Loading...
Searching...
No Matches
Region2.hpp
Go to the documentation of this file.
// -*- 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_IAPWS_REGION2_HPP
#define OPM_IAPWS_REGION2_HPP
#include <opm/material/common/MathToolbox.hpp>
#include <cmath>
namespace Opm {
namespace IAPWS {
template <class Scalar>
class Region2
{
public:
template <class Evaluation>
static bool isValid(const Evaluation& temperature, const Evaluation& pressure)
{
return
temperature <= 623.15 && pressure <= 100e6;
// actually this is:
/*
return
(273.15 <= temperature && temperature <= 623.15 && pressure <= vaporPressure(temperature)) ||
(623.15 < temperature && temperature <= 863.15 && pressure <= auxPressure(temperature)) ||
(863.15 < temperature && temperature <= 1073.15 && pressure < 100e6);
*/
}
template <class Evaluation>
static Evaluation tau(const Evaluation& temperature)
{ return 540.0 / temperature; }
template <class Evaluation>
static Evaluation dtau_dT(const Evaluation& temperature)
{ return - 540.0 / (temperature*temperature); }
template <class Evaluation>
static Evaluation pi(const Evaluation& pressure)
{ return pressure / 1e6; }
template <class Evaluation>
static Scalar dpi_dp(const Evaluation& /*pressure*/)
{ return 1.0 / 1e6; }
template <class Evaluation>
static Evaluation dp_dpi(const Evaluation& /*pressure*/)
{ return 1e6; }
template <class Evaluation>
static Evaluation gamma(const Evaluation& temperature, const Evaluation& pressure)
{
const Evaluation& tau_ = tau(temperature); /* reduced temperature */
const Evaluation& pi_ = pi(pressure); /* reduced pressure */
Evaluation result;
// ideal gas part
result = log(pi_);
for (int i = 0; i < 9; ++i)
result += n_g(i)*pow(tau_, J_g(i));
// residual part
for (int i = 0; i < 43; ++i)
result +=
n_r(i)*
pow(pi_, I_r(i))*
pow(tau_ - 0.5, J_r(i));
return result;
}
template <class Evaluation>
static Evaluation dgamma_dtau(const Evaluation& temperature, const Evaluation& pressure)
{
const Evaluation& tau_ = tau(temperature); /* reduced temperature */
const Evaluation& pi_ = pi(pressure); /* reduced pressure */
// ideal gas part
Evaluation result = 0.0;
for (int i = 0; i < 9; i++) {
result +=
n_g(i) *
J_g(i) *
pow(tau_, static_cast<Scalar>(J_g(i) - 1));
}
// residual part
for (int i = 0; i < 43; i++) {
result +=
n_r(i) *
pow(pi_, static_cast<Scalar>(I_r(i))) *
J_r(i) *
pow(tau_ - 0.5, static_cast<Scalar>(J_r(i) - 1));
}
return result;
}
template <class Evaluation>
static Evaluation dgamma_dpi(const Evaluation& temperature, const Evaluation& pressure)
{
const Evaluation& tau_ = tau(temperature); /* reduced temperature */
const Evaluation& pi_ = pi(pressure); /* reduced pressure */
// ideal gas part
Evaluation result = 1/pi_;
// residual part
for (int i = 0; i < 43; i++) {
result +=
n_r(i) *
I_r(i) *
pow(pi_, static_cast<Scalar>(I_r(i) - 1)) *
pow(tau_ - 0.5, static_cast<Scalar>(J_r(i)));
}
return result;
}
template <class Evaluation>
static Evaluation ddgamma_dtaudpi(const Evaluation& temperature, const Evaluation& pressure)
{
const Evaluation& tau_ = tau(temperature); /* reduced temperature */
const Evaluation& pi_ = pi(pressure); /* reduced pressure */
// ideal gas part
Evaluation result = 0.0;
// residual part
for (int i = 0; i < 43; i++) {
result +=
n_r(i) *
I_r(i) *
J_r(i) *
pow(pi_, static_cast<Scalar>(I_r(i) - 1)) *
pow(tau_ - 0.5, static_cast<Scalar>(J_r(i) - 1));
}
return result;
}
template <class Evaluation>
static Evaluation ddgamma_ddpi(const Evaluation& temperature, const Evaluation& pressure)
{
const Evaluation& tau_ = tau(temperature); /* reduced temperature */
const Evaluation& pi_ = pi(pressure); /* reduced pressure */
// ideal gas part
Evaluation result = -1/(pi_*pi_);
// residual part
for (int i = 0; i < 43; i++) {
result +=
n_r(i) *
I_r(i) *
(I_r(i) - 1) *
pow(pi_, static_cast<Scalar>(I_r(i) - 2)) *
pow(tau_ - 0.5, static_cast<Scalar>(J_r(i)));
}
return result;
}
template <class Evaluation>
static Evaluation ddgamma_ddtau(const Evaluation& temperature, const Evaluation& pressure)
{
const Evaluation& tau_ = tau(temperature); /* reduced temperature */
const Evaluation& pi_ = pi(pressure); /* reduced pressure */
// ideal gas part
Evaluation result = 0.0;
for (int i = 0; i < 9; i++) {
result +=
n_g(i) *
J_g(i) *
(J_g(i) - 1) *
pow(tau_, static_cast<Scalar>(J_g(i) - 2));
}
// residual part
for (int i = 0; i < 43; i++) {
result +=
n_r(i) *
pow(pi_, I_r(i)) *
J_r(i) *
(J_r(i) - 1.) *
pow(tau_ - 0.5, static_cast<Scalar>(J_r(i) - 2));
}
return result;
}
private:
static Scalar n_g(int i)
{
static const Scalar n[9] = {
-0.96927686500217e1, 0.10086655968018e2, -0.56087911283020e-2,
0.71452738081455e-1, -0.40710498223928, 0.14240819171444e1,
-0.43839511319450e1, -0.28408632460772, 0.21268463753307e-1
};
return n[i];
}
static Scalar n_r(int i)
{
static const Scalar n[43] = {
-0.17731742473213e-2, -0.17834862292358e-1, -0.45996013696365e-1,
-0.57581259083432e-1, -0.50325278727930e-1, -0.33032641670203e-4,
-0.18948987516315e-3, -0.39392777243355e-2, -0.43797295650573e-1,
-0.26674547914087e-4, 0.20481737692309e-7, 0.43870667284435e-6,
-0.32277677238570e-4, -0.15033924542148e-2, -0.40668253562649e-1,
-0.78847309559367e-9, 0.12790717852285e-7, 0.48225372718507e-6,
0.22922076337661e-5, -0.16714766451061e-10, -0.21171472321355e-2,
-0.23895741934104e2, -0.59059564324270e-17, -0.12621808899101e-5,
-0.38946842435739e-1, 0.11256211360459e-10, -0.82311340897998e1,
0.19809712802088e-7, 0.10406965210174e-18, -0.10234747095929e-12,
-0.10018179379511e-8, -0.80882908646985e-10, 0.10693031879409,
-0.33662250574171, 0.89185845355421e-24, 0.30629316876232e-12,
-0.42002467698208e-5, -0.59056029685639e-25, 0.37826947613457e-5,
-0.12768608934681e-14, 0.73087610595061e-28, 0.55414715350778e-16,
-0.94369707241210e-6
};
return n[i];
}
static Scalar I_r(int i)
{
static const short int I[43] = {
1, 1, 1,
1, 1, 2,
2, 2, 2,
2, 3, 3,
3, 3, 3,
4, 4, 4,
5, 6, 6,
6, 7, 7,
7, 8, 8,
9, 10, 10,
10, 16, 16,
18, 20, 20,
20, 21, 22,
23, 24, 24,
24
};
return I[i];
}
static Scalar J_g(int i)
{
static const short int J[9] = {
0, 1, -5,
-4, -3, -2,
-1, 2, 3
};
return J[i];
}
static Scalar J_r(int i)
{
static const short int J[43] = {
0, 1, 2,
3, 6, 1,
2, 4, 7,
36, 0, 1,
3, 6, 35,
1, 2, 3,
7, 3, 16,
35, 0, 11,
25, 8, 36,
13, 4, 10,
14, 29, 50,
57, 20, 35,
48, 21, 53,
39, 26, 40,
58
};
return J[i];
}
};
} // namespace IAPWS
} // namespace Opm
#endif
MathToolbox.hpp
A traits class which provides basic mathematical functions for arbitrary scalar floating point values...
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::dtau_dT
static Evaluation dtau_dT(const Evaluation &temperature)
Returns the derivative of the reduced temperature to the temperature for IAPWS region 2.
Definition Region2.hpp:92
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::dp_dpi
static Evaluation dp_dpi(const Evaluation &)
Returns the derivative of the pressure to the reduced pressure for IAPWS region 2 (dimensionless).
Definition Region2.hpp:121
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::gamma
static Evaluation gamma(const Evaluation &temperature, const Evaluation &pressure)
The Gibbs free energy for IAPWS region 2 (i.e.
Definition Region2.hpp:136
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
This class implements a small container which holds the transmissibility mulitpliers for all the face...
Definition Exceptions.hpp:30