Convex hull method for the determination of vapour-liquid equilibria (VLE) phase diagrams for binary and ternary systems

Amieibibama Joseph, Christine M. Sands, Peter D. Hicks, Howard W. Chandler

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
12 Downloads (Pure)


Flash calculations are widely used and constitute an integral part of modelling vapour-liquid equilibria in compositional simulators. However, it has been discovered that during compositional simulations, flash calculations take 50–70% of the overall computational time because the procedure currently used is iterative. Hence, several methods such as the reduced variable method, compositional space adaptive tabulation (CSAT) and the tie-line table look-up (TTL) have been developed to improve on the computational speed of most flash calculations during compositional simulations. Unfortunately, most of these methods are still iterative, and pose convergence problems, even though some are developed with efficient Newton-Raphson algorithms. Non-iterative techniques may be the best option to speed up the computational time during simulations. This paper presents a non-iterative procedure for the determination of fluid phase diagrams using the convex hull method and Peng-Robinson equation of state. Convex hull is a mathematical method, and algorithmic implementations of this method are available in many software packages, of which Matlab was used in this work. Unlike the conventional flash calculation method, programs developed with convex hull does not the need an accurate start value to make fluid phase diagrams and determine phase properties for binary and ternary mixtures. The time taken to complete a simulation run using convex hull and the conventional flash calculation method were noted, and the numerical results from both methods was validated against a range of experimental data for different mixtures. The results show good agreement in all the cases investigated. From the analyses, it was shown that the convex hull method is faster than the conventional flash calculation method in achieving convergence and also gave better predictions close to the critical point. The reliability of the results and the additional time benefits are indication that the convex hull method has a promising prospect of becoming an efficient procedure for modelling vapour-liquid phase equilibria calculations for compositional simulations.
Original languageEnglish
Pages (from-to)34-47
Number of pages14
JournalFluid Phase Equilibria
Early online date22 Sept 2016
Publication statusPublished - 15 Jan 2017

Bibliographical note

Amieibibama Joseph wishes to thank Petroleum Technology Development Fund (PTDF) for their financial support which has made this research possible.


  • convex hull
  • Peng-Robinson EoS
  • Excess Gibbs energy
  • phase diagram
  • vapour-liquid equilibria
  • flash calculation


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