Analytically approximate solution to the VLE problem with the SRK equation of state

TL;DR

This paper introduces an analytical approximation method for vapor-liquid equilibrium calculations using the SRK equation of state, reducing computational effort and enabling easier thermodynamic property estimation across the entire coexistence curve.

Contribution

It presents a novel analytical approximation procedure for VLE with cubic EoS, applicable to the SRK EoS and potentially other cubic EoS, simplifying calculations and reducing iterative efforts.

Findings

Analytical solutions can replace iterative numerical methods in VLE calculations.

A one-time effort to develop a databank of coefficients enables quick property retrieval.

The approach simplifies the solution of the transcendental equation in cubic EoS-based VLE problems.

Abstract

Since a transcendental equation is involved in vapor liquid equilibrium (VLE) calculations with a cubic equation of state (EoS), any exact solution has to be carried out numerically with an iterative approach [1,2]. This causes significant wastes of repetitive human efforts and computing resources. Based on a recent study [3] on the Maxwell construction [4] and the van der Waals EoS [5], here we propose a procedure for developing analytically approximate solutions to the VLE calculation with the Soave-Redlich-Kwong (SRK) EoS [6] for the entire coexistence curve. This procedure can be applied to any cubic EoS and thus opens a new area for the EoS study. For industrial applications, a simple databank can be built containing only the coefficients of a newly defined function and other thermodynamic properties will be obtained with analytical forms. For each system there is only a one-time effort, and therefore, the wastes caused by the repetitive efforts can be avoided. By the way, we also show that for exact solutions, the VLE problem with any cubic EoS can be reduced to solving a transcendental equation with one unknown, which can significantly simplify the methods currently employed [2,7].