Select thermodynamic models for process simulation
A Practical Guide to a Three Steps Methodology

Chapter 4 – Abstract

It is impossible to choose correctly a model if the phase behaviour of the system is unknown. The aim of this fourth chapter is therefore to provide a phenomenological understanding of the various phases that may exist in mixtures of industrial interest, and the behaviour of the properties as a function of pressure and temperature. Obviously, the reader should not expect an exhaustive review, since it would extend far beyond the scope of this book. The interested reader will be invited to consult other documents for further study [1-3].

Generalities about phase behaviour are discussed in section 2.1.3. The phases are often labelled as vapour, liquid and solid. Solid phases are generally easy to differentiate from the fluid phases because of their specific crystalline character. Amorphous (i.e. highly viscous, but non-crystalline) solids may be treated as liquids, and will not be considered here. Concerning vapour and liquid phases, it has been mentioned that it may not always be obvious to differentiate between them. The best criterion considers the density of the phase and its compressibility with respect to pressure. The critical vapour-liquid zone may require special attention since the mathematical expressions used for property calculations must display continuous behaviour.

In this chapter, we intend to present the recommended thermodynamic methods, in the sense that was introduced in the first chapter: a method is a combination of models that provide a final numerical value for the requested property(-ies), possibly through the use of an algorithmic computation. The recommendations depend on the phases at hand. This is why these various phases will be first defined in a somewhat more detailed manner. The fluid property behaviour within these phases will be discussed. The recommended calculation method for single phase properties will be provided, both for pure components as for mixtures. On this subject, it is important to mention the well-known book of Poling et al. 2001 [4] and the previous versions of Reid et al. [5, 6], who investigate and recommend a large number of methods in very specific conditions.

In the second section of this chapter, the type of phase equilibrium behaviour will be reviewed considering the main components in the mixture. For each subsection, the conditions of occurrence of the various phase equilibria will be mentioned; the order of magnitude of the solubilities will be given and some recommended models will be proposed.

In a concluding section, some general guidelines are provided, including a decision tree that covers the most frequently encountered situations.

The interest of using the homogeneous or heterogeneous approach is discussed and illustrated in table 4.6. The decision tree (figure 4.59) and its comments refers back to all specialized sections of the chapter. Table 4.6: Heterogeneous and homogeneous approaches for vapour- liquid distribution coefficients calculation (taken from [7]).

  • High pressures
  • Phase envelope calculation, including the near-critical region
  • Improved accuracy because of the large choice of models, in particular for non-ideal mixtures
  • Limited by the choice of an appropriate mixing rule
  • Limited to pressures below 1.0 MPa*
  • No phase envelope calculation
  • Requires the asymmetric convetions in case of superficial components
  • Unable to take into account free-volume effects in polymer-solvent systems

*: there is no truly theorical reason for this limit to 1.0 MPa: use of a Poynting correction can enlarge the validity domain to 1.5 Mpa, but above this pressure, one of the components is often supercritical, resulting in the need to use the asymmetric convetion.

Figure 4.59: Decision tree for fluid phase equilibrium calculations
click here for a full view


  1. de Swaan Arons, J. and de Loos, T. “Phase Behavior: Phenomena, Significance and Models”; Ed. Sandler, S. I.; Marcel Dekker, Inc., 1994.
  2. Kiran, E. and Levelt Sengers, J. M. H. “Supercritical Fluids; Fundamentals for Applications”; Kluwer Academic Publishers, 1994.
  3. Sadus, R. J. “High Pressure Phase Behaviour of Multicomponent Fluid Mixtures”; Elsevier Science Publisher: Amsterdam, 1992.
  4. Poling, B. E., Prausnitz, J. M. and O’Connell, J. P. “The Properties of Gases and Liquids” 5th Ed.; McGraw-Hill: New York, 2000.
  5. Reid, R. C., Prausnitz, J. M. and Sherwood, T. K. “The Properties of Gases and Liquids”; McGraw-Hill Book Company: New York, 1977.
  6. Reid, R. C., Prausnitz, J. M. and Poling, B. E. “The Properties of Gases and Liquids” 4th Ed. McGraw-Hill Book Company: New York, 1987.
  7. de Hemptinne, J. C. and Behar, E. “Thermodynamic Modelling of Petroleum Fluids” Oil & Gas Science and Technology-Revue de l'Institut Français du Pétrole 2006, 61 (3), 303-317.