluidState), Brine::liquidPhaseIdx); | |
| 636 | // This assumes NaCl not to be present in the gas phase | ||
| 637 |
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103268 | else if (phaseIdx == gasPhaseIdx) |
| 638 | 309796 | return Air::gasThermalConductivity(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx)) * fluidState.massFraction(gasPhaseIdx, AirIdx) | |
| 639 | 309796 | + H2O::gasThermalConductivity(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx)) * fluidState.massFraction(gasPhaseIdx, H2OIdx); | |
| 640 | |||
| 641 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx); | |
| 642 | } | ||
| 643 | |||
| 644 | using Base<Scalar, ThisType>::heatCapacity; | ||
| 645 | /*! | ||
| 646 | * \brief Specific isobaric heat capacity of a fluid phase. | ||
| 647 | * \f$\mathrm{[J/(kg*K)}\f$. | ||
| 648 | * \param fluidState An arbitrary fluid state | ||
| 649 | * \param phaseIdx The index of the fluid phase to consider | ||
| 650 | * | ||
| 651 | * \note We assume an ideal mixture for the gas-phase specific isobaric heat capacity, as a first approximation. | ||
| 652 | * In porous media, gas-phase heat capacities are, due to the usually low densities of gases, negligible anyway. | ||
| 653 | * A better implementation might be relevant for free-flow systems. | ||
| 654 | */ | ||
| 655 | template <class FluidState> | ||
| 656 | 4 | static Scalar heatCapacity(const FluidState &fluidState, int phaseIdx) | |
| 657 | { | ||
| 658 | 4 | const Scalar T = fluidState.temperature(phaseIdx); | |
| 659 | 4 | const Scalar p = fluidState.pressure(phaseIdx); | |
| 660 | |||
| 661 | 4 | if (phaseIdx == liquidPhaseIdx) | |
| 662 | 4 | return Brine::heatCapacity(BrineAdapter<FluidState>(fluidState), Brine::liquidPhaseIdx); | |
| 663 | |||
| 664 | // We assume NaCl not to be present in the gas phase here | ||
| 665 | 2 | else if (phaseIdx == gasPhaseIdx) | |
| 666 | 2 | return Air::gasHeatCapacity(T, p)*fluidState.massFraction(gasPhaseIdx, AirIdx) | |
| 667 | 2 | + H2O::gasHeatCapacity(T, p)*fluidState.massFraction(gasPhaseIdx, H2OIdx); | |
| 668 | |||
| 669 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx); | |
| 670 | } | ||
| 671 | }; | ||
| 672 | |||
| 673 | } // end namespace FluidSystems | ||
| 674 | } // end namespace Dumux | ||
| 675 | |||
| 676 | #endif | ||
| 677 |