Critical Point Calculations by Numerical Inversion of Functions

TL;DR

This paper introduces a novel numerical inversion method for calculating critical points of mixtures, offering a robust and accurate alternative to existing techniques by transforming the problem into a system of nonlinear equations.

Contribution

It presents a new approach based on function inversion for critical point prediction, improving robustness and providing a global view of the nonlinear problem.

Findings

Method is robust and accurate in predicting critical points.

Compared favorably with classical and stochastic algorithms.

Offers a unified framework for critical point calculation.

Abstract

In this work, we propose a new approach to the problem of critical point calculation, based on the formulation of Heidemann and Khalil (1980). This leads to a $2 \times 2$ system of nonlinear algebraic equations in temperature and molar volume, which makes possible the prediction of critical points of the mixture through an adaptation of the technique of inversion of functions from the plane to the plane, proposed by Malta, Saldanha, and Tomei (1993). The results are compared to those obtained by three methodologies: ($i$) the classical method of Heidemann and Khalil (1980), which uses a double-loop structure, also in terms of temperature and molar volume; ($ii$) the algorithm of Dimitrakopoulos, Jia, and Li (2014), which employs a damped Newton algorithm and ($iii$) the methodology proposed by Nichita and Gomez (2010), based on a stochastic algorithm. The proposed methodology proves to be robust and accurate in the prediction of critical points, as well as provides a global view of the nonlinear problem.