066601ae52
Most H2 properties are calculated using Helmholtz free energy EOS. Moved Helmholtz equations from Brine_H2 to H2 class. New file with simple H2 property calculations based on ideal gas.
194 lines
7.5 KiB
C++
194 lines
7.5 KiB
C++
// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
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// vi: set et ts=4 sw=4 sts=4:
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/*
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This file is part of the Open Porous Media project (OPM).
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OPM is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 2 of the License, or
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(at your option) any later version.
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OPM is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with OPM. If not, see <http://www.gnu.org/licenses/>.
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Consult the COPYING file in the top-level source directory of this
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module for the precise wording of the license and the list of
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copyright holders.
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*/
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/*!
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* \file
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*
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* \copydoc Opm::BinaryCoeff::Brine_H2
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*/
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#ifndef OPM_BINARY_COEFF_BRINE_H2_HPP
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#define OPM_BINARY_COEFF_BRINE_H2_HPP
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#include <opm/material/binarycoefficients/FullerMethod.hpp>
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namespace Opm {
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namespace BinaryCoeff {
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/*!
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* \ingroup Binarycoefficients
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* \brief Binary coefficients for brine and H2.
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*/
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template<class Scalar, class H2O, class H2, bool verbose = true>
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class Brine_H2 {
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static const int liquidPhaseIdx = 0; // index of the liquid phase
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static const int gasPhaseIdx = 1; // index of the gas phase
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public:
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/*!
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* \brief Returns the _mol_ (!) fraction of H2 in the liquid phase for a given temperature, pressure, and brine
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* salinity. Implemented according to Li et al., Int. J. Hydrogen Energ., 2018.
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*
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* \param temperature temperature [K]
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* \param pg gas phase pressure [Pa]
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* \param salinity salinity [mol NaCl / kg solution]
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* \param knownPhaseIdx indicates which phases are present
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* \param xlH2 mole fraction of H2 in brine [mol/mol]
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*/
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template <class Evaluation>
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static void calculateMoleFractions(const Evaluation& temperature,
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const Evaluation& pg,
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Scalar salinity,
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Evaluation& xH2)
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{
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// All intermediate calculations
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Evaluation lnYH2 = moleFractionGasH2_(temperature, pg);
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Evaluation lnPg = log(pg / 1e6); // Pa --> MPa before ln
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Evaluation lnPhiH2 = fugacityCoefficientH2(temperature, pg);
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Evaluation lnKh = henrysConstant_(temperature);
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Evaluation PF = computePoyntingFactor_(temperature, pg);
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Evaluation lnGammaH2 = activityCoefficient_(temperature, salinity);
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// Eq. (4) to get mole fraction of H2 in brine
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xH2 = exp(lnYH2 + lnPg + lnPhiH2 - lnKh - PF - lnGammaH2);
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}
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/*!
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* \brief Returns the Poynting Factor (PF) which is needed in calculation of H2 solubility in Li et al (2018).
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*
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* \param temperature temperature [K]
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* \param pg gas phase pressure [Pa]
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*/
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template <class Evaluation>
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static Evaluation computePoyntingFactor_(const Evaluation& temperature, const Evaluation& pg)
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{
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// PF is approximated as a polynomial expansion in terms of temperature and pressure with the following
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// parameters (Table 4)
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static const Scalar a[4] = {6.156755, -2.502396e-2, 4.140593e-5, -1.322988e-3};
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// Eq. (16)
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Evaluation pg_mpa = pg / 1.0e6; // convert from Pa to MPa
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Evaluation PF = a[0]*pg_mpa/temperature + a[1]*pg_mpa + a[2]*temperature*pg_mpa + a[3]*pg_mpa*pg_mpa/temperature;
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return PF;
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}
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/*!
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* \brief Returns the activity coefficient of H2 in brine which is needed in calculation of H2 solubility in Li et
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* al (2018). Note that we only include NaCl effects. Could be extended with other salts, e.g. from Duan & Sun,
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* Chem. Geol., 2003.
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*
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* \param temperature temperature [K]
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* \param salinity salinity [mol NaCl / kg solution]
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*/
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template <class Evaluation>
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static Evaluation activityCoefficient_(const Evaluation& temperature, Scalar salinity)
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{
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// Linear approximation in temperature with following parameters (Table 5)
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static const Scalar a[2] = {0.64485, 0.00142};
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// Eq. (17)
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Evaluation lnGamma = (a[0] - a[1]*temperature)*salinity;
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return lnGamma;
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}
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/*!
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* \brief Returns Henry's constant of H2 in brine which is needed in calculation of H2 solubility in Li et al (2018).
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*
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* \param temperature temperature [K]
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*/
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template <class Evaluation>
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static Evaluation henrysConstant_(const Evaluation& temperature)
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{
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// Polynomic approximation in temperature with following parameters (Table 2)
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static const Scalar a[5] = {2.68721e-5, -0.05121, 33.55196, -3411.0432, -31258.74683};
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// Eq. (13)
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Evaluation lnKh = a[0]*temperature*temperature + a[1]*temperature + a[2] + a[3]/temperature
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+ a[4]/(temperature*temperature);
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return lnKh;
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}
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/*!
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* \brief Returns mole fraction of H2 in gasous phase which is needed in calculation of H2 solubility in Li et al
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* (2018).
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*
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* \param temperature temperature [K]
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* \param pg gas phase pressure [Pa]
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*/
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template <class Evaluation>
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static Evaluation moleFractionGasH2_(const Evaluation& temperature, const Evaluation& pg)
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{
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// Need saturaturated vapor pressure of pure water
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Evaluation pw_sat = H2O::vaporPressure(temperature);
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// Eq. (12)
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Evaluation lnyH2 = log(1 - (pw_sat / pg));
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return lnyH2;
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}
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/*!
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* \brief Calculate fugacity coefficient for H2 which is needed in calculation of H2 solubility in Li et al (2018).
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* The equation used is based on Helmoltz free energy EOS. The formulas here are taken from Span et al., J. Phys.
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* Chem. Ref. Data 29, 2000 and Leachman et al., J. Phys. Chem. Ref. Data 38, 2009, and Li et al. (2018).
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*
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* \param temperature temperature [K]
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* \param pg gas phase pressure [Pa]
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*/
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template <class Evaluation>
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static Evaluation fugacityCoefficientH2(const Evaluation& temperature, const Evaluation& pg)
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{
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// Convert pressure to reduced density and temperature to reduced temperature
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Evaluation rho_red = H2::reducedMolarDensity(temperature, pg);
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Evaluation T_red = H2::criticalTemperature() / temperature;
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// Residual Helmholtz energy, Eq. (7) in Li et al. (2018)
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Evaluation resHelm = H2::residualPartHelmholtz(T_red, rho_red);
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// Derivative of residual Helmholtz energy wrt to reduced density, Eq. (73) in Span et al. (2018)
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Evaluation dResHelm_dRedRho = H2::derivResHelmholtzWrtRedRho(T_red, rho_red);
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// Fugacity coefficient, Eq. (8) in Li et al. (2018)
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Evaluation lnPhiH2 = resHelm + rho_red * dResHelm_dRedRho - log(rho_red * dResHelm_dRedRho + 1);
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return lnPhiH2;
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}
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/*!
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* \brief Binary diffusion coefficent [m^2/s] for molecular water and H2 as an approximation for brine-H2 diffusion.
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*
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* To calculate the values, the \ref fullerMethod is used.
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*/
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template <class Evaluation>
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static Evaluation gasDiffCoeff(const Evaluation& temperature, const Evaluation& pressure)
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{
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// atomic diffusion volumes
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const Scalar SigmaNu[2] = { 13.1 /* H2O */, 7.07 /* H2 */ };
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// molar masses [g/mol]
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const Scalar M[2] = { H2O::molarMass()*1e3, H2::molarMass()*1e3 };
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return fullerMethod(M, SigmaNu, temperature, pressure);
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}
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}; // end class Brine_H2
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} // end namespace BinaryCoeff
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} // end namespace Opm
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#endif
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