#!/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 scipy.constants import R
from lib.EoS.cubic import Cubic
# K1 values from Table 1 from [1]_
# K2 and K3 values from Table 2 from reference for PRSV2
dat = {
46: (0.01996, 0.3162, 0.535),
47: (0.01512, -0.0090, 0.490),
49: (0.04285, 0.0000, 0.000),
63: (0.00100, -0.1265, 0.510),
62: (-0.06635, 0.0199, 0.443),
104: (0.01989, -0.0036, 0.310),
2: (-0.00159, 0.1521, 0.517),
3: (0.02669, 0.1358, 0.424),
22: (0.04191, 0.2610, 0.424),
4: (0.03136, 0.2757, 0.447),
6: (0.03443, 0.6767, 0.461),
8: (0.03946, 0.3940, 0.457),
9: (0.04303, 0.8697, 0.615),
10: (0.05104, 0.8634, 0.460),
11: (0.04648, 0.9331, 0.496),
12: (0.04464, 0.6214, 0.509),
13: (0.04104, 0.6621, 0.519),
14: (0.04510, 0.8549, 0.527),
15: (0.02919, 1.3288, 0.568),
16: (0.05426, 0.8744, 0.505),
17: (0.04157, 0.9387, 0.528),
18: (0.02686, 0.9408, 0.528),
19: (0.01892, 1.0908, 0.559),
20: (0.02665, 0.0334, 0.767),
21: (0.04048, 2.9805, 0.571),
90: (0.08291, 4.1441, 0.577),
38: (0.07023, 0.6146, 0.530),
888: (0.01805, 3.0438, 0.606),
40: (0.07019, 0.7939, 0.523),
41: (0.03849, 0.5261, 0.510),
45: (0.03994, 0.5342, 0.519),
44: (0.01277, 0.5963, 0.524),
182: (0.01173, 0.9246, 0.548),
70: (0.02715, 0.7310, 0.530),
75: (-0.01384, 0.4777, 0.538),
185: (0.03297, 0.6634, 0.510),
191: (-0.01842, -0.8140, 0.577),
192: (-0.01639, -0.0750, 0.597),
194: (0.11487, 0.1077, 0.407),
406: (0.05955, 0.3703, 0.587),
# : (-0.01393, -5.8256, 0.587), # 9,10-Dihydrophenanthrene
140: (-0.00888, 0.2871, 0.537),
448: (0.00554, 0.6847, 0.613),
304: (0.01681, 0.7787, 0.620),
165: (0.03558, 0.6180, 0.610),
305: (0.04113, 0.5138, 0.615),
771: (0.00984, 0.8448, 0.550),
# 1356: (0.02321, 0.8891, 0.619),
# 1354: (0.04005, 0.7451, 0.535),
809: (0.02731, 0.9236, 0.561),
610: (0.02002, 0.9649, 0.579),
117: (-0.16816, -1.3400, 0.588),
134: (-0.03374, -2.6846, 0.592),
146: (0.21419, -3.6816, 0.640),
145: (0.23264, -3.5578, 0.652),
160: (0.33431, -1.1748, 0.642),
159: (0.39045, 0.0026, 0.676),
314: (0.37200, -1.2792, 0.642),
316: (0.43099, -0.0480, 0.658),
313: (0.36781, 0.2918, 0.621),
335: (-0.00237, -3.3938, 0.551),
360: (0.82940, 2.7372, 0.543),
396: (0.80898, 1.4978, 0.470),
133: (0.05717, -0.1211, 0.481),
486: (0.16948, 0.0515, 0.768),
# 1287: 0.02300, 0.9179, 0.558),
# 1286: 0.04123, 0.3833, 0.562),
# 1317: 0.01622, 0.6140, 0.548),
456: (0.05129, -0.2022, 0.585),
318: (-0.01668, 1.1679, 0.553),
778: (-0.03162, 1.4094, 0.577),
337: (0.03751, 0.8810, 0.590),
344: (0.01610, 1.0478, 0.616),
226: (-0.10299, 0.5905, 0.463),
125: (-0.13991, -0.3777, 0.522),
130: (-0.19724, 0.8136, 0.541),
144: (0.18999, -0.1857, 0.470),
688: (-0.42503, 0.0020, 0.407),
270: (0.14326, 1.1002, 0.614),
271: (0.06001, 2.2851, 0.603),
# 1285: (-0.09508, 0.0033, 0.931),
# : (0.13440, 0.9308, 0.635), # 2-Methyl-2-Propylamine
281: (0.03961, 0.5029, 0.573),
295: (0.06946, 0.4241, 0.575),
164: (-0.03471, 4.5512, 0.539),
497: (0.11367, -0.7871, 0.537),
319: (0.02752, 0.8172, 0.565),
796: (-0.00901, 0.5425, 0.582),
346: (0.24705, 5.6910, 0.597),
# : (0.06043, -0.1210, 0.592), # Thianaphthene
# Aditional parameter from Table 1 in [2]_, only for PRSV equation
# Inorganic
51: (0.03962, 0, 0),
48: (0.04279, 0, 0),
50: (0.03160, 0, 0),
105: (0.03641, 0, 0),
110: (0.06325, 0, 0),
# Hydrocarbons
65: (0.09919, 0, 0),
5: (-0.00238, 0, 0),
24: (0.02222, 0, 0),
68: (-0.00516, 0, 0),
25: (0.04457, 0, 0),
26: (0.00435, 0, 0),
28: (0.02327, 0, 0),
7: (0.02840, 0, 0),
29: (0.03521, 0, 0),
82: (0.03363, 0, 0),
36: (0.04602, 0, 0),
39: (0.04859, 0, 0),
42: (0.02291, 0, 0),
43: (0.01610, 0, 0),
71: (0.05509, 0, 0),
178: (0.16109, 0, 0),
# Acids
143: (-0.03093, 0, 0),
154: (-0.14012, 0, 0),
306: (-0.08171, 0, 0),
# Aldehydes
261: (-0.03642, 0, 0),
# Esters
141: (0.11372, 0, 0),
142: (0.05791, 0, 0),
155: (0.06464, 0, 0),
166: (0.06531, 0, 0),
330: (0.07587, 0, 0),
309: (0.06362, 0, 0),
# Ethers
162: (0.05004, 0, 0),
# Ketones
327: (-0.29473, 0, 0),
# Halogen Compounds
100: (0.05212, 0, 0),
218: (0.02136, 0, 0),
636: (0.04014, 0, 0),
215: (0.05054, 0, 0),
216: (0.04722, 0, 0),
217: (0.03708, 0, 0),
112: (0.02899, 0, 0),
642: (0.07915, 0, 0),
220: (0.04513, 0, 0),
643: (0.00535, 0, 0),
645: (-0.02874, 0, 0),
115: (0.01160, 0, 0),
225: (-0.00374, 0, 0),
229: (0.03220, 0, 0),
231: (0.06095, 0, 0),
232: (0.05596, 0, 0),
126: (-0.00984, 0, 0),
127: (-0.04659, 0, 0),
132: (0.03982, 0, 0),
172: (0.03123, 0, 0),
# Nitrogen Compounds
118: (0.10475, 0, 0),
138: (0.03536, 0, 0),
249: (0.20709, 0, 0),
147: (0.06414, 0, 0),
294: (0.11210, 0, 0),
339: (0.02951, 0, 0),
175: (0.00316, 0, 0),
353: (0.03690, 0, 0),
354: (0.08293, 0, 0),
# Oxygen Compounds
129: (0.01757, 0, 0),
444: (0.03693, 0, 0),
174: (0.02100, 0, 0),
177: (-0.00849, 0, 0),
347: (-0.04098, 0, 0),
# Sulful Compounds
149: (0.07654, 0, 0)}
[docs]
class PRSV(Cubic):
r"""Peng-Robinson cubic equation of state with a modified dependence of
temperature by Stryjek-Vera [1]_
.. 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 + k\left(1-Tr^{0.5}\right)\\
k = k_0+k_1\left(1+\sqrt{T_r}\right)\left(0.7-T_r\right)\\
k_0 = 0.378893+1.4897153\omega-0.17131848\omega^2+0.0196554\omega^3\\
\end{array}
:math:`k_1` is a parameter characteristic to each compound given in [1]_
and [2]_
Examples
--------
Example 4.3 from [3]_, Propane saturated at 300K
>>> from lib.mezcla import Mezcla
>>> mix = Mezcla(5, ids=[4], caudalMolar=1, fraccionMolar=[1])
>>> eq = PRSV(300, 9.9742e5, mix)
>>> '%0.1f' % (eq.Vl.ccmol)
'86.8'
>>> eq = PRSV(300, 42.477e5, mix)
>>> '%0.1f' % (eq.Vg.ccmol)
'84.2'
"""
__title__ = "PRSV (1986)"
__status__ = "PRSV"
__doi__ = (
{"autor": "Stryjek, R., Vera, J.H.",
"title": "PRSV: An Improved Peng—Robinson Equation of State for Pure "
"Compounds and Mixtures",
"ref": "Can. J. Chem. Eng. 64 (1986) 323-333",
"doi": "10.1002/cjce.5450640224"},
{"autor": "Proust, P., Vera, J.H.",
"title": "PRSV: The Stryjek-Vera Modification of the Peng-Robinson"
"Equation of Stte. Parameters for Other Pure Compounds of "
"Industrial Interest",
"ref": "Can. J. Chem. Eng. 67 (1989) 170-173",
"doi": "10.1002/cjce.5450670125"},
{"autor": "Poling, B.E, Prausnitz, J.M, O'Connell, J.P",
"title": "The Properties of Gases and Liquids 5th Edition",
"ref": "McGraw-Hill, New York, 2001",
"doi": ""})
[docs]
def _cubicDefinition(self, T):
"""Definition of individual components coefficients"""
ai = []
bi = []
for cmp in self.componente:
Tr = T/cmp.Tc
k = self._k(cmp, Tr)
alfa = (1 + k*(1-Tr**0.5))**2
ao = 0.457235*R**2*cmp.Tc**2/cmp.Pc
b = 0.077796*R*cmp.Tc/cmp.Pc
ai.append(ao*alfa)
bi.append(b)
self.ai = ai
self.bi = bi
[docs]
def _GEOS(self, xi):
am, bm = self._mixture(None, xi, [self.ai, self.bi])
delta = 2*bm
epsilon = -bm**2
return am, bm, delta, epsilon
[docs]
def _k(self, cmp, Tr):
# Eq 11
ko = 0.378893 + 1.4897153*cmp.f_acent - \
0.17131848*cmp.f_acent**2 + 0.0196554*cmp.f_acent**3
if cmp.id in dat and Tr < 1:
k1 = dat[cmp.id][0]
else:
k1 = 0
k = ko + k1*(1+Tr**0.5)*(0.7-Tr)
return k
if __name__ == "__main__":
from lib.mezcla import Mezcla
mix = Mezcla(5, ids=[4], caudalMolar=1, fraccionMolar=[1])
eq = PRSV(300, 9.9742e5, mix)
print('%0.0f %0.1f' % (eq.Vg.ccmol, eq.Vl.ccmol))
eq = PRSV(300, 42.477e5, mix)
print('%0.1f' % (eq.Vl.ccmol))
