Calculation of Vapor-Liquid Equilibria by Making Use of Implicit Function

Kengo Shimizu, Hayatoshi Sayama, Yoshimasa Kameyama, Kazuhiko Suzuki

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


A number of computational methods have been proposed for solving multicomponent vapor-liquid equilibrium and distillation problems. Many of these methods employing a gradient-type algorithm involve numerical differentiation for evaluation of the partial derivatives. This may require a large amount of computation time and often gives rise to numerical instability, especially in problems with microcomponent. This paper presents a new computation procedure for multicomponent nonideal vapor-liquid equilibrium problems. The liquid compositions are chosen as the independent variables and the temperature is considered as the dependent variable. The partial derivatives of vapor compositions with respect to the liquid compositions are derived analytically by making use of the implicit function theorem. The iterative solution procedure is based on the gradient method (Newton-Raphson or Gauss-Newton method), which uses analytical equations for the partial derivatives and approach to the solutions with the liquid and vapor composition constraints satisfied. The iteration procedure gives numerically stable and rigorous solutions to multicomponent dew point problems.

Original languageEnglish
Pages (from-to)1095-1101
Number of pages7
Issue number6
Publication statusPublished - 1989


  • Dew Point
  • Gauss-Newton Method
  • Gradient Method
  • Implicit Function
  • Vapor-Liquid Equilibria

ASJC Scopus subject areas

  • Chemistry(all)
  • Chemical Engineering(all)


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