Elsevier

Fluid Phase Equilibria

Volume 354, 25 September 2013, Pages 212-235
Fluid Phase Equilibria

Prediction of the phase behavior of alkene-containing binary systems with the PPR78 model

https://doi.org/10.1016/j.fluid.2013.06.040Get rights and content

Abstract

The study of the phase equilibria of alkene-containing mixtures is fundamental to the petroleum and chemical industries. Therefore, the development of a predictive model for these systems is a necessary and challenging task. The PPR78 (predictive 1978, Peng–Robinson EoS) model is a predictive thermodynamic model that combines the widely used Peng–Robinson equation of state and a group contribution method aimed at estimating the temperature-dependent binary interaction parameters, kij(T), involved in the Van der Waals one-fluid mixing rules. In our previous papers, 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. It was thus possible to estimate kij for any mixture containing alkanes, aromatics, naphthenes, CO2, N2, H2S, mercaptans and hydrogen regardless of the temperature. In this work, four alkene groups are added in order to accurately predict not only the mutual solubility of petroleum components and alkenes but also the critical loci of binary alkene-containing systems.

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:P=RTvbiai(T)v(v+bi)+bi(vbi)andR=8.314472 J mol1 K1X=1+62+83628330.253076587bi=ΩbRTc,iPc,iwith:Ωb=XX+30.0777960739ai=ΩaR2Tc,i2Pc,iα(T)with:Ωa=8(5X+1)4937X0.457235529andα(T)=1+mi1TTc,i2ifωi0.491mi=0.37464+1.54226ωi0.26992ωi2ifωi>0.491mi=0.379642+1.48503ωi0.164423ωi2+0.016666ωi3where 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:Δx1¯=i=1nbubble(|x1,expx1,cal|)inbubble=0.023.Moreover,Fobj,bubblenbubble=8.06%.

The average overall deviation in the gas-phase composition is:Δy1¯=i=1ndew(|y1,expy1,cal|)indew=0.016.Moreover,Fobj,dewndew=10.66%.

The average overall deviation in the critical composition is:Δxc1¯=i=1ncrit(|xc1,expxc1,cal|)incrit=

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.

References (286)

  • J.-N. Jaubert et al.

    Fluid Phase Equilib.

    (2004)
  • J.-N. Jaubert et al.

    Fluid Phase Equilib.

    (2005)
  • S. Vitu et al.

    Fluid Phase Equilib.

    (2006)
  • S. Vitu et al.

    J. Supercrit. Fluids

    (2008)
  • R. Privat et al.

    J. Chem. Thermodyn.

    (2008)
  • R. Privat et al.

    Fluid Phase Equilib.

    (2012)
  • J.-W. Qian et al.

    J. Supercrit. Fluids

    (2013)
  • V. Machat et al.

    Fluid Phase Equilib.

    (1985)
  • J. Gregorowicz

    J. Supercrit. Fluids

    (2003)
  • J. Gregorowicz

    Fluid Phase Equilib.

    (2006)
  • R.C. Miller et al.

    J. Chem. Thermodyn.

    (1977)
  • P.T. Eubank et al.

    Fluid Phase Equilib.

    (1989)
  • C.R. Coan et al.

    J. Chromatogr.

    (1969)
  • L.-S. Lee et al.

    Fluid Phase Equilib.

    (2005)
  • K.A.M. Gasem et al.

    Fluid Phase Equilib.

    (1981)
  • L. Grauso et al.

    Fluid Phase Equilib.

    (1977)
  • S. Zeck et al.

    Fluid Phase Equilib.

    (1986)
  • R. Privat et al.

    Ind. Eng. Chem. Res.

    (2008)
  • R. Privat et al.

    Ind. Eng. Chem. Res.

    (2008)
  • R. Privat et al.

    Ind. Eng. Chem. Res.

    (2008)
  • J.-N. Jaubert et al.

    AIChE J.

    (2010)
  • D.B. Robinson et al.

    GPA Research Report RR-28

    (1978)
  • B.E. Poling et al.

    The Properties of Gases and Liquids

    (2000)
  • Confidential Company Research Report

    (1982)
  • I.M. Elshayal et al.

    Can. J. Chem. Eng.

    (1975)
  • M.S. Rozhnov et al.

    Khim. Prom-st. (Moscow)

    (1988)
  • P. Smith, Ph.D. thesis, University of Wisconsin,...
  • B. Williams, Pressure-Volume-Temperature Relationships and Phase Equilibria in the System Ethylene-Normal Butane, Ph.D....
  • M.T. Raetzsch et al.

    Z. Phys. Chem. (Leipzig)

    (1975)
  • Confidential Company Research Report

    (1979)
  • B.I. Konobeev et al.

    Khim. Prom-st. (Moscow)

    (1967)
  • I. Nagy et al.

    J. Chem. Eng. Data

    (2005)
  • T.P. Zhuze et al.

    Bull. Acad. Sci. USSR Div. Chem. Sci.

    (1960)
  • T.P. Zhuze et al.

    Bull. Acad. Sci. USSR Div. Chem. Sci.

    (1960)
  • W.B. Kay

    J. Ind. Eng. Chem. (Washington, D.C.)

    (1948)
  • C.R.N. Pacheco et al.
  • A. Sahgal et al.

    Can. J. Chem. Eng.

    (1978)
  • I. Thoedtmann et al.

    FIZ Report

    (1989)
  • V.S. Zernov et al.

    J. Appl. Chem. USSR

    (1990)
  • W.L. Weng et al.

    J. Chem. Eng. Data

    (1992)
  • G.W. Nederbragt

    Appl. Sci. Res. A

    (1948)
  • D.B. Todd et al.

    AIChE J.

    (1955)
  • J.V. Ribeiro et al.

    J. Chem. Eng. Data

    (1972)
  • B.K. Kaul, Solubilities and Dew-Point Temperature in Hydrocarbon and Coal Processing, Ph.D. thesis, University of...
  • J.S. Chou et al.

    J. Chem. Eng. Data

    (1989)
  • T.W. De Loos et al.

    Ber. Bunsen-Ges. Phys. Chem.

    (1984)
  • J.P. Kohn et al.

    J. Chem. Eng. Data

    (1980)
  • A.A. Naumova et al.

    Zh. Prikl. Khim. (Leningrad)

    (1981)
  • A.A. Naumova et al.

    J. Appl. Chem. USSR

    (1981)
  • F.H. Fallaha, Phase Equilibria at high Pressures with Application to Vapor Phase Extraction, Ph.D. thesis, University...
  • Cited by (0)

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