International Journal of Thermophysics

, Volume 10, Issue 1, pp 61–73 | Cite as

Perturbation method for phase-equilibrium calculations

  • E. M. Hendriks


In phase equilibrium problems, the thermodynamic model used often contains a small parameter. For example, for cubic equations of state the interaction coefficients occurring in van der Waals-type mixing rules are often numerically small. The small parameter (ɛ) enters the model then via the formula
$$a = \sum\limits_{i = 1}^n {\sum\limits_{j = 1}^n {x_i x_j \sqrt {a_i a_j } (1 - \varepsilon \theta _{ij} )} }$$
Other examples include mixtures with compounds whose characteristic parameters cover a narrow range, diluted solutions, small amounts of polydisperse material in a solvent, and so on. In this paper we develop a general scheme to obtain the solution of thermodynamic problems such as the prediction of phase equilibria, using an expansion in the small parameter ε. We also give a method to obtain a suitable zero-order (ɛ = 0) system. The perturbation scheme may be helpful in the solution of difficult problems or as a tool in a sensitivity analysis. As an example we apply it to multicomponent mixtures, described through a two-parameter equation of state with small interaction coefficients. We show that for that case, if the number of components is large, it leads to computational savings.

Key words

perturbation method mixtures thermodynamic properties vapor-liquid equilibrium 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. A. Gualtieri, J. M. Kincaid, and G. Morrison, J. Chem. Phys. 77:521 (1982).Google Scholar
  2. 2.
    A. G. Schlijper, Fluid Phase Equil. 34:149 (1987).Google Scholar
  3. 3.
    E. M. Hendriks, I&EC Research 27:1728 (1988).Google Scholar
  4. 4.
    M. L. Michelsen, Ind. Eng. Chem. Process Des. Dev. 25:184 (1986).Google Scholar
  5. 5.
    E. M. Hendriks, Fluid Phase Equil. 33:207 (1987).Google Scholar
  6. 6.
    B. H. Jensen and A. Fredeslund, Ind. Eng. Chem. Res. 26:2129 (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • E. M. Hendriks
    • 1
  1. 1.Koninklijke/Shell LaboratoriumAmsterdamThe Netherlands

Personalised recommendations