395 lines
17 KiB
C++
395 lines
17 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_CO2
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*/
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#ifndef OPM_BINARY_COEFF_BRINE_CO2_HPP
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#define OPM_BINARY_COEFF_BRINE_CO2_HPP
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#include <opm/material/IdealGas.hpp>
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#include <opm/material/common/Valgrind.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 CO2.
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*/
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template<class Scalar, class H2O, class CO2, bool verbose = true>
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class Brine_CO2 {
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typedef ::Opm::IdealGas<Scalar> IdealGas;
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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 Binary diffusion coefficent [m^2/s] of water in the CO2 phase.
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*
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* According to "Diffusion of Water in Liquid and Supercritical Carbon Dioxide: An NMR Study",Bin Xu et al., 2002
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* \param temperature the temperature [K]
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* \param pressure the phase pressure [Pa]
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*/
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template <class Evaluation>
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static Evaluation gasDiffCoeff(const Evaluation& temperature, const Evaluation& pressure, bool extrapolate = false)
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{
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//Diffusion coefficient of water in the CO2 phase
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Scalar k = 1.3806504e-23; // Boltzmann constant
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Scalar c = 4; // slip parameter, can vary between 4 (slip condition) and 6 (stick condition)
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Scalar R_h = 1.72e-10; // hydrodynamic radius of the solute
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const Evaluation& mu = CO2::gasViscosity(temperature, pressure, extrapolate); // CO2 viscosity
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return k / (c * M_PI * R_h) * (temperature / mu);
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}
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/*!
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* \brief Binary diffusion coefficent [m^2/s] of CO2 in the brine phase.
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*
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* \param temperature the temperature [K]
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* \param pressure the phase pressure [Pa]
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*/
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template <class Evaluation>
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static Evaluation liquidDiffCoeff(const Evaluation& /*temperature*/, const Evaluation& /*pressure*/)
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{
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//Diffusion coefficient of CO2 in the brine phase
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return 2e-9;
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}
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/*!
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* \brief Returns the _mol_ (!) fraction of CO2 in the liquid
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* phase and the mol_ (!) fraction of H2O in the gas phase
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* for a given temperature, pressure, CO2 density and brine
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* salinity.
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*
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* Implemented according to "Spycher and Pruess 2005"
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* applying the activity coefficient expression of "Duan and Sun 2003"
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* and the correlations for pure water given in "Spycher, Pruess and Ennis-King 2003"
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*
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* \param temperature the temperature [K]
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* \param pg the gas phase pressure [Pa]
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* \param salinity the salinity [kg NaCl / kg solution]
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* \param knownPhaseIdx indicates which phases are present
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* \param xlCO2 mole fraction of CO2 in brine [mol/mol]
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* \param ygH2O mole fraction of water in the gas phase [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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const Evaluation& salinity,
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const int knownPhaseIdx,
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Evaluation& xlCO2,
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Evaluation& ygH2O,
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bool extrapolate = false)
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{
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Evaluation A = computeA_(temperature, pg, extrapolate);
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/* salinity: conversion from mass fraction to mol fraction */
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Evaluation x_NaCl = salinityToMolFrac_(salinity);
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// if both phases are present the mole fractions in each phase can be calculate
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// with the mutual solubility function
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if (knownPhaseIdx < 0) {
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Evaluation molalityNaCl = moleFracToMolality_(x_NaCl); // molality of NaCl //CHANGED
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Evaluation m0_CO2 = molalityCO2inPureWater_(temperature, pg, extrapolate); // molality of CO2 in pure water
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Evaluation gammaStar = activityCoefficient_(temperature, pg, molalityNaCl);// activity coefficient of CO2 in brine
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Evaluation m_CO2 = m0_CO2 / gammaStar; // molality of CO2 in brine
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xlCO2 = m_CO2 / (molalityNaCl + 55.508 + m_CO2); // mole fraction of CO2 in brine
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ygH2O = A * (1 - xlCO2 - x_NaCl); // mole fraction of water in the gas phase
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}
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// if only liquid phase is present the mole fraction of CO2 in brine is given and
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// and the virtual equilibrium mole fraction of water in the non-existing gas phase can be estimated
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// with the mutual solubility function
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if (knownPhaseIdx == liquidPhaseIdx)
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ygH2O = A * (1 - xlCO2 - x_NaCl);
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// if only gas phase is present the mole fraction of water in the gas phase is given and
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// and the virtual equilibrium mole fraction of CO2 in the non-existing liquid phase can be estimated
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// with the mutual solubility function
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if (knownPhaseIdx == gasPhaseIdx)
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//y_H2o = fluidstate.
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xlCO2 = 1 - x_NaCl - ygH2O / A;
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}
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/*!
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* \brief Henry coefficent \f$\mathrm{[N/m^2]}\f$ for CO2 in brine.
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*/
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template <class Evaluation>
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static Evaluation henry(const Evaluation& temperature, bool extrapolate = false)
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{ return fugacityCoefficientCO2(temperature, /*pressure=*/1e5, extrapolate)*1e5; }
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/*!
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* \brief Returns the fugacity coefficient of the CO2 component in a water-CO2 mixture
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*
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* (given in Spycher, Pruess and Ennis-King (2003))
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*
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* \param T the temperature [K]
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* \param pg the gas phase pressure [Pa]
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*/
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template <class Evaluation>
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static Evaluation fugacityCoefficientCO2(const Evaluation& temperature, const Evaluation& pg, bool extrapolate = false)
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{
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Valgrind::CheckDefined(temperature);
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Valgrind::CheckDefined(pg);
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Evaluation V = 1 / (CO2::gasDensity(temperature, pg, extrapolate) / CO2::molarMass()) * 1.e6; // molar volume in cm^3/mol
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Evaluation pg_bar = pg / 1.e5; // gas phase pressure in bar
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Evaluation a_CO2 = (7.54e7 - 4.13e4 * temperature); // mixture parameter of Redlich-Kwong equation
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Scalar b_CO2 = 27.8; // mixture parameter of Redlich-Kwong equation
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Scalar R = IdealGas::R * 10.; // ideal gas constant with unit bar cm^3 /(K mol)
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Evaluation lnPhiCO2;
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lnPhiCO2 = log(V / (V - b_CO2));
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lnPhiCO2 += b_CO2 / (V - b_CO2);
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lnPhiCO2 -= 2 * a_CO2 / (R * pow(temperature, 1.5) * b_CO2) * log((V + b_CO2) / V);
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lnPhiCO2 +=
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a_CO2 * b_CO2
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/ (R
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* pow(temperature, 1.5)
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* b_CO2
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* b_CO2)
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* (log((V + b_CO2) / V)
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- b_CO2 / (V + b_CO2));
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lnPhiCO2 -= log(pg_bar * V / (R * temperature));
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return exp(lnPhiCO2); // fugacity coefficient of CO2
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}
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/*!
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* \brief Returns the fugacity coefficient of the H2O component in a water-CO2 mixture
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*
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* (given in Spycher, Pruess and Ennis-King (2003))
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*
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* \param temperature the temperature [K]
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* \param pg the gas phase pressure [Pa]
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*/
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template <class Evaluation>
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static Evaluation fugacityCoefficientH2O(const Evaluation& temperature, const Evaluation& pg, bool extrapolate = false)
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{
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const Evaluation& V = 1 / (CO2::gasDensity(temperature, pg, extrapolate) / CO2::molarMass()) * 1.e6; // molar volume in cm^3/mol
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const Evaluation& pg_bar = pg / 1.e5; // gas phase pressure in bar
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const Evaluation& a_CO2 = (7.54e7 - 4.13e4 * temperature);// mixture parameter of Redlich-Kwong equation
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Scalar a_CO2_H2O = 7.89e7;// mixture parameter of Redlich-Kwong equation
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Scalar b_CO2 = 27.8;// mixture parameter of Redlich-Kwong equation
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Scalar b_H2O = 18.18;// mixture parameter of Redlich-Kwong equation
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Scalar R = IdealGas::R * 10.; // ideal gas constant with unit bar cm^3 /(K mol)
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Evaluation lnPhiH2O;
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lnPhiH2O =
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log(V/(V - b_CO2))
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+ b_H2O/(V - b_CO2) - 2*a_CO2_H2O
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/ (R*pow(temperature, 1.5)*b_CO2)*log((V + b_CO2)/V)
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+ a_CO2*b_H2O/(R*pow(temperature, 1.5)*b_CO2*b_CO2)
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*(log((V + b_CO2)/V) - b_CO2/(V + b_CO2))
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- log(pg_bar*V/(R*temperature));
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return exp(lnPhiH2O); // fugacity coefficient of H2O
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}
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private:
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/*!
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* \brief Returns the molality of NaCl (mol NaCl / kg water) for a given mole fraction
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*
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* \param salinity the salinity [kg NaCl / kg solution]
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*/
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template <class Evaluation>
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static Evaluation salinityToMolFrac_(const Evaluation& salinity) {
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const Scalar Mw = H2O::molarMass(); /* molecular weight of water [kg/mol] */
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const Scalar Ms = 58.44e-3; /* molecular weight of NaCl [kg/mol] */
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const Evaluation X_NaCl = salinity;
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/* salinity: conversion from mass fraction to mol fraction */
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const Evaluation x_NaCl = -Mw * X_NaCl / ((Ms - Mw) * X_NaCl - Ms);
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return x_NaCl;
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}
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/*!
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* \brief Returns the molality of NaCl (mol NaCl / kg water) for a given mole fraction (mol NaCl / mol solution)
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*
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* \param x_NaCl mole fraction of NaCL in brine [mol/mol]
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*/
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template <class Evaluation>
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static Evaluation moleFracToMolality_(const Evaluation& x_NaCl)
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{
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// conversion from mol fraction to molality (dissolved CO2 neglected)
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return 55.508 * x_NaCl / (1 - x_NaCl);
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}
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/*!
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* \brief Returns the equilibrium molality of CO2 (mol CO2 / kg water) for a
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* CO2-water mixture at a given pressure and temperature
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*
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* \param temperature The temperature [K]
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* \param pg The gas phase pressure [Pa]
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*/
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template <class Evaluation>
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static Evaluation molalityCO2inPureWater_(const Evaluation& temperature, const Evaluation& pg, bool extrapolate = false)
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{
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const Evaluation& A = computeA_(temperature, pg, extrapolate); // according to Spycher, Pruess and Ennis-King (2003)
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const Evaluation& B = computeB_(temperature, pg, extrapolate); // according to Spycher, Pruess and Ennis-King (2003)
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const Evaluation& yH2OinGas = (1 - B) / (1. / A - B); // equilibrium mol fraction of H2O in the gas phase
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const Evaluation& xCO2inWater = B * (1 - yH2OinGas); // equilibrium mol fraction of CO2 in the water phase
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return (xCO2inWater * 55.508) / (1 - xCO2inWater); // CO2 molality
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}
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/*!
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* \brief Returns the activity coefficient of CO2 in brine for a
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* molal description. According to "Duan and Sun 2003"
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* given in "Spycher and Pruess 2005"
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*
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* \param temperature the temperature [K]
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* \param pg the gas phase pressure [Pa]
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* \param molalityNaCl molality of NaCl (mol NaCl / kg water)
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*/
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template <class Evaluation>
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static Evaluation activityCoefficient_(const Evaluation& temperature,
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const Evaluation& pg,
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const Evaluation& molalityNaCl)
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{
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const Evaluation& lambda = computeLambda_(temperature, pg); // lambda_{CO2-Na+}
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const Evaluation& xi = computeXi_(temperature, pg); // Xi_{CO2-Na+-Cl-}
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const Evaluation& lnGammaStar =
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2*molalityNaCl*lambda + xi*molalityNaCl*molalityNaCl;
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return exp(lnGammaStar);
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}
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/*!
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* \brief Returns the paramater A for the calculation of
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* them mutual solubility in the water-CO2 system.
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* Given in Spycher, Pruess and Ennis-King (2003)
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*
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* \param T the temperature [K]
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* \param pg the gas phase pressure [Pa]
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*/
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template <class Evaluation>
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static Evaluation computeA_(const Evaluation& temperature, const Evaluation& pg, bool extrapolate = false)
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{
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const Evaluation& deltaP = pg / 1e5 - 1; // pressure range [bar] from p0 = 1bar to pg[bar]
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Scalar v_av_H2O = 18.1; // average partial molar volume of H2O [cm^3/mol]
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Scalar R = IdealGas::R * 10;
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const Evaluation& k0_H2O = equilibriumConstantH2O_(temperature); // equilibrium constant for H2O at 1 bar
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const Evaluation& phi_H2O = fugacityCoefficientH2O(temperature, pg, extrapolate); // fugacity coefficient of H2O for the water-CO2 system
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const Evaluation& pg_bar = pg / 1.e5;
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return k0_H2O/(phi_H2O*pg_bar)*exp(deltaP*v_av_H2O/(R*temperature));
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}
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/*!
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* \brief Returns the paramater B for the calculation of
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* the mutual solubility in the water-CO2 system.
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* Given in Spycher, Pruess and Ennis-King (2003)
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*
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* \param temperature the temperature [K]
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* \param pg the gas phase pressure [Pa]
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*/
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template <class Evaluation>
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static Evaluation computeB_(const Evaluation& temperature, const Evaluation& pg, bool extrapolate = false)
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{
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const Evaluation& deltaP = pg / 1e5 - 1; // pressure range [bar] from p0 = 1bar to pg[bar]
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const Scalar v_av_CO2 = 32.6; // average partial molar volume of CO2 [cm^3/mol]
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const Scalar R = IdealGas::R * 10;
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const Evaluation& k0_CO2 = equilibriumConstantCO2_(temperature); // equilibrium constant for CO2 at 1 bar
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const Evaluation& phi_CO2 = fugacityCoefficientCO2(temperature, pg, extrapolate); // fugacity coefficient of CO2 for the water-CO2 system
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const Evaluation& pg_bar = pg / 1.e5;
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return phi_CO2*pg_bar/(55.508*k0_CO2)*exp(-(deltaP*v_av_CO2)/(R*temperature));
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}
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/*!
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* \brief Returns the parameter lambda, which is needed for the
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* calculation of the CO2 activity coefficient in the brine-CO2 system.
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* Given in Spycher and Pruess (2005)
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* \param temperature the temperature [K]
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* \param pg the gas phase pressure [Pa]
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*/
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template <class Evaluation>
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static Evaluation computeLambda_(const Evaluation& temperature, const Evaluation& pg)
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{
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static const Scalar c[6] =
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{ -0.411370585, 6.07632013E-4, 97.5347708, -0.0237622469, 0.0170656236, 1.41335834E-5 };
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Evaluation pg_bar = pg / 1.0E5; /* conversion from Pa to bar */
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return
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c[0]
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+ c[1]*temperature
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+ c[2]/temperature
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+ c[3]*pg_bar/temperature
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+ c[4]*pg_bar/(630.0 - temperature)
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+ c[5]*temperature*log(pg_bar);
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}
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/*!
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* \brief Returns the parameter xi, which is needed for the
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* calculation of the CO2 activity coefficient in the brine-CO2 system.
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* Given in Spycher and Pruess (2005)
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* \param temperature the temperature [K]
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* \param pg the gas phase pressure [Pa]
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*/
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template <class Evaluation>
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static Evaluation computeXi_(const Evaluation& temperature, const Evaluation& pg)
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{
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static const Scalar c[4] =
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{ 3.36389723E-4, -1.98298980E-5, 2.12220830E-3, -5.24873303E-3 };
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Evaluation pg_bar = pg / 1.0E5; /* conversion from Pa to bar */
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return c[0] + c[1]*temperature + c[2]*pg_bar/temperature + c[3]*pg_bar/(630.0 - temperature);
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}
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/*!
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* \brief Returns the equilibrium constant for CO2, which is needed for the
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* calculation of the mutual solubility in the water-CO2 system
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* Given in Spycher, Pruess and Ennis-King (2003)
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* \param temperature the temperature [K]
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*/
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template <class Evaluation>
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static Evaluation equilibriumConstantCO2_(const Evaluation& temperature)
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{
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Evaluation temperatureCelcius = temperature - 273.15;
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static const Scalar c[3] = { 1.189, 1.304e-2, -5.446e-5 };
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Evaluation logk0_CO2 = c[0] + temperatureCelcius*(c[1] + temperatureCelcius*c[2]);
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Evaluation k0_CO2 = pow(10.0, logk0_CO2);
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return k0_CO2;
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}
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/*!
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* \brief Returns the equilibrium constant for H2O, which is needed for the
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* calculation of the mutual solubility in the water-CO2 system
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* Given in Spycher, Pruess and Ennis-King (2003)
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* \param temperature the temperature [K]
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*/
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template <class Evaluation>
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static Evaluation equilibriumConstantH2O_(const Evaluation& temperature)
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{
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Evaluation temperatureCelcius = temperature - 273.15;
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static const Scalar c[4] = { -2.209, 3.097e-2, -1.098e-4, 2.048e-7 };
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Evaluation logk0_H2O =
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c[0] + temperatureCelcius*(c[1] + temperatureCelcius*(c[2] + temperatureCelcius*c[3]));
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return pow(10.0, logk0_H2O);
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}
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};
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} // namespace BinaryCoeff
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} // namespace Opm
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#endif
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