Prediction of the phase behavior of alkene-containing binary systems with the PPR78 model
Introduction
Over the past several years, the use of alkenes and cycloalkenes as reactants, intermediates and end products has significantly increased in the chemical, petrochemical and polymer industries. Consequently, accurate knowledge of the phase equilibria of alkene-containing systems is vital for the optimal design of processes and products. In order to obtain a thermodynamic model capable of predicting the equilibrium properties without requiring experimental data, Jaubert and coworkers [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11] developed a group contribution method allowing for the estimation of the temperature-dependent binary interaction parameters, kij(T), for the widely used equation of state (EoS) published in 1978 by Peng and Robinson [12]. The resulting model was thus simply called PPR78 (predictive 1978, Peng–Robinson EoS). A cubic EoS was chosen because it allows for the fast screening of a large number of design alternatives and preselection of the most favorable candidate structures due to its low complexity and high accuracy for non-polar compounds. The Peng–Robinson EoS was selected because it is certainly the most widely used by chemical engineers at petroleum companies and because it is available in any process simulator.
In our previous work [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], sixteen groups were defined: CH3, CH2, CH, C, CH4 (methane), C2H6 (ethane), CHaro, Caro, Cfused aromatic rings, CH2,cyclic, CHcyclic ⇔ Ccyclic, CO2, N2, H2S, SH and H2. In this study, the applicability range of the PPR78 model was extended to systems containing not only linear or branched alkenes but also cycloalkenes. To do so, four groups were defined: C2H4 (ethylene), CH2,alkenic ⇔ CHalkenic, Calkenic and CHcycloalkenic ⇔ Ccycloalkenic. When developing a group contribution model, the choice of a decomposition scheme – that is, the definition of the elementary groups – is of the first importance. It is, however, well known that these methods are often not suitable for the first molecules of a homologous chemical series. Therefore, as in the case of ethane, the ethylene molecule was considered as a separate group and not as the addition of two CH2,alkenic groups.
When sufficient experimental data were available, the interactions between these four new groups and the sixteen previously defined ones were determined. It therefore becomes possible to estimate, at any temperature, the kij value between two components i and j in any mixture containing paraffins, aromatics, naphthenes, CO2, N2, H2S, mercaptans, hydrogen and alkenes.
Section snippets
The PPR78 model
In 1978, Peng and Robinson [12] published an improved version of their well-known equation of state, referred as PR78 in this paper. For a pure component, the PR78 EoS is:andwhere P is the
Database and reduction procedure
Table 2 lists the 76 pure components involved in this study. The pure fluid physical properties (Tc, Pc and ω) were obtained from two sources. Poling et al. [13] was used for alkanes, cycloalkanes, aromatic compounds, CO2, N2, H2S and most of the alkenes. For the missing components (some alkenes), the DIPPR database was employed. Table 3 details the sources of the binary experimental data used in our evaluations [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27],
Uncertainty in the pure-component vapor pressures
Table 3 shows that many experimental data are available for binary systems in which the two components have the same carbon-atom number. For such systems, the resulting solution can either be ideal (mixture of two very similar components such as 1-butene + n-butane) or give rise to an azeotrope (when the two compounds, such as 2-methyl-1,3-butadiene + n-pentane, do not have the same chemical structure). As a general rule, the corresponding isothermal or isobaric phase diagrams are particularly
Results and discussion
For all the data points included in our database, the objective function defined by Eq. (8) is Fobj = 9.06%.
The average overall deviation in the liquid-phase composition is:
The average overall deviation in the gas-phase composition is:
The average overall deviation in the critical composition is:
Conclusion
In this paper, four alkenic or cycloalkenic groups were added to the PPR78 model, and as a general rule, satisfactory results are obtained over a wide range of temperatures and pressures. Accurate results were expected because most of the 198 binary systems investigated in this study exhibit Type I or Type II phase behavior according to the classification scheme of Van Konynenburg and Scott and we know from experience [5] that a cubic EoS can capture Type I and II phase behaviors with much
Acknowledgments
The French Petroleum Company TOTAL and more particularly Dr. Pierre Duchet-Suchaux (expert in thermodynamics) are gratefully acknowledged for sponsoring this research.
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