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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 EffectiveHeatConductivity | ||
| 10 | * \brief Effective thermal conductivity after Somerton | ||
| 11 | */ | ||
| 12 | |||
| 13 | #ifndef DUMUX_MATERIAL_FLUIDMATRIX_THERMALCONDUCTIVITY_SOMERTON_THREE_P_HH | ||
| 14 | #define DUMUX_MATERIAL_FLUIDMATRIX_THERMALCONDUCTIVITY_SOMERTON_THREE_P_HH | ||
| 15 | |||
| 16 | #include <algorithm> | ||
| 17 | #include <cmath> | ||
| 18 | |||
| 19 | namespace Dumux { | ||
| 20 | |||
| 21 | /*! | ||
| 22 | * \addtogroup EffectiveHeatConductivity | ||
| 23 | * \copydetails Dumux::ThermalConductivitySomertonThreeP | ||
| 24 | */ | ||
| 25 | |||
| 26 | /*! | ||
| 27 | * \ingroup EffectiveHeatConductivity | ||
| 28 | * \brief Effective thermal conductivity after Somerton | ||
| 29 | * | ||
| 30 | * ### Somerton (three fluid phases) | ||
| 31 | * | ||
| 32 | * The Somerton method \cite somerton1974 computes the thermal conductivity of dry and the wet soil material. | ||
| 33 | * It is extended here to a three phase system of water (w), NAPL (n) and gas (g). | ||
| 34 | * It uses a root function of the water and NAPL saturation to compute the | ||
| 35 | * effective thermal conductivity for a three-phase fluidsystem. The individual thermal | ||
| 36 | * conductivities are calculated as geometric mean of the thermal conductivity of the porous | ||
| 37 | * material and of the respective fluid phase. | ||
| 38 | * | ||
| 39 | * The effective thermal conductivity of `ThermalConductivitySomertonThreeP` is given by | ||
| 40 | * \f[ | ||
| 41 | * \lambda_\text{eff} = \lambda_\text{g,eff} + \sqrt{S_\text{w}} \left(\lambda_\text{w,eff} - \lambda_\text{g,eff}\right) + | ||
| 42 | * \sqrt{S_\text{n}} \left(\lambda_\text{n,eff} - \lambda_\text{g,eff}\right) | ||
| 43 | * \f] | ||
| 44 | * | ||
| 45 | * with \f$ S_\text{w} \f$ the water saturation, | ||
| 46 | * \f$ S_\text{n} \f$ the NAPL saturation, the effective phase saturations given by | ||
| 47 | * \f$ \lambda_{\alpha,\text{eff}} = (\lambda_\text{s})^{\left(1-\phi\right)} (\lambda_\alpha)^\phi, \alpha \in \{\text{w,n,g}\}\f$ | ||
| 48 | * (geometric mean) and \f$ \lambda_\text{s} \f$ is the thermal conductivity of the solid phase. | ||
| 49 | */ | ||
| 50 | template<class Scalar> | ||
| 51 | class ThermalConductivitySomertonThreeP | ||
| 52 | { | ||
| 53 | public: | ||
| 54 | /*! | ||
| 55 | * \brief Effective thermal conductivity in \f$\mathrm{W/(m K)}\f$ for three phases | ||
| 56 | * \param volVars volume variables | ||
| 57 | * \return Effective thermal conductivity in \f$\mathrm{W/(m K)}\f$ for three phases | ||
| 58 | */ | ||
| 59 | template<class VolumeVariables> | ||
| 60 | 9041184 | static Scalar effectiveThermalConductivity(const VolumeVariables& volVars) | |
| 61 | { | ||
| 62 | using FluidSystem = typename VolumeVariables::FluidSystem; | ||
| 63 | |||
| 64 | 9041184 | const Scalar sw = volVars.saturation(FluidSystem::wPhaseIdx); | |
| 65 | 9041184 | const Scalar sn = volVars.saturation(FluidSystem::nPhaseIdx); | |
| 66 | 9041184 | const Scalar lambdaW = volVars.fluidThermalConductivity(FluidSystem::wPhaseIdx); | |
| 67 | 9041184 | const Scalar lambdaN = volVars.fluidThermalConductivity(FluidSystem::nPhaseIdx); | |
| 68 | 9041184 | const Scalar lambdaG = volVars.fluidThermalConductivity(FluidSystem::gPhaseIdx); | |
| 69 | 9041184 | const Scalar lambdaSolid = volVars.solidThermalConductivity(); | |
| 70 | 9041184 | const Scalar porosity = volVars.porosity(); | |
| 71 | |||
| 72 | 9041184 | return effectiveThermalConductivity(sw, sn, lambdaW, lambdaN, lambdaG, lambdaSolid, porosity); | |
| 73 | } | ||
| 74 | |||
| 75 | /*! | ||
| 76 | * \brief Effective thermal conductivity in \f$\mathrm{W/(m K)}\f$ for three phases | ||
| 77 | * | ||
| 78 | * \param sw The saturation of the wetting phase | ||
| 79 | * \param sn The saturation of the nonwetting phase | ||
| 80 | * \param lambdaW The thermal conductivity of the water phase in \f$\mathrm{W/(m K)}\f$ | ||
| 81 | * \param lambdaN The thermal conductivity of the NAPL phase in \f$\mathrm{W/(m K)}\f$ | ||
| 82 | * \param lambdaG The thermal conductivity of the gas phase in \f$\mathrm{W/(m K)}\f$ | ||
| 83 | * \param lambdaSolid The thermal conductivity of the solid phase in \f$\mathrm{W/(m K)}\f$ | ||
| 84 | * \param porosity The porosity | ||
| 85 | * | ||
| 86 | * \return Effective thermal conductivity in \f$\mathrm{W/(m K)}\f$ for three phases | ||
| 87 | */ | ||
| 88 | 9041184 | static Scalar effectiveThermalConductivity(const Scalar sw, | |
| 89 | const Scalar sn, | ||
| 90 | const Scalar lambdaW, | ||
| 91 | const Scalar lambdaN, | ||
| 92 | const Scalar lambdaG, | ||
| 93 | const Scalar lambdaSolid, | ||
| 94 | const Scalar porosity) | ||
| 95 | { | ||
| 96 | using std::max; | ||
| 97 | using std::pow; | ||
| 98 | using std::sqrt; | ||
| 99 |
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9041184 | const Scalar satW = max<Scalar>(0.0, sw); |
| 100 |
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9041184 | const Scalar satN = max<Scalar>(0.0, sn); |
| 101 | |||
| 102 | // porosity weighted geometric mean | ||
| 103 | 9041184 | const Scalar lSw = pow(lambdaSolid, (1.0 - porosity)) * pow(lambdaW, porosity); | |
| 104 | 9041184 | const Scalar lSn = pow(lambdaSolid, (1.0 - porosity)) * pow(lambdaN, porosity); | |
| 105 | 9041184 | const Scalar lSg = pow(lambdaSolid, (1.0 - porosity)) * pow(lambdaG, porosity); | |
| 106 | 9041184 | const Scalar lambdaEff = lSg + sqrt(satW) * (lSw - lSg) + sqrt(satN) * (lSn -lSg); | |
| 107 | |||
| 108 | 9041184 | return lambdaEff; | |
| 109 | |||
| 110 | } | ||
| 111 | }; | ||
| 112 | |||
| 113 | |||
| 114 | } // end namespace Dumux | ||
| 115 | |||
| 116 | #endif | ||
| 117 |