#!/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.PR78 import PR78
# Group interaction parameters, from Table 1 in [3]_, values in MPa
Aij = [[74.81, 261.5, 396.7, 32.94, 8.579, 90.25, 62.8, 40.38, 98.48],
[51.47, 88.53, 36.72, 31.23, 29.78, 3.775, 12.78, -54.9],
[-305.7, 145.2, 174.3, 103.3, 6.177, 101.9, -226.5],
[263.9, 333.2, 158.9, 79.61, 177.1, 17.84],
[13.04, 67.26, 139.3, 36.37, 40.15],
[41.18, -3.088, 8.579, 10.29],
[-13.38, 29.17, -26.42],
[34.31, -105.7],
[-50.1]]
Bij = [[165.7, 388.8, 804.3, -35, -29.51, 146.1, 41.86, 95.9, 231.6],
[79.61, 315, 108.4, 84.76, 58.17, 144.8, 28.37, -319.5],
[-250.8, 301.6, 352.1, 191.8, -33.97, -90.93, -51.47],
[531.5, 203.8, 613.2, -326.0, 601.9, -109.5],
[6.863, 167.5, 464.3, 26.42, 255.3],
[50.79, 13.04, 76.86, -52.84],
[20.25, 69.32, -789.2],
[95.39, -286.5],
[-891.1]]
# Map unifac group in compound database to group used in the PPR78 EoS
MAP_UNIFAC = {}
[docs]
class PPR78(PR78):
r"""Predictive 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\\
k_{ij} = \frac{-\frac{1}{2}\sum_{k=1}^{Ng} \sum_{l=1}^{Ng}
\left(\alpha_{ik}-\alpha_{jk}\right)\left(\alpha_{il}-\alpha_{jl}\right)
A_{kl} \left(\frac{298.15}{T}\right)^{\left(\frac{B_{kl}}{A_{kl}}-1\right)}
-\left(\frac{\sqrt{a_i}}{b_i}-\frac{\sqrt{a_j}}{b_j}\right)^2}
{2\frac{\sqrt{a_i a_j}}{b_i b_j}}
\end{array}
Examples
--------
kij between propane and n-butane at T=303.15 from Appendix A of [1]_, tiny
variation because differences in critical properties of components
>>> mix = Mezcla(5, ids=[4, 6], caudalMolar=1, fraccionMolar=[0.5, 0.5])
>>> eq = PPR78(303.15, 101325, mix)
>>> print("%0.4f" % self.kij[0][1])
0.0029
"""
__title__ = "Predictive Peng-Robinson (1978)"
__status__ = "PPR78"
__doi__ = (
{"autor": "Jaubert, J.-N., Mutelet, F.",
"title": "VLE predictions with the Peng–Robinson equation of state and "
"temperature dependent kij calculated through a group "
"contribution method",
"ref": "Fluid Phase Equilibria 224 (2004) 285-304",
"doi": "10.1016/j.fluid.2004.06.059"},
{"autor": "Jaubert, J.-N., Vitu, S., Mutelet, F., Corriou, J.-P.",
"title": "Extension of the PPR78 model (predictive 1978, "
"Peng-Robinson EOS with temperature dependent kij calculated "
"through a group contribution method) to systems containing "
"aromatic compounds",
"ref": "Fluid Phase Equilibria 237 (2005) 193-211",
"doi": "10.1016/j.fluid.2005.09.003"},
{"autor": "Vitu, S., Jaubert, J.-N., Mutelet, F.",
"title": "Extension of the PPR78 model (predictive 1978, "
"Peng-Robinson EOS with temperature dependent kij calculated "
"through a group contribution method) to systems containing "
"naphtenic compounds",
"ref": "Fluid Phase Equilibria 243 (2006) 9-28",
"doi": "10.1016/j.fluid.2006.02.004"})
[docs]
def _Kij(self, eq=None):
"""Calculate binary interaction parameters"""
group = self.mapUNIFAC()
alfa = []
for i, cmp in enumerate(self.componente):
alfai = []
for gi in group[i]:
total = sum(group[i].values())
alfai.append(group[i][gi]/total)
alfa.append(alfai)
# Eq 5 in [1]_
kij = []
for i, ci in enumerate(self.componente):
kiji = []
for j, cj in enumerate(self.componente):
suma = 0
for alfaik, alfajk, Aki, Bki in zip(alfa[i], alfa[j], Aij, Bij):
for alfail, alfajl, Akl, Bkl in zip(alfa[i], alfa[j], Aki, Bki):
suma += (alfaik-alfajk)*(alfail-alfajl)*Akl*1e6 \
* (298.15/self.T)**(Bkl/Akl-1)
k = -0.5*suma
k -= (self.ai[i]**0.5/self.bi[i]-self.ai[j]**0.5/self.bi[j])**2
k /= 2*(self.ai[i]*self.ai[j])**0.5/self.bi[i]/self.bi[j]
# Applying recomentation of unphysical result for kij > 1
# Polishuk, I.
# Comments on “VLE predictions with the Peng–Robinson equation
# of state and temperature dependent kij calculated through a
# group contribution method” by J.-N. Jaubert and F. Mutelet
# [Fluid Phase Equilibria, 224 (2004) 285–304]
# Fluid Phase Equilibria 249(1-2) (2006) 198-199
# doi: 10.1016/j.fluid.2006.09.002
if k > 1:
k = 1
kiji.append(k)
kij.append(kiji)
return kij
[docs]
def mapUNIFAC(self):
"""Convert UNIFAC group saved in compound database to group
contribution as used in PPR78"""
group = []
for cmp in self.componente:
gi = {}
gi[1] = cmp.UNIFAC.get(1, 0)
gi[2] = cmp.UNIFAC.get(2, 0)
gi[3] = cmp.UNIFAC.get(3, 0)
gi[4] = cmp.UNIFAC.get(4, 0)
# Special case for methane
if cmp.id == 2:
gi[5] = 1
else:
gi[5] = 0
# Special case for ethane
if cmp.id == 3:
gi[6] = 1
else:
gi[6] = 0
gi[7] = cmp.UNIFAC.get(10, 0)
gi[8] = sum([cmp.UNIFAC.get(i, 0) for i in range(11, 15)])
group.append(gi)
return group
if __name__ == "__main__":
from lib.mezcla import Mezcla
# mix = Mezcla(5, ids=[4], caudalMolar=1, fraccionMolar=[1])
mix = Mezcla(5, ids=[4, 6, 40, 41], caudalMolar=1, fraccionMolar=[0.4, 0.4, 0.1, 0.1])
# mix = Mezcla(5, ids=[4, 6], caudalMolar=1, fraccionMolar=[0.5, 0.5])
eq = PPR78(303.15, 101325, mix)
print(eq.kij)
# print('%0.0f %0.1f' % (eq.Vg.ccmol, eq.Vl.ccmol))
# eq = PR78(300, 42.477e5, mix)
# print('%0.1f' % (eq.Vl.ccmol))
