Ii can only notice that almost any cubic equation of state can be applied to VLE if pure component parameters (e.g., the alpha parameter in cubic EOS's) are fitted to the components' vapor pressures. That automatatically improves the calculation of thermal properties also. And by proper mixing rules (VdW ones with a single adjustable kij, for non polar components, or more complex rules with more parameters for others) VLE behaviour can be reproduced fairly. Regardless of the volumetric proprties, which are used only as calculation parameters.

Anyway I must remember that the classical quadratic mixing rules in general perform well for VLE of mixtures of polar components also, if none of them is non associating; i.e. none of them exhibits self association like in water and alkanols

Based on my experience in simulation of Gas Processing and comparing the result with the reality, you are right, cubic EOS's are using largely in predicting behavior of non-polar species like hydrocarbon. But few changes required: e.g. Lee-Kesler correlation for enthalpy.

PC-SAFT based EOS I used before for aforementioned simulation and comparison between the results and reality failed and I think many effort has been remained to accurate statistical based models.

There is no concern to use cubic EOS. The results are acceptable. 

Massimiliano, as you said and as far as I know cubic EoS's can produce highly acceptable results, are you working on a specific system phase equilibrium? 

In case you did not read it, check the book "molecular thermodynamic of phase equilibria" by Prausnitz, not only you can find comprehensive discussion about each type it also addresses the main reference papers on Stat. Mech based models.

If the focus is on polar and associating species, then yes, statistical associating fluid theory (SAFT) is better than a classical cubic equation of state. There is however a hybrid of the two called Cubic-Plus-Association (CPA), which uses a cubic equation of state along with a slightly modified version of the association term in SAFT. The CPA has been found to be effective at polar and associating mixtures. In the absence of associating species it also returns to the cubic form. However, along the lines of modified cubic equations of state, there are also advanced mixing rule cubic equations of state which use activity coefficients inside the cubics mixing rules. These are also good at polar and associating mixtures. There are also Phi-Gamma models such as pairing the Hayden O'Connell vapor phase model with an activity coefficient model such as the NRTL or UNIQUAC, but that is deviating from your question.

The advantage cubic equations of state have over "statistical" models is that they are very fast and also very easy to implement. SAFT and its variants such as perturbed chain (PC)-SAFT are much harder to code/use and aren't as fast because they involve nested iteration loops. The complexity of SAFT is most of its downfall, the speed isn't so much of an issue.

The advantage of SAFT is that while "bulkier" it is capable of handling associating components. Cubics can't; you can only try to tune their interaction parameters to specific(small) ranges if you need to use them for associating and polar components.

At the end of the day, despite SAFT having a more advanced theoretical foundation it still requires parameter regression i.e. it takes the same amount of optimizing as a cubic equation prior to being used.

I strongly recommend the textbook by Professor Georgios Kontogeorgis and Dr. Georgios Folas titles "Thermodynamic Models for industrial Applications: From classical and advanced mixing rules to Association Theories" as well as the textbook by Professors Michael Michelson and Jorgen Mollerup titled "Thermodynamic Models: Fundamentals & Computational Aspects".

The first covers everything you need to know about your question, and the second dives deeper into the computational aspects of coding/using each for phase equilibrium and chemical reactions.

Here is a link to the first book that will let you see the table of contents. https://books.google.ca/books?hl=en&lr=&id=xJchfLU5T1QC&oi=fnd&pg=PR7&dq=thermodynamic+models+for+industrial+application&ots=ZKiLTAQFWI&sig=tDLDV1yKXvFw74zwFME_TsHRs4k#v=onepage&q=thermodynamic%20models%20for%20industrial%20application&f=false

And here is a paper which shows just how poorly cubic equations of state perform when attempting VLLE of associating and polar mixtures: http://pubs.acs.org/doi/abs/10.1021/acs.iecr.5b02616

Ii can only notice that almost any cubic equation of state can be applied to VLE if pure component parameters (e.g., the alpha parameter in cubic EOS's) are fitted to the components' vapor pressures. That automatatically improves the calculation of thermal properties also. And by proper mixing rules (VdW ones with a single adjustable kij, for non polar components, or more complex rules with more parameters for others) VLE behaviour can be reproduced fairly. Regardless of the volumetric proprties, which are used only as calculation parameters.

Anyway I must remember that the classical quadratic mixing rules in general perform well for VLE of mixtures of polar components also, if none of them is non associating; i.e. none of them exhibits self association like in water and alkanols

Dear Mr Soave,

It is with pleasure to see your comment.

As you mentioned,in addition to non-polars, based on my experience in simulation of NGL recovery, some times, presence of a (weak) polar components like CO2 and other (weak) polar component in hydrocarbon mixtures will results in unreliable prediction of kij factors. Because kij is set constant vs. temperature in conventional simulators.

In Gas Processing , I tried to improve CO2-C2 kij parameter, using experimental data.

The result was acceptable but using of Perturbed model was not.

For non-polar component, results of cubic EOS like PR, and SRK are acceptable but with presence of dipole or quad poles, the results will deviate. It is necessary to adjust kij for any case and it is recommended for process simulators to tune adjustable parameters kij's.