fluidsystems/brine.hh

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#ifndef DUMUX_BRINE_FLUID_SYSTEM_HH
#define DUMUX_BRINE_FLUID_SYSTEM_HH
 
#include <dune/common/math.hh>
 
#include <dumux/common/exceptions.hh>
#include <dumux/io/name.hh>
#include <dumux/material/fluidsystems/base.hh>
#include <dumux/material/constants.hh>
#include <dumux/material/components/h2o.hh>
#include <dumux/material/components/nacl.hh>
#include <dumux/material/components/tabulatedcomponent.hh>
 
namespace Dumux {
namespace FluidSystems {
 
template< class Scalar, class H2OType = Components::TabulatedComponent<Dumux::Components::H2O<Scalar>> >
class Brine : public Base< Scalar, Brine<Scalar, H2OType>>
{
    using ThisType = Brine<Scalar, H2OType>;
    using Base = Dumux::FluidSystems::Base<Scalar, ThisType>;
 
public:
    using H2O = H2OType;
    using NaCl = Dumux::Components::NaCl<Scalar>;
 
    static const int numPhases = 1;     
    static const int numComponents = 2; 
 
    static constexpr int phase0Idx = 0; 
    static constexpr int liquidPhaseIdx = phase0Idx; 
 
    static constexpr int H2OIdx = 0;         
    static constexpr int NaClIdx = 1;        
    static constexpr int comp0Idx = H2OIdx;  
    static constexpr int comp1Idx = NaClIdx; 
 
    static const std::string phaseName(int phaseIdx = liquidPhaseIdx)
    {
        assert(phaseIdx == liquidPhaseIdx);
        return IOName::liquidPhase();
    }
 
    static constexpr bool isMiscible()
    {
        return false;
    }
 
    static constexpr bool isGas(int phaseIdx = liquidPhaseIdx)
    {
        assert(phaseIdx == liquidPhaseIdx);
        return false;
    }
 
    static bool isIdealMixture(int phaseIdx = liquidPhaseIdx)
    {
        assert(phaseIdx == liquidPhaseIdx);
        return true;
    }
 
    static bool isCompressible(int phaseIdx = liquidPhaseIdx)
    {
        assert(phaseIdx == liquidPhaseIdx);
        return H2O::liquidIsCompressible();
    }
 
    static bool isIdealGas(int phaseIdx = liquidPhaseIdx)
    {
        assert(phaseIdx == liquidPhaseIdx);
        return false; /*we're a liquid!*/
    }
 
    /****************************************
     * Component related static parameters
     ****************************************/
 
    static std::string componentName(int compIdx)
    {
        switch (compIdx)
        {
            case H2OIdx: return H2O::name();
            case NaClIdx: return NaCl::name();
        };
        DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << compIdx);
    }
 
    static Scalar molarMass(int compIdx)
    {
        switch (compIdx)
        {
            case H2OIdx: return H2O::molarMass();
            case NaClIdx: return NaCl::molarMass();
        };
        DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << compIdx);
    }
 
    /****************************************
     * thermodynamic relations
     ****************************************/
     static void init()
     {
         init(/*tempMin=*/273.15,
              /*tempMax=*/623.15,
              /*numTemp=*/100,
              /*pMin=*/-10.,
              /*pMax=*/20e6,
              /*numP=*/200);
     }
 
    static void init(Scalar tempMin, Scalar tempMax, unsigned nTemp,
                     Scalar pressMin, Scalar pressMax, unsigned nPress)
    {
 
        if (H2O::isTabulated)
        {
            std::cout << "Initializing tables for the H2O fluid properties ("
                      << nTemp*nPress
                      << " entries).\n";
 
            H2O::init(tempMin, tempMax, nTemp, pressMin, pressMax, nPress);
        }
    }
 
    using Base::density;
    template <class FluidState>
    static Scalar density(const FluidState& fluidState, int phaseIdx = liquidPhaseIdx)
    {
        assert(phaseIdx == liquidPhaseIdx);
        const Scalar temperature = fluidState.temperature(phaseIdx);
        const Scalar pressure = fluidState.pressure(phaseIdx);
        const Scalar xNaCl = fluidState.massFraction(phaseIdx, NaClIdx);
 
        using std::max;
        const Scalar TempC = temperature - 273.15;
        const Scalar pMPa = pressure/1.0E6;
        const Scalar salinity = max(0.0, xNaCl);
 
        const Scalar rhow = H2O::liquidDensity(temperature, pressure);
        const Scalar density = rhow + 1000*salinity*(0.668 +
                                                     0.44*salinity +
                                                     1.0E-6*(300*pMPa -
                                                             2400*pMPa*salinity +
                                                             TempC*(80.0 +
                                                                    3*TempC -
                                                                    3300*salinity -
                                                                    13*pMPa +
                                                                    47*pMPa*salinity)));
        assert(density > 0.0);
        return density;
    }
 
    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);
 
        if (phaseIdx == compIdx)
            // We could calculate the real fugacity coefficient of
            // the component in the fluid. Probably that's not worth
            // the effort, since the fugacity coefficient of the other
            // component is infinite anyway...
            return 1.0;
        return std::numeric_limits<Scalar>::infinity();
    }
 
    using Base::viscosity;
    template <class FluidState>
    static Scalar viscosity(const FluidState& fluidState, int phaseIdx = liquidPhaseIdx)
    {
        assert(phaseIdx == liquidPhaseIdx);
        const Scalar temperature = fluidState.temperature(phaseIdx);
        const Scalar xNaCl = fluidState.massFraction(phaseIdx, NaClIdx);
 
        using std::pow;
        using Dune::power;
        using std::exp;
        using std::max;
        const Scalar T = max(temperature, 275.0);
        const Scalar salinity = max(0.0, xNaCl);
 
        const Scalar T_C = T - 273.15;
        const Scalar A = ((0.42*power((pow(salinity, 0.8)-0.17), 2)) + 0.045)*pow(T_C, 0.8);
        const Scalar mu_brine = 0.1 + (0.333*salinity) + (1.65+(91.9*salinity*salinity*salinity))*exp(-A); // [cP]
        assert(mu_brine > 0.0);
        return mu_brine/1000.0; // [Pa·s]
    }
 
    template <class FluidState>
    static Scalar vaporPressure(const FluidState& fluidState, int compIdx)
    {
        if (compIdx == H2OIdx)
        {
            const Scalar temperature = fluidState.temperature(H2OIdx);
            // Raoult's law, see Thomas Fetzer's Dissertation Eq. 2.11.
            return H2O::vaporPressure(temperature)*fluidState.moleFraction(phase0Idx, H2OIdx);
        }
        else if (compIdx == NaClIdx)
            DUNE_THROW(Dune::NotImplemented, "NaCl::vaporPressure(t)");
        else
            DUNE_THROW(Dune::NotImplemented, "Invalid component index " << compIdx);
    }
 
    using Base::enthalpy;
    template <class FluidState>
    static Scalar enthalpy(const FluidState& fluidState, int phaseIdx)
    {
        //use private enthalpy function to recycle it for the heat capacity calculation
        return enthalpy_(fluidState.pressure(phaseIdx),
                        fluidState.temperature(phaseIdx),
                        fluidState.massFraction(phase0Idx, NaClIdx)); /*J/kg*/
    }
 
    template <class FluidState>
    static Scalar componentEnthalpy(const FluidState &fluidState,
                                    int phaseIdx,
                                    int componentIdx)
    {
        const Scalar T = fluidState.temperature(liquidPhaseIdx);
        const Scalar p = fluidState.pressure(liquidPhaseIdx);
 
        if (phaseIdx == liquidPhaseIdx)
        {
            if (componentIdx == H2OIdx)
                return H2O::liquidEnthalpy(T, p);
            else if (componentIdx == NaClIdx)
                DUNE_THROW(Dune::NotImplemented, "The component enthalpy for NaCl is not implemented.");
            DUNE_THROW(Dune::InvalidStateException, "Invalid component index " << componentIdx);
        }
        DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx);
    }
 
    using Base::molarDensity;
    template <class FluidState>
    static Scalar molarDensity(const FluidState& fluidState, int phaseIdx = liquidPhaseIdx)
    {
        return density(fluidState, phaseIdx)/fluidState.averageMolarMass(phaseIdx);
    }
 
    using Base::diffusionCoefficient;
    template <class FluidState>
    static Scalar diffusionCoefficient(const FluidState& fluidState, int phaseIdx, int compIdx)
    {
        DUNE_THROW(Dune::NotImplemented, "FluidSystems::Brine::diffusionCoefficient()");
    }
 
    using Base::binaryDiffusionCoefficient;
    template <class FluidState>
    static Scalar binaryDiffusionCoefficient(const FluidState& fluidState,
                                             int phaseIdx,
                                             int compIIdx,
                                             int compJIdx)
    {
        if (phaseIdx == liquidPhaseIdx)
        {
            if (compIIdx > compJIdx)
            {
                using std::swap;
                swap(compIIdx, compJIdx);
            }
 
            if (compJIdx == NaClIdx)
                return 1.54e-9;
            else
                DUNE_THROW(Dune::NotImplemented, "Binary diffusion coefficient of components "
                                                 << compIIdx << " and " << compJIdx
                                                 << " in phase " << phaseIdx);
         }
 
         DUNE_THROW(Dune::InvalidStateException, "Invalid phase index: " << phaseIdx);
    }
 
    using Base::thermalConductivity;
    template <class FluidState>
    static Scalar thermalConductivity(const FluidState& fluidState, int phaseIdx)
    {
        if (phaseIdx == liquidPhaseIdx)
        {
            Scalar tempC = fluidState.temperature(phaseIdx)-273.15;
            Scalar m = fluidState.moleFraction(phaseIdx, NaClIdx)/(molarMass(H2OIdx)*(1- fluidState.moleFraction(phaseIdx, NaClIdx))); // molality of NaCl
            Scalar S = 5844.3 * m / (1000 + 58.443 *m);
            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;
            return contribNaClFactor * H2O::liquidThermalConductivity(fluidState.temperature(phaseIdx), fluidState.pressure(phaseIdx));
        }
        DUNE_THROW(Dune::InvalidStateException, "Invalid phase index: " << phaseIdx);
    }
 
    using Base::heatCapacity;
    template <class FluidState>
    static Scalar heatCapacity(const FluidState &fluidState, int phaseIdx)
    {
        if (phaseIdx == liquidPhaseIdx){
            const Scalar eps = fluidState.temperature(phaseIdx)*1e-8;
            //calculate heat capacity from the difference in enthalpy with temperature at constant pressure.
            return (enthalpy_(fluidState.pressure(phaseIdx),
                        fluidState.temperature(phaseIdx) +eps ,
                        fluidState.massFraction(phase0Idx, NaClIdx))
                        - enthalpy_(fluidState.pressure(phaseIdx),
                        fluidState.temperature(phaseIdx),
                        fluidState.massFraction(phase0Idx, NaClIdx)))/eps; /*J/kg*/
        }
        DUNE_THROW(Dune::InvalidStateException, "Invalid phase index " << phaseIdx);
    }
 
private:
    static Scalar enthalpy_(const Scalar p, const Scalar T, const Scalar xNaCl)
    {
        /*Numerical coefficients from PALLISER*/
        static const Scalar f[] = { 2.63500E-1, 7.48368E-6, 1.44611E-6, -3.80860E-10 };
 
        /*Numerical coefficients from MICHAELIDES for the enthalpy of brine*/
        static const Scalar a[4][3] = { { +9633.6, -4080.0, +286.49 },
                                        { +166.58, +68.577, -4.6856 },
                                        { -0.90963, -0.36524, +0.249667E-1 },
                                        { +0.17965E-2, +0.71924E-3, -0.4900E-4 } };
 
        const Scalar theta = T - 273.15;
        const Scalar salSat = f[0] + f[1]*theta + f[2]*theta*theta + f[3]*theta*theta*theta;
 
        /*Regularization*/
        using std::min;
        using std::max;
        const Scalar salinity = min(max(xNaCl,0.0), salSat);
 
        const Scalar hw = H2O::liquidEnthalpy(T, p)/1E3; /* kJ/kg */
 
        /*component enthalpy of soluted NaCl after DAUBERT and DANNER*/
        const Scalar h_NaCl = (3.6710E4*T + 0.5*(6.2770E1)*T*T - ((6.6670E-2)/3)*T*T*T
                              + ((2.8000E-5)/4)*(T*T*T*T))/(58.44E3)- 2.045698e+02; /* U [kJ/kg] */
 
        const Scalar m = (1E3/58.44)*(salinity/(1-salinity));
 
        using Dune::power;
        Scalar d_h = 0;
        for (int i = 0; i<=3; i++)
            for (int j=0; j<=2; j++)
                d_h = d_h + a[i][j] * power(theta, i) * power(m, j);
 
        /* heat of dissolution for halite according to Michaelides 1981 */
        const Scalar delta_h = (4.184/(1E3 + (58.44 * m)))*d_h;
 
        /* Enthalpy of brine without any dissolved gas */
        const Scalar h_ls1 =(1-salinity)*hw + salinity*h_NaCl + salinity*delta_h; /* kJ/kg */
        return h_ls1*1E3; /*J/kg*/
    }
};
 
} // end namespace FluidSystems
} // end namespace Dumux
 
#endif