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Brine_CO2.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.
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/>.
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_BINARY_COEFF_BRINE_CO2_HPP
#define OPM_BINARY_COEFF_BRINE_CO2_HPP
#include <opm/material/IdealGas.hpp>
#include <opm/material/common/Valgrind.hpp>
#include <opm/common/TimingMacros.hpp>
#include <array>
namespace Opm {
namespace BinaryCoeff {
template<class Scalar, class H2O, class CO2, bool verbose = true>
class Brine_CO2 {
typedef ::Opm::IdealGas<Scalar> IdealGas;
static const int liquidPhaseIdx = 0; // index of the liquid phase
static const int gasPhaseIdx = 1; // index of the gas phase
public:
template <class Evaluation>
static Evaluation gasDiffCoeff(const Evaluation& temperature, const Evaluation& pressure, bool extrapolate = false)
{
//Diffusion coefficient of water in the CO2 phase
Scalar k = 1.3806504e-23; // Boltzmann constant
Scalar c = 4; // slip parameter, can vary between 4 (slip condition) and 6 (stick condition)
Scalar R_h = 1.72e-10; // hydrodynamic radius of the solute
const Evaluation& mu = CO2::gasViscosity(temperature, pressure, extrapolate); // CO2 viscosity
return k / (c * M_PI * R_h) * (temperature / mu);
}
template <class Evaluation>
static Evaluation liquidDiffCoeff(const Evaluation& /*temperature*/, const Evaluation& /*pressure*/)
{
//Diffusion coefficient of CO2 in the brine phase
return 2e-9;
}
template <class Evaluation>
static void calculateMoleFractions(const Evaluation& temperature,
const Evaluation& pg,
const Evaluation& salinity,
const int knownPhaseIdx,
Evaluation& xlCO2,
Evaluation& ygH2O,
const int& activityModel,
bool extrapolate = false)
{
OPM_TIMEFUNCTION_LOCAL();
// Iterate or not?
bool iterate = false;
if ((activityModel == 1 && salinity > 0.0) || (activityModel == 2 && temperature > 372.15)) {
iterate = true;
}
// If both phases are present the mole fractions in each phase can be calculate with the mutual solubility
// function
if (knownPhaseIdx < 0) {
Evaluation molalityNaCl = massFracToMolality_(salinity); // mass fraction to molality of NaCl
// Duan-Sun model as given in Spycher & Pruess (2005) have a different fugacity coefficient formula and
// activity coefficient definition (not a true activity coefficient but a ratio).
// Technically only valid below T = 100 C, but we use low-temp. parameters and formulas even above 100 C as
// an approximation.
if (activityModel == 3) {
auto [xCO2, yH2O] = mutualSolubilitySpycherPruess2005_(temperature, pg, molalityNaCl, extrapolate);
xlCO2 = xCO2;
ygH2O = yH2O;
}
else {
// Fixed-point iterations to calculate solubility
if (iterate) {
auto [xCO2, yH2O] = fixPointIterSolubility_(temperature, pg, molalityNaCl, activityModel, extrapolate);
xlCO2 = xCO2;
ygH2O = yH2O;
}
// Solve mutual solubility equation with back substitution (no need for iterations)
else {
auto [xCO2, yH2O] = nonIterSolubility_(temperature, pg, molalityNaCl, activityModel, extrapolate);
xlCO2 = xCO2;
ygH2O = yH2O;
}
}
}
// if only liquid phase is present the mole fraction of CO2 in brine is given and
// and the virtual equilibrium mole fraction of water in the non-existing gas phase can be estimated
// with the mutual solubility function
else if (knownPhaseIdx == liquidPhaseIdx && activityModel == 3) {
Evaluation x_NaCl = salinityToMolFrac_(salinity);
const Evaluation& A = computeA_(temperature, pg, Evaluation(0.0), Evaluation(0.0), false, extrapolate, true);
ygH2O = A * (1 - xlCO2 - x_NaCl);
}
// if only gas phase is present the mole fraction of water in the gas phase is given and
// and the virtual equilibrium mole fraction of CO2 in the non-existing liquid phase can be estimated
// with the mutual solubility function
else if (knownPhaseIdx == gasPhaseIdx && activityModel == 3) {
//y_H2o = fluidstate.
Evaluation x_NaCl = salinityToMolFrac_(salinity);
const Evaluation& A = computeA_(temperature, pg, Evaluation(0.0), Evaluation(0.0), false, extrapolate, true);
xlCO2 = 1 - x_NaCl - ygH2O / A;
}
}
template <class Evaluation>
static Evaluation henry(const Evaluation& temperature, bool extrapolate = false)
{ return fugacityCoefficientCO2(temperature, /*pressure=*/1e5, extrapolate)*1e5; }
template <class Evaluation>
static Evaluation fugacityCoefficientCO2(const Evaluation& temperature,
const Evaluation& pg,
const Evaluation& yH2O,
const bool highTemp,
bool extrapolate = false,
bool spycherPruess2005 = false)
{
OPM_TIMEFUNCTION_LOCAL();
Valgrind::CheckDefined(temperature);
Valgrind::CheckDefined(pg);
Evaluation V = 1 / (CO2::gasDensity(temperature, pg, extrapolate) / CO2::molarMass()) * 1.e6; // molar volume in cm^3/mol
Evaluation pg_bar = pg / 1.e5; // gas phase pressure in bar
Scalar R = IdealGas::R * 10.; // ideal gas constant with unit bar cm^3 /(K mol)
// Parameters in Redlich-Kwong equation
Evaluation a_CO2 = aCO2_(temperature, highTemp);
Evaluation a_CO2_H2O = aCO2_H2O_(temperature, yH2O, highTemp);
Evaluation a_mix = aMix_(temperature, yH2O, highTemp);
Scalar b_CO2 = bCO2_(highTemp);
Evaluation b_mix = bMix_(yH2O, highTemp);
Evaluation lnPhiCO2;
if (spycherPruess2005) {
lnPhiCO2 = log(V / (V - b_CO2));
lnPhiCO2 += b_CO2 / (V - b_CO2);
lnPhiCO2 -= 2 * a_CO2 / (R * pow(temperature, 1.5) * b_CO2) * log((V + b_CO2) / V);
lnPhiCO2 +=
a_CO2 * b_CO2
/ (R
* pow(temperature, 1.5)
* b_CO2
* b_CO2)
* (log((V + b_CO2) / V)
- b_CO2 / (V + b_CO2));
lnPhiCO2 -= log(pg_bar * V / (R * temperature));
}
else {
lnPhiCO2 = (b_CO2 / b_mix) * (pg_bar * V / (R * temperature) - 1);
lnPhiCO2 -= log(pg_bar * (V - b_mix) / (R * temperature));
lnPhiCO2 += (2 * (yH2O * a_CO2_H2O + (1 - yH2O) * a_CO2) / a_mix - (b_CO2 / b_mix)) *
a_mix / (b_mix * R * pow(temperature, 1.5)) * log(V / (V + b_mix));
}
return exp(lnPhiCO2); // fugacity coefficient of CO2
}
template <class Evaluation>
static Evaluation fugacityCoefficientH2O(const Evaluation& temperature,
const Evaluation& pg,
const Evaluation& yH2O,
const bool highTemp,
bool extrapolate = false,
bool spycherPruess2005 = false)
{
OPM_TIMEFUNCTION_LOCAL();
Valgrind::CheckDefined(temperature);
Valgrind::CheckDefined(pg);
const Evaluation& V = 1 / (CO2::gasDensity(temperature, pg, extrapolate) / CO2::molarMass()) * 1.e6; // molar volume in cm^3/mol
const Evaluation& pg_bar = pg / 1.e5; // gas phase pressure in bar
Scalar R = IdealGas::R * 10.; // ideal gas constant with unit bar cm^3 /(K mol)
// Mixture parameter of Redlich-Kwong equation
Evaluation a_H2O = aH2O_(temperature, highTemp);
Evaluation a_CO2_H2O = aCO2_H2O_(temperature, yH2O, highTemp);
Evaluation a_mix = aMix_(temperature, yH2O, highTemp);
Scalar b_H2O = bH2O_(highTemp);
Evaluation b_mix = bMix_(yH2O, highTemp);
Evaluation lnPhiH2O;
if (spycherPruess2005) {
lnPhiH2O =
log(V/(V - b_mix))
+ b_H2O/(V - b_mix) - 2*a_CO2_H2O
/ (R*pow(temperature, 1.5)*b_mix)*log((V + b_mix)/V)
+ a_mix*b_H2O/(R*pow(temperature, 1.5)*b_mix*b_mix)
*(log((V + b_mix)/V) - b_mix/(V + b_mix))
- log(pg_bar*V/(R*temperature));
}
else {
lnPhiH2O = (b_H2O / b_mix) * (pg_bar * V / (R * temperature) - 1);
lnPhiH2O -= log(pg_bar * (V - b_mix) / (R * temperature));
lnPhiH2O += (2 * (yH2O * a_H2O + (1 - yH2O) * a_CO2_H2O) / a_mix - (b_H2O / b_mix)) *
a_mix / (b_mix * R * pow(temperature, 1.5)) * log(V / (V + b_mix));
}
return exp(lnPhiH2O); // fugacity coefficient of H2O
}
private:
template <class Evaluation>
static Evaluation aCO2_(const Evaluation& temperature, const bool& highTemp)
{
if (highTemp) {
return 8.008e7 - 4.984e4 * temperature;
}
else {
return 7.54e7 - 4.13e4 * temperature;
}
}
template <class Evaluation>
static Evaluation aH2O_(const Evaluation& temperature, const bool& highTemp)
{
if (highTemp) {
return 1.337e8 - 1.4e4 * temperature;
}
else {
return 0.0;
}
}
template <class Evaluation>
static Evaluation aCO2_H2O_(const Evaluation& temperature, const Evaluation& yH2O, const bool& highTemp)
{
if (highTemp) {
// Pure parameters
Evaluation aCO2 = aCO2_(temperature, highTemp);
Evaluation aH2O = aH2O_(temperature, highTemp);
// Mixture Eq. (A-6)
Evaluation K_CO2_H2O = 0.4228 - 7.422e-4 * temperature;
Evaluation K_H2O_CO2 = 1.427e-2 - 4.037e-4 * temperature;
Evaluation k_CO2_H2O = yH2O * K_H2O_CO2 + (1 - yH2O) * K_CO2_H2O;
// Eq. (A-5)
return sqrt(aCO2 * aH2O) * (1 - k_CO2_H2O);
}
else {
return 7.89e7;
}
}
template <class Evaluation>
static Evaluation aMix_(const Evaluation& temperature, const Evaluation& yH2O, const bool& highTemp)
{
if (highTemp) {
// Parameters
Evaluation aCO2 = aCO2_(temperature, highTemp);
Evaluation aH2O = aH2O_(temperature, highTemp);
Evaluation a_CO2_H2O = aCO2_H2O_(temperature, yH2O, highTemp);
return yH2O * yH2O * aH2O + 2 * yH2O * (1 - yH2O) * a_CO2_H2O + (1 - yH2O) * (1 - yH2O) * aCO2;
}
else {
return aCO2_(temperature, highTemp);
}
}
static Scalar bCO2_(const bool& highTemp)
{
if (highTemp) {
return 28.25;
}
else {
return 27.8;
}
}
static Scalar bH2O_(const bool& highTemp)
{
if (highTemp) {
return 15.7;
}
else {
return 18.18;
}
}
template <class Evaluation>
static Evaluation bMix_(const Evaluation& yH2O, const bool& highTemp)
{
if (highTemp) {
// Parameters
Scalar bCO2 = bCO2_(highTemp);
Scalar bH2O = bH2O_(highTemp);
return yH2O * bH2O + (1 - yH2O) * bCO2;
}
else {
return bCO2_(highTemp);
}
}
template <class Evaluation>
static Evaluation V_avg_CO2_(const Evaluation& temperature, const bool& highTemp)
{
if (highTemp && (temperature > 373.15)) {
return 32.6 + 3.413e-2 * (temperature - 373.15);
}
else {
return 32.6;
}
}
template <class Evaluation>
static Evaluation V_avg_H2O_(const Evaluation& temperature, const bool& highTemp)
{
if (highTemp && (temperature > 373.15)) {
return 18.1 + 3.137e-2 * (temperature - 373.15);
}
else {
return 18.1;
}
}
template <class Evaluation>
static Evaluation AM_(const Evaluation& temperature, const bool& highTemp)
{
if (highTemp && temperature > 373.15) {
Evaluation deltaTk = temperature - 373.15;
return deltaTk * (-3.084e-2 + 1.927e-5 * deltaTk);
}
else {
return 0.0;
}
}
template <class Evaluation>
static Evaluation Pref_(const Evaluation& temperature, const bool& highTemp)
{
if (highTemp && temperature > 373.15) {
const Evaluation& temperatureCelcius = temperature - 273.15;
static const Scalar c[5] = { -1.9906e-1, 2.0471e-3, 1.0152e-4, -1.4234e-6, 1.4168e-8 };
return c[0] + temperatureCelcius * (c[1] + temperatureCelcius * (c[2] +
temperatureCelcius * (c[3] + temperatureCelcius * c[4])));
}
else {
return 1.0;
}
}
template <class Evaluation>
static Evaluation activityCoefficientCO2_(const Evaluation& temperature,
const Evaluation& xCO2,
const bool& highTemp)
{
if (highTemp) {
// Eq. (13)
Evaluation AM = AM_(temperature, highTemp);
Evaluation lnGammaCO2 = 2 * AM * xCO2 * (1 - xCO2) * (1 - xCO2);
return exp(lnGammaCO2);
}
else {
return 1.0;
}
}
template <class Evaluation>
static Evaluation activityCoefficientH2O_(const Evaluation& temperature,
const Evaluation& xCO2,
const bool& highTemp)
{
if (highTemp) {
// Eq. (12)
Evaluation AM = AM_(temperature, highTemp);
Evaluation lnGammaH2O = (1 - 2 * (1 - xCO2)) * AM * xCO2 * xCO2;
return exp(lnGammaH2O);
}
else {
return 1.0;
}
}
template <class Evaluation>
static Evaluation salinityToMolFrac_(const Evaluation& salinity) {
OPM_TIMEFUNCTION_LOCAL();
const Scalar Mw = H2O::molarMass(); /* molecular weight of water [kg/mol] */
const Scalar Ms = 58.44e-3; /* molecular weight of NaCl [kg/mol] */
const Evaluation X_NaCl = salinity;
/* salinity: conversion from mass fraction to mol fraction */
const Evaluation x_NaCl = -Mw * X_NaCl / ((Ms - Mw) * X_NaCl - Ms);
return x_NaCl;
}
#if 0
template <class Evaluation>
static Evaluation moleFracToMolality_(const Evaluation& x_NaCl)
{
// conversion from mol fraction to molality (dissolved CO2 neglected)
return 55.508 * x_NaCl / (1 - x_NaCl);
}
#endif
template <class Evaluation>
static Evaluation massFracToMolality_(const Evaluation& X_NaCl)
{
const Scalar MmNaCl = 58.44e-3;
return X_NaCl / (MmNaCl * (1 - X_NaCl));
}
template <class Evaluation>
static Evaluation molalityToMoleFrac_(const Evaluation& m_NaCl)
{
// conversion from molality to mole fractio (dissolved CO2 neglected)
return m_NaCl / (55.508 + m_NaCl);
}
template <class Evaluation>
static std::pair<Evaluation, Evaluation> fixPointIterSolubility_(const Evaluation& temperature,
const Evaluation& pg,
const Evaluation& m_NaCl,
const int& activityModel,
bool extrapolate = false)
{
OPM_TIMEFUNCTION_LOCAL();
// Start point for fixed-point iterations as recommended below in section 2.2
Evaluation yH2O = H2O::vaporPressure(temperature) / pg; // ideal mixing
Evaluation xCO2 = 0.009; // same as ~0.5 mol/kg
Evaluation gammaNaCl = 1.0; // default salt activity coeff = 1.0
// We can pre-calculate Duan-Sun, Spycher & Pruess (2009) salt activity coeff.
if (m_NaCl > 0.0 && activityModel == 2) {
gammaNaCl = activityCoefficientSalt_(temperature, pg, m_NaCl, Evaluation(0.0), activityModel);
}
// Options
int max_iter = 100;
Scalar tol = 1e-8;
bool highTemp = true;
if (activityModel == 1) {
highTemp = false;
}
const bool iterate = true;
// Fixed-point loop x_i+1 = F(x_i)
for (int i = 0; i < max_iter; ++i) {
// Calculate activity coefficient for Rumpf et al (1994) model
if (m_NaCl > 0.0 && activityModel == 1) {
gammaNaCl = activityCoefficientSalt_(temperature, pg, m_NaCl, xCO2, activityModel);
}
// F(x_i) is the mutual solubilities
auto [xCO2_new, yH2O_new] = mutualSolubility_(temperature, pg, xCO2, yH2O, m_NaCl, gammaNaCl, highTemp,
iterate, extrapolate);
// Check for convergence
if (abs(xCO2_new - xCO2) < tol && abs(yH2O_new - yH2O) < tol) {
xCO2 = xCO2_new;
yH2O = yH2O_new;
break;
}
// Else update mole fractions for next iteration
else {
xCO2 = xCO2_new;
yH2O = yH2O_new;
}
}
return {xCO2, yH2O};
}
template <class Evaluation>
static std::pair<Evaluation, Evaluation> nonIterSolubility_(const Evaluation& temperature,
const Evaluation& pg,
const Evaluation& m_NaCl,
const int& activityModel,
bool extrapolate = false)
{
// Calculate activity coefficient for salt
Evaluation gammaNaCl = 1.0;
if (m_NaCl > 0.0 && activityModel > 0 && activityModel < 3) {
gammaNaCl = activityCoefficientSalt_(temperature, pg, m_NaCl, Evaluation(0.0), activityModel);
}
// Calculate mutual solubility.
// Note that we don't use xCO2 and yH2O input in low-temperature case, so we set them to 0.0
const bool highTemp = false;
const bool iterate = false;
auto [xCO2, yH2O] = mutualSolubility_(temperature, pg, Evaluation(0.0), Evaluation(0.0), m_NaCl, gammaNaCl,
highTemp, iterate, extrapolate);
return {xCO2, yH2O};
}
template <class Evaluation>
static std::pair<Evaluation, Evaluation> mutualSolubility_(const Evaluation& temperature,
const Evaluation& pg,
const Evaluation& xCO2,
const Evaluation& yH2O,
const Evaluation& m_NaCl,
const Evaluation& gammaNaCl,
const bool& highTemp,
const bool& iterate,
bool extrapolate = false)
{
// Calculate A and B (without salt effect); Eqs. (8) and (9)
const Evaluation& A = computeA_(temperature, pg, yH2O, xCO2, highTemp, extrapolate);
Evaluation B = computeB_(temperature, pg, yH2O, xCO2, highTemp, extrapolate);
// Add salt effect to B, Eq. (17)
B /= gammaNaCl;
// Compute yH2O and xCO2, Eqs. (B-7) and (B-2)
Evaluation yH2O_new = (1. - B) * 55.508 / ((1. / A - B) * (2 * m_NaCl + 55.508) + 2 * m_NaCl * B);
Evaluation xCO2_new;
if (iterate) {
xCO2_new = B * (1 - yH2O);
}
else {
xCO2_new = B * (1 - yH2O_new);
}
return {xCO2_new, yH2O_new};
}
template <class Evaluation>
static std::pair<Evaluation, Evaluation> mutualSolubilitySpycherPruess2005_(const Evaluation& temperature,
const Evaluation& pg,
const Evaluation& m_NaCl,
bool extrapolate = false)
{
// Calculate A and B (without salt effect); Eqs. (8) and (9)
const Evaluation& A = computeA_(temperature, pg, Evaluation(0.0), Evaluation(0.0), false, extrapolate, true);
const Evaluation& B = computeB_(temperature, pg, Evaluation(0.0), Evaluation(0.0), false, extrapolate, true);
// Mole fractions and molality in pure water
Evaluation yH2O = (1 - B) / (1. / A - B);
Evaluation xCO2 = B * (1 - yH2O);
// Modifiy mole fractions with Duan-Sun "activity coefficient" if salt is involved
if (m_NaCl > 0.0) {
const Evaluation& gammaNaCl = activityCoefficientSalt_(temperature, pg, m_NaCl, Evaluation(0.0), 3);
// Molality with salt
Evaluation mCO2 = (xCO2 * 55.508) / (1 - xCO2); // pure water
mCO2 /= gammaNaCl;
xCO2 = mCO2 / (m_NaCl + 55.508 + mCO2);
// new yH2O with salt
const Evaluation& xNaCl = molalityToMoleFrac_(m_NaCl);
yH2O = A * (1 - xCO2 - xNaCl);
}
return {xCO2, yH2O};
}
template <class Evaluation>
static Evaluation computeA_(const Evaluation& temperature,
const Evaluation& pg,
const Evaluation& yH2O,
const Evaluation& xCO2,
const bool& highTemp,
bool extrapolate = false,
bool spycherPruess2005 = false)
{
OPM_TIMEFUNCTION_LOCAL();
// Intermediate calculations
const Evaluation& deltaP = pg / 1e5 - Pref_(temperature, highTemp); // pressure range [bar] from pref to pg[bar]
Evaluation v_av_H2O = V_avg_H2O_(temperature, highTemp); // average partial molar volume of H2O [cm^3/mol]
Evaluation k0_H2O = equilibriumConstantH2O_(temperature, highTemp); // equilibrium constant for H2O at 1 bar
Evaluation phi_H2O = fugacityCoefficientH2O(temperature, pg, yH2O, highTemp, extrapolate, spycherPruess2005); // fugacity coefficient of H2O for the water-CO2 system
Evaluation gammaH2O = activityCoefficientH2O_(temperature, xCO2, highTemp);
// In the intermediate temperature range 99-109 C, equilibrium constants and fugacity coeff. are linearly
// weighted
if ( temperature > 372.15 && temperature < 382.15 && !spycherPruess2005) {
const Evaluation weight = (382.15 - temperature) / 10.;
const Evaluation& k0_H2O_low = equilibriumConstantH2O_(temperature, false);
const Evaluation& phi_H2O_low = fugacityCoefficientH2O(temperature, pg, Evaluation(0.0), false, extrapolate);
k0_H2O = k0_H2O * (1 - weight) + k0_H2O_low * weight;
phi_H2O = phi_H2O * (1 - weight) + phi_H2O_low * weight;
}
// Eq. (10)
const Evaluation& pg_bar = pg / 1.e5;
Scalar R = IdealGas::R * 10;
return k0_H2O * gammaH2O / (phi_H2O * pg_bar) * exp(deltaP * v_av_H2O / (R * temperature));
}
template <class Evaluation>
static Evaluation computeB_(const Evaluation& temperature,
const Evaluation& pg,
const Evaluation& yH2O,
const Evaluation& xCO2,
const bool& highTemp,
bool extrapolate = false,
bool spycherPruess2005 = false)
{
OPM_TIMEFUNCTION_LOCAL();
// Intermediate calculations
const Evaluation& deltaP = pg / 1e5 - Pref_(temperature, highTemp); // pressure range [bar] from pref to pg[bar]
Evaluation v_av_CO2 = V_avg_CO2_(temperature, highTemp); // average partial molar volume of CO2 [cm^3/mol]
Evaluation k0_CO2 = equilibriumConstantCO2_(temperature, pg, highTemp, spycherPruess2005); // equilibrium constant for CO2 at 1 bar
Evaluation phi_CO2 = fugacityCoefficientCO2(temperature, pg, yH2O, highTemp, extrapolate, spycherPruess2005); // fugacity coefficient of CO2 for the water-CO2 system
Evaluation gammaCO2 = activityCoefficientCO2_(temperature, xCO2, highTemp);
// In the intermediate temperature range 99-109 C, equilibrium constants and fugacity coeff. are linearly
// weighted
if ( temperature > 372.15 && temperature < 382.15 && !spycherPruess2005) {
const Evaluation weight = (382.15 - temperature) / 10.;
const Evaluation& k0_CO2_low = equilibriumConstantCO2_(temperature, pg, false, spycherPruess2005);
const Evaluation& phi_CO2_low = fugacityCoefficientCO2(temperature, pg, Evaluation(0.0), false, extrapolate);
k0_CO2 = k0_CO2 * (1 - weight) + k0_CO2_low * weight;
phi_CO2 = phi_CO2 * (1 - weight) + phi_CO2_low * weight;
}
// Eq. (11)
const Evaluation& pg_bar = pg / 1.e5;
const Scalar R = IdealGas::R * 10;
return phi_CO2 * pg_bar / (55.508 * k0_CO2 * gammaCO2) * exp(-deltaP * v_av_CO2 / (R * temperature));
}
template <class Evaluation>
static Evaluation activityCoefficientSalt_(const Evaluation& temperature,
const Evaluation& pg,
const Evaluation& m_NaCl,
const Evaluation& xCO2,
const int& activityModel)
{
OPM_TIMEFUNCTION_LOCAL();
// Lambda and xi parameter for either Rumpf et al (1994) (activityModel = 1) or Duan-Sun as modified by Spycher
// & Pruess (2009) (activityModel = 2) or Duan & Sun (2003) as given in Spycher & Pruess (2005) (activityModel =
// 3)
Evaluation lambda;
Evaluation xi;
Evaluation convTerm;
if (activityModel == 1) {
lambda = computeLambdaRumpfetal_(temperature);
xi = -0.0028 * 3.0;
Evaluation m_CO2 = xCO2 * (2 * m_NaCl + 55.508) / (1 - xCO2);
convTerm = (1 + (m_CO2 + 2 * m_NaCl) / 55.508) / (1 + m_CO2 / 55.508);
}
else if (activityModel == 2) {
lambda = computeLambdaSpycherPruess2009_(temperature);
xi = computeXiSpycherPruess2009_(temperature);
convTerm = 1 + 2 * m_NaCl / 55.508;
}
else if (activityModel == 3) {
lambda = computeLambdaDuanSun_(temperature, pg);
xi = computeXiDuanSun_(temperature, pg);
convTerm = 1.0;
}
else {
throw std::runtime_error("Activity model for salt-out effect has not been implemented!");
}
// Eq. (18)
const Evaluation& lnGamma = 2 * lambda * m_NaCl + xi * m_NaCl * m_NaCl;
// Eq. (18), return activity coeff. on mole-fraction scale
return convTerm * exp(lnGamma);
}
template <class Evaluation>
static Evaluation computeLambdaSpycherPruess2009_(const Evaluation& temperature)
{
// Table 1
static const Scalar c[3] = { 2.217e-4, 1.074, 2648. };
// Eq. (19)
return c[0] * temperature + c[1] / temperature + c[2] / (temperature * temperature);
}
template <class Evaluation>
static Evaluation computeXiSpycherPruess2009_(const Evaluation& temperature)
{
// Table 1
static const Scalar c[3] = { 1.3e-5, -20.12, 5259. };
// Eq. (19)
return c[0] * temperature + c[1] / temperature + c[2] / (temperature * temperature);
}
template <class Evaluation>
static Evaluation computeLambdaRumpfetal_(const Evaluation& temperature)
{
// B^(0) below Eq. (A-6)
static const Scalar c[4] = { 0.254, -76.82, -10656, 6312e3 };
return c[0] + c[1] / temperature + c[2] / (temperature * temperature) +
c[3] / (temperature * temperature * temperature);
}
template <class Evaluation>
static Evaluation computeLambdaDuanSun_(const Evaluation& temperature, const Evaluation& pg)
{
static const Scalar c[6] =
{ -0.411370585, 6.07632013E-4, 97.5347708, -0.0237622469, 0.0170656236, 1.41335834E-5 };
Evaluation pg_bar = pg / 1.0E5; /* conversion from Pa to bar */
return c[0] + c[1]*temperature + c[2]/temperature + c[3]*pg_bar/temperature + c[4]*pg_bar/(630.0 - temperature)
+ c[5]*temperature*log(pg_bar);
}
template <class Evaluation>
static Evaluation computeXiDuanSun_(const Evaluation& temperature, const Evaluation& pg)
{
static const Scalar c[4] =
{ 3.36389723E-4, -1.98298980E-5, 2.12220830E-3, -5.24873303E-3 };
Evaluation pg_bar = pg / 1.0E5; /* conversion from Pa to bar */
return c[0] + c[1]*temperature + c[2]*pg_bar/temperature + c[3]*pg_bar/(630.0 - temperature);
}
template <class Evaluation>
static Evaluation equilibriumConstantCO2_(const Evaluation& temperature,
const Evaluation& pg,
const bool& highTemp,
bool spycherPruess2005 = false)
{
OPM_TIMEFUNCTION_LOCAL();
Evaluation temperatureCelcius = temperature - 273.15;
std::array<Scalar, 4> c;
if (highTemp) {
c = { 1.668, 3.992e-3, -1.156e-5, 1.593e-9 };
}
else {
// For temperature below 31 C and pressures above saturation pressure, separate parameters are needed
Evaluation psat = CO2::vaporPressure(temperature);
if (temperatureCelcius < 31 && pg > psat && !spycherPruess2005) {
c = { 1.169, 1.368e-2, -5.38e-5, 0.0 };
}
else {
c = { 1.189, 1.304e-2, -5.446e-5, 0.0 };
}
}
Evaluation logk0_CO2 = c[0] + temperatureCelcius * (c[1] + temperatureCelcius *
(c[2] + temperatureCelcius * c[3]));
Evaluation k0_CO2 = pow(10.0, logk0_CO2);
return k0_CO2;
}
template <class Evaluation>
static Evaluation equilibriumConstantH2O_(const Evaluation& temperature, const bool& highTemp)
{
Evaluation temperatureCelcius = temperature - 273.15;
std::array<Scalar, 5> c;
if (highTemp){
c = { -2.1077, 2.8127e-2, -8.4298e-5, 1.4969e-7, -1.1812e-10 };
}
else {
c = { -2.209, 3.097e-2, -1.098e-4, 2.048e-7, 0.0 };
}
Evaluation logk0_H2O = c[0] + temperatureCelcius * (c[1] + temperatureCelcius * (c[2] +
temperatureCelcius * (c[3] + temperatureCelcius * c[4])));
return pow(10.0, logk0_H2O);
}
};
} // namespace BinaryCoeff
} // namespace Opm
#endif
IdealGas.hpp
Relations valid for an ideal gas.
Valgrind.hpp
Some templates to wrap the valgrind client request macros.
Opm::BinaryCoeff::Brine_CO2
Binary coefficients for brine and CO2.
Definition Brine_CO2.hpp:45
Opm::BinaryCoeff::Brine_CO2::calculateMoleFractions
static void calculateMoleFractions(const Evaluation &temperature, const Evaluation &pg, const Evaluation &salinity, const int knownPhaseIdx, Evaluation &xlCO2, Evaluation &ygH2O, const int &activityModel, bool extrapolate=false)
Returns the mol (!) fraction of CO2 in the liquid phase and the mol_ (!) fraction of H2O in the gas p...
Definition Brine_CO2.hpp:100
Opm::BinaryCoeff::Brine_CO2::fugacityCoefficientH2O
static Evaluation fugacityCoefficientH2O(const Evaluation &temperature, const Evaluation &pg, const Evaluation &yH2O, const bool highTemp, bool extrapolate=false, bool spycherPruess2005=false)
Returns the fugacity coefficient of the H2O component in a water-CO2 mixture.
Definition Brine_CO2.hpp:240
Opm::BinaryCoeff::Brine_CO2::gasDiffCoeff
static Evaluation gasDiffCoeff(const Evaluation &temperature, const Evaluation &pressure, bool extrapolate=false)
Binary diffusion coefficent [m^2/s] of water in the CO2 phase.
Definition Brine_CO2.hpp:59
Opm::BinaryCoeff::Brine_CO2::fugacityCoefficientCO2
static Evaluation fugacityCoefficientCO2(const Evaluation &temperature, const Evaluation &pg, const Evaluation &yH2O, const bool highTemp, bool extrapolate=false, bool spycherPruess2005=false)
Returns the fugacity coefficient of the CO2 component in a water-CO2 mixture.
Definition Brine_CO2.hpp:185
Opm::BinaryCoeff::Brine_CO2::liquidDiffCoeff
static Evaluation liquidDiffCoeff(const Evaluation &, const Evaluation &)
Binary diffusion coefficent [m^2/s] of CO2 in the brine phase.
Definition Brine_CO2.hpp:76
Opm::BinaryCoeff::Brine_CO2::henry
static Evaluation henry(const Evaluation &temperature, bool extrapolate=false)
Henry coefficent for CO2 in brine.
Definition Brine_CO2.hpp:173
Opm::CO2::gasViscosity
static Evaluation gasViscosity(Evaluation temperature, const Evaluation &pressure, bool extrapolate=false)
The dynamic viscosity [Pa s] of CO2.
Definition CO2.hpp:208
Opm::CO2::vaporPressure
static Evaluation vaporPressure(const Evaluation &T)
Returns the pressure [Pa] at CO2's triple point.
Definition CO2.hpp:135
Opm::CO2::molarMass
static Scalar molarMass()
The mass in [kg] of one mole of CO2.
Definition CO2.hpp:71
Opm::CO2::gasDensity
static Evaluation gasDensity(const Evaluation &temperature, const Evaluation &pressure, bool extrapolate=false)
The density of CO2 at a given pressure and temperature [kg/m^3].
Definition CO2.hpp:194
Opm::H2O::vaporPressure
static Evaluation vaporPressure(Evaluation temperature)
The vapor pressure in of pure water at a given temperature.
Definition H2O.hpp:143
Opm::H2O::molarMass
static const Scalar molarMass()
The molar mass in of water.
Definition H2O.hpp:85
Opm::IdealGas
Relations valid for an ideal gas.
Definition IdealGas.hpp:38
Opm::IdealGas::R
static const Scalar R
The ideal gas constant .
Definition IdealGas.hpp:41
Opm
This class implements a small container which holds the transmissibility mulitpliers for all the face...
Definition Exceptions.hpp:30