phasepy.equilibrium¶

Phase equilibrium conditions are obtained from a differential entropy balance of a system. The following equationes must be solved:

\[\begin{split}T^\alpha = T^\beta = ... &= T^\pi\\ P^\alpha = P^\beta = ... &= P^\pi\\ \mu_i^\alpha = \mu_i^\beta = ... &= \mu_i^\pi \quad i = 1,...,c\end{split}\]

Where \(T\), \(P\) and \(\mu\) are the temperature, pressure and chemical potencial, \(\alpha\), \(\beta\) and \(\pi\) are the phases and \(i\) is component index.

For the continuous (\(\phi-\phi\)) phase equilibrium approach, equilibrium is defined using fugacity coefficients \(\phi\):

\[x_i^\alpha\hat{\phi}_i^\alpha = x_i^\beta \hat{\phi}_i^\beta = ... = x_i^\pi \hat{\phi}_i^\pi \quad i = 1,...,c\]

For the discontinuous (\(\gamma-\phi\)) phase equilibrium approach, the equilibrium is defined with vapor fugacity coefficient and liquid phase activity coefficients \(\gamma\):

\[x_i^\alpha\hat{\gamma}_i^\alpha f_i^0 = x_i^\beta \hat{\gamma}_i^\beta f_i^0 = ... = x_i^\pi\hat{\phi}_i^\pi P \quad i = 1,...,c\]

where \(f_i^0\) is standard state fugacity.