h2oairmesitylene.hh

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#ifndef DUMUX_H2O_AIR_MESITYLENE_FLUID_SYSTEM_HH
#define DUMUX_H2O_AIR_MESITYLENE_FLUID_SYSTEM_HH
 
#include <dumux/material/idealgas.hh>
#include <dumux/material/components/air.hh>
#include <dumux/material/components/h2o.hh>
#include <dumux/material/components/tabulatedcomponent.hh>
#include <dumux/material/components/mesitylene.hh>
#include <dumux/material/components/tabulatedcomponent.hh>
 
#include <dumux/material/binarycoefficients/h2o_air.hh>
#include <dumux/material/binarycoefficients/h2o_mesitylene.hh>
#include <dumux/material/binarycoefficients/air_mesitylene.hh>
 
#include <dumux/material/fluidsystems/base.hh>
 
#include <dumux/io/name.hh>
 
namespace Dumux {
namespace FluidSystems {

template <class Scalar,
          class H2OType = Components::TabulatedComponent<Components::H2O<Scalar> > >
class H2OAirMesitylene
    : public Base<Scalar, H2OAirMesitylene<Scalar, H2OType> >
{
    using ThisType = H2OAirMesitylene<Scalar, H2OType>;
    using Base = Dumux::FluidSystems::Base<Scalar, ThisType>;
 
public:
    using NAPL = Components::Mesitylene<Scalar>;
    using Air = Dumux::Components::Air<Scalar>;
    using H2O = H2OType;
 
 
    static const int numPhases = 3;
    static const int numComponents = 3;
 
    static const int wPhaseIdx = 0; // index of the water phase
    static const int nPhaseIdx = 1; // index of the NAPL phase
    static const int gPhaseIdx = 2; // index of the gas phase
 
    static const int H2OIdx = 0;
    static const int NAPLIdx = 1;
    static const int AirIdx = 2;
 
    // export component indices to indicate the main component
    // of the corresponding phase at atmospheric pressure 1 bar
    // and room temperature 20°C:
    static const int wCompIdx = H2OIdx;
    static const int nCompIdx = NAPLIdx;
    static const int gCompIdx = AirIdx;

    static void init()
    {
        init(/*tempMin=*/273.15,
             /*tempMax=*/623.15,
             /*numTemp=*/100,
             /*pMin=*/0.0,
             /*pMax=*/20e6,
             /*numP=*/200);
    }

    static void init(Scalar tempMin, Scalar tempMax, unsigned nTemp,
                     Scalar pressMin, Scalar pressMax, unsigned nPress)
    {
        if (H2O::isTabulated)
        {
            H2O::init(tempMin, tempMax, nTemp,
                      pressMin, pressMax, nPress);
        }
    }

    static constexpr bool isMiscible()
    { return true; }

    static constexpr bool isGas(int phaseIdx)
    {
        assert(0 <= phaseIdx && phaseIdx < numPhases);
        return phaseIdx == gPhaseIdx;
    }

    static bool isIdealGas(int phaseIdx)
    { return phaseIdx == gPhaseIdx && H2O::gasIsIdeal() && Air::gasIsIdeal() && NAPL::gasIsIdeal(); }

    static bool isIdealMixture(int phaseIdx)
    {
        assert(0 <= phaseIdx && phaseIdx < numPhases);
        // we assume Henry's and Raoult's laws for the water phase and
        // and no interaction between gas molecules of different
        // components, so all phases are ideal mixtures!
        return true;
    }

    static constexpr bool isCompressible(int phaseIdx)
    {
        assert(0 <= phaseIdx && phaseIdx < numPhases);
        // gases are always compressible
        if (phaseIdx == gPhaseIdx)
            return true;
        else if (phaseIdx == wPhaseIdx)
            // the water component decides for the water phase...
            return H2O::liquidIsCompressible();
 
        // the NAPL component decides for the napl phase...
        return NAPL::liquidIsCompressible();
    }

    static std::string phaseName(int phaseIdx)
    {
        assert(0 <= phaseIdx && phaseIdx < numPhases);
        switch (phaseIdx)
        {
            case wPhaseIdx: return IOName::aqueousPhase();
            case nPhaseIdx: return IOName::naplPhase();
            case gPhaseIdx: return IOName::gaseousPhase();
        }
        DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx);
    }

    static std::string componentName(int compIdx)
    {
        switch (compIdx) {
            case H2OIdx: return H2O::name();
            case AirIdx: return Air::name();
            case NAPLIdx: return NAPL::name();
        }
        DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << compIdx);
    }

    static Scalar molarMass(int compIdx)
    {
        switch (compIdx) {
            case H2OIdx: return H2O::molarMass();
            case AirIdx: return Air::molarMass();
            case NAPLIdx: return NAPL::molarMass();
        }
        DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << compIdx);
    }
 
    using Base::density;
    template <class FluidState>
    static Scalar density(const FluidState &fluidState, int phaseIdx)
    {
        if (phaseIdx == wPhaseIdx) {
            // See: Eq. (7) in Class et al. (2002a)
            // this assumes each dissolved molecule displaces exactly one
            // water molecule in the liquid
            return H2O::liquidMolarDensity(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx))
                   * (H2O::molarMass()*fluidState.moleFraction(wPhaseIdx, H2OIdx)
                      + Air::molarMass()*fluidState.moleFraction(wPhaseIdx, AirIdx)
                      + NAPL::molarMass()*fluidState.moleFraction(wPhaseIdx, NAPLIdx));
        }
        else if (phaseIdx == nPhaseIdx) {
            // assume pure NAPL for the NAPL phase
            Scalar pressure = NAPL::liquidIsCompressible()?fluidState.pressure(phaseIdx):1e100;
            return NAPL::liquidDensity(fluidState.temperature(phaseIdx), pressure);
        }
 
        assert (phaseIdx == gPhaseIdx);
        Scalar pH2O =
            fluidState.moleFraction(gPhaseIdx, H2OIdx)  *
            fluidState.pressure(gPhaseIdx);
        Scalar pAir =
            fluidState.moleFraction(gPhaseIdx, AirIdx)  *
            fluidState.pressure(gPhaseIdx);
        Scalar pNAPL =
            fluidState.moleFraction(gPhaseIdx, NAPLIdx)  *
            fluidState.pressure(gPhaseIdx);
        return H2O::gasDensity(fluidState.temperature(phaseIdx), pH2O)
               + Air::gasDensity(fluidState.temperature(phaseIdx), pAir)
               + NAPL::gasDensity(fluidState.temperature(phaseIdx), pNAPL);
    }
 
    using Base::molarDensity;
    template <class FluidState>
    static Scalar molarDensity(const FluidState &fluidState, int phaseIdx)
    {
        Scalar temperature = fluidState.temperature(phaseIdx);
        Scalar pressure = fluidState.pressure(phaseIdx);
 
        if (phaseIdx == nPhaseIdx)
        {
            // assume pure NAPL for the NAPL phase
            return NAPL::liquidMolarDensity(temperature, pressure);
        }
        else if (phaseIdx == wPhaseIdx)
        {
            return H2O::liquidMolarDensity(temperature, pressure);
        }
        else
        {
            return H2O::gasMolarDensity(temperature, fluidState.partialPressure(gPhaseIdx, H2OIdx))
                   + NAPL::gasMolarDensity(temperature, fluidState.partialPressure(gPhaseIdx, NAPLIdx))
                   + Air::gasMolarDensity(temperature, fluidState.partialPressure(gPhaseIdx, AirIdx));
        }
    }
 
    using Base::viscosity;
    template <class FluidState>
    static Scalar viscosity(const FluidState &fluidState,
                            int phaseIdx)
    {
        if (phaseIdx == wPhaseIdx) {
            // assume pure water viscosity
            return H2O::liquidViscosity(fluidState.temperature(phaseIdx),
                                        fluidState.pressure(phaseIdx));
        }
        else if (phaseIdx == nPhaseIdx) {
            // assume pure NAPL viscosity
            return NAPL::liquidViscosity(fluidState.temperature(phaseIdx),
                                         fluidState.pressure(phaseIdx));
        }
 
        assert (phaseIdx == gPhaseIdx);
 
        /* Wilke method. See:
         *
         * See: R. Reid, et al.: The Properties of Gases and Liquids,
         * 4th edition, McGraw-Hill, 1987, 407-410
         * 5th edition, McGraw-Hill, 2001, p. 9.21/22
         *
         * in this case, we use a simplified version in order to avoid
         * computationally costly evaluation of sqrt and pow functions and
         * divisions
         * -- compare e.g. with Promo Class p. 32/33
         */
        Scalar muResult;
        const Scalar mu[numComponents] = {
            h2oGasViscosityInMixture(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx)),
            Air::gasViscosity(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx)),
            NAPL::gasViscosity(fluidState.temperature(phaseIdx), NAPL::vaporPressure(fluidState.temperature(phaseIdx)))
        };
        // molar masses
        const Scalar M[numComponents] = {
            H2O::molarMass(),
            Air::molarMass(),
            NAPL::molarMass()
        };
 
        Scalar muAW = mu[AirIdx]*fluidState.moleFraction(gPhaseIdx, AirIdx)
                      + mu[H2OIdx]*fluidState.moleFraction(gPhaseIdx, H2OIdx)
                        / (fluidState.moleFraction(gPhaseIdx, AirIdx)
                           + fluidState.moleFraction(gPhaseIdx, H2OIdx));
        Scalar xAW = fluidState.moleFraction(gPhaseIdx, AirIdx)
                     + fluidState.moleFraction(gPhaseIdx, H2OIdx);
 
        Scalar MAW = (fluidState.moleFraction(gPhaseIdx, AirIdx)*Air::molarMass()
                      + fluidState.moleFraction(gPhaseIdx, H2OIdx)*H2O::molarMass())
                     / xAW;
 
        Scalar phiCAW = 0.3; // simplification for this particular system
        /* actually like this
        * using std::sqrt;
        * using std::pow;
         * Scalar phiCAW = pow(1.+sqrt(mu[NAPLIdx]/muAW)*pow(MAW/M[NAPLIdx],0.25),2)
         *                 / sqrt(8.*(1.+M[NAPLIdx]/MAW));
         */
        Scalar phiAWC = phiCAW * muAW*M[NAPLIdx]/(mu[NAPLIdx]*MAW);
 
        muResult = (xAW*muAW)/(xAW+fluidState.moleFraction(gPhaseIdx, NAPLIdx)*phiAWC)
                   + (fluidState.moleFraction(gPhaseIdx, NAPLIdx) * mu[NAPLIdx])
                     / (fluidState.moleFraction(gPhaseIdx, NAPLIdx) + xAW*phiCAW);
        return muResult;
    }
 
 
    using Base::diffusionCoefficient;
    template <class FluidState>
    static Scalar diffusionCoefficient(const FluidState &fluidState,
                                       int phaseIdx,
                                       int compIdx)
    {
        switch (phaseIdx)
        {
            case gPhaseIdx:
            {
                switch (compIdx)
                {
                    case NAPLIdx:
                    {
                        Scalar diffWC = BinaryCoeff::H2O_Mesitylene::gasDiffCoeff(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx));
                        Scalar diffAW = BinaryCoeff::H2O_Air::gasDiffCoeff(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx));
                        const Scalar xga = fluidState.moleFraction(gPhaseIdx, AirIdx);
                        const Scalar xgw = fluidState.moleFraction(gPhaseIdx, H2OIdx);
                        const Scalar xgc = fluidState.moleFraction(gPhaseIdx, NAPLIdx);
                        return (1.- xgw)/(xga/diffAW + xgc/diffWC);
                    }
                    case H2OIdx:
                    {
                        Scalar diffAC = BinaryCoeff::Air_Mesitylene::gasDiffCoeff(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx));
                        Scalar diffWC = BinaryCoeff::H2O_Mesitylene::gasDiffCoeff(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx));
                        const Scalar xga = fluidState.moleFraction(gPhaseIdx, AirIdx);
                        const Scalar xgw = fluidState.moleFraction(gPhaseIdx, H2OIdx);
                        const Scalar xgc = fluidState.moleFraction(gPhaseIdx, NAPLIdx);
                        return (1.- xgc)/(xgw/diffWC + xga/diffAC);
                    }
                    case AirIdx:
                        DUNE_THROW(Dune::InvalidStateException, "Diffusivity of Air in the gas phase is constraint by sum of diffusive fluxes = 0 !");
                }
            }
            case wPhaseIdx:
            {
                Scalar diffACl = BinaryCoeff::Air_Mesitylene::liquidDiffCoeff(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx));
                Scalar diffWCl = BinaryCoeff::H2O_Mesitylene::liquidDiffCoeff(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx));
                Scalar diffAWl = BinaryCoeff::H2O_Air::liquidDiffCoeff(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx));
 
                Scalar xwa = fluidState.moleFraction(wPhaseIdx, AirIdx);
                Scalar xww = fluidState.moleFraction(wPhaseIdx, H2OIdx);
                Scalar xwc = fluidState.moleFraction(wPhaseIdx, NAPLIdx);
 
                switch (compIdx)
                {
                    case NAPLIdx:
                        return (1.- xww)/(xwa/diffAWl + xwc/diffWCl);
                    case AirIdx:
                        return (1.- xwc)/(xww/diffWCl + xwa/diffACl);
                    case H2OIdx:
                        DUNE_THROW(Dune::InvalidStateException,
                                   "Diffusivity of water in the water phase "
                                   "is constraint by sum of diffusive fluxes = 0 !\n");
                }
            }
            case nPhaseIdx:
            {
                return 0;
            }
        }
        return 0;
    }
 
    using Base::binaryDiffusionCoefficient;
    template <class FluidState>
    static Scalar binaryDiffusionCoefficient(const FluidState &fluidState,
                                             int phaseIdx,
                                             int compIIdx,
                                             int compJIdx)
    {
        DUNE_THROW(Dune::NotImplemented, "FluidSystems::H2OAirMesitylene::binaryDiffusionCoefficient()");
    }
 
    using Base::fugacityCoefficient;
    template <class FluidState>
    static Scalar fugacityCoefficient(const FluidState &fluidState,
                                      int phaseIdx,
                                      int compIdx)
    {
        assert(0 <= phaseIdx  && phaseIdx < numPhases);
        assert(0 <= compIdx  && compIdx < numComponents);
 
        Scalar T = fluidState.temperature(phaseIdx);
        Scalar p = fluidState.pressure(phaseIdx);
 
        if (phaseIdx == wPhaseIdx) {
            if (compIdx == H2OIdx)
                return H2O::vaporPressure(T)/p;
            else if (compIdx == AirIdx)
                return BinaryCoeff::H2O_Air::henry(T)/p;
            else if (compIdx == NAPLIdx)
                return BinaryCoeff::H2O_Mesitylene::henry(T)/p;
        }
 
        // for the NAPL phase, we assume currently that nothing is
        // dissolved. this means that the affinity of the NAPL
        // component to the NAPL phase is much higher than for the
        // other components, i.e. the fugacity coefficient is much
        // smaller.
        if (phaseIdx == nPhaseIdx) {
            Scalar phiNapl = NAPL::vaporPressure(T)/p;
            if (compIdx == NAPLIdx)
                return phiNapl;
            else if (compIdx == AirIdx)
                return 1e6*phiNapl;
            else if (compIdx == H2OIdx)
                return 1e6*phiNapl;
        }
 
        // for the gas phase, assume an ideal gas when it comes to
        // fugacity (-> fugacity == partial pressure)
        assert(phaseIdx == gPhaseIdx);
        return 1.0;
    }
 
    template <class FluidState>
    static Scalar kelvinVaporPressure(const FluidState &fluidState,
                                      const int phaseIdx,
                                      const int compIdx)
    {
        DUNE_THROW(Dune::NotImplemented, "FluidSystems::H2OAirMesitylene::kelvinVaporPressure()");
    }
 
    using Base::enthalpy;
    template <class FluidState>
    static Scalar enthalpy(const FluidState &fluidState,
                           int phaseIdx)
    {
        if (phaseIdx == wPhaseIdx) {
            return H2O::liquidEnthalpy(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx));
        }
        else if (phaseIdx == nPhaseIdx) {
            return NAPL::liquidEnthalpy(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx));
        }
        else if (phaseIdx == gPhaseIdx) {  // gas phase enthalpy depends strongly on composition
            Scalar hgc = NAPL::gasEnthalpy(fluidState.temperature(phaseIdx),
                                           fluidState.pressure(phaseIdx));
            Scalar hgw = H2O::gasEnthalpy(fluidState.temperature(phaseIdx),
                                          fluidState.pressure(phaseIdx));
            // pressure is only a dummy here (not dependent on pressure, just temperature)
            Scalar hga = Air::gasEnthalpy(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx));
 
            Scalar result = 0;
            result += hgw * fluidState.massFraction(gPhaseIdx, H2OIdx);
            result += hga * fluidState.massFraction(gPhaseIdx, AirIdx);
            result += hgc * fluidState.massFraction(gPhaseIdx, NAPLIdx);
 
            return result;
        }
        DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx);
    }

    template <class FluidState>
    static Scalar componentEnthalpy(const FluidState& fluidState, int phaseIdx, int componentIdx)
    {
        const Scalar T = fluidState.temperature(phaseIdx);
        const Scalar p = fluidState.pressure(phaseIdx);
 
        if (phaseIdx == wPhaseIdx)
        {
            if (componentIdx == H2OIdx)
                return H2O::liquidEnthalpy(T, p);
            else if (componentIdx == NAPLIdx)
                DUNE_THROW(Dune::NotImplemented, "The component enthalpy for NAPL in water is not implemented.");
            else if (componentIdx == AirIdx)
                DUNE_THROW(Dune::NotImplemented, "The component enthalpy for Air in water is not implemented.");
            DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << componentIdx);
        }
        else if (phaseIdx == nPhaseIdx)
        {
            if (componentIdx == H2OIdx)
                DUNE_THROW(Dune::NotImplemented, "The component enthalpy for water in NAPL is not implemented.");
            else if (componentIdx == NAPLIdx)
                return NAPL::liquidEnthalpy(T, p);
            else if (componentIdx == AirIdx)
                DUNE_THROW(Dune::NotImplemented, "The component enthalpy for air in NAPL is not implemented.");
            DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << componentIdx);
        }
        else if (phaseIdx == gPhaseIdx)
        {
            if (componentIdx == H2OIdx)
                return H2O::gasEnthalpy(T, p);
            else if (componentIdx == NAPLIdx)
                return NAPL::gasEnthalpy(T, p);
            else if (componentIdx == AirIdx)
                return Air::gasEnthalpy(T,p);
            DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << componentIdx);
        }
        DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx);
    }
 
    using Base::heatCapacity;
    template <class FluidState>
    static Scalar heatCapacity(const FluidState &fluidState,
                               int phaseIdx)
    {
        DUNE_THROW(Dune::NotImplemented, "FluidSystems::H2OAirMesitylene::heatCapacity()");
    }
 
    using Base::thermalConductivity;
    template <class FluidState>
    static Scalar thermalConductivity(const FluidState &fluidState,
                                      int phaseIdx)
    {
        const Scalar temperature  = fluidState.temperature(phaseIdx) ;
        const Scalar pressure = fluidState.pressure(phaseIdx);
        if (phaseIdx == wPhaseIdx)
        {
            return H2O::liquidThermalConductivity(temperature, pressure);
        }
        else if (phaseIdx == nPhaseIdx)
        {
            return NAPL::liquidThermalConductivity(temperature, pressure);
        }
        else if (phaseIdx == gPhaseIdx)
        {
            return Air::gasThermalConductivity(temperature, pressure);
        }
        DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx);
    }
 
private:
    static Scalar waterPhaseDensity_(Scalar T, Scalar pw, Scalar xww, Scalar xwa, Scalar xwc)
    {
        Scalar rholH2O = H2O::liquidDensity(T, pw);
        Scalar clH2O = rholH2O/H2O::molarMass();
 
        // this assumes each dissolved molecule displaces exactly one
        // water molecule in the liquid
        return clH2O*(xww*H2O::molarMass() + xwa*Air::molarMass() + xwc*NAPL::molarMass());
    }
 
    static Scalar gasPhaseDensity_(Scalar T, Scalar pg, Scalar xgw, Scalar xga, Scalar xgc)
    {
        return H2O::gasDensity(T, pg*xgw) + Air::gasDensity(T, pg*xga) + NAPL::gasDensity(T, pg*xgc);
    }
 
    static Scalar NAPLPhaseDensity_(Scalar T, Scalar pn)
    {
        return NAPL::liquidDensity(T, pn);
    }
 
};
 
} // end namespace FluidSystems
} // end namespace Dumux
 
#endif