lib.PT module

class lib.EoS.Cubic.PT.PT(T, P, mezcla, **kwargs)[source]

Bases: Cubic

Patel-Teja cubic equation of state implementation

\[\begin{split}\begin{array}[t]{l} P = \frac{RT}{V-b}-\frac{a}{V\left(V+b\right)+c\left(V-b\right)}\\ a = \Omega_a\frac{R^2T_c^2}{P_c}\alpha\\ b = \Omega_b\frac{RT_c}{P_c}\\ c = \Omega_c\frac{RT_c}{P_c}\\ \Omega_c = 1 - 3\zeta_c\\ \Omega_a = 3\zeta_c^2 + 3\left(1-2\zeta_c\right)\Omega_b + \Omega_b^2 + 1 - 3\zeta_c\\ \end{array}\end{split}\]

\(\Omega_b\) is the smallest positive root or the equation:

\[\Omega_b^3 + \left(2-3\zeta_c\right)\Omega_b^2 + 3\zeta_c^2\Omega_b - \zeta_c^3 = 0\]

The paper give generation correlation for F and ζc, valid only for nonpolar compounds.

\[\begin{split}\begin{array}[t]{l} F = 0.452413 + 1.30982\omega - 0.295937\omega^2\\ \zeta_c = 0.329032 - 0.076799\omega + 0.0211947\omega^2\\ \end{array}\end{split}\]

In [1] and [3] there are values for these parameters for several compounds.

The temperature dependence of alpha is defined in [2]

\[\alpha = 1 + c_1\left(T_r-1\right) + c_2\left(\sqrt{T_r}-1\right) + c_3\left(T_r^N-1\right)\]

where c₁, c₂, c₃ and N are compound specific parameters available for several compounds from [2]. In compound with no parameters available use the SRK original temperature dependence:

\[\begin{split}\alpha^{0.5} = 1 + F\left(1-Tr^{0.5}\right)\\\end{split}\]

Examples

Example 4.3 from [4], Propane saturated at 300K

>>> from lib.mezcla import Mezcla
>>> mix = Mezcla(5, ids=[4], caudalMolar=1, fraccionMolar=[1])
>>> eq = PT(300, 9.9742e5, mix)
>>> '%0.1f' % (eq.Vl.ccmol)
'90.9'
>>> eq = PT(300, 42.477e5, mix)
>>> '%0.1f' % (eq.Vg.ccmol)
'88.1'
_cubicDefinition(T)[source]

Definition of individual components coefficients

_GEOS(xi)[source]

Definition of parameters of generalized cubic equation of state, each child class must define in this procedure the values of mixture a, b, delta, epsilon. The returned values are not dimensionless.

Parameters:
xilist

Molar fraction of component in mixture, [-]

Returns:
parameterslist

Mixture parameters of equation, a, b, c, d

_lib(cmp, T)[source]

References