A Very Cool Rumination on Vapor-Liquid Cubic Equations of State.
The paper to which I'll refer here, written by scientists at Institute of Process System Engineering, Qingdao University of Science & Technology, People’s Republic of China is this one: Research into the Polynomial Alpha Function for the Cubic Equation of State (Wenying Zhao , Xiaoyan Sun, Li Xia, and Shuguang Xiang, Ind. Eng. Chem. Res., 2018, 57 (38), pp 12602–12623)
When I was a kid, I was doing a bunch of hydrogenations and because this sort of thing can be a little boring, I decided to program my HP41C calculator to solve cubic equations for the Van der Waals. The traditional way to monitor these things was to wait until the reaction stopped taking up hydrogen and work it up, but I was a dorky kid and so I programmed the calculator to do it. If I recall correctly, it came in within 2 or 3 percent of the theoretical value, so it kind of worked, but was more or less useless, because the reaction worked just as well if you didn't calculate the number of moles of hydrogen uptake from the P,V,T data.
Before my son went off to college, I challenged him to do the same thing (using Mathematica) for the Peng Robinson cubic equation, and he sort of made a decent stab at it, but largely blew it off to spend the last free days with his high school friends.
More and more, as I contemplate the awful state of our environment with respect to carbon dioxide (and other gases), I fantasize about reactors with mixtures of gases in them at high temperature - often involving supercritical fluids, especially the strange supercritical state of water - and I find myself thinking how I should find the time to think more about equations of states and their refinements.
It was thus with some joy that I came across the interesting paper linked herein. Here's a graphic from the paper:
The intro:
Formally, alpha functions can be divided into polynomial and exponential functions. In this work, we review and analyze the functional forms, parameter correlations, and scope of the polynomial alpha functions developed over the past 40 years. The research methods and developing trend for this kind of function are also reported. A review of exponential alpha functions will be made in a separate publication.
The "evolutionary tree" of cubic equations of state:
I suppose only a dork could be filled with joy at this sort of thing, but I'm a dork, and damned proud of it too.
I have to find some time to play with this paper.
I'd send it to my son, but he, apparently, has a life.
I'd just thought I'd throw this out there, because I think it beautiful, and more than ever, we need beautiful things.
I just realized the paper is open sourced if you'd like to try it.
= new reply since forum marked as read
I'm damn well pleased. And you're right: we do need beautiful things in our lives. 
