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H2.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_H2_HPP
#define OPM_H2_HPP
#include <opm/material/IdealGas.hpp>
#include <opm/material/components/Component.hpp>
#include <opm/material/common/UniformTabulated2DFunction.hpp>
#include <opm/material/densead/Math.hpp>
#include <cmath>
namespace Opm {
template <class Scalar>
class H2 : public Component<Scalar, H2<Scalar> >
{
using IdealGas = Opm::IdealGas<Scalar>;
static const UniformTabulated2DFunction<double>& tabulatedEnthalpy;
static const UniformTabulated2DFunction<double>& tabulatedDensity;
public:
// For H2Tables class
static const Scalar brineSalinity;
static std::string name()
{ return "H2"; }
static constexpr Scalar molarMass()
{ return 2.01588e-3; }
static Scalar criticalTemperature()
{ return 33.145; /* [K] */ }
static Scalar criticalPressure()
{ return 1.2964e6; /* [N/m^2] */ }
static Scalar criticalDensity()
{ return 15.508e-3; /* [mol/cm^3] */ }
static Scalar tripleTemperature()
{ return 13.957; /* [K] */ }
static Scalar triplePressure()
{ return 0.00736e6; /* [N/m^2] */ }
static Scalar tripleDensity()
{ return 38.2e-3; /* [mol/cm^3] */ }
static Scalar criticalVolume() {return 6.45e-2; }
static Scalar acentricFactor() { return -0.22; }
template <class Evaluation>
static Evaluation vaporPressure(Evaluation temperature)
{
if (temperature > criticalTemperature())
return criticalPressure();
if (temperature < tripleTemperature())
return 0; // H2 is solid: We don't take sublimation into
// account
// Intermediate calculations involving temperature
Evaluation sigma = 1 - temperature/criticalTemperature();
Evaluation T_recp = criticalTemperature() / temperature;
// Parameters for normal hydrogen in Table 8
static const Scalar N[4] = {-4.89789, 0.988558, 0.349689, 0.499356};
static const Scalar k[4] = {1.0, 1.5, 2.0, 2.85};
// Eq. (33)
Evaluation s = 0.0; // sum calculation
for (int i = 0; i < 4; ++i) {
s += N[i] * pow(sigma, k[i]);
}
Evaluation lnPsigmaPc = T_recp * s;
return exp(lnPsigmaPc) * criticalPressure();
}
template <class Evaluation>
static Evaluation gasDensity(Evaluation temperature, Evaluation pressure, bool extrapolate = false)
{
return tabulatedDensity.eval(temperature, pressure, extrapolate);
}
template <class Evaluation>
static Evaluation gasMolarDensity(Evaluation temperature, Evaluation pressure, bool extrapolate = false)
{ return gasDensity(temperature, pressure, extrapolate) / molarMass(); }
static constexpr bool gasIsCompressible()
{ return true; }
static constexpr bool gasIsIdeal()
{ return false; }
template <class Evaluation>
static Evaluation gasPressure(Evaluation temperature, Evaluation density)
{
// Eq. (56) in Span et al. (2000)
Scalar R = IdealGas::R;
Evaluation rho_red = density / (molarMass() * criticalDensity() * 1e6);
Evaluation T_red = H2::criticalTemperature() / temperature;
return rho_red * criticalDensity() * R * temperature
* (1 + rho_red * derivResHelmholtzWrtRedRho(T_red, rho_red));
}
template <class Evaluation>
static Evaluation gasInternalEnergy(const Evaluation& temperature,
const Evaluation& pressure,
bool extrapolate = false)
{
const Evaluation h = gasEnthalpy(temperature, pressure, extrapolate);
const Evaluation rho = gasDensity(temperature, pressure, extrapolate);
return h - (pressure / rho);
}
template <class Evaluation>
static const Evaluation gasEnthalpy(Evaluation temperature,
Evaluation pressure,
bool extrapolate = false)
{
return tabulatedEnthalpy.eval(temperature, pressure, extrapolate);
}
template <class Evaluation>
static Evaluation gasViscosity(const Evaluation& temperature,
const Evaluation& pressure,
bool extrapolate = false)
{
// Some needed parameters and variables
const Scalar M = molarMass() * 1e3; // g/mol
const Scalar epsilon_div_kb = 30.41;
const Scalar sigma = 0.297; // nm
const Scalar Na = 6.022137e23; // Avogadro's number
Evaluation T_star = temperature / epsilon_div_kb;
Evaluation ln_T_star = log(T_star);
Evaluation T_r = temperature / criticalTemperature();
Evaluation rho = gasDensity(temperature, pressure, extrapolate);
Evaluation rho_r = rho / 90.909090909; // see corrections
//
// Eta_0 terms (zero-density viscocity)
//
// Parameters in Table 2 for Eq. (4)
static constexpr Scalar a[5] =
{2.0963e-1, -4.55274e-1, 1.43602e-1, -3.35325e-2, 2.76981e-3};
// Eq. (4)
Evaluation ln_S_star = 0.0;
for (int i = 0; i < 5; ++i) {
ln_S_star += a[i] * pow(ln_T_star, i);
}
// Eq. (3)
Evaluation eta_0 = 0.021357 * sqrt(M * temperature) / (sigma * sigma * exp(ln_S_star));
//
// Eta_1 terms (excess contribution)
//
//
// Parameters in Table 3 for Eq. (7)
static constexpr Scalar b[7] =
{-0.187, 2.4871, 3.7151, -11.0972, 9.0965, -3.8292, 0.5166};
// Eq. (7) with corrections
Evaluation B_star = 0.0;
for (int i = 0; i < 7; ++i) {
B_star += b[i] * pow(T_star, -i);
}
// Eq. (9) (eta_1 part) using Eq. (5-7) with corrections and sigma in m (instead of nm). Note that Na * sigma_m
// ^ 3 have unit [m3/mol], so we need to multiply with molar density (= rho / molarMass) and not mass density in
// Eq. (9)
const Scalar sigma_m = sigma * 1e-9;
Evaluation eta_1 = B_star * Na * sigma_m * sigma_m * sigma_m * eta_0 * rho / M;
//
// delta eta_h terms (higher-order effects)
//
// Parameters in Table 4 for Eq. (9)
static constexpr Scalar c[6] =
{6.43449673, 4.56334068e-2, 2.32797868e-1, 9.58326120e-1, 1.27941189e-1, 3.63576595e-1};
// delta eta_h terms in Eq. (9)
Evaluation delta_eta_h = c[0] * rho_r * rho_r * exp(c[1] * T_r + c[2] / T_r +
(c[3] * rho_r * rho_r) / (c[4] + T_r) + c[5] * pow(rho_r, 6));
// return all terms in Eq. (9) converted from muPa*s to Pa*s
return (eta_0 + eta_1 + delta_eta_h) * 1e-6;
}
template <class Evaluation>
static const Evaluation gasHeatCapacity(Evaluation temperature,
Evaluation pressure)
{
// Reduced variables
Evaluation rho_red = reducedMolarDensity(temperature, pressure);
Evaluation T_red = criticalTemperature() / temperature;
// Need Eq. (62) in Span et al. (2000)
Evaluation cv = gasIsochoricHeatCapacity(temperature, pressure); // [J/(kg*K)]
// Some intermediate calculations
Evaluation numerator = pow(1 + rho_red * derivResHelmholtzWrtRedRho(T_red, rho_red)
- rho_red * T_red * secDerivResHelmholtzWrtRecipRedTempAndRedRho(T_red, rho_red), 2);
Evaluation denominator = 1 + 2 * rho_red * derivResHelmholtzWrtRedRho(T_red, rho_red)
+ pow(rho_red, 2) * secDerivResHelmholtzWrtRedRho(T_red, rho_red);
// Eq. (63) in Span et al. (2000).
Scalar R = IdealGas::R;
Evaluation cp = cv + R * (numerator / denominator) / molarMass(); // divide by M to get [J/(kg*K)]
// Return
return cp;
}
template <class Evaluation>
static const Evaluation gasIsochoricHeatCapacity(Evaluation temperature,
Evaluation pressure)
{
// Reduced variables
Evaluation rho_red = reducedMolarDensity(temperature, pressure);
Evaluation T_red = criticalTemperature() / temperature;
// Eq. (62) in Span et al. (2000)
Scalar R = IdealGas::R;
Evaluation cv = R * (-pow(T_red, 2) * (secDerivIdealHelmholtzWrtRecipRedTemp(T_red)
+ secDerivResHelmholtzWrtRecipRedTemp(T_red, rho_red))); // [J/(mol*K)]
return cv / molarMass();
}
template <class Evaluation>
static Evaluation reducedMolarDensity(const Evaluation& temperature,
const Evaluation& pg,
bool extrapolate = false)
{
return gasDensity(temperature, pg, extrapolate) / (molarMass() * criticalDensity() * 1e6);
}
template <class Evaluation>
static Evaluation idealGasPartHelmholtz(const Evaluation& T_red, const Evaluation& rho_red)
{
// Eq. (31), which can be compared with Eq. (53) in Span et al. (2000)
// Terms not in sum
Evaluation s1 = log(rho_red) + 1.5*log(T_red) + a_[0] + a_[1] * T_red;
// Sum term
Evaluation s2 = 0.0;
for (int i = 2; i < 7; ++i) {
s1 += a_[i] * log(1 - exp(b_[i-2] * T_red));
}
// Return total
Evaluation s = s1 + s2;
return s;
}
template <class Evaluation>
static Evaluation derivIdealHelmholtzWrtRecipRedTemp(const Evaluation& T_red)
{
// Derivative of Eq. (31) wrt. reciprocal reduced temperature, which can be compared with Eq. (79) in Span et
// al. (2000)
// Terms not in sum
Evaluation s1 = (1.5 / T_red) + a_[1];
// Sum term
Evaluation s2 = 0.0;
for (int i = 2; i < 7; ++i) {
s2 += (-a_[i] * b_[i-2] * exp(b_[i-2] * T_red)) / (1 - exp(b_[i-2] * T_red));
}
// Return total
Evaluation s = s1 + s2;
return s;
}
template <class Evaluation>
static Evaluation secDerivIdealHelmholtzWrtRecipRedTemp(const Evaluation& T_red)
{
// Second derivative of Eq. (31) wrt. reciprocal reduced temperature, which can be compared with Eq. (80) in
// Span et al. (2000)
// Sum term
Evaluation s1 = 0.0;
for (int i = 2; i < 7; ++i) {
s1 += (-a_[i] * pow(b_[i-2], 2) * exp(b_[i-2] * T_red)) / pow(1 - exp(b_[i-2] * T_red), 2);
}
// Return total
Evaluation s = (-1.5 / pow(T_red, 2)) + s1;
return s;
}
template <class Evaluation>
static Evaluation residualPartHelmholtz(const Evaluation& T_red, const Evaluation& rho_red)
{
// Eq. (32), which can be compared with Eq. (55) in Span et al. (2000)
// First sum term
Evaluation s1 = 0.0;
for (int i = 0; i < 7; ++i) {
s1 += N_[i] * pow(rho_red, d_[i]) * pow(T_red, t_[i]);
}
// Second sum term
Evaluation s2 = 0.0;
for (int i = 7; i < 9; ++i) {
s2 += N_[i] * pow(T_red, t_[i]) * pow(rho_red, d_[i]) * exp(-pow(rho_red, p_[i-7]));
}
// Third, and last, sum term
Evaluation s3 = 0.0;
for (int i = 9; i < 14; ++i) {
s3 += N_[i] * pow(T_red, t_[i]) * pow(rho_red, d_[i]) *
exp(phi_[i-9] * pow(rho_red - D_[i-9], 2) + beta_[i-9] * pow(T_red - gamma_[i-9], 2));
}
// Return total sum
Evaluation s = s1 + s2 + s3;
return s;
}
template <class Evaluation>
static Evaluation derivResHelmholtzWrtRedRho(const Evaluation& T_red, const Evaluation& rho_red)
{
// Derivative of Eq. (32) wrt to reduced density, which can be compared with Eq. (81) in Span et al. (2000)
// First sum term
Evaluation s1 = 0.0;
for (int i = 0; i < 7; ++i) {
s1 += d_[i] * N_[i] * pow(rho_red, d_[i]-1) * pow(T_red, t_[i]);
}
// Second sum term
Evaluation s2 = 0.0;
for (int i = 7; i < 9; ++i) {
s2 += N_[i] * pow(T_red, t_[i]) * pow(rho_red, d_[i]-1) * exp(-pow(rho_red, p_[i-7])) *
(d_[i] - p_[i-7]*pow(rho_red, p_[i-7]));
}
// Third, and last, sum term
Evaluation s3 = 0.0;
for (int i = 9; i < 14; ++i) {
s3 += N_[i] * pow(T_red, t_[i]) * pow(rho_red, d_[i]-1) *
exp(phi_[i-9] * pow(rho_red - D_[i-9], 2) + beta_[i-9] * pow(T_red - gamma_[i-9], 2)) *
(d_[i] + 2 * phi_[i-9] * rho_red * (rho_red - D_[i-9]));
}
// Return total sum
Evaluation s = s1 + s2 + s3;
return s;
}
template <class Evaluation>
static Evaluation secDerivResHelmholtzWrtRedRho(const Evaluation& T_red, const Evaluation& rho_red)
{
// Second derivative of Eq. (32) wrt to reduced density, which can be compared with Eq. (82) in Span et al.
// (2000)
// First sum term
Evaluation s1 = 0.0;
for (int i = 0; i < 7; ++i) {
s1 += d_[i] * (d_[i] - 1) * N_[i] * pow(rho_red, d_[i]-2) * pow(T_red, t_[i]);
}
// Second sum term
Evaluation s2 = 0.0;
for (int i = 7; i < 9; ++i) {
s2 += N_[i] * pow(T_red, t_[i]) * pow(rho_red, d_[i]-2) * exp(-pow(rho_red, p_[i-7])) *
((d_[i] - p_[i-7] * pow(rho_red, p_[i-7])) * (d_[i] - p_[i-7] * pow(rho_red, p_[i-7]) - 1.0)
- pow(p_[i-7], 2) * pow(rho_red, p_[i-7]));
}
// Third, and last, sum term
Evaluation s3 = 0.0;
for (int i = 9; i < 14; ++i) {
s3 += N_[i] * pow(T_red, t_[i]) * pow(rho_red, d_[i]-2) *
exp(phi_[i-9] * pow(rho_red - D_[i-9], 2) + beta_[i-9] * pow(T_red - gamma_[i-9], 2)) *
(pow(d_[i] + 2 * phi_[i-9] * rho_red * (rho_red - D_[i-9]), 2)
- d_[i] + 2 * phi_[i-9] * pow(rho_red, 2));
}
// Return total sum
Evaluation s = s1 + s2 + s3;
return s;
}
template <class Evaluation>
static Evaluation derivResHelmholtzWrtRecipRedTemp(const Evaluation& T_red, const Evaluation& rho_red)
{
// Derivative of Eq. (32) wrt to reciprocal reduced temperature, which can be compared with Eq. (84) in Span et
// al. (2000).
// First sum term
Evaluation s1 = 0.0;
for (int i = 0; i < 7; ++i) {
s1 += t_[i] * N_[i] * pow(rho_red, d_[i]) * pow(T_red, t_[i]-1);
}
// Second sum term
Evaluation s2 = 0.0;
for (int i = 7; i < 9; ++i) {
s2 += t_[i] * N_[i] * pow(T_red, t_[i]-1) * pow(rho_red, d_[i]) * exp(-pow(rho_red, p_[i-7]));
}
// Third, and last, sum term
Evaluation s3 = 0.0;
for (int i = 9; i < 14; ++i) {
s3 += N_[i] * pow(T_red, t_[i]-1) * pow(rho_red, d_[i]) *
exp(phi_[i-9] * pow(rho_red - D_[i-9], 2) + beta_[i-9] * pow(T_red - gamma_[i-9], 2)) *
(t_[i] + 2 * beta_[i-9] * T_red * (T_red - gamma_[i-9]));
}
// Return total sum
Evaluation s = s1 + s2 + s3;
return s;
}
template <class Evaluation>
static Evaluation secDerivResHelmholtzWrtRecipRedTemp(const Evaluation& T_red, const Evaluation& rho_red)
{
// Second derivative of Eq. (32) wrt to reciprocal reduced temperature, which can be compared with Eq. (85) in
// Span et al. (2000).
// First sum term
Evaluation s1 = 0.0;
for (int i = 0; i < 7; ++i) {
s1 += t_[i] * (t_[i] - 1) * N_[i] * pow(rho_red, d_[i]) * pow(T_red, t_[i]-2);
}
// Second sum term
Evaluation s2 = 0.0;
for (int i = 7; i < 9; ++i) {
s2 += t_[i] * (t_[i] - 1) * N_[i] * pow(T_red, t_[i]-2) * pow(rho_red, d_[i]) * exp(-pow(rho_red, p_[i-7]));
}
// Third, and last, sum term
Evaluation s3 = 0.0;
for (int i = 9; i < 14; ++i) {
s3 += N_[i] * pow(T_red, t_[i]-2) * pow(rho_red, d_[i]) *
exp(phi_[i-9] * pow(rho_red - D_[i-9], 2) + beta_[i-9] * pow(T_red - gamma_[i-9], 2)) *
(pow(t_[i] + 2 * beta_[i-9] * T_red * (T_red - gamma_[i-9]), 2)
- t_[i] + 2 * beta_[i-9] * pow(T_red, 2));
}
// Return total sum
Evaluation s = s1 + s2 + s3;
return s;
}
template <class Evaluation>
static Evaluation secDerivResHelmholtzWrtRecipRedTempAndRedRho(const Evaluation& T_red, const Evaluation& rho_red)
{
// Second derivative of Eq. (32) wrt to reciprocal reduced temperature and reduced density, which can be
// compared with Eq. (86) in Span et al. (2000).
// First sum term
Evaluation s1 = 0.0;
for (int i = 0; i < 7; ++i) {
s1 += t_[i] * d_[i] * N_[i] * pow(rho_red, d_[i]-1) * pow(T_red, t_[i]-1);
}
// Second sum term
Evaluation s2 = 0.0;
for (int i = 7; i < 9; ++i) {
s2 += t_[i] * N_[i] * pow(T_red, t_[i]-1) * pow(rho_red, d_[i]-1) * exp(-pow(rho_red, p_[i-7]))
* (d_[i] - p_[i-7] * pow(rho_red, p_[i-7]));
}
// Third, and last, sum term
Evaluation s3 = 0.0;
for (int i = 9; i < 14; ++i) {
s3 += N_[i] * pow(T_red, t_[i]-1) * pow(rho_red, d_[i]-1) *
exp(phi_[i-9] * pow(rho_red - D_[i-9], 2) + beta_[i-9] * pow(T_red - gamma_[i-9], 2)) *
(t_[i] + 2 * beta_[i-9] * T_red * (T_red - gamma_[i-9]))
* (d_[i] + 2 * phi_[i-9] * rho_red * (rho_red - D_[i-9]));
}
// Return total sum
Evaluation s = s1 + s2 + s3;
return s;
}
private:
// Parameter values need in the ideal-gas contribution to the reduced Helmholtz free energy given in Table 4
static constexpr Scalar a_[7] = {-1.4579856475, 1.888076782, 1.616, -0.4117, -0.792, 0.758, 1.217};
static constexpr Scalar b_[5] = {-16.0205159149, -22.6580178006, -60.0090511389, -74.9434303817, -206.9392065168};
// Parameter values needed in the residual contribution to the reduced Helmholtz free energy given in Table 5.
static constexpr Scalar N_[14] = {-6.93643, 0.01, 2.1101, 4.52059, 0.732564, -1.34086, 0.130985, -0.777414,
0.351944, -0.0211716, 0.0226312, 0.032187, -0.0231752, 0.0557346};
static constexpr Scalar t_[14] = {0.6844, 1.0, 0.989, 0.489, 0.803, 1.1444, 1.409, 1.754, 1.311, 4.187, 5.646,
0.791, 7.249, 2.986};
static constexpr Scalar d_[14] = {1, 4, 1, 1, 2, 2, 3, 1, 3, 2, 1, 3, 1, 1};
static constexpr Scalar p_[2] = {1, 1};
static constexpr Scalar phi_[5] = {-1.685, -0.489, -0.103, -2.506, -1.607};
static constexpr Scalar beta_[5] = {-0.1710, -0.2245, -0.1304, -0.2785, -0.3967};
static constexpr Scalar gamma_[5] = {0.7164, 1.3444, 1.4517, 0.7204, 1.5445};
static constexpr Scalar D_[5] = {1.506, 0.156, 1.736, 0.670, 1.662};
#if 0
template <class Evaluation>
static Evaluation rootFindingObj_(const Evaluation& rho_red, const Evaluation& temperature, const Evaluation& pg)
{
// Temporary calculations
Evaluation T_red = criticalTemperature() / temperature; // reciprocal reduced temp.
Evaluation p_MPa = pg / 1.0e6; // Pa --> MPa
Scalar R = IdealGas::R;
Evaluation rho_cRT = criticalDensity() * R * temperature;
// Eq. (56) in Span et al. (2000)
Evaluation dResHelm_dRedRho = derivResHelmholtzWrtRedRho(T_red, rho_red);
Evaluation obj = rho_red * rho_cRT * (1 + rho_red * dResHelm_dRedRho) - p_MPa;
return obj;
}
#endif
};
} // end namespace Opm
#endif
Component.hpp
Abstract base class of a pure chemical species.
IdealGas.hpp
Relations valid for an ideal gas.
Math.hpp
A number of commonly used algebraic functions for the localized OPM automatic differentiation (AD) fr...
UniformTabulated2DFunction.hpp
Implements a scalar function that depends on two variables and which is sampled on an uniform X-Y gri...
Opm::Component
Abstract base class of a pure chemical species.
Definition Component.hpp:44
Opm::H2
Properties of pure molecular hydrogen .
Definition H2.hpp:58
Opm::H2::secDerivResHelmholtzWrtRedRho
static Evaluation secDerivResHelmholtzWrtRedRho(const Evaluation &T_red, const Evaluation &rho_red)
Second derivative of the residual part of Helmholtz energy wrt.
Definition H2.hpp:534
Opm::H2::name
static std::string name()
A human readable name for the .
Definition H2.hpp:71
Opm::H2::secDerivResHelmholtzWrtRecipRedTempAndRedRho
static Evaluation secDerivResHelmholtzWrtRecipRedTempAndRedRho(const Evaluation &T_red, const Evaluation &rho_red)
Second derivative of the residual part of Helmholtz energy first wrt.
Definition H2.hpp:647
Opm::H2::vaporPressure
static Evaluation vaporPressure(Evaluation temperature)
The vapor pressure in of pure molecular hydrogen at a given temperature.
Definition H2.hpp:134
Opm::H2::residualPartHelmholtz
static Evaluation residualPartHelmholtz(const Evaluation &T_red, const Evaluation &rho_red)
The residual part of Helmholtz energy.
Definition H2.hpp:464
Opm::H2::criticalTemperature
static Scalar criticalTemperature()
Returns the critical temperature of molecular hydrogen.
Definition H2.hpp:83
Opm::H2::gasIsIdeal
static constexpr bool gasIsIdeal()
Returns true if the gas phase is assumed to be ideal.
Definition H2.hpp:191
Opm::H2::tripleDensity
static Scalar tripleDensity()
Returns the density of molecular hydrogen's triple point.
Definition H2.hpp:113
Opm::H2::acentricFactor
static Scalar acentricFactor()
Acentric factor of .
Definition H2.hpp:124
Opm::H2::criticalDensity
static Scalar criticalDensity()
Returns the critical density of molecular hydrogen.
Definition H2.hpp:95
Opm::H2::gasIsochoricHeatCapacity
static const Evaluation gasIsochoricHeatCapacity(Evaluation temperature, Evaluation pressure)
Specific isochoric heat capacity of pure hydrogen gas.
Definition H2.hpp:358
Opm::H2::secDerivResHelmholtzWrtRecipRedTemp
static Evaluation secDerivResHelmholtzWrtRecipRedTemp(const Evaluation &T_red, const Evaluation &rho_red)
Second derivative of the residual part of Helmholtz energy wrt.
Definition H2.hpp:609
Opm::H2::criticalPressure
static Scalar criticalPressure()
Returns the critical pressure of molecular hydrogen.
Definition H2.hpp:89
Opm::H2::gasPressure
static Evaluation gasPressure(Evaluation temperature, Evaluation density)
The pressure of gaseous in at a given density and temperature.
Definition H2.hpp:201
Opm::H2::tripleTemperature
static Scalar tripleTemperature()
Returns the temperature at molecular hydrogen's triple point.
Definition H2.hpp:101
Opm::H2::idealGasPartHelmholtz
static Evaluation idealGasPartHelmholtz(const Evaluation &T_red, const Evaluation &rho_red)
The ideal-gas part of Helmholtz energy.
Definition H2.hpp:394
Opm::H2::reducedMolarDensity
static Evaluation reducedMolarDensity(const Evaluation &temperature, const Evaluation &pg, bool extrapolate=false)
Calculate reduced density (rho/rho_crit) from pressure and temperature.
Definition H2.hpp:380
Opm::H2::derivResHelmholtzWrtRedRho
static Evaluation derivResHelmholtzWrtRedRho(const Evaluation &T_red, const Evaluation &rho_red)
Derivative of the residual part of Helmholtz energy wrt.
Definition H2.hpp:498
Opm::H2::gasInternalEnergy
static Evaluation gasInternalEnergy(const Evaluation &temperature, const Evaluation &pressure, bool extrapolate=false)
Specific internal energy of H2 [J/kg].
Definition H2.hpp:215
Opm::H2::gasHeatCapacity
static const Evaluation gasHeatCapacity(Evaluation temperature, Evaluation pressure)
Specific isobaric heat capacity of pure hydrogen gas.
Definition H2.hpp:325
Opm::H2::criticalVolume
static Scalar criticalVolume()
Critical volume of [m2/kmol].
Definition H2.hpp:119
Opm::H2::gasViscosity
static Evaluation gasViscosity(const Evaluation &temperature, const Evaluation &pressure, bool extrapolate=false)
The dynamic viscosity of at a given pressure and temperature.
Definition H2.hpp:249
Opm::H2::derivResHelmholtzWrtRecipRedTemp
static Evaluation derivResHelmholtzWrtRecipRedTemp(const Evaluation &T_red, const Evaluation &rho_red)
Derivative of the residual part of Helmholtz energy wrt.
Definition H2.hpp:573
Opm::H2::gasIsCompressible
static constexpr bool gasIsCompressible()
Returns true if the gas phase is assumed to be compressible.
Definition H2.hpp:185
Opm::H2::secDerivIdealHelmholtzWrtRecipRedTemp
static Evaluation secDerivIdealHelmholtzWrtRecipRedTemp(const Evaluation &T_red)
Second derivative of the ideal-gas part of Helmholtz energy wrt to reciprocal reduced temperature.
Definition H2.hpp:442
Opm::H2::molarMass
static constexpr Scalar molarMass()
The molar mass in of molecular hydrogen.
Definition H2.hpp:77
Opm::H2::triplePressure
static Scalar triplePressure()
Returns the pressure of molecular hydrogen's triple point.
Definition H2.hpp:107
Opm::H2::gasDensity
static Evaluation gasDensity(Evaluation temperature, Evaluation pressure, bool extrapolate=false)
The density of at a given pressure and temperature.
Definition H2.hpp:167
Opm::H2::gasMolarDensity
static Evaluation gasMolarDensity(Evaluation temperature, Evaluation pressure, bool extrapolate=false)
The molar density of in , depending on pressure and temperature.
Definition H2.hpp:179
Opm::H2::derivIdealHelmholtzWrtRecipRedTemp
static Evaluation derivIdealHelmholtzWrtRecipRedTemp(const Evaluation &T_red)
Derivative of the ideal-gas part of Helmholtz energy wrt to reciprocal reduced temperature.
Definition H2.hpp:417
Opm::H2::gasEnthalpy
static const Evaluation gasEnthalpy(Evaluation temperature, Evaluation pressure, bool extrapolate=false)
Specific enthalpy of pure hydrogen gas.
Definition H2.hpp:232
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::UniformTabulated2DFunction
Implements a scalar function that depends on two variables and which is sampled on an uniform X-Y gri...
Definition UniformTabulated2DFunction.hpp:52
Opm::UniformTabulated2DFunction::eval
Evaluation eval(const Evaluation &x, const Evaluation &y, bool extrapolate) const
Evaluate the function at a given (x,y) position.
Definition UniformTabulated2DFunction.hpp:196
Opm
This class implements a small container which holds the transmissibility mulitpliers for all the face...
Definition Exceptions.hpp:30