BrineH2Pvt.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:
/*
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.
 
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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/>.
 
Consult the COPYING file in the top-level source directory of this
module for the precise wording of the license and the list of
copyright holders.
*/
#ifndef OPM_BRINE_H2_PVT_HPP
#define OPM_BRINE_H2_PVT_HPP
 
#include <opm/common/Exceptions.hpp>
 
#include <opm/material/binarycoefficients/Brine_H2.hpp>
#include <opm/material/components/SimpleHuDuanH2O.hpp>
#include <opm/material/components/BrineDynamic.hpp>
#include <opm/material/components/H2.hpp>
#include <opm/material/common/UniformTabulated2DFunction.hpp>
#include <opm/material/common/Valgrind.hpp>
#include <opm/material/fluidsystems/BlackOilFunctions.hpp>
 
#include <cstddef>
#include <vector>
 
namespace Opm {
 
class EclipseState;
class Schedule;

template <class Scalar>
class BrineH2Pvt
{
    static const bool extrapolate = true;
public:
    using H2O = SimpleHuDuanH2O<Scalar>;
    using Brine = ::Opm::BrineDynamic<Scalar, H2O>;
    using H2 = ::Opm::H2<Scalar>;
 
    // The binary coefficients for brine and H2 used by this fluid system
    using BinaryCoeffBrineH2 = BinaryCoeff::Brine_H2<Scalar, H2O, H2>;
 
    explicit BrineH2Pvt() = default;
 
    explicit BrineH2Pvt(const std::vector<Scalar>& salinity,
                        Scalar T_ref = 288.71, //(273.15 + 15.56)
                        Scalar P_ref = 101325);

    void initFromState(const EclipseState& eclState, const Schedule&);
 
    void setNumRegions(std::size_t numRegions);
 
    void setVapPars(const Scalar, const Scalar)
    {
    }

    void setReferenceDensities(unsigned regionIdx,
                               Scalar rhoRefBrine,
                               Scalar rhoRefH2,
                               Scalar /*rhoRefWater*/);

    void initEnd()
    {
    }

    void setEnableDissolvedGas(bool yesno)
    { enableDissolution_ = yesno; }

    void setEnableSaltConcentration(bool yesno)
    { enableSaltConcentration_ = yesno; }

    unsigned numRegions() const
    { return brineReferenceDensity_.size(); }

    Scalar hVap(unsigned /*regionIdx*/) const
    { return 0.0; }
 
    template <class Evaluation>
    Evaluation internalEnergy(unsigned regionIdx,
                        const Evaluation& temperature,
                        const Evaluation& pressure,
                        const Evaluation& Rs,
                        const Evaluation& saltConcentration) const
    {
        const Evaluation salinity = salinityFromConcentration(regionIdx, temperature,
                                                              pressure, saltConcentration);
        const Evaluation xlH2 = convertRsToXoG_(Rs,regionIdx);
        return liquidEnthalpyBrineH2_(temperature,
                                      pressure,
                                      salinity,
                                      xlH2)
             - pressure / density_(regionIdx, temperature, pressure, Rs, salinity);
    }

    template <class Evaluation>
    Evaluation internalEnergy(unsigned regionIdx,
                        const Evaluation& temperature,
                        const Evaluation& pressure,
                        const Evaluation& Rs) const
    {
        const Evaluation xlH2 = convertRsToXoG_(Rs,regionIdx);
        return liquidEnthalpyBrineH2_(temperature,
                                      pressure,
                                      Evaluation(salinity_[regionIdx]),
                                      xlH2)
             - pressure / density_(regionIdx, temperature, pressure,
                                   Rs, Evaluation(salinity_[regionIdx]));
    }

    template <class Evaluation>
    Evaluation viscosity(unsigned regionIdx,
                         const Evaluation& temperature,
                         const Evaluation& pressure,
                         const Evaluation& /*Rs*/) const
    {
        //TODO: The viscosity does not yet depend on the composition
        return saturatedViscosity(regionIdx, temperature, pressure);
    }

    template <class Evaluation>
    Evaluation saturatedViscosity(unsigned regionIdx,
                                 const Evaluation& temperature,
                                 const Evaluation& pressure,
                                 const Evaluation& saltConcentration) const
    {
        const Evaluation salinity = salinityFromConcentration(regionIdx, temperature,
                                                              pressure, saltConcentration);
        return Brine::liquidViscosity(temperature, pressure, salinity);
    }

    template <class Evaluation>
    Evaluation viscosity(unsigned regionIdx,
                         const Evaluation& temperature,
                         const Evaluation& pressure,
                         const Evaluation& /*Rsw*/,
                         const Evaluation& saltConcentration) const
    {
        //TODO: The viscosity does not yet depend on the composition
        return saturatedViscosity(regionIdx, temperature, pressure, saltConcentration);
    }

    template <class Evaluation>
    Evaluation saturatedViscosity(unsigned regionIdx,
                                  const Evaluation& temperature,
                                  const Evaluation& pressure) const
    {
        return Brine::liquidViscosity(temperature, pressure, Evaluation(salinity_[regionIdx]));
    }

    template <class Evaluation>
    Evaluation saturatedInverseFormationVolumeFactor(unsigned regionIdx,
                                                     const Evaluation& temperature,
                                                     const Evaluation& pressure,
                                                     const Evaluation& saltconcentration) const
    {
        const Evaluation salinity = salinityFromConcentration(regionIdx, temperature,
                                                              pressure, saltconcentration);
        Evaluation rsSat = rsSat_(regionIdx, temperature, pressure, salinity);
        return (1.0 - convertRsToXoG_(rsSat,regionIdx))
             * density_(regionIdx, temperature, pressure, rsSat, salinity)
             / brineReferenceDensity_[regionIdx];
    }

    template <class Evaluation>
    Evaluation inverseFormationVolumeFactor(unsigned regionIdx,
                                            const Evaluation& temperature,
                                            const Evaluation& pressure,
                                            const Evaluation& Rs,
                                            const Evaluation& saltConcentration) const
    {
        const Evaluation salinity = salinityFromConcentration(regionIdx, temperature,
                                                              pressure, saltConcentration);
        return (1.0 - convertRsToXoG_(Rs,regionIdx))
             * density_(regionIdx, temperature, pressure, Rs, salinity)
             / brineReferenceDensity_[regionIdx];
    }

    template <class Evaluation>
    Evaluation inverseFormationVolumeFactor(unsigned regionIdx,
                                            const Evaluation& temperature,
                                            const Evaluation& pressure,
                                            const Evaluation& Rs) const
    {
        return (1.0 - convertRsToXoG_(Rs, regionIdx))
             * density_(regionIdx, temperature, pressure, Rs, Evaluation(salinity_[regionIdx]))
             / brineReferenceDensity_[regionIdx];
    }

    template <class FluidState, class LhsEval = typename FluidState::ValueType>
    std::pair<LhsEval, LhsEval>
    inverseFormationVolumeFactorAndViscosity(const FluidState& fluidState, unsigned regionIdx)
    {
        // Deal with the possibility that we are in a two-phase H2STORE with OIL and GAS as phases.
        const bool waterIsActive = fluidState.phaseIsActive(FluidState::waterPhaseIdx);
        const int myPhaseIdx = waterIsActive ? FluidState::waterPhaseIdx : FluidState::oilPhaseIdx;
        const LhsEval& Rsw = waterIsActive ? decay<LhsEval>(fluidState.Rsw()) : decay<LhsEval>(fluidState.Rs());
 
        const LhsEval& T = decay<LhsEval>(fluidState.temperature(myPhaseIdx));
        const LhsEval& p = decay<LhsEval>(fluidState.pressure(myPhaseIdx));
        const LhsEval& saltConcentration
            = BlackOil::template getSaltConcentration_<FluidState, LhsEval>(fluidState, regionIdx);
        // TODO: The viscosity does not yet depend on the composition
        return { this->inverseFormationVolumeFactor(regionIdx, T, p, Rsw, saltConcentration) ,
                this->saturatedViscosity(regionIdx, T, p, saltConcentration) };
    }

    template <class Evaluation>
    Evaluation saturatedInverseFormationVolumeFactor(unsigned regionIdx,
                                                     const Evaluation& temperature,
                                                     const Evaluation& pressure) const
    {
        Evaluation rsSat = rsSat_(regionIdx, temperature,
                                  pressure, Evaluation(salinity_[regionIdx]));
        return (1.0 - convertRsToXoG_(rsSat, regionIdx))
             * density_(regionIdx, temperature, pressure, rsSat,
                        Evaluation(salinity_[regionIdx]))
             /  brineReferenceDensity_[regionIdx];
    }

    template <class Evaluation>
    Evaluation saturationPressure(unsigned /*regionIdx*/,
                                  const Evaluation& /*temperature*/,
                                  const Evaluation& /*Rs*/) const
    {
        throw std::runtime_error("Saturation pressure for the Brine-H2 PVT module "
                                 "has not been implemented yet!");
    }

    template <class Evaluation>
    Evaluation saturationPressure(unsigned /*regionIdx*/,
                                  const Evaluation& /*temperature*/,
                                  const Evaluation& /*Rs*/,
                                  const Evaluation& /*saltConcentration*/) const
    {
        throw std::runtime_error("Saturation pressure for the Brine-H2 PVT module "
                                 "has not been implemented yet!");
    }

    template <class Evaluation>
    Evaluation saturatedGasDissolutionFactor(unsigned regionIdx,
                                             const Evaluation& temperature,
                                             const Evaluation& pressure,
                                             const Evaluation& /*oilSaturation*/,
                                             const Evaluation& /*maxOilSaturation*/) const
    {
        //TODO support VAPPARS
        return rsSat_(regionIdx, temperature, pressure, Evaluation(salinity_[regionIdx]));
    }

    template <class Evaluation>
    Evaluation saturatedGasDissolutionFactor(unsigned regionIdx,
                                             const Evaluation& temperature,
                                             const Evaluation& pressure,
                                             const Evaluation& saltConcentration) const
    {
        const Evaluation salinity = salinityFromConcentration(regionIdx, temperature,
                                                              pressure, saltConcentration);
        return rsSat_(regionIdx, temperature, pressure, salinity);
    }

    template <class Evaluation>
    Evaluation saturatedGasDissolutionFactor(unsigned regionIdx,
                                             const Evaluation& temperature,
                                             const Evaluation& pressure) const
    {
        return rsSat_(regionIdx, temperature, pressure, Evaluation(salinity_[regionIdx]));
    }
 
    Scalar oilReferenceDensity(unsigned regionIdx) const
    { return brineReferenceDensity_[regionIdx]; }
 
    Scalar waterReferenceDensity(unsigned regionIdx) const
    { return brineReferenceDensity_[regionIdx]; }
 
    Scalar gasReferenceDensity(unsigned regionIdx) const
    { return h2ReferenceDensity_[regionIdx]; }
 
    Scalar salinity(unsigned regionIdx) const
    { return salinity_[regionIdx]; }

    template <class Evaluation>
    Evaluation diffusionCoefficient(const Evaluation& temperature,
                                    const Evaluation& pressure,
                                    unsigned /*compIdx*/,
                                    unsigned regionIdx = 0) const
    {
        // Diffusion coefficient of H2 in pure water according to
        // Ferrell & Himmelbau, AIChE Journal, 13(4), 1967 (Eq. 23)
        // Some intermediate calculations and definitions
 
        // molar volume at normal boiling point (20.271 K and 1 atm) in cm2/mol
        const Scalar vm = 28.45;
        const Scalar sigma = 2.96 * 1e-8; // Lennard-Jones 6-12 potential in cm (1 Å = 1e-8 cm)
        const Scalar avogadro = 6.022e23; // Avogrado's number in mol^-1
        const Scalar alpha = sigma / pow((vm / avogadro), 1 / 3);  // Eq. (19)
        const Scalar lambda = 1.729; // quantum parameter [-]
        const Evaluation mu_pure = H2O::liquidViscosity(temperature, pressure, extrapolate) * 1e3;  // [cP]
        const Evaluation mu_brine = Brine::liquidViscosity(temperature, pressure,
                                                           Evaluation(salinity_[regionIdx])) * 1e3;
 
        // Diffusion coeff in pure water in cm2/s
        const Evaluation D_pure = ((4.8e-7 * temperature) / pow(mu_pure, alpha)) *
                                  pow((1 + pow(lambda, 2)) / vm, 0.6);
 
        // Diffusion coefficient in brine using Ratcliff and Holdcroft,
        // J. G. Trans. Inst. Chem. Eng, 1963. OBS: Value
        // of n is noted as the recommended single value according to
        // Akita, Ind. Eng. Chem. Fundam., 1981.
        const Evaluation log_D_brine = log10(D_pure) - 0.637 * log10(mu_brine / mu_pure);
 
        return pow(Evaluation(10), log_D_brine) * 1e-4;  // convert from cm2/s to m2/s
    }
 
private:
    template <class LhsEval>
    LhsEval density_(unsigned regionIdx,
                     const LhsEval& temperature,
                     const LhsEval& pressure,
                     const LhsEval& Rs,
                     const LhsEval& salinity) const
    {
        // convert Rs to mole fraction (via mass fraction)
        LhsEval xlH2 = convertXoGToxoG_(convertRsToXoG_(Rs,regionIdx), salinity);
 
        // calculate the density of solution
        LhsEval result = liquidDensity_(temperature,
                                        pressure,
                                        xlH2,
                                        salinity);
 
        Valgrind::CheckDefined(result);
        return result;
    }

    template <class LhsEval>
    LhsEval liquidDensity_(const LhsEval& T,
                           const LhsEval& pl,
                           const LhsEval& xlH2,
                           const LhsEval& salinity) const
    {
        // check input variables
        Valgrind::CheckDefined(T);
        Valgrind::CheckDefined(pl);
        Valgrind::CheckDefined(xlH2);
 
        // check if pressure and temperature is valid
        if (!extrapolate && T < 273.15) {
            const std::string msg =
                "Liquid density for Brine and H2 is only "
                "defined above 273.15K (is " +
                std::to_string(getValue(T)) + "K)";
            throw NumericalProblem(msg);
        }
        if (!extrapolate && pl >= 2.5e8) {
            const std::string msg  =
                "Liquid density for Brine and H2 is only "
                "defined below 250MPa (is " +
                std::to_string(getValue(pl)) + "Pa)";
            throw NumericalProblem(msg);
        }
 
        // calculate individual contribution to density
        const LhsEval& rho_pure = H2O::liquidDensity(T, pl, extrapolate);
        const LhsEval& rho_brine = Brine::liquidDensity(T, pl, salinity, rho_pure);
        const LhsEval& rho_lH2 = liquidDensityWaterH2_(T, pl, xlH2);
        const LhsEval& contribH2 = rho_lH2 - rho_pure;
 
        return rho_brine + contribH2;
    }

    template <class LhsEval>
    LhsEval liquidDensityWaterH2_(const LhsEval& temperature,
                                          const LhsEval& pl,
                                          const LhsEval& xlH2) const
    {
        // molar masses
        Scalar M_H2 = H2::molarMass();
        Scalar M_H2O = H2O::molarMass();
 
        // density of pure water
        const LhsEval& rho_pure = H2O::liquidDensity(temperature, pl, extrapolate);
 
        // (apparent) molar volume of H2, Eq. (14) in Li et al. (2018)
        const LhsEval& A1 = 51.1904 - 0.208062 * temperature +
                            3.4427e-4 * temperature * temperature;
        const LhsEval& A2 = -0.022;
        // pressure in [MPa] and Vphi in [m3/mol] (from [cm3/mol])
        const LhsEval& V_phi = (A1 + A2 * (pl / 1e6)) / 1e6;
 
        // density of solution, Eq. (19) in Garcia (2001)
        const LhsEval xlH2O = 1.0 - xlH2;
        const LhsEval& M_T = M_H2O * xlH2O + M_H2 * xlH2;
        const LhsEval& rho_aq = 1 / (xlH2 * V_phi/M_T + M_H2O * xlH2O / (rho_pure * M_T));
 
        return rho_aq;
    }

    template <class LhsEval>
    LhsEval convertRsToXoG_(const LhsEval& Rs, unsigned regionIdx) const
    {
        Scalar rho_oRef = brineReferenceDensity_[regionIdx];
        Scalar rho_gRef = h2ReferenceDensity_[regionIdx];
 
        const LhsEval& rho_oG = Rs*rho_gRef;
        return rho_oG/(rho_oRef + rho_oG);
    }

    template <class LhsEval>
    LhsEval convertXoGToxoG_(const LhsEval& XoG, const LhsEval& salinity) const
    {
        Scalar M_H2 = H2::molarMass();
        LhsEval M_Brine = Brine::molarMass(salinity);
        return XoG*M_Brine / (M_H2*(1 - XoG) + XoG*M_Brine);
    }

    template <class LhsEval>
    LhsEval convertxoGToXoG(const LhsEval& xoG, const LhsEval& salinity) const
    {
        Scalar M_H2 = H2::molarMass();
        LhsEval M_Brine = Brine::molarMass(salinity);
 
        return xoG*M_H2 / (xoG*(M_H2 - M_Brine) + M_Brine);
    }

    template <class LhsEval>
    LhsEval convertXoGToRs(const LhsEval& XoG, unsigned regionIdx) const
    {
        Scalar rho_oRef = brineReferenceDensity_[regionIdx];
        Scalar rho_gRef = h2ReferenceDensity_[regionIdx];
 
        return XoG/(1.0 - XoG)*(rho_oRef/rho_gRef);
    }

    template <class LhsEval>
    LhsEval rsSat_(unsigned regionIdx,
                   const LhsEval& temperature,
                   const LhsEval& pressure,
                   const LhsEval& salinity) const
    {
        // Return Rs=0.0 if dissolution is disabled
        if (!enableDissolution_)
            return 0.0;
 
        // calulate the equilibrium composition for the given temperature and pressure
        LhsEval xlH2 = BinaryCoeffBrineH2::calculateMoleFractions(temperature, pressure,
                                                                  salinity, extrapolate);
 
        // normalize the phase compositions
        xlH2 = max(0.0, min(1.0, xlH2));
 
        return convertXoGToRs(convertxoGToXoG(xlH2, salinity), regionIdx);
    }
 
    template <class LhsEval>
    static LhsEval liquidEnthalpyBrineH2_(const LhsEval& T,
                                           const LhsEval& p,
                                           const LhsEval& salinity,
                                           const LhsEval& X_H2_w)
    {
        /* X_H2_w : mass fraction of H2 in brine */
        /*NOTE: The heat of dissolution of H2 in brine is not included at the moment!*/
 
        /*Numerical coefficents from PALLISER*/
        static constexpr Scalar f[] = {
            2.63500E-1, 7.48368E-6, 1.44611E-6, -3.80860E-10
        };
 
        /*Numerical coefficents from MICHAELIDES for the enthalpy of brine*/
        static constexpr 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 }
        };
 
        LhsEval theta, h_NaCl;
        LhsEval h_ls1, d_h;
        LhsEval delta_h;
        LhsEval hg, hw;
 
        // Temperature in Celsius
        theta = T - 273.15;
 
        // Regularization
        Scalar scalarTheta = scalarValue(theta);
        Scalar S_lSAT = f[0] + scalarTheta*(f[1] + scalarTheta*(f[2] + scalarTheta*f[3]));
 
        LhsEval S = salinity;
        if (S > S_lSAT) {
            S = S_lSAT;
        }
 
        hw = H2O::liquidEnthalpy(T, p) /1E3; /* kJ/kg */
 
        /*DAUBERT and DANNER*/
        /*U=*/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; /* kJ/kg */
 
        LhsEval m = 1E3/58.44 * S/(1-S);
        d_h = 0;
 
        for (int i = 0; i <=3 ; ++i) {
            for (int j = 0; j <= 2; ++j) {
                d_h = d_h + a[i][j] * pow(theta, static_cast<Scalar>(i)) * pow(m, j);
            }
        }
        /* heat of dissolution for halite according to Michaelides 1971 */
        delta_h = (4.184/(1E3 + (58.44 * m)))*d_h;
 
        /* Enthalpy of brine without H2 */
        h_ls1 =(1-S)*hw + S*h_NaCl + S*delta_h; /* kJ/kg */
 
        /* enthalpy contribution of H2 gas (kJ/kg) */
        hg = H2::gasEnthalpy(T, p, extrapolate) / 1E3;
 
        /* Enthalpy of brine with dissolved H2 */
        return (h_ls1 - X_H2_w*hw + hg*X_H2_w)*1E3; /*J/kg*/
    }
 
    template <class LhsEval>
    const LhsEval salinityFromConcentration(unsigned regionIdx,
                                            const LhsEval&T,
                                            const LhsEval& P,
                                            const LhsEval& saltConcentration) const
    {
        if (enableSaltConcentration_) {
            // Convert concentration [kg/m³] to mass fraction [kg_salt/kg_solution].
            // First approximation using pure water density
            const LhsEval rho_w = H2O::liquidDensity(T, P, true);
            const LhsEval S_approx = saltConcentration / rho_w;
            // Improved estimate using Batzle-Wang brine density
            const LhsEval rho_brine = Brine::liquidDensity(T, P, S_approx, rho_w);
            return saltConcentration / rho_brine;
        }
 
        return salinity(regionIdx);
    }
 
    std::vector<Scalar> brineReferenceDensity_{};
    std::vector<Scalar> h2ReferenceDensity_{};
    std::vector<Scalar> salinity_{};
    bool enableDissolution_ = true;
    bool enableSaltConcentration_ = false;
};  // end class BrineH2Pvt
 
}  // end namespace Opm
 
#endif