"""Implementation of Asymmetric NRTL Model"""
import numpy as np
from pyrast.activity_coefficients.activity_coefficient import ActivityCoefficient
[docs]
class ANRTL(ActivityCoefficient, model_name='aNRTL'):
r"""
The Asymmetric NRTL model is analagous to the Asymmetric NRTL model for vapor liquid
equlibria. The Asymmetric NRTL model is best suited for: UPDATE
The excess Gibbs free energy in the Asymmetric NRTL model is given by:
.. math::
\frac{g^E}{RT} = \frac{x_1 x_2 \tau_{12} (G_{12} - 1)}
{x_1 G_{12} + x_2} (1 - e^{-C \phi})
G_{12} = \exp(-\alpha \tau_{12}), \ \tau_{12} = -\tau_{21}, \ \alpha = 0.3
Sources: Kaur, H., Tun, H., Sees, M. & Chen, C.-C. Local composition activity
coefficient model for mixed-gas adsorption equilibria. Adsorption 25, 951-964
(2019).
Kopatsis, A., Salinger, A. & Myers, A. L. Thermodynamics of solutions with solvent
and solute in different pure states. AIChE Journal 34, 1275-1286 (1988).
"""
# Class variables for every instance
name = 'aNRTL'
param_names = ('t12', 'C')
param_default_bounds = ((-np.inf, np.inf), (0.0, np.inf))
param_ideal_values = (1.0,)
alpha = 0.3
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def ln_gamma(self, x, phi):
r"""Calculates the natural log of the activity coefficients for each component.
In the Asymmetric NRTL model, the activity coefficients are calculated as:
.. math::
\ln \gamma_1 = \frac{x_2^2 \tau_{12} (G_{12} - 1)}{(x_1 G_{12} + x_2)^2}
(1 - e^{-C \phi})
\ln \gamma_2 = \frac{x_1^2 \tau_{21} (G_{21} - 1)}{(x_2 G_{21} + x_1)^2}
(1 - e^{-C \phi})
Args:
x (array-like): Mole fractions of the components in the mixture.
phi (float): Spreading pressure for the mixture.
Returns:
np.ndarray: Natural log of the activity coefficients for each component.
"""
t12 = self.model_parameters['t12']
t21 = -t12
c = self.model_parameters['C']
f = 1.0 - np.exp(-c * phi)
alpha = self.alpha
g12 = np.exp(-alpha*t12)
g21 = np.exp(-alpha*t21)
ln_gamma0 = x[1]**2 * f * t12 * (g12 - 1.0) / (x[0] * g12 + x[1])**2
ln_gamma1 = x[0]**2 * f * t21 * (g21 - 1.0) / (x[1] * g21 + x[0])**2
return np.array([ln_gamma0, ln_gamma1])
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def inverse_excess_loading(self, x, phi):
r"""Calculates the inverse of the excess loading given composition and phi.
The excess loading in the Asymmetric NRTL model is calculated as:
.. math:: \left(\frac{1}{q}\right)^E = \frac{x_1 x_2 \tau_{12} (G_{12} - 1)}
{x_1 G_{12} + x_2} C e^{-C \phi}
Args:
x (array-like): Mole fractions of the components in the mixture.
phi (float): Spreading pressure for the mixture.
Returns:
float: Inverse of the excess loading for the mixture.
"""
t12 = self.model_parameters['t12']
g12 = np.exp(-self.alpha*t12)
c = self.model_parameters['C']
return c * x[0] * x[1] * t12 * (g12 - 1.0) * np.exp(-c * phi) / \
(x[0]*g12 + x[1])