Virial - Activity coefficient Model

This phase equilibrium model class uses a virial correlation for the vapor phase and an activity coefficient model for the liquid phase. For the gas phase, the virial coefficient can be estimated using ideal gas law, Abbott or Tsonopoulos correlations. For liquid phase, NRTL, Wilson, Redlich-Kister and Modified-UNIFAC activity coefficient models are available.

Before creating a phase equilibrium model object, it is necessary to supply the interactions parameters of the activity coefficient model to the mixture object, for example using the NRTL model:

>>> import numpy as np
>>> from phasepy import component, mixture, virialgamma
>>> water = component(name='water', Tc=647.13, Pc=220.55, Zc=0.229, Vc=55.948, w=0.344861,
                      Ant=[11.64785144, 3797.41566067, -46.77830444],
                      GC={'H2O':1})
>>> ethanol = component(name='ethanol', Tc=514.0, Pc=61.37, Zc=0.241, Vc=168.0, w=0.643558,
                        Ant=[11.61809279, 3423.0259436, -56.48094263],
                        GC={'CH3':1, 'CH2':1, 'OH(P)':1})
>>> mix = mixture(ethanol, water)
>>> alpha = np.array([[0.0, 0.5597628],
                      [0.5597628, 0.0]])
>>> g = np.array([[0.0, -57.6880881],
                  [668.682368, 0.0]])
>>> g1 = np.array([[0.0, 0.46909821],
                   [-0.37982045, 0.0]])
>>> mix.NRTL(alpha, g, g1)
>>> model = virialgamma(mix, virialmodel='Abbott', actmodel='nrtl')

Parameters for Redlich-Kister are specified as follows:

>>> C0 = np.array([1.20945699, -0.62209997, 3.18919339])
>>> C1 = np.array([-13.271128, 101.837857, -1100.29221])
>>> mix.rk(C0, C1)
>>> model = virialgamma(mix, actmodel='rk')

Modified-UNIFAC with an ideal gas model is set up simply:

>>> mix.unifac()
>>> model = virialgamma(mix, virialmodel='ideal_gas', actmodel='unifac')
class virialgamma(mix, virialmodel='Tsonopoulos', actmodel='nrtl')[source]

Bases: object

Returns a phase equilibrium model with mixture using a virial EOS to describe vapour phase, and an activity coefficient model for liquid phase.

Parameters:
  • mix (object) – mixture created with mixture class
  • virialmodel (string) – function to compute virial coefficients, available options are ‘Tsonopoulos’, ‘Abbott’ or ‘ideal_gas’
  • actmodel (string) – function to compute activity coefficients, available optiones are ‘nrtl’, ‘wilson’, ‘original_unifac’, ‘unifac’, ‘uniquac’, ‘rkb’ or ‘rk’
temperature_aux: computes temperature dependent parameters.
logfugef: computes effective fugacity coefficients.
dlogfugef: computes effective fugacity coefficients and its

composition derivatives.

lngama: computes activity coefficients.
dlngama: computes activity coefficients and its

composition derivatives.

dlngama(X, T)[source]

Computes the natural logarithm of activy coefficients and its composition derivatives matrix.

Parameters:
  • X (array) – molar fractions
  • T (float) – absolute temperature [K]
Returns:

  • lngama (array_like) – activity coefficient
  • dlngama (array_like) – derivatives of the activity coefficients
dlogfugef(X, T, P, state, v0=None)[source]

Returns array of effective fugacity coefficients at given composition, temperature and pressure as first return value, array of partial fugacity coefficients as second return value, and passes through argument v0 as third value.

Parameters:
  • X (array) – molar fractions
  • T (float) – absolute temperature [K]
  • P (float) – pressure [bar]
  • state (string) – ‘L’ for liquid phase, or ‘V’ for vapour phase
  • v0 (float, optional) – volume of phase
Returns:

  • logfug (array_like) – effective fugacity coefficients
  • dlogfug (array_like) – derivatives of effective fugacity coefficients
  • v0 (float) – volume of phase, if calculated
lngama(X, T)[source]

Computes the natural logarithm of activy coefficients.

Parameters:
  • X (array) – molar fractions
  • T (float) – absolute temperature [K]
Returns:

lngama – activity coefficients
Return type:

array_like
logfugef(X, T, P, state, v0=None)[source]

Returns array of effective fugacity coefficients at given composition, temperature and pressure as first return value, and passes through argument v0 as second value.

Parameters:
  • X (array) – molar fractions
  • T (float) – absolute temperature [K]
  • P (float) – pressure [bar]
  • state (string) – ‘L’ for liquid phase, or ‘V’ for vapour phase
  • v0 (float, optional) – volume of phase
Returns:

  • logfug (array_like) – effective fugacity coefficients
  • v0 (float) – volume of phase, if calculated