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

Example 4-10: Example of a vapour-liquid-liquid equilibrium of an acid gas system in the presence of water

In this example, we illustrate how some selected models are capable to predict the phase envelope of a quaternary system composed of H2O, H2S, CH4, CO2 (50/40/5/5 molar percent). This system has been examined experimentally by Robinson et al (1982) [1] and figure 1 shows its phase diagram. This system is quite interesting as it shows both non-ideal mixing behaviour as high pressure effects, in a small range of temperature and pressure.

At high temperature and low pressure, the system is a vapour phase. When the temperature and pressure are large (upper right corner of the diagram), the water forms an aqueous phase and a liquid- vapour domain is observed. For lower temperatures, the hydrogen sulphide forms a second liquid phase and we obtain a three-phase equilibrium. Finally, at lower temperatures and high pressure, the vapour phase disappears and we have only liquid-liquid equilibrium.

The chosen models are presented in table 1, along with the number of empirical binary parameters that have been adjusted. The fitting used binary VLE data, i.e. other than those presented in figure 1: calculation of the phase diagram is performed in a predictive mode. The origin of the parameters is also provided in the table. The fewer binary parameters, the better the theoretical foundation of the model must be.

Table 1: characteristic properties of propane (C3) and n-pentane (C5)
Name Detail of the model Number of binary parameters Origin of binary parameters
SW (Soreide Whitson) Peng-Robinson EoS with kij≠0 for aqueous phase
Peng-Robinson EoS with kij≠0 for organic phase
12 (6 for each EoS) Aqueous: Soreide-Witson Organic: state of the art published values
PRHV (Peng Robinson Huron Vidal) Peng-Robinson EoS with Huron Vidal mixing rules with NRTL-V GE approach 12 (2 for each binary) Parameters fitted on each binary systems
PSRK Soave Redlich Kwong EoS with MHV1 mixing rules with UNIFAC GE approach - UNIFAC matrix
CPA Cubic Plus Association with kij parameters 6 (1 for each binary) Parameters fitted on each binary systems


The phase diagrams predicted by these models are shown on figure 1.

The water dew curve (lowest curve) is well described by all models: the deviation between experimental and calculated pressure is less than 2.5 %.

The prediction of the three phase equilibrium is more difficult. Since we deal with a multicomponent mixture, this three-phase equilibrium appears in a zone (it would have been a line for a binary mixture) that is limited by a hydrocarbon dew curve on the bottom and a hydrocarbon bubble curve on top. A liquid-vapour critical point (not drawn) is found at the limit between dew and bubble lines. The dew curve corresponding to the appearance, upon pressure increase, of the hydrogen sulphide-rich liquid phase is close to the pure H2S vapour pressure curve and is well predicted by all models (except PSRK).

On the other hand, the bubble curve of the three phase equilibrium is difficult to estimate and there are large differences between the models. For PRH and SW, agreement with experimental data is close to perfection. This result illustrates that it is possible to describe this type of complex mixture phase diagrams knowing its binary sub-systems.

PSRK and CPA produce the worst results: bubble temperature is underestimated by up to 40 K for PSRK and up to 10 K for CPA; bubble pressure is over-estimated by 4 MPa for PSRK and 3 MPa for CPA . We must bear in mind that PSRK is used in a totally predictive manner and that the equation of state gives a good qualitative idea of the phase behaviour. For CPA, the result is very interesting since it uses fewer parameters. It may even produce better results if the binary H2O + H2S is described with more detail, as shown by Tsivintzelis et al. [2].

To conclude this example, we can note that in opposition with the other models, SW uses a heterogeneous approach (hence no continuity between the aqueous and the hydrocarbon phases). As a result, SW would be incapable of calculating the critical point between the aqueous and a hydrocarbon phase. This has no real impact on the figure since the only critical point seen is that between the liquid and the vapour hydrocarbon phases.

image Figure 1: Phase envelope of the water + hydrogen sulphide + methane + carbon dioxide (data from [1]).


[1] ROBINSON D.B., HUANG S.H., LEU A.D., NG H.J., The Phase Behavior of Two Mixtures of Methane, Carbon Dioxide, Hydrogen Sulfide and Water, 1982, GPA RR-57.

[2] TSIVINTZELIS I., KONTOGEORGIS G.M., MICHELSEN M.L., STENBY E.H., Modeling phase equilibria for acid gas mixtures using the CPA equation of state. I. Mixtures with H2S, AIChE Journal, 2010, 56, n°11, p. 2965-2982.