LBCco2rich.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 2022 NORCE.
 
  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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  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
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  Consult the COPYING file in the top-level source directory of this
  module for the precise wording of the license and the list of
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*/
#ifndef OPM_LBC_CO2RICH_HPP
#define OPM_LBC_CO2RICH_HPP
 
#include <cmath>
#include <vector>
 
namespace Opm
{
template <class Scalar, class FluidSystem>
class ViscosityModels
{
 
public:
 
        // Improved LBC model for CO2 rich mixtures. (Lansangan, Taylor, Smith & Kovarik - 1993)
        template <class FluidState, class Params, class LhsEval = typename FluidState::Scalar>
        static LhsEval LBCco2rich(const FluidState& fluidState,
                          const Params& /*paramCache*/,
                          unsigned phaseIdx)
        {
        const Scalar MPa_atm = 0.101325;
        const auto& T = Opm::decay<LhsEval>(fluidState.temperature(phaseIdx));
        const auto& rho = Opm::decay<LhsEval>(fluidState.density(phaseIdx));
 
        LhsEval sumMm = 0.0;
        LhsEval sumVolume = 0.0;
        for (unsigned compIdx = 0; compIdx < FluidSystem::numComponents; ++compIdx) {
            const Scalar& p_c = FluidSystem::criticalPressure(compIdx)/1e6; // in Mpa;
            const Scalar& T_c = FluidSystem::criticalTemperature(compIdx);
            const Scalar Mm = FluidSystem::molarMass(compIdx) * 1000; //in kg/kmol;
            const auto& x = Opm::decay<LhsEval>(fluidState.moleFraction(phaseIdx, compIdx));
            const Scalar v_c = FluidSystem::criticalVolume(compIdx);  // in m3/kmol
            sumMm += x*Mm;
            sumVolume += x*v_c;
        }
 
        LhsEval rho_pc = sumMm/sumVolume; //mixture pseudocritical density
        LhsEval rho_r = rho/rho_pc;
 
        LhsEval xxT_p = 0.0;  // x*x*T_c/p_c
        LhsEval xxT2_p = 0.0; // x*x*T^2_c/p_c
        for (unsigned i_compIdx = 0; i_compIdx < FluidSystem::numComponents; ++i_compIdx) {
            const Scalar& T_c_i = FluidSystem::criticalTemperature(i_compIdx);
            const Scalar& p_c_i = FluidSystem::criticalPressure(i_compIdx)/1e6; // in Mpa;
            const auto& x_i = Opm::decay<LhsEval>(fluidState.moleFraction(phaseIdx, i_compIdx));
            for (unsigned j_compIdx = 0; j_compIdx < FluidSystem::numComponents; ++j_compIdx) {
                const Scalar& T_c_j = FluidSystem::criticalTemperature(j_compIdx);
                const Scalar& p_c_j = FluidSystem::criticalPressure(j_compIdx)/1e6; // in Mpa;
                const auto& x_j = Opm::decay<LhsEval>(fluidState.moleFraction(phaseIdx, j_compIdx));
 
                const Scalar T_c_ij = std::sqrt(T_c_i*T_c_j);
                const Scalar p_c_ij = 8.0*T_c_ij / Opm::pow(Opm::pow(T_c_i/p_c_i,1.0/3)+Opm::pow(T_c_j/p_c_j,1.0/3),3);
 
                xxT_p += x_i*x_j*T_c_ij/p_c_ij;
                xxT2_p += x_i*x_j*T_c_ij*T_c_ij/p_c_ij;
            }
        }
 
        const LhsEval T_pc = xxT2_p/xxT_p; //mixture pseudocritical temperature
        const LhsEval p_pc = T_pc/xxT_p;   //mixture pseudocritical pressure
 
        LhsEval p_pca = p_pc / MPa_atm;
        LhsEval zeta_tot = Opm::pow(T_pc / (Opm::pow(sumMm,3.0) * Opm::pow(p_pca,4.0)),1./6);
 
        LhsEval my0 = 0.0;
        LhsEval sumxrM = 0.0;
        for (unsigned compIdx = 0; compIdx < FluidSystem::numComponents; ++compIdx) {
            const Scalar& p_c = FluidSystem::criticalPressure(compIdx)/1e6; // in Mpa;
            const Scalar& T_c = FluidSystem::criticalTemperature(compIdx);
            const Scalar Mm = FluidSystem::molarMass(compIdx) * 1000; //in kg/kmol;
            const auto& x = Opm::decay<LhsEval>(fluidState.moleFraction(phaseIdx, compIdx));
            Scalar p_ca = p_c / MPa_atm;
            Scalar zeta = std::pow(T_c / (std::pow(Mm,3.0) * std::pow(p_ca,4.0)),1./6);
            LhsEval T_r = T/T_c;
            LhsEval xrM = x * std::pow(Mm,0.5);
            LhsEval mys = 0.0;
            if (T_r <=1.5) {
                mys = 34.0e-5*Opm::pow(T_r,0.94)/zeta;
            } else {
                mys = 17.78e-5*Opm::pow(4.58*T_r - 1.67, 0.625)/zeta;
            }
            my0 += xrM*mys;
            sumxrM += xrM;
            }
            my0 /= sumxrM;
 
            std::vector<Scalar> LBC = {0.10230,
                                   0.023364,
                                   0.058533,
                                   -0.040758,  // typo in 1964-paper: -0.40758
                                   0.0093324};
 
            LhsEval sumLBC = 0.0;
            for (int i = 0; i < 5; ++i) {
                sumLBC += Opm::pow(rho_r,i)*LBC[i];
            }
 
            return (my0 + (Opm::pow(sumLBC,4.0) - 1e-4)/zeta_tot -1.8366e-8*Opm::pow(rho_r,13.992))/1e3; // mPas-> Pas
        }
};
 
}; // namespace Opm
 
#endif // OPM_LBC_CO2RICH_HPP