H2ON2FluidSystem.hpp

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// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
// vi: set et ts=4 sw=4 sts=4:
/*
  Copyright (C) 2009-2013 by Andreas Lauser

  This file is part of the Open Porous Media project (OPM).

  OPM is free software: you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation, either version 2 of the License, or
  (at your option) any later version.

  OPM is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.

  You should have received a copy of the GNU General Public License
  along with OPM.  If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef OPM_H2O_N2_FLUID_SYSTEM_HPP
#define OPM_H2O_N2_FLUID_SYSTEM_HPP

#include "BaseFluidSystem.hpp"
#include "NullParameterCache.hpp"

#include <opm/material/IdealGas.hpp>
#include <opm/material/components/N2.hpp>
#include <opm/material/components/H2O.hpp>
#include <opm/material/components/SimpleH2O.hpp>
#include <opm/material/components/TabulatedComponent.hpp>
#include <opm/material/binarycoefficients/H2O_N2.hpp>
#include <opm/material/common/Valgrind.hpp>

#include <opm/common/Exceptions.hpp>
#include <opm/common/ErrorMacros.hpp>

#include <iostream>
#include <cassert>

namespace Opm {
namespace FluidSystems {

template <class Scalar, bool useComplexRelations = true>
class H2ON2
    : public BaseFluidSystem<Scalar, H2ON2<Scalar, useComplexRelations> >
{
    typedef H2ON2<Scalar, useComplexRelations> ThisType;
    typedef BaseFluidSystem<Scalar, ThisType> Base;

    // convenience typedefs
    typedef Opm::IdealGas<Scalar> IdealGas;
    typedef Opm::H2O<Scalar> IapwsH2O;
    typedef Opm::TabulatedComponent<Scalar, IapwsH2O > TabulatedH2O;
    typedef Opm::N2<Scalar> SimpleN2;

public:
    typedef NullParameterCache ParameterCache;

    /****************************************
     * Fluid phase related static parameters
     ****************************************/

    static const int numPhases = 2;

    static const int liquidPhaseIdx = 0;
    static const int gasPhaseIdx = 1;

    static const char *phaseName(unsigned phaseIdx)
    {
        static const char *name[] = {
            "liquid",
            "gas"
        };

        assert(0 <= phaseIdx && phaseIdx < numPhases);
        return name[phaseIdx];
    }

    static bool isLiquid(unsigned phaseIdx)
    {
        //assert(0 <= phaseIdx && phaseIdx < numPhases);
        return phaseIdx != gasPhaseIdx;
    }

    static bool isCompressible(unsigned phaseIdx)
    {
        //assert(0 <= phaseIdx && phaseIdx < numPhases);
        // gases are always compressible
        return
            (phaseIdx == gasPhaseIdx)
            ? true
            :H2O::liquidIsCompressible();// the water component decides for the liquid phase...
    }

    static bool isIdealGas(unsigned phaseIdx)
    {
        //assert(0 <= phaseIdx && phaseIdx < numPhases);

        return
            (phaseIdx == gasPhaseIdx)
            ? H2O::gasIsIdeal() && N2::gasIsIdeal() // let the components decide
            : false; // not a gas
    }

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

    /****************************************
     * Component related static parameters
     ****************************************/

    static const int numComponents = 2;

    static const int H2OIdx = 0;
    static const int N2Idx = 1;

    typedef TabulatedH2O H2O;
    //typedef SimpleH2O H2O;
    //typedef IapwsH2O H2O;

    typedef SimpleN2 N2;

    static const char *componentName(unsigned compIdx)
    {
        static const char *name[] = {
            H2O::name(),
            N2::name()
        };

        assert(0 <= compIdx && compIdx < numComponents);
        return name[compIdx];
    }

    static Scalar molarMass(unsigned compIdx)
    {
        //assert(0 <= compIdx && compIdx < numComponents);
        return (compIdx == H2OIdx)
            ? H2O::molarMass()
            : (compIdx == N2Idx)
            ? N2::molarMass()
            : 1e100;
    }

    static Scalar criticalTemperature(unsigned compIdx)
    {
        return (compIdx == H2OIdx)
            ? H2O::criticalTemperature()
            : (compIdx == N2Idx)
            ? N2::criticalTemperature()
            : 1e100;
    }

    static Scalar criticalPressure(unsigned compIdx)
    {
        return (compIdx == H2OIdx)
            ? H2O::criticalPressure()
            : (compIdx == N2Idx)
            ? N2::criticalPressure()
            : 1e100;
    }

    static Scalar acentricFactor(unsigned compIdx)
    {
        return (compIdx == H2OIdx)
            ? H2O::acentricFactor()
            : (compIdx == N2Idx)
            ? N2::acentricFactor()
            : 1e100;
    }

    /****************************************
     * thermodynamic relations
     ****************************************/

    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) {
            TabulatedH2O::init(tempMin, tempMax, nTemp,
                               pressMin, pressMax, nPress);
        }
    }

    template <class FluidState, class LhsEval = typename FluidState::Scalar>
    static LhsEval density(const FluidState &fluidState,
                           const ParameterCache &/*paramCache*/,
                           unsigned phaseIdx)
    {
        assert(0 <= phaseIdx  && phaseIdx < numPhases);

        typedef Opm::MathToolbox<LhsEval> LhsToolbox;
        typedef Opm::MathToolbox<typename FluidState::Scalar> FsToolbox;

        const auto& T = FsToolbox::template toLhs<LhsEval>(fluidState.temperature(phaseIdx));
        const auto& p = FsToolbox::template toLhs<LhsEval>(fluidState.pressure(phaseIdx));

        LhsEval sumMoleFrac = 0;
        for (unsigned compIdx = 0; compIdx < numComponents; ++compIdx)
            sumMoleFrac += FsToolbox::template toLhs<LhsEval>(fluidState.moleFraction(phaseIdx, compIdx));

        // liquid phase
        if (phaseIdx == liquidPhaseIdx) {
            if (!useComplexRelations)
                // assume pure water
                return H2O::liquidDensity(T, p);
            else
            {
                // See: Ochs 2008
                const auto& rholH2O = H2O::liquidDensity(T, p);
                const auto& clH2O = rholH2O/H2O::molarMass();

                const auto& xlH2O = FsToolbox::template toLhs<LhsEval>(fluidState.moleFraction(liquidPhaseIdx, H2OIdx));
                const auto& xlN2 = FsToolbox::template toLhs<LhsEval>(fluidState.moleFraction(liquidPhaseIdx, N2Idx));

                // this assumes each nitrogen molecule displaces exactly one
                // water molecule in the liquid
                return clH2O*(H2O::molarMass()*xlH2O + N2::molarMass()*xlN2)/sumMoleFrac;
            }
        }

        // gas phase
        assert(phaseIdx == gasPhaseIdx);

        if (!useComplexRelations)
            // for the gas phase assume an ideal gas
            return
                IdealGas::molarDensity(T, p)
                * FsToolbox::template toLhs<LhsEval>(fluidState.averageMolarMass(gasPhaseIdx))
                / LhsToolbox::max(1e-5, sumMoleFrac);

        // assume ideal mixture: steam and nitrogen don't "see" each
        // other
        const auto& xgH2O = FsToolbox::template toLhs<LhsEval>(fluidState.moleFraction(gasPhaseIdx, H2OIdx));
        const auto& xgN2 = FsToolbox::template toLhs<LhsEval>(fluidState.moleFraction(gasPhaseIdx, N2Idx));
        const auto& rho_gH2O = H2O::gasDensity(T, p*xgH2O);
        const auto& rho_gN2 = N2::gasDensity(T, p*xgN2);
        return (rho_gH2O + rho_gN2)/LhsToolbox::max(1e-5, sumMoleFrac);
    }

    template <class FluidState, class LhsEval = typename FluidState::Scalar>
    static LhsEval viscosity(const FluidState &fluidState,
                             const ParameterCache &/*paramCache*/,
                             unsigned phaseIdx)
    {
        assert(0 <= phaseIdx  && phaseIdx < numPhases);

        typedef Opm::MathToolbox<LhsEval> LhsToolbox;
        typedef Opm::MathToolbox<typename FluidState::Scalar> FsToolbox;

        const auto& T = FsToolbox::template toLhs<LhsEval>(fluidState.temperature(phaseIdx));
        const auto& p = FsToolbox::template toLhs<LhsEval>(fluidState.pressure(phaseIdx));

        // liquid phase
        if (phaseIdx == liquidPhaseIdx)
            // assume pure water for the liquid phase
            return H2O::liquidViscosity(T, p);

        // gas phase
        assert(phaseIdx == gasPhaseIdx);

        if (!useComplexRelations)
            // assume pure nitrogen for the gas phase
            return N2::gasViscosity(T, p);
        else {
            /* 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, 20001, p. 9.21/22
             */
            LhsEval muResult = 0;
            const LhsEval mu[numComponents] = {
                H2O::gasViscosity(T, H2O::vaporPressure(T)),
                N2::gasViscosity(T, p)
            };

            LhsEval sumx = 0.0;
            for (unsigned compIdx = 0; compIdx < numComponents; ++compIdx)
                sumx += FsToolbox::template toLhs<LhsEval>(fluidState.moleFraction(phaseIdx, compIdx));
            sumx = LhsToolbox::max(1e-10, sumx);

            for (unsigned i = 0; i < numComponents; ++i) {
                LhsEval divisor = 0;
                for (unsigned j = 0; j < numComponents; ++j) {
                    LhsEval phiIJ = 1 + LhsToolbox::sqrt(mu[i]/mu[j]) * std::pow(molarMass(j)/molarMass(i), 1/4.0);
                    phiIJ *= phiIJ;
                    phiIJ /= std::sqrt(8*(1 + molarMass(i)/molarMass(j)));
                    divisor +=
                        FsToolbox::template toLhs<LhsEval>(fluidState.moleFraction(phaseIdx, j))
                        /sumx*phiIJ;
                }
                muResult +=
                    FsToolbox::template toLhs<LhsEval>(fluidState.moleFraction(phaseIdx, i))
                    /sumx*mu[i]/divisor;
            }
            return muResult;
        }
    }

    template <class FluidState, class LhsEval = typename FluidState::Scalar>
    static LhsEval fugacityCoefficient(const FluidState &fluidState,
                                       const ParameterCache &/*paramCache*/,
                                       unsigned phaseIdx,
                                       unsigned compIdx)
    {
        assert(0 <= phaseIdx  && phaseIdx < numPhases);
        assert(0 <= compIdx  && compIdx < numComponents);

        typedef Opm::MathToolbox<typename FluidState::Scalar> FsToolbox;

        const auto& T = FsToolbox::template toLhs<LhsEval>(fluidState.temperature(phaseIdx));
        const auto& p = FsToolbox::template toLhs<LhsEval>(fluidState.pressure(phaseIdx));

        // liquid phase
        if (phaseIdx == liquidPhaseIdx) {
            if (compIdx == H2OIdx)
                return H2O::vaporPressure(T)/p;
            return Opm::BinaryCoeff::H2O_N2::henry(T)/p;
        }

        assert(phaseIdx == gasPhaseIdx);

        // for the gas phase, assume an ideal gas when it comes to
        // fugacity (-> fugacity == partial pressure)
        return 1.0;
    }

    template <class FluidState, class LhsEval = typename FluidState::Scalar>
    static LhsEval diffusionCoefficient(const FluidState &fluidState,
                                        const ParameterCache &/*paramCache*/,
                                        unsigned phaseIdx,
                                        unsigned /*compIdx*/)

    {
        typedef Opm::MathToolbox<typename FluidState::Scalar> FsToolbox;

        const auto& T = FsToolbox::template toLhs<LhsEval>(fluidState.temperature(phaseIdx));
        const auto& p = FsToolbox::template toLhs<LhsEval>(fluidState.pressure(phaseIdx));

        // liquid phase
        if (phaseIdx == liquidPhaseIdx)
            return BinaryCoeff::H2O_N2::liquidDiffCoeff(T, p);

        // gas phase
        assert(phaseIdx == gasPhaseIdx);
        return BinaryCoeff::H2O_N2::gasDiffCoeff(T, p);
    }

    template <class FluidState, class LhsEval = typename FluidState::Scalar>
    static LhsEval enthalpy(const FluidState &fluidState,
                            const ParameterCache &/*paramCache*/,
                            unsigned phaseIdx)
    {
        typedef Opm::MathToolbox<typename FluidState::Scalar> FsToolbox;

        const auto& T = FsToolbox::template toLhs<LhsEval>(fluidState.temperature(phaseIdx));
        const auto& p = FsToolbox::template toLhs<LhsEval>(fluidState.pressure(phaseIdx));
        Valgrind::CheckDefined(T);
        Valgrind::CheckDefined(p);

        // liquid phase
        if (phaseIdx == liquidPhaseIdx) {
            // TODO: correct way to deal with the solutes???
            return H2O::liquidEnthalpy(T, p);
        }

        // gas phase
        assert(phaseIdx == gasPhaseIdx);

        // assume ideal mixture: Molecules of one component don't
        // "see" the molecules of the other component, which means
        // that the total specific enthalpy is the sum of the
        // "partial specific enthalpies" of the components.
        const auto& XgH2O = FsToolbox::template toLhs<LhsEval>(fluidState.massFraction(gasPhaseIdx, H2OIdx));
        const auto& XgN2 = FsToolbox::template toLhs<LhsEval>(fluidState.massFraction(gasPhaseIdx, N2Idx));

        LhsEval hH2O = XgH2O*H2O::gasEnthalpy(T, p);
        LhsEval hN2 = XgN2*N2::gasEnthalpy(T, p);
        return hH2O + hN2;
    }

    template <class FluidState, class LhsEval = typename FluidState::Scalar>
    static LhsEval thermalConductivity(const FluidState &fluidState,
                                       const ParameterCache &/*paramCache*/,
                                       unsigned phaseIdx)
    {
        assert(0 <= phaseIdx  && phaseIdx < numPhases);

        typedef Opm::MathToolbox<typename FluidState::Scalar> FsToolbox;

        const auto& T = FsToolbox::template toLhs<LhsEval>(fluidState.temperature(phaseIdx));
        const auto& p = FsToolbox::template toLhs<LhsEval>(fluidState.pressure(phaseIdx));
        if (phaseIdx == liquidPhaseIdx) // liquid phase
            return H2O::liquidThermalConductivity(T, p);

        // gas phase
        assert(phaseIdx == gasPhaseIdx);

        if (useComplexRelations){
            // return the sum of the partial conductivity of Nitrogen and Steam
            const auto& xH2O = FsToolbox::template toLhs<LhsEval>(fluidState.moleFraction(phaseIdx, H2OIdx));
            const auto& xN2 = FsToolbox::template toLhs<LhsEval>(fluidState.moleFraction(phaseIdx, N2Idx));

            // Assuming Raoult's, Daltons law and ideal gas in order to obtain the
            // partial pressures in the gas phase
            const auto& lambdaN2 = N2::gasThermalConductivity(T, p*xN2);
            const auto& lambdaH2O = H2O::gasThermalConductivity(T, p*xH2O);

            return lambdaN2 + lambdaH2O;
        }
        else
            // return the conductivity of dry Nitrogen
            return N2::gasThermalConductivity(T, p);
    }

    template <class FluidState, class LhsEval = typename FluidState::Scalar>
    static LhsEval heatCapacity(const FluidState &fluidState,
                                const ParameterCache &/*paramCache*/,
                                unsigned phaseIdx)
    {
        typedef Opm::MathToolbox<typename FluidState::Scalar> FsToolbox;

        const auto& T = FsToolbox::template toLhs<LhsEval>(fluidState.temperature(phaseIdx));
        const auto& p = FsToolbox::template toLhs<LhsEval>(fluidState.pressure(phaseIdx));
        const auto& xAlphaH2O = FsToolbox::template toLhs<LhsEval>(fluidState.moleFraction(phaseIdx, H2OIdx));
        const auto& xAlphaN2 = FsToolbox::template toLhs<LhsEval>(fluidState.moleFraction(phaseIdx, N2Idx));
        const auto& XAlphaH2O = FsToolbox::template toLhs<LhsEval>(fluidState.massFraction(phaseIdx, H2OIdx));
        const auto& XAlphaN2 = FsToolbox::template toLhs<LhsEval>(fluidState.massFraction(phaseIdx, N2Idx));

        if (phaseIdx == liquidPhaseIdx)
            return H2O::liquidHeatCapacity(T, p);

        assert(phaseIdx == gasPhaseIdx);

        // for the gas phase, assume ideal mixture, i.e. molecules of
        // one component don't "see" the molecules of the other
        // component
        LhsEval c_pN2;
        LhsEval c_pH2O;
        // let the water and nitrogen components do things their own way
        if (useComplexRelations) {
            c_pN2 = N2::gasHeatCapacity(T, p*xAlphaN2);
            c_pH2O = H2O::gasHeatCapacity(T, p*xAlphaH2O);
        }
        else {
            // assume an ideal gas for both components. See:
            //
            // http://en.wikipedia.org/wiki/Heat_capacity
            Scalar c_vN2molar = Opm::Constants<Scalar>::R*2.39;
            Scalar c_pN2molar = Opm::Constants<Scalar>::R + c_vN2molar;

            Scalar c_vH2Omolar = Opm::Constants<Scalar>::R*3.37; // <- correct??
            Scalar c_pH2Omolar = Opm::Constants<Scalar>::R + c_vH2Omolar;

            c_pN2 = c_pN2molar/molarMass(N2Idx);
            c_pH2O = c_pH2Omolar/molarMass(H2OIdx);
        }

        // mingle both components together. this assumes that there is no "cross
        // interaction" between both flavors of molecules.
        return XAlphaH2O*c_pH2O + XAlphaN2*c_pN2;
    }
};

} // namespace FluidSystems

} // namespace Opm

#endif