lib.PRMathiasCopeman module

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

Bases: Cubic

Mathias-Copeman alpha temperature dependency modification of Peng-Robinson cubic equation of state, [1]

\[\begin{split}\begin{array}[t]{l} P = \frac{RT}{V-b}-\frac{a}{V\left(V+b\right)+b\left(V-b\right)}\\ a = 0.45747\frac{R^2T_c^2}{P_c}\alpha\\ b = 0.0778\frac{RT_c}{P_c}\\ \alpha^{0.5} = 1 + c_1\left(1-Tr^{0.5}\right) + c_2\left(1-Tr^{0.5}\right)^2 + c_3\left(1-Tr^{0.5}\right)^3\\ \end{array}\end{split}\]

In case T > Tc it use a special alpha temperature dependence give in [3]

\[\alpha^{0.5} = 1 + c_1\left(1-Tr^{0.5}\right)\]

The C1, C2 and C3 parameters are those given in [2]

Parameters:
alphaint
Correlation index for alpha expresion at supercritical temperatures:

  • 0 - Original

  • 1 - Coquelet formulation

Examples

Helmholtz energy formulation example for supplementary documentatión from [4], the critical parameter are override for the valued used in paper to get the values of test

>>> from lib.mezcla import Mezcla
>>> from lib.compuestos import Componente
>>> ch4 = Componente(2)
>>> ch4.Tc, ch4.Pc, ch4.f_acent = 190.564, 4599200, 0.011
>>> o2 = Componente(47)
>>> o2.Tc, o2.Pc, o2.f_acent = 154.581, 5042800, 0.022
>>> ar = Componente(98)
>>> ar.Tc, ar.Pc, ar.f_acent = 150.687, 4863000, -0.002
>>> zi = [0.5, 0.3, 0.2]
>>> cmpList = [ch4, o2, ar]
>>> mix = Mezcla(5, customCmp=cmpList, caudalMolar=1, fraccionMolar=zi)
>>> eq = PRMathiasCopeman(800, 34933409.8798343, mix, R=8.3144598)
>>> fir = eq._phir(800, 5000, eq.yi)
>>> delta = 5000
>>> tau = 1/800
>>> print("fir: %0.15f" % (fir["fir"]))
fir: 0.034118184296355
>>> print("fird: %0.15f" % (fir["fird"]*delta))
fird: 0.050381225002564
>>> print("firt: %0.14f" % (fir["firt"]*tau))
firt: 0.10841024634867
>>> print("firdd: %0.15f" % (fir["firdd"]*delta**2))
firdd: 0.031329489702333
>>> print("firdt: %0.15f" % (fir["firdt"]*delta*tau))
firdt: 0.098515746761245
>>> print("firtt: %0.14f" % (fir["firtt"]*tau**2))
firtt: -0.55088266208097
>>> print("firddd: %0.16f" % (fir["firddd"]*delta**3))
firddd: -0.0018875965519497
>>> print("firddt: %0.15f" % (fir["firddt"]*delta**2*tau))
firddt: -0.016659995071735
>>> print("firdtt: %0.14f" % (fir["firdtt"]*delta*tau**2))
firdtt: -0.50060412793624
>>> print("firttt: %0.13f" % (fir["firttt"]*tau**3))
firttt: 2.5911592464473
_cubicDefinition(T)[source]

Definition of coefficients for generic cubic equation of state

_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

_da(tau, x)[source]

Calculate the derivatives of α, this procedure is used for Helmholtz energy formulation of EoS for calculation of properties, alternate alfa formulation must define this procedure for any change of formulation

References