lib.SRK module

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

Bases: Cubic

Equation of state of Soave-Redlich-Kwong (1972)

\[\begin{split}\begin{array}[t]{l} P = \frac{RT}{V-b}-\frac{a}{V\left(V+b\right)}\\ a = 0.42747\frac{R^2T_c^2}{P_c}\alpha\\ b = 0.08664\frac{RT_c}{P_c}\\ \alpha^{0.5} = 1 + m\left(1-Tr^{0.5}\right)\\ m = 0.48 + 1.574\omega - 0.176\omega^2\\ \end{array}\end{split}\]

In supercritical states, the α temperature dependence can use different extrapolation correlation:

  • Boston-Mathias expression, [3]

\[\begin{split}\begin{array}[t]{l} \alpha = \exp\left(c\left(1-T_r^d\right)\right)\\ d = 1+\frac{m}{2}\\ c = \frac{m}{d}\\ \end{array}\end{split}\]

  • Nasrifar-Bolland expression, [4]

\[\begin{split}\begin{array}[t]{l} \alpha = \frac{b_1}{T_r} + \frac{b_2}{T_r^2} + \frac{b_3}{T_r^3}\\ b_1 = 0.25\left(12 - 11m + m^2\right)\\ b_2 = 0.5\left(-6 + 9m - m^2\right)\\ b_3 = 0.25\left(4 - 7m + m^2\right)\\ \end{array}\end{split}\]
Parameters:
alphaint
Correlation index for alpha expresion at supercritical temperatures:

  • 0 - Original

  • 1 - Boston

  • 2 - Nasrifar

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 = SRK(300, 9.9742e5, mix)
>>> '%0.1f' % (eq.Vl.ccmol)
'98.4'
>>> eq = SRK(300, 42.477e5, mix)
>>> '%0.1f' % (eq.Vg.ccmol)
'95.1'

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 with high precision

>>> from lib.mezcla import Mezcla
>>> from lib import unidades
>>> 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
>>> mix = Mezcla(5, customCmp=[ch4, o2, ar], caudalMolar=1,
...              fraccionMolar=[0.5, 0.3, 0.2])
>>> eq = SRK(800, 36451227.52066596, mix, R=8.3144598)
>>> fir = eq._phir(800, 5000, eq.yi)
>>> delta = 5000
>>> tau = 1/800
>>> print("fir: %0.14f" % (fir["fir"]))
fir: 0.11586323513845
>>> print("fird: %0.14f" % (fir["fird"]*delta))
fird: 0.12741566551477
>>> print("firt: %0.15f" % (fir["firt"]*tau))
firt: -0.082603152680518
>>> print("firdd: %0.15f" % (fir["firdd"]*delta**2))
firdd: 0.024895937945147
>>> print("firdt: %0.15f" % (fir["firdt"]*delta*tau))
firdt: -0.077752734990782
>>> print("firtt: %0.14f" % (fir["firtt"]*tau**2))
firtt: -0.10404751064185
>>> print("firddd: %0.16f" % (fir["firddd"]*delta**3))
firddd: 0.0060986538256190
>>> print("firddt: %0.16f" % (fir["firddt"]*delta**2*tau))
firddt: 0.0089488831000362
>>> print("firdtt: %0.15f" % (fir["firdtt"]*delta*tau**2))
firdtt: -0.097937890490398
>>> print("firttt: %0.14f" % (fir["firttt"]*tau**3))
firttt: 0.15607126596277
_cubicDefinition(T)[source]

Definition of coefficients for generic cubic equation of state

_lib(cmp)[source]
_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

_alfa(cmp, T)[source]

α parameter calculation procedure, separate of general procedure to let define derived equation where only change this term.

This method use the original alpha formulation for temperatures below the critical temperature and can choose by configuration between:

  • Boston-Mathias formulation

  • Nasrifar-Bolland formulation

Parameters:
cmpcomponente.Componente

Componente instance

Tfloat

Temperature, [K]

Returns:
alphafloat

alpha parameter of equation, [-]

_m(cmp)[source]

Calculate the intermediate parameter for alpha expression

_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