Source code for lib.EoS.Cubic.Kubic
#!/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
[docs]
class Kubic(Cubic):
r"""Kubic cubic equation of state, [1]_
This is a two parameter cubic equation of state with both parameters
temperature dependent
.. math::
\begin{array}[t]{l}
P = \frac{RT}{V-b}-\frac{a(T)}{\left(V+c\right)^2}\\
a(T) = \frac{27}{64} \frac{R^2T_c^2}{P_c}
\left(\alpha^0\left(T_r\right)+\omega'\alpha^1\left(T_r\right)\right)\\
\alpha^0 = -0.1514T_r + 0.7895 + \frac{0.3314}{T_r} +
\frac{0.029}{T_r^2} + \frac{0.0015}{T_r^7}\\
\alpha^1 = -0.237T_r - \frac{0.7846}{T_r} + \frac{1.0026}{T_r^2} +
\frac{0.019}{T_r^7}\\
b = \left(0.082-0.0715\omega'\right)\frac{RT_c}{P_c}\\
c = \left(0.043\gamma^0\left(T_r\right)+0.0713\omega'\gamma^1
\left(T_r\right)\right)\frac{RT_c}{P_c}\\
\gamma^0 = 4.275051 - \frac{8.878889}{T_r} + \frac{8.508932}{T_r^2} -
\frac{3.481408}{T_r^3} + \frac{0.576312}{T_r^4}\\
\gamma^1 = 12.856404 - \frac{34.744125}{T_r} + \frac{37.433095}{T_r^2}
- \frac{18.059421}{T_r^3} + \frac{3.514050}{T_r^4}\\
\omega' = 0.000756+0.90984\omega+0.16226\omega^2+0.14549\omega^3\\
\end{array}
"""
__title__ = "Kubic (1982)"
__status__ = "Kubic"
__doi__ = {
"autor": "Kubic, W.L.",
"title": "A Modification of the Martin Equation of State for "
"Calculating Vapour-Liquid Equilibria",
"ref": "Fluid Phase Equilibria 9 (1982) 79-97",
"doi": "10.1016/0378-3812(82)85006-1"},
[docs]
def _cubicDefinition(self, T):
"""Definition of individual components coefficients"""
ai = []
bi = []
ci = []
for cmp in self.componente:
a, b, c = self._lib(cmp, T)
ai.append(a)
bi.append(b)
ci.append(c)
self.ai = ai
self.bi = bi
self.ci = ci
[docs]
def _GEOS(self, xi):
am, bm, cm = self._mixture(None, xi, [self.ai, self.bi, self.ci])
delta = 2*cm
epsilon = cm**2
return am, bm, delta, epsilon
[docs]
def _lib(self, cmp, T):
Tr = T/cmp.Tc
# Eq 26
omega = 0.000756 + 0.90984*cmp.f_acent + 0.16226*cmp.f_acent**2 + \
0.14549*cmp.f_acent**3
# Eq 24
g0 = 4.275051 - 8.878889/Tr + 8.508932/Tr**2 - 3.481408/Tr**3 + \
0.576312/Tr**4
# Eq 25
g1 = 12.856404 - 34.744125/Tr + 37.433095/Tr**2 - 18.059421/Tr**3 + \
3.514050/Tr**4
# Eq 20
a0 = -0.1514*Tr + 0.7895 + 0.3314/Tr + 0.029/Tr**2 + 0.0015/Tr**7
# Eq 21
a1 = -0.237*Tr - 0.7846/Tr + 1.0026/Tr**2 + 0.019/Tr**7
b = (0.082 - 0.0713*omega)*R*cmp.Tc/cmp.Pc # Eq 22
c = (0.043*g0 + 0.0713*omega*g1)*R*cmp.Tc/cmp.Pc # Eq 23
a = 27/64*(a0+omega*a1)*R**2*cmp.Tc**2/cmp.Pc # Eq 19
return a, b, c
if __name__ == "__main__":
from lib.mezcla import Mezcla
mix = Mezcla(5, ids=[4], caudalMolar=1, fraccionMolar=[1])
eq = Kubic(300, 9.9742e5, mix)
print('%0.0f %0.1f' % (eq.Vg.ccmol, eq.Vl.ccmol))
eq = Kubic(300, 42.477e5, mix)
print('%0.1f' % (eq.Vl.ccmol))
