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H2O.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_H2O_HPP
#define OPM_H2O_HPP
#include "iapws/Common.hpp"
#include "iapws/Region1.hpp"
#include "iapws/Region2.hpp"
#include "iapws/Region4.hpp"
#include "Component.hpp"
#include <opm/common/Exceptions.hpp>
#include <opm/material/IdealGas.hpp>
#include <opm/material/common/Valgrind.hpp>
#include <opm/material/common/quad.hpp>
#include <opm/material/densead/Evaluation.hpp>
#include <cmath>
#include <cassert>
namespace Opm {
template <class Scalar>
class H2O : public Component<Scalar, H2O<Scalar> >
{
typedef IAPWS::Common<Scalar> Common;
typedef IAPWS::Region1<Scalar> Region1;
typedef IAPWS::Region2<Scalar> Region2;
typedef IAPWS::Region4<Scalar> Region4;
static const Scalar Rs; // specific gas constant of water
public:
using Component<Scalar, H2O<Scalar>>::isTabulated;
static std::string_view name()
{ return "H2O"; }
static const Scalar molarMass()
{ return Common::molarMass; }
static const Scalar acentricFactor()
{ return Common::acentricFactor; }
static const Scalar criticalTemperature()
{ return Common::criticalTemperature; }
static const Scalar criticalPressure()
{ return Common::criticalPressure; }
static const Scalar criticalVolume()
{ return Common::criticalVolume; }
static const Scalar criticalMolarVolume()
{ return Common::criticalMolarVolume; }
static const Scalar tripleTemperature()
{ return Common::tripleTemperature; }
static const Scalar triplePressure()
{ return Common::triplePressure; }
template <class Evaluation>
static Evaluation vaporPressure(Evaluation temperature)
{
if (temperature > criticalTemperature())
temperature = criticalTemperature();
if (temperature < tripleTemperature())
temperature = tripleTemperature();
return Region4::saturationPressure(temperature);
}
template <class Evaluation>
static Evaluation vaporTemperature(const Evaluation& pressure)
{
if (pressure > criticalPressure())
pressure = criticalPressure();
if (pressure < triplePressure())
pressure = triplePressure();
return Region4::vaporTemperature(pressure);
}
template <class Evaluation>
static Evaluation gasEnthalpy(const Evaluation& temperature,
const Evaluation& pressure)
{
if (!Region2::isValid(temperature, pressure))
{
throw NumericalProblem(domainError("Enthalphy of steam",
temperature,
pressure));
}
// regularization
if (pressure < triplePressure() - 100) {
// We assume an ideal gas for low pressures to avoid the
// 0/0 for the gas enthalpy at very low pressures. The
// enthalpy of an ideal gas does not exhibit any
// dependence on pressure, so we can just return the
// specific enthalpy at the point of regularization, i.e.
// the triple pressure - 100Pa
return enthalpyRegion2_<Evaluation>(temperature, triplePressure() - 100);
}
Evaluation pv = vaporPressure(temperature);
if (pressure > pv) {
// the pressure is too high, in this case we use the slope
// of the enthalpy at the vapor pressure to regularize
Evaluation dh_dp =
Rs*temperature*
Region2::tau(temperature)*
Region2::dpi_dp(pv)*
Region2::ddgamma_dtaudpi(temperature, pv);
return
enthalpyRegion2_(temperature, pv) +
(pressure - pv)*dh_dp;
};
return enthalpyRegion2_(temperature, pressure);
}
template <class Evaluation>
static Evaluation liquidEnthalpy(const Evaluation& temperature,
const Evaluation& pressure)
{
if (!Region1::isValid(temperature, pressure))
{
throw NumericalProblem(domainError("Enthalphy of water",
temperature,
pressure));
}
// regularization
const Evaluation& pv = vaporPressure(temperature);
if (pressure < pv) {
// the pressure is too low, in this case we use the slope
// of the enthalpy at the vapor pressure to regularize
const Evaluation& dh_dp =
Rs * temperature*
Region1::tau(temperature)*
Region1::dpi_dp(pv)*
Region1::ddgamma_dtaudpi(temperature, pv);
return
enthalpyRegion1_(temperature, pv) +
(pressure - pv)*dh_dp;
};
return enthalpyRegion1_(temperature, pressure);
}
template <class Evaluation>
static Evaluation gasHeatCapacity(const Evaluation& temperature,
const Evaluation& pressure)
{
if (!Region2::isValid(temperature, pressure))
{
throw NumericalProblem(domainError("Heat capacity of steam",
temperature,
pressure));
}
// regularization
if (pressure < triplePressure() - 100)
return heatCap_p_Region2_(temperature, Evaluation(triplePressure() - 100));
const Evaluation& pv = vaporPressure(temperature);
if (pressure > pv)
// the pressure is too high, in this case we use the heat
// cap at the vapor pressure to regularize
return heatCap_p_Region2_(temperature, pv);
return heatCap_p_Region2_(temperature, pressure);
}
template <class Evaluation>
static Evaluation liquidHeatCapacity(const Evaluation& temperature,
const Evaluation& pressure)
{
if (!Region1::isValid(temperature, pressure))
{
throw NumericalProblem(domainError("Heat capacity of water",
temperature,
pressure));
}
// regularization
const Evaluation& pv = vaporPressure(temperature);
if (pressure < pv) {
// the pressure is too low, in this case we use the heat capacity at the
// vapor pressure to regularize
return heatCap_p_Region1_(temperature, pv);
};
return heatCap_p_Region1_(temperature, pressure);
}
template <class Evaluation>
static Evaluation liquidInternalEnergy(const Evaluation& temperature,
const Evaluation& pressure)
{
if (!Region1::isValid(temperature, pressure))
{
throw NumericalProblem(domainError("Internal energy of water",
temperature,
pressure));
}
// regularization
Scalar pv = vaporPressure<Scalar>(scalarValue(temperature));
if (pressure < pv) {
// the pressure is too low, in this case we use the slope
// of the internal energy at the vapor pressure to
// regularize
/*
// calculate the partial derivative of the internal energy
// to the pressure at the vapor pressure.
Scalar tau = Region1::tau(temperature);
Scalar dgamma_dpi = Region1::dgamma_dpi(temperature, pv);
Scalar ddgamma_dtaudpi = Region1::ddgamma_dtaudpi(temperature, pv);
Scalar ddgamma_ddpi = Region1::ddgamma_ddpi(temperature, pv);
Scalar pi = Region1::pi(pv);
Scalar dpi_dp = Region1::dpi_dp(pv);
Scalar du_dp =
Rs*temperature*
(tau*dpi_dp*ddgamma_dtaudpi + dpi_dp*dpi_dp*dgamma_dpi + pi*dpi_dp*ddgamma_ddpi);
*/
// use a straight line for extrapolation. use forward
// differences to calculate the partial derivative to the
// pressure at the vapor pressure
Scalar eps = 1e-7;
const Evaluation& uv = internalEnergyRegion1_(temperature, Evaluation(pv));
const Evaluation& uvPEps = internalEnergyRegion1_(temperature, Evaluation(pv + eps));
const Evaluation& du_dp = (uvPEps - uv)/eps;
return uv + du_dp*(pressure - pv);
};
return internalEnergyRegion1_(temperature, pressure);
}
template <class Evaluation>
static Evaluation gasInternalEnergy(const Evaluation& temperature, const Evaluation& pressure)
{
if (!Region2::isValid(temperature, pressure))
{
throw NumericalProblem(domainError("Internal energy of steam",
temperature,
pressure));
}
// regularization
if (pressure < triplePressure() - 100) {
// We assume an ideal gas for low pressures to avoid the
// 0/0 for the internal energy of gas at very low
// pressures. The enthalpy of an ideal gas does not
// exhibit any dependence on pressure, so we can just
// return the specific enthalpy at the point of
// regularization, i.e. the triple pressure - 100Pa, and
// subtract the work required to change the volume for an
// ideal gas.
return
enthalpyRegion2_(temperature, Evaluation(triplePressure() - 100.0))
-
Rs*temperature; // = p*v for an ideal gas!
}
Scalar pv = vaporPressure(scalarValue(temperature));
if (pressure > pv) {
// the pressure is too high, in this case we use the slope
// of the internal energy at the vapor pressure to
// regularize
/*
// calculate the partial derivative of the internal energy
// to the pressure at the vapor pressure.
Scalar tau = Region2::tau(temperature);
Scalar dgamma_dpi = Region2::dgamma_dpi(temperature, pv);
Scalar ddgamma_dtaudpi = Region2::ddgamma_dtaudpi(temperature, pv);
Scalar ddgamma_ddpi = Region2::ddgamma_ddpi(temperature, pv);
Scalar pi = Region2::pi(pv);
Scalar dpi_dp = Region2::dpi_dp(pv);
Scalar du_dp =
Rs*temperature*
(tau*dpi_dp*ddgamma_dtaudpi + dpi_dp*dpi_dp*dgamma_dpi + pi*dpi_dp*ddgamma_ddpi);
// use a straight line for extrapolation
Scalar uv = internalEnergyRegion2_(temperature, pv);
return uv + du_dp*(pressure - pv);
*/
// use a straight line for extrapolation. use backward
// differences to calculate the partial derivative to the
// pressure at the vapor pressure
Scalar eps = 1e-7;
const Evaluation& uv = internalEnergyRegion2_(temperature, Evaluation(pv));
const Evaluation& uvMEps = internalEnergyRegion2_(temperature, Evaluation(pv - eps));
const Evaluation& du_dp = (uv - uvMEps)/eps;
return uv + du_dp*(pressure - pv);
};
return internalEnergyRegion2_(temperature, pressure);
}
template <class Evaluation>
static Evaluation liquidHeatCapacityConstVolume(const Evaluation& temperature,
const Evaluation& pressure)
{
if (!Region1::isValid(temperature, pressure))
{
throw NumericalProblem(domainError("Heat capacity of water",
temperature,
pressure));
}
// regularization
Scalar pv = vaporPressure(temperature);
if (pressure < pv) {
// the pressure is too low, in this case we use the heat cap at the vapor pressure to regularize
return heatCap_v_Region1_(temperature, pv);
}
return heatCap_v_Region1_(temperature, pressure);
}
template <class Evaluation>
static Evaluation gasHeatCapacityConstVolume(const Evaluation& temperature, const Evaluation& pressure)
{
if (!Region2::isValid(temperature, pressure))
{
throw NumericalProblem(domainError("Heat capacity of steam",
temperature,
pressure));
}
// regularization
if (pressure < triplePressure() - 100) {
return
heatCap_v_Region2_(temperature, triplePressure() - 100);
}
Scalar pv = vaporPressure(temperature);
if (pressure > pv) {
return heatCap_v_Region2_(temperature, pv);
};
return heatCap_v_Region2_(temperature, pressure);
}
static bool gasIsCompressible()
{ return true; }
static bool liquidIsCompressible()
{ return true; }
template <class Evaluation>
static Evaluation gasDensity(const Evaluation& temperature, const Evaluation& pressure)
{
if (!Region2::isValid(temperature, pressure))
{
throw NumericalProblem(domainError("Density of steam",
temperature,
pressure));
}
// regularization
if (pressure < triplePressure() - 100) {
// We assume an ideal gas for low pressures to avoid the
// 0/0 for the internal energy and enthalpy.
const Evaluation& rho0IAPWS =
1.0/volumeRegion2_(temperature,
Evaluation(triplePressure() - 100));
const Evaluation& rho0Id =
IdealGas<Scalar>::density(Evaluation(molarMass()),
temperature,
Evaluation(triplePressure() - 100));
return
rho0IAPWS/rho0Id
*IdealGas<Scalar>::density(Evaluation(molarMass()),
temperature,
pressure);
}
Evaluation pv = vaporPressure(temperature);
if (pressure > pv) {
// the pressure is too high, in this case we use the slope
// of the density energy at the vapor pressure to
// regularize
// calculate the partial derivative of the specific volume
// to the pressure at the vapor pressure.
Scalar eps = scalarValue(pv)*1e-8;
Evaluation v0 = volumeRegion2_(temperature, pv);
Evaluation v1 = volumeRegion2_(temperature, pv + eps);
Evaluation dv_dp = (v1 - v0)/eps;
/*
Scalar pi = Region2::pi(pv);
Scalar dp_dpi = Region2::dp_dpi(pv);
Scalar dgamma_dpi = Region2::dgamma_dpi(temperature, pv);
Scalar ddgamma_ddpi = Region2::ddgamma_ddpi(temperature, pv);
Scalar RT = Rs*temperature;
Scalar dv_dp =
RT/(dp_dpi*pv)
*
(dgamma_dpi + pi*ddgamma_ddpi - v0*dp_dpi/RT);
*/
// calculate the partial derivative of the density to the
// pressure at vapor pressure
Evaluation drho_dp = - 1/(v0*v0)*dv_dp;
// use a straight line for extrapolation
return 1.0/v0 + (pressure - pv)*drho_dp;
};
return 1.0/volumeRegion2_(temperature, pressure);
}
static bool gasIsIdeal()
{ return false; }
template <class Evaluation>
static Evaluation gasPressure(const Evaluation& temperature, Scalar density)
{
Valgrind::CheckDefined(temperature);
Valgrind::CheckDefined(density);
// We use the newton method for this. For the initial value we
// assume steam to be an ideal gas
Evaluation pressure = IdealGas<Scalar>::pressure(temperature, density/molarMass());
Scalar eps = pressure*1e-7;
Evaluation deltaP = pressure*2;
Valgrind::CheckDefined(pressure);
Valgrind::CheckDefined(deltaP);
for (int i = 0; i < 5 && std::abs(scalarValue(pressure)*1e-9) < std::abs(scalarValue(deltaP)); ++i) {
Evaluation f = gasDensity(temperature, pressure) - density;
Evaluation df_dp;
df_dp = gasDensity(temperature, pressure + eps);
df_dp -= gasDensity(temperature, pressure - eps);
df_dp /= 2*eps;
deltaP = - f/df_dp;
pressure += deltaP;
Valgrind::CheckDefined(pressure);
Valgrind::CheckDefined(deltaP);
}
return pressure;
}
template <class Evaluation>
static Evaluation liquidDensity(const Evaluation& temperature,
const Evaluation& pressure,
bool extrapolate = false)
{
if (!extrapolate && !Region1::isValid(temperature, pressure))
{
throw NumericalProblem(domainError("Density of water",
temperature,
pressure));
}
// regularization
Evaluation pv = vaporPressure(temperature);
if (pressure < pv) {
// the pressure is too low, in this case we use the slope
// of the density at the vapor pressure to regularize
// calculate the partial derivative of the specific volume
// to the pressure at the vapor pressure.
Scalar eps = scalarValue(pv)*1e-8;
Evaluation v0 = volumeRegion1_(temperature, pv);
Evaluation v1 = volumeRegion1_(temperature, pv + eps);
Evaluation dv_dp = (v1 - v0)/eps;
/*
Scalar v0 = volumeRegion1_(temperature, pv);
Scalar pi = Region1::pi(pv);
Scalar dp_dpi = Region1::dp_dpi(pv);
Scalar dgamma_dpi = Region1::dgamma_dpi(temperature, pv);
Scalar ddgamma_ddpi = Region1::ddgamma_ddpi(temperature, pv);
Scalar RT = Rs*temperature;
Scalar dv_dp =
RT/(dp_dpi*pv)
*
(dgamma_dpi + pi*ddgamma_ddpi - v0*dp_dpi/RT);
*/
// calculate the partial derivative of the density to the
// pressure at vapor pressure
Evaluation drho_dp = - 1/(v0*v0)*dv_dp;
// use a straight line for extrapolation
return 1.0/v0 + (pressure - pv)*drho_dp;
};
return 1/volumeRegion1_(temperature, pressure);
}
template <class Evaluation>
static Evaluation liquidPressure(const Evaluation& temperature, Scalar density)
{
// We use the Newton method for this. For the initial value we
// assume the pressure to be 10% higher than the vapor
// pressure
Evaluation pressure = 1.1*vaporPressure(temperature);
Scalar eps = scalarValue(pressure)*1e-7;
Evaluation deltaP = pressure*2;
for (int i = 0; i < 5 && std::abs(scalarValue(pressure)*1e-9) < std::abs(scalarValue(deltaP)); ++i) {
Evaluation f = liquidDensity(temperature, pressure) - density;
Evaluation df_dp;
df_dp = liquidDensity(temperature, pressure + eps);
df_dp -= liquidDensity(temperature, pressure - eps);
df_dp /= 2*eps;
deltaP = - f/df_dp;
pressure += deltaP;
}
return pressure;
}
template <class Evaluation>
static Evaluation gasViscosity(const Evaluation& temperature, const Evaluation& pressure)
{
if (!Region2::isValid(temperature, pressure))
{
throw NumericalProblem(domainError("Viscosity of steam",
temperature,
pressure));
}
Evaluation rho = gasDensity(temperature, pressure);
return Common::viscosity(temperature, rho);
}
template <class Evaluation>
static Evaluation liquidViscosity(const Evaluation& temperature,
const Evaluation& pressure,
bool extrapolate = false)
{
if (!extrapolate && !Region1::isValid(temperature, pressure))
{
throw NumericalProblem(domainError("Viscosity of water",
temperature,
pressure));
};
const Evaluation& rho = liquidDensity(temperature, pressure, extrapolate);
return Common::viscosity(temperature, rho);
}
template <class Evaluation>
static Evaluation liquidThermalConductivity(const Evaluation& temperature, const Evaluation& pressure)
{
const Evaluation& rho = liquidDensity(temperature, pressure);
return Common::thermalConductivityIAPWS(temperature, rho);
}
template <class Evaluation>
static Evaluation gasThermalConductivity(const Evaluation& temperature, const Evaluation& pressure)
{
const Evaluation& rho = gasDensity(temperature, pressure);
return Common::thermalConductivityIAPWS(temperature, rho);
}
private:
// the unregularized specific enthalpy for liquid water
template <class Evaluation>
static Evaluation enthalpyRegion1_(const Evaluation& temperature, const Evaluation& pressure)
{
return
Region1::tau(temperature) *
Region1::dgamma_dtau(temperature, pressure) *
Rs*temperature;
}
// the unregularized specific isobaric heat capacity
template <class Evaluation>
static Evaluation heatCap_p_Region1_(const Evaluation& temperature, const Evaluation& pressure)
{
return
- pow(Region1::tau(temperature), 2.0) *
Region1::ddgamma_ddtau(temperature, pressure) *
Rs;
}
// the unregularized specific isochoric heat capacity
template <class Evaluation>
static Evaluation heatCap_v_Region1_(const Evaluation& temperature, const Evaluation& pressure)
{
double tau = Region1::tau(temperature);
double num = Region1::dgamma_dpi(temperature, pressure) - tau * Region1::ddgamma_dtaudpi(temperature, pressure);
double diff = std::pow(num, 2) / Region1::ddgamma_ddpi(temperature, pressure);
return
- std::pow(tau, 2 ) *
Region1::ddgamma_ddtau(temperature, pressure) * Rs +
diff;
}
// the unregularized specific internal energy for liquid water
template <class Evaluation>
static Evaluation internalEnergyRegion1_(const Evaluation& temperature, const Evaluation& pressure)
{
return
Rs * temperature *
( Region1::tau(temperature)*Region1::dgamma_dtau(temperature, pressure) -
Region1::pi(pressure)*Region1::dgamma_dpi(temperature, pressure));
}
// the unregularized specific volume for liquid water
template <class Evaluation>
static Evaluation volumeRegion1_(const Evaluation& temperature, const Evaluation& pressure)
{
return
Region1::pi(pressure)*
Region1::dgamma_dpi(temperature, pressure) *
Rs * temperature / pressure;
}
// the unregularized specific enthalpy for steam
template <class Evaluation>
static Evaluation enthalpyRegion2_(const Evaluation& temperature, const Evaluation& pressure)
{
return
Region2::tau(temperature) *
Region2::dgamma_dtau(temperature, pressure) *
Rs*temperature;
}
// the unregularized specific internal energy for steam
template <class Evaluation>
static Evaluation internalEnergyRegion2_(const Evaluation& temperature, const Evaluation& pressure)
{
return
Rs * temperature *
( Region2::tau(temperature)*Region2::dgamma_dtau(temperature, pressure) -
Region2::pi(pressure)*Region2::dgamma_dpi(temperature, pressure));
}
// the unregularized specific isobaric heat capacity
template <class Evaluation>
static Evaluation heatCap_p_Region2_(const Evaluation& temperature, const Evaluation& pressure)
{
return
- pow(Region2::tau(temperature), 2 ) *
Region2::ddgamma_ddtau(temperature, pressure) *
Rs;
}
// the unregularized specific isochoric heat capacity
template <class Evaluation>
static Evaluation heatCap_v_Region2_(const Evaluation& temperature, const Evaluation& pressure)
{
const Evaluation& tau = Region2::tau(temperature);
const Evaluation& pi = Region2::pi(pressure);
const Evaluation& num = 1 + pi * Region2::dgamma_dpi(temperature, pressure) + tau * pi * Region2::ddgamma_dtaudpi(temperature, pressure);
const Evaluation& diff = num * num / (1 - pi * pi * Region2::ddgamma_ddpi(temperature, pressure));
return
- std::pow(tau, 2 ) *
Region2::ddgamma_ddtau(temperature, pressure) * Rs
- diff;
}
// the unregularized specific volume for steam
template <class Evaluation>
static Evaluation volumeRegion2_(const Evaluation& temperature, const Evaluation& pressure)
{
return
Region2::pi(pressure)*
Region2::dgamma_dpi(temperature, pressure) *
Rs * temperature / pressure;
}
private:
template<class Evaluation>
static std::string domainError(const std::string& type,
const Evaluation& temperature,
const Evaluation& pressure)
{
auto cast = [](const auto d)
{
#if HAVE_QUAD
if constexpr (std::is_same_v<decltype(d), const quad>)
return static_cast<double>(d);
else
#endif
return d;
};
auto tostring = [cast](const auto& val) -> std::string
{
if constexpr (DenseAd::is_evaluation<Evaluation>::value) {
return std::to_string(cast(getValue(val.value())));
}
else
return std::to_string(cast(getValue(val)));
};
return type + " is only implemented for temperatures "
"below 623.15K and pressures below 100MPa. (T = " +
tostring(temperature) + ", p=" + tostring(pressure);
}
}; // end class
template <class Scalar>
const Scalar H2O<Scalar>::Rs = Common::Rs;
} // namespace Opm
#endif
Common.hpp
Implements relations which are common for all regions of the IAPWS '97 formulation.
Component.hpp
Abstract base class of a pure chemical species.
Evaluation.hpp
Representation of an evaluation of a function and its derivatives w.r.t.
Exceptions.hpp
Provides the OPM specific exception classes.
IdealGas.hpp
Relations valid for an ideal gas.
Region1.hpp
Implements the equations for region 1 of the IAPWS '97 formulation.
Region2.hpp
Implements the equations for region 2 of the IAPWS '97 formulation.
Region4.hpp
Implements the equations for region 4 of the IAPWS '97 formulation.
Valgrind.hpp
Some templates to wrap the valgrind client request macros.
Opm::Component
Abstract base class of a pure chemical species.
Definition Component.hpp:44
Opm::H2O
Material properties of pure water .
Definition H2O.hpp:65
Opm::H2O::liquidDensity
static Evaluation liquidDensity(const Evaluation &temperature, const Evaluation &pressure, bool extrapolate=false)
The density of pure water in at a given pressure and temperature.
Definition H2O.hpp:689
Opm::H2O::criticalTemperature
static const Scalar criticalTemperature()
Returns the critical temperature of water.
Definition H2O.hpp:97
Opm::H2O::gasDensity
static Evaluation gasDensity(const Evaluation &temperature, const Evaluation &pressure)
The density of steam in at a given pressure and temperature.
Definition H2O.hpp:564
Opm::H2O::name
static std::string_view name()
A human readable name for the water.
Definition H2O.hpp:79
Opm::H2O::gasIsCompressible
static bool gasIsCompressible()
Returns true iff the gas phase is assumed to be compressible.
Definition H2O.hpp:542
Opm::H2O::gasPressure
static Evaluation gasPressure(const Evaluation &temperature, Scalar density)
The pressure of steam in at a given density and temperature.
Definition H2O.hpp:645
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::gasViscosity
static Evaluation gasViscosity(const Evaluation &temperature, const Evaluation &pressure)
The dynamic viscosity of steam.
Definition H2O.hpp:792
Opm::H2O::gasHeatCapacityConstVolume
static Evaluation gasHeatCapacityConstVolume(const Evaluation &temperature, const Evaluation &pressure)
Specific isochoric heat capacity of steam and water vapor .
Definition H2O.hpp:517
Opm::H2O::gasHeatCapacity
static Evaluation gasHeatCapacity(const Evaluation &temperature, const Evaluation &pressure)
Specific isobaric heat capacity of water steam .
Definition H2O.hpp:281
Opm::H2O::criticalMolarVolume
static const Scalar criticalMolarVolume()
Returns the molar volume of water at the critical point.
Definition H2O.hpp:115
Opm::H2O::liquidEnthalpy
static Evaluation liquidEnthalpy(const Evaluation &temperature, const Evaluation &pressure)
Specific enthalpy of liquid water .
Definition H2O.hpp:239
Opm::H2O::liquidThermalConductivity
static Evaluation liquidThermalConductivity(const Evaluation &temperature, const Evaluation &pressure)
Thermal conductivity of water (IAPWS) .
Definition H2O.hpp:846
Opm::H2O::acentricFactor
static const Scalar acentricFactor()
The acentric factor of water.
Definition H2O.hpp:91
Opm::H2O::liquidInternalEnergy
static Evaluation liquidInternalEnergy(const Evaluation &temperature, const Evaluation &pressure)
Specific internal energy of liquid water .
Definition H2O.hpp:350
Opm::H2O::gasIsIdeal
static bool gasIsIdeal()
Returns true iff the gas phase is assumed to be ideal.
Definition H2O.hpp:629
Opm::H2O::criticalPressure
static const Scalar criticalPressure()
Returns the critical pressure of water.
Definition H2O.hpp:103
Opm::H2O::molarMass
static const Scalar molarMass()
The molar mass in of water.
Definition H2O.hpp:85
Opm::H2O::vaporTemperature
static Evaluation vaporTemperature(const Evaluation &pressure)
The vapor temperature in of pure water at a given pressure.
Definition H2O.hpp:165
Opm::H2O::liquidIsCompressible
static bool liquidIsCompressible()
Returns true iff the liquid phase is assumed to be compressible.
Definition H2O.hpp:548
Opm::H2O::liquidViscosity
static Evaluation liquidViscosity(const Evaluation &temperature, const Evaluation &pressure, bool extrapolate=false)
The dynamic viscosity of pure water.
Definition H2O.hpp:817
Opm::H2O::gasInternalEnergy
static Evaluation gasInternalEnergy(const Evaluation &temperature, const Evaluation &pressure)
Specific internal energy of steam and water vapor .
Definition H2O.hpp:408
Opm::H2O::gasThermalConductivity
static Evaluation gasThermalConductivity(const Evaluation &temperature, const Evaluation &pressure)
Thermal conductivity of water (IAPWS) .
Definition H2O.hpp:866
Opm::H2O::gasEnthalpy
static Evaluation gasEnthalpy(const Evaluation &temperature, const Evaluation &pressure)
Specific enthalpy of water steam .
Definition H2O.hpp:188
Opm::H2O::liquidHeatCapacityConstVolume
static Evaluation liquidHeatCapacityConstVolume(const Evaluation &temperature, const Evaluation &pressure)
Specific isochoric heat capacity of liquid water .
Definition H2O.hpp:482
Opm::H2O::liquidPressure
static Evaluation liquidPressure(const Evaluation &temperature, Scalar density)
The pressure of liquid water in at a given density and temperature.
Definition H2O.hpp:752
Opm::H2O::tripleTemperature
static const Scalar tripleTemperature()
Returns the temperature at water's triple point.
Definition H2O.hpp:121
Opm::H2O::liquidHeatCapacity
static Evaluation liquidHeatCapacity(const Evaluation &temperature, const Evaluation &pressure)
Specific isobaric heat capacity of liquid water .
Definition H2O.hpp:316
Opm::H2O::triplePressure
static const Scalar triplePressure()
Returns the pressure at water's triple point.
Definition H2O.hpp:127
Opm::H2O::criticalVolume
static const Scalar criticalVolume()
Returns the critical volume of water.
Definition H2O.hpp:109
Opm::IAPWS::Common
Implements relations which are common for all regions of the IAPWS '97 formulation.
Definition Common.hpp:55
Opm::IAPWS::Common::criticalVolume
static const Scalar criticalVolume
Critical volume of water .
Definition Common.hpp:73
Opm::IAPWS::Common::criticalPressure
static const Scalar criticalPressure
Critical pressure of water .
Definition Common.hpp:67
Opm::IAPWS::Common::viscosity
static Evaluation viscosity(const Evaluation &temperature, const Evaluation &rho)
The dynamic viscosity of pure water.
Definition Common.hpp:102
Opm::IAPWS::Common::criticalMolarVolume
static const Scalar criticalMolarVolume
Critical molar volume of water .
Definition Common.hpp:76
Opm::IAPWS::Common::criticalTemperature
static const Scalar criticalTemperature
Critical temperature of water .
Definition Common.hpp:64
Opm::IAPWS::Common::thermalConductivityIAPWS
static Evaluation thermalConductivityIAPWS(const Evaluation &T, const Evaluation &rho)
Thermal conductivity water (IAPWS) .
Definition Common.hpp:162
Opm::IAPWS::Common::tripleTemperature
static const Scalar tripleTemperature
Triple temperature of water .
Definition Common.hpp:82
Opm::IAPWS::Common::triplePressure
static const Scalar triplePressure
Triple pressure of water .
Definition Common.hpp:85
Opm::IAPWS::Common::molarMass
static const Scalar molarMass
The molar mass of water .
Definition Common.hpp:58
Opm::IAPWS::Common::acentricFactor
static const Scalar acentricFactor
The acentric factor of water .
Definition Common.hpp:79
Opm::IAPWS::Region1
Implements the equations for region 1 of the IAPWS '97 formulation.
Definition Region1.hpp:51
Opm::IAPWS::Region1::ddgamma_ddpi
static Evaluation ddgamma_ddpi(const Evaluation &temperature, const Evaluation &pressure)
The second partial derivative of the Gibbs free energy to the normalized pressure for IAPWS region 1 ...
Definition Region1.hpp:252
Opm::IAPWS::Region1::tau
static Evaluation tau(const Evaluation &temperature)
Returns the reduced temperature for IAPWS region 1.
Definition Region1.hpp:83
Opm::IAPWS::Region1::ddgamma_ddtau
static Evaluation ddgamma_ddtau(const Evaluation &temperature, const Evaluation &pressure)
The second partial derivative of the Gibbs free energy to the normalized temperature for IAPWS region...
Definition Region1.hpp:282
Opm::IAPWS::Region1::pi
static Evaluation pi(const Evaluation &pressure)
Returns the reduced pressure for IAPWS region 1.
Definition Region1.hpp:102
Opm::IAPWS::Region1::dgamma_dtau
static Evaluation dgamma_dtau(const Evaluation &temperature, const Evaluation &pressure)
The partial derivative of the Gibbs free energy to the normalized temperature for IAPWS region 1 (i....
Definition Region1.hpp:162
Opm::IAPWS::Region1::isValid
static bool isValid(const Evaluation &temperature, const Evaluation &pressure)
Returns true if IAPWS region 1 applies for a (temperature in , pressure in ) pair.
Definition Region1.hpp:61
Opm::IAPWS::Region1::ddgamma_dtaudpi
static Evaluation ddgamma_dtaudpi(const Evaluation &temperature, const Evaluation &pressure)
The partial derivative of the Gibbs free energy to the normalized pressure and to the normalized temp...
Definition Region1.hpp:221
Opm::IAPWS::Region1::dpi_dp
static Scalar dpi_dp(const Evaluation &)
Returns the derivative of the reduced pressure to the pressure for IAPWS region 1 in .
Definition Region1.hpp:112
Opm::IAPWS::Region1::dgamma_dpi
static Evaluation dgamma_dpi(const Evaluation &temperature, const Evaluation &pressure)
The partial derivative of the Gibbs free energy to the normalized pressure for IAPWS region 1 (i....
Definition Region1.hpp:191
Opm::IAPWS::Region2
Implements the equations for region 2 of the IAPWS '97 formulation.
Definition Region2.hpp:52
Opm::IAPWS::Region2::dpi_dp
static Scalar dpi_dp(const Evaluation &)
Returns the derivative of the reduced pressure to the pressure for IAPWS region 2 in .
Definition Region2.hpp:111
Opm::IAPWS::Region2::ddgamma_ddtau
static Evaluation ddgamma_ddtau(const Evaluation &temperature, const Evaluation &pressure)
The second partial derivative of the Gibbs free energy to the normalized temperature for IAPWS region...
Definition Region2.hpp:310
Opm::IAPWS::Region2::ddgamma_ddpi
static Evaluation ddgamma_ddpi(const Evaluation &temperature, const Evaluation &pressure)
The second partial derivative of the Gibbs free energy to the normalized pressure for IAPWS region 2 ...
Definition Region2.hpp:276
Opm::IAPWS::Region2::pi
static Evaluation pi(const Evaluation &pressure)
Returns the reduced pressure (dimensionless) for IAPWS region 2.
Definition Region2.hpp:101
Opm::IAPWS::Region2::dgamma_dtau
static Evaluation dgamma_dtau(const Evaluation &temperature, const Evaluation &pressure)
The partial derivative of the Gibbs free energy to the normalized temperature for IAPWS region 2 (i....
Definition Region2.hpp:170
Opm::IAPWS::Region2::tau
static Evaluation tau(const Evaluation &temperature)
Returns the reduced temperature (dimensionless) for IAPWS region 2.
Definition Region2.hpp:82
Opm::IAPWS::Region2::ddgamma_dtaudpi
static Evaluation ddgamma_dtaudpi(const Evaluation &temperature, const Evaluation &pressure)
The partial derivative of the Gibbs free energy to the normalized pressure and to the normalized temp...
Definition Region2.hpp:242
Opm::IAPWS::Region2::isValid
static bool isValid(const Evaluation &temperature, const Evaluation &pressure)
Returns true if IAPWS region 2 applies for a (temperature, pressure) pair.
Definition Region2.hpp:62
Opm::IAPWS::Region2::dgamma_dpi
static Evaluation dgamma_dpi(const Evaluation &temperature, const Evaluation &pressure)
The partial derivative of the Gibbs free energy to the normalized pressure for IAPWS region 2 (i....
Definition Region2.hpp:209
Opm::IAPWS::Region4
Implements the equations for region 4 of the IAPWS '97 formulation.
Definition Region4.hpp:52
Opm::IAPWS::Region4::vaporTemperature
static Evaluation vaporTemperature(const Evaluation &pressure)
Returns the saturation temperature in of pure water at a given pressure.
Definition Region4.hpp:94
Opm::IAPWS::Region4::saturationPressure
static Evaluation saturationPressure(const Evaluation &temperature)
Returns the saturation pressure in of pure water at a given temperature.
Definition Region4.hpp:63
Opm::IdealGas::pressure
static Evaluation pressure(const Evaluation &temperature, const Evaluation &rhoMolar)
The pressure of the gas in , depending on the molar density and temperature.
Definition IdealGas.hpp:58
Opm::IdealGas::density
static Evaluation density(const Evaluation &avgMolarMass, const Evaluation &temperature, const Evaluation &pressure)
The density of the gas in , depending on pressure, temperature and average molar mass of the gas.
Definition IdealGas.hpp:48
Opm::NumericalProblem
Definition Exceptions.hpp:40
Opm
This class implements a small container which holds the transmissibility mulitpliers for all the face...
Definition Exceptions.hpp:30
quad.hpp
This file provides the infrastructure to use quad-precision floating point values in the numerical mo...