SGT for pure components

When working with pure components, SGT implementation is direct as there is a continuous path from the vapor to the liquid phase. SGT can be reformulated using the density as an independent variable.

\[\sigma = \sqrt{2} \int_{\rho^\alpha}^{\rho_\beta} \sqrt{c_i \Delta \Omega} d\rho\]

Here, \(\Delta \Omega\) represents the grand thermodynamic potential difference, obtained from:

\[\Delta \Omega = a_0 - \rho \mu^0 + P^0\]

Where \(P^0\) is the equilibrium pressure.

In SGTPy this integration is done using orthogonal collocation, which reduces the number of nodes needed for a desired error. This calculation is done with the sgt_pure function and it requires the equilibrium densities, temperature and pressure as inputs.

>>> from SGTPy import component, saftvrmie
>>> # The pure component is defined with the influence parameter
>>> 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 = 1.5371939422641703e-20)
>>> eos = saftvrmie(water)

First, vapor-liquid equilibria have to be computed. This is done with the psat method from the EoS, which returns the pressure and densities at equilibrium. Then the interfacial can be computed as it is shown. >>> from SGTPy.sgt import sgt_pure >>> T = 373. # K >>> P0 = 1e5 # Pa >>> P, vl, vv = eos.psat(T, P0=P0) >>> rhol = 1/vl >>> rhov = 1/vv >>> sgt_pure(rhol, rhov, T, P, eos) … array([58.84475645])

Optionally, full_output allows getting all the computation information as the density profile, interfacial length and grand thermodynamic potential.

>>> solution = sgt_pure(rhol, rhov, T, Psat, eos, full_output = True)
>>> solution.z # interfacial lenght array
>>> solution.rho # density path array
>>> solution.tension # IFT computed value