lib.PR module

class lib.EoS.Cubic.PR.PR(T, P, mezcla, **kwargs)

Bases: Cubic

Peng-Robinson cubic equation of state, [1]

\[\begin{split}\begin{array}[t]{l} P = \frac{RT}{V-b}-\frac{a}{V\left(V+b\right)+b\left(V-b\right)}\\ a = 0.45747\frac{R^2T_c^2}{P_c}\alpha\\ b = 0.0778\frac{RT_c}{P_c}\\ \alpha^{0.5} = 1 + m\left(1-Tr^{0.5}\right)\\ m = 0.37464 + 1.54226\omega-0.26992\omega^2\\ \end{array}\end{split}\]

This EoS include too a special alpha temperature dependence for water as described in [2]

In supercritical states, the α temperature dependence use the Boston-Mathias expression, [4].

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

Examples

Example 4.3 from [3], Propane saturated at 300K

>>> from lib.mezcla import Mezcla
>>> mix = Mezcla(5, ids=[4], caudalMolar=1, fraccionMolar=[1])
>>> eq = PR(300, 9.9742e5, mix)
>>> '%0.1f' % (eq.Vl.ccmol)
'86.7'
>>> eq = PR(300, 42.477e5, mix)
>>> '%0.1f' % (eq.Vg.ccmol)
'84.1'

OmegaA = 0.45724

OmegaB = 0.0778

_cubicDefinition(T)

Definition of individual components coefficients

_lib(cmp)

_alfa(cmp, T)

α parameter calculation procedure, separate of general procedure to let define derived equation where only change this term like the 1978 version.

This method use the original alpha formulation for temperatures below the critical temperature and the Boston-Mathias formulation for supercritical states.

The procedure return too the m parameters because it’s used in Helmholtz formulation

Parameters:

cmpcomponente.Componente

Componente instance

Tfloat

Temperature, [K]

Returns:

mfloat

m parameter of equation, [-]

alphafloat

Correlation for alpha expresion at supercritical temperatures: * 0 - Original * 1 - Boston-Mathias

_GEOS(xi)

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)

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

_fugl2(Z, zi, a, b)

References

[1]

Peng, D.-Y., Robinson, D.B.; A New Two-Constant Equation of State, Ind. Eng. Chem. Fund. 15(1) (1976) 59-64, http://dx.doi.org/10.1021/i160057a011

[2]

Peng, D.-Y., Robinson, D.B.; Two- and Three-Phase Equilibrium Calculations for Coal Gasification and Related Processes, in Newman, Barner, Klein, Sandler (Eds.). Thermodynamic of Aqueous Systems with Industrial Applications. ACS (1980), pag. 393-414, http://dx.doi.org/10.1021/bk-1980-0133.ch020

[3]

Poling, B.E, Prausnitz, J.M, O’Connell, J.P; The Properties of Gases and Liquids 5th Edition, McGraw-Hill, New York, 2001

[4]

Boston, J.F., Mathias, P.M.; Phase Equilibria in a Third-Generation Process Simulator, Presented at: ‘Phase Equilibria and Fluid Properties in the Chemical Industries’, Berlin, March 17-21, 1980.