#!/usr/bin/python3
# -*- coding: utf-8 -*-
r"""Pychemqt, Chemical Engineering Process simulator
Copyright (C) 2009-2025, Juan José Gómez Romera <jjgomera@gmail.com>
This program 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 3 of the License, or
(at your option) any later version.
This program 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 this program. If not, see <http://www.gnu.org/licenses/>."""
from lib.EoS.Cubic.PR import PR
[docs]
class PR78(PR):
r"""Peng-Robinson cubic equation of state
.. math::
\begin{array}[t]{l}
P = \frac{RT}{V-b}-\frac{a}{V\left(V+b\right)+b\left(V-b\right)}\\
a = 0.45747\frac{R^2T_c^2}{P_c}\alpha\\
b = 0.0778\frac{RT_c}{P_c}\\
\alpha^{0.5} = 1 + m\left(1-Tr^{0.5}\right)\\
m = 0.37464 + 1.54226\omega-0.26992\omega^2 if \omega < 0.491\\
m = 0.379642 + 1.48503\omega - 0.164423*\omega^2 + 0.016666*\omega^3\\
\end{array}
Examples
--------
Helmholtz energy formulation example for supplementary documentatión from
[4]_, the critical parameter are override for the valued used in paper to
get the values of test with high precision
>>> from lib.mezcla import Mezcla
>>> from lib import unidades
>>> from lib.compuestos import Componente
>>> ch4 = Componente(2)
>>> ch4.Tc, ch4.Pc, ch4.f_acent = 190.564, 4599200, 0.011
>>> o2 = Componente(47)
>>> o2.Tc, o2.Pc, o2.f_acent = 154.581, 5042800, 0.022
>>> ar = Componente(98)
>>> ar.Tc, ar.Pc, ar.f_acent = 150.687, 4863000, -0.002
>>> mix = Mezcla(5, customCmp=[ch4, o2, ar], caudalMolar=1,
... fraccionMolar=[0.5, 0.3, 0.2])
>>> eq = PR78(800, 36451227.52066596, mix, R=8.3144598)
>>> fir = eq._phir(800, 5000, eq.yi)
>>> delta = 5000
>>> tau = 1/800
>>> print("fir: %0.15f" % (fir["fir"]))
fir: 0.084339749584296
>>> print("fird: %0.15f" % (fir["fird"]*delta))
fird: 0.096019116018396
>>> print("firt: %0.14f" % (fir["firt"]*tau))
firt: -0.10134978074971
>>> print("firdd: %0.15f" % (fir["firdd"]*delta**2))
firdd: 0.023611667278971
>>> print("firdt: %0.15f" % (fir["firdt"]*delta*tau))
firdt: -0.092099683110520
>>> print("firtt: %0.15f" % (fir["firtt"]*tau**2))
firtt: -0.078186052271240
>>> print("firddd: %0.16f" % (fir["firddd"]*delta**3))
firddd: 0.0017433108161805
>>> print("firddt: %0.15f" % (fir["firddt"]*delta**2*tau))
firddt: 0.015574974734224
>>> print("firdtt: %0.15f" % (fir["firdtt"]*delta*tau**2))
firdtt: -0.071050085995025
>>> print("firttt: %0.14f" % (fir["firttt"]*tau**3))
firttt: 0.11727907840686
"""
__title__ = "Peng-Robinson (1978)"
__status__ = "PR78"
__doi__ = (
{
"autor": "Peng, D.-Y., Robinson, D.B.",
"title": "A New Two-Constant Equation of State",
"ref": "Ind. Eng. Chem. Fund. 15(1) (1976) 59-64",
"doi": "10.1021/i160057a011"},
{
"autor": "Peng, D.-Y., Robinson, D.B.",
"title": "Two- and Three-Phase Equilibrium Calculations for Coal "
"Gasification and Related Processes",
"ref": "in Newman, Barner, Klein, Sandler (Eds.). Thermodynamic of "
"Aqueous Systems with Industrial Applications. ACS (1980), pag."
" 393-414",
"doi": "10.1021/bk-1980-0133.ch020"})
[docs]
def _alfa(self, cmp, T):
"""Custom expression for α"""
if cmp.f_acent <= 0.491:
m = 0.37464 + 1.54226*cmp.f_acent - 0.26992*cmp.f_acent**2
else:
m = 0.379642 + 1.48503*cmp.f_acent - 0.164423*cmp.f_acent**2 + \
0.016666*cmp.f_acent**3
alfa = (1+m*(1-(T/cmp.Tc)**0.5))**2 # Eq 17
return m, alfa
if __name__ == "__main__":
from lib.mezcla import Mezcla
mix = Mezcla(5, ids=[4], caudalMolar=1, fraccionMolar=[1])
eq = PR78(300, 9.9742e5, mix)
print('%0.0f %0.1f' % (eq.Vg.ccmol, eq.Vl.ccmol))
eq = PR78(300, 42.477e5, mix)
print('%0.1f' % (eq.Vl.ccmol))
