#!/usr/bin/python3
# -*- coding: utf-8 -*-
'''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 vdW(Cubic):
r"""Equation of state of van der Waals (1873), [1]_.
.. math::
\begin{array}[t]{l}
P = \frac{RT}{V-b}-\frac{a}{V^2}\\
a = 0.421875\frac{R^2T_c^2}{P_c}\\
b = 0.125\frac{RT_c}{P_c}\\
\end{array}
This equation is not accuracy and it's implemented only by its historic
relevance because it's the first cubic equation of state.
Examples
--------
Example 4.3 from [2]_, Propane saturated at 300K
>>> from lib.mezcla import Mezcla
>>> mix = Mezcla(5, ids=[4], caudalMolar=1, fraccionMolar=[1])
>>> eq = vdW(300, 9.9742e5, mix)
>>> '%0.1f' % (eq.Vl.ccmol)
'145.4'
>>> eq = vdW(300, 42.477e5, mix)
>>> '%0.1f' % (eq.Vg.ccmol)
'135.5'
"""
__title__ = "van der Waals (1890)"
__status__ = "vdW"
__doi__ = (
{"autor": "van der Waals, J.D.",
"title": "Over de Continuiteit van den Gas- En Vloestoftoestand",
"ref": "Dissertation, Leiden University, Leiden, Niederlande, 1873",
"doi": ""},
{"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=None):
"""Definition of individual components coefficients"""
# Schmidt-Wenzel factorization of terms
self.u = 0
self.w = 0
ai = []
bi = []
for cmp in self.componente:
a = 0.421875*R**2*cmp.Tc**2/cmp.Pc
b = 0.125*R*cmp.Tc/cmp.Pc
ai.append(a)
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 = 0
epsilon = 0
return am, bm, delta, epsilon
if __name__ == "__main__":
from lib.mezcla import Mezcla
mix = Mezcla(5, ids=[4], caudalMolar=1, fraccionMolar=[1])
eq = vdW(300, 9.9742e5, mix)
print(eq.Vl.ccmol)
eq = vdW(300, 42.477e5, mix)
print(eq._Z())
print('%0.1f' % (eq.Vg.ccmol))
