SGTPy
SGTPy is an object-oriented python software for phase equilibria and interfacial properties calculation using SAFT-VR-Mie EoS. The SAFT-VR-Mie Equation of State describes the Helmholtz free energy as follows:
Where, \(a\) is the total Helmholtz free energy, \(a^{IG}\) is the ideal gas reference, \(a^{MONO}\) represents monomer (unbounded) contribution, \(a^{CHARI}\) accounts for the formation of chain and ring molecule while \(a^{ASSOC}\) accounts for the intermolecular association contribution and \(a^{POL}\) represents the polar contribution. For further information about each contribution, we recommend the original references [1], [2], [3].
The coded equation of state was tested to pass the following molar partial property test and Gibbs-Duhem consistency:
\[\begin{split}\ln \phi - \sum_{i=1}^c x_i \ln \hat{\phi_i} = 0 \\ \frac{d \ln \phi}{dP} - \frac{Z - 1}{P} = 0 \\ \sum_{i=1}^c x_i d \ln \hat{\phi_i} = 0\end{split}\]
Here, \(\phi\) is the fugacity coefficient of the mixture, \(x_i\) and \(\hat{\phi_i}\) is the mole fraction and fugacity coefficient of component \(i\), \(P\) refers to pressure and \(Z\) to the compressibility factor.
To use SGTPy, first, it is required to create components and mixtures, and then combine them with the equation of state to create a final model object, which can be used to carry out the desired calculations.
With the class SGTPy.component, only pure component info is saved. These parameters are required to evaluate SAFT-VR-Mie EoS. This includes numbers of segments (\(m_s\)), well-depth of Mie potential (\(\epsilon\)) in K units, size parameter of Mie potential (\(\sigma\)) in Å (\(10^{-10}\) m) , attractive (\(\lambda_a\)) and repulsive (\(\lambda_r\)) exponents of Mie Potential. If the fluid is modeled as a ring it requires a geometric factor (\(\chi\)) [2]. For the case of pure self-associating fluid, three extra parameters are needed: the association energy (\(\epsilon^{AB}\)) in K units, the association range (\(r_c^{AB}/\sigma\)) and association center position (\(r_d^{AB}/\sigma\)). Additionally, the association scheme is characterized by the triple [B, P, N], which indicates the number of bipolar, positive and negative association sites, respectively. The polar contribution requires the definition of a dipolar moment (\(\mu\)) in Debye units, and the number of polar sites (\(n_p\)).
Finally, the influence parameter (\(c_{ii}\)) in J m \(^5\) / mol \(^2\) is required to study the interfacial behavior using Square Gradient Theory.
>>> from SGTPy import component
>>> water = component('water', ms = 1.7311, sigma = 2.4539 , eps = 110.85,
... lambda_r = 8.308, lambda_a = 6., eAB = 1991.07, rcAB = 0.5624,
... rdAB = 0.4, sites = [0,2,2], cii = 1.5371939421515458e-20)
>>> water.sigma
... 2.4539e-10 # stored in meters
>>> water.eps
... 1.5304491948e-21 # stored in Joules
>>> butanol = component('butanol2C', ms = 1.9651, sigma = 4.1077 , eps = 277.892,
... lambda_r = 10.6689, lambda_a = 6., eAB = 3300.0, rcAB = 0.2615,
... rdAB = 0.4, sites = [1,0,1], npol = 1.45, mupol = 1.6609,
... cii = 1.5018715324070352e-19)
>>> butanol.rcAB
... 1.0741635500000002e-10 # stored in meters
>>> butanol.eAB
... 4.55614104e-20 # stored in Joules
A mixture can be created from two components and the SGTPy.mixture class:
>>> from SGTPy import mixture
>>> mix = mixture(water, butanol)
>>> mix.sigma
... [2.4539e-10, 4.1077000000000007e-10]
>>> mix.mupol
... [0, 1.6609] # dipolar moment in Debye
The mix object stores pure component molecular parameters and allows to set interaction corrections for the cross-association energy and the Mie potential interaction energy. Both pure component or fluid mixture can be modeled with SAFT-VR-Mie EoS, examples of how to use obtain properties from the EoS are shown in the following sections.
A complete list of available calculations in SGTPy is found here.