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

Fluid Phase Equilibria 354 (2013) 212–235

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Prediction of the phase behavior of alkene-containing binary systems with the PPR78 model Jun-Wei Qian, Jean-Noël Jaubert ∗ , Romain Privat Université de Lorraine, Ecole Nationale Supérieure des Industries Chimiques, Laboratoire Réactions et Génie des Procédés (UMR CNRS 7274), 1 rue Grandville, 54000 Nancy, France

a r t i c l e

i n f o

Article history: Received 20 January 2013 Received in revised form 12 June 2013 Accepted 14 June 2013 Available online 28 June 2013 Keywords: Equation of state Vapor–liquid equilibrium Binary interaction parameters PPR78 Alkenes Critical locus

a b s t r a c t 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), C2 H6 (ethane), CHaro , Caro , Cfused aromatic rings , CH2,cyclic , CHcyclic ⇔ Ccyclic , CO2 , N2 , H2 S, SH and H2 . It was thus possible to estimate kij for any mixture containing alkanes, aromatics, naphthenes, CO2 , N2 , H2 S, 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. © 2013 Elsevier B.V. All rights reserved.

1. 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 [1–11] 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 [1–11], sixteen groups were defined: CH3 , CH2 , CH, C, CH4 (methane), C2 H6 (ethane), CHaro , Caro ,

∗ Corresponding author. Tel.: +33 3 83 17 50 81; fax: +33 3 83 17 51 52. E-mail address: [email protected] (J.-N. Jaubert). 0378-3812/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2013.06.040

Cfused aromatic rings , CH2,cyclic , CHcyclic ⇔ Ccyclic , CO2 , N2 , H2 S, 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: C2 H4 (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 , H2 S, mercaptans, hydrogen and alkenes. 2. 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=

RT

v − bi

−

ai (T )

v(v + bi ) + bi (v − bi )

(1)

J.-W. Qian et al. / Fluid Phase Equilibria 354 (2013) 212–235

a(T) Akl , Bkl b kij m P Pc R T Tc

v xi , yi , zi

temperature-dependent function of the equation of state constant parameters allowing the calculation of the binary interaction parameters covolume binary interaction parameter shape parameter pressure critical pressure ideal gas constant temperature critical temperature volume mole fractions

Greek letters ω acentric factor fraction occupied by group k in the molecule i ˛ik

213

In Eq. (4), T is the temperature. The ai and bi values are given in Eq. (2). The Ng variable is the number of different groups defined by the group contribution method (for the time being, twenty groups are defined, and Ng = 20). The ˛ik variable is the fraction of molecule i occupied by group k (occurrence of group k in molecule i divided by the total number of groups present in molecule i). The constant parameters, Akl = Alk and Bkl = Blk (where k and l are two different groups), were determined either in this study or in our previous papers (Akk = Bkk = 0) [1–11]. For the four new groups added in this paper (group 17: C2 H4 (ethylene), group 18: CH2,alkenic or CHalkenic , group 19: Calkenic and group 20: CHcycloalkenic or Ccycloalkenic ), 140 interactions (70 Akl and 70 Bkl values) between the new groups and the ones defined previously must be estimated. However, due to a lack of experimental data, it was only possible to determine 100 new parameters, which will be highlighted in the next sections. These parameters were obtained by minimizing the deviations between calculated and experimental data from an extended database. The corresponding Akl and Bkl values (expressed in MPa) are summarized in Table 1. To be really complete, let us recall that the PPR78 model may also be seen as the combination of the PR EoS and a Van Laar type activity coefficient (gE ) model under infinite pressure. Indeed, as

and

⎧ R = 8.314472 J mol−1 K−1 ⎪ ⎪ ⎪   ⎪ √ √ ⎪ 3 3 ⎪ ⎪ X = −1 + 6 2 + 8 − 6 2 − 8 ≈ 0.253076587 ⎪ ⎪ ⎪ 3 ⎪ ⎪ ⎪ ⎪ RT ⎪ ⎨ bi = ˝b c,i with : ˝b = X ≈ 0.0777960739 X +3

Pc,i

(2)

  2 ⎪ 2 ⎪ R2 Tc,i ⎪ 8(5X + 1) T ⎪ ⎪ a = ˝ ˛(T ) with : ˝ = 0.457235529 and ˛(T ) = 1 + m 1− ≈ a a i ⎪ i ⎪ Pc,i 49 − 37X Tc,i ⎪ ⎪ ⎪ ⎪ 2 ⎪ ⎪ ⎪ if ωi ≤ 0.491 mi = 0.37464 + 1.54226ωi − 0.26992ωi ⎪ ⎩ 3 2 if ωi > 0.491 mi = 0.379642 + 1.48503ωi − 0.164423ωi + 0.016666ωi

where P is the pressure, R is the gas constant, T is the temperature, ai and bi are the EoS parameters of pure component i, v is the molar volume, Tc,i is the critical temperature, Pc,i is the critical pressure and ωi is the acentric factor of pure i. To apply this EoS to a mixture, mixing rules are necessary to calculate the values of a and b of the mixture. Classical Van der Waals one-fluid mixing rules are used in the PPR78 model:

⎧ N N  ⎪ ⎪ ⎪ a(T, z) = zi zj ai aj [1 − kij (T )] ⎪ ⎨ i=1 j=1

(3)

N ⎪ ⎪ ⎪ ⎪ = zi bi b(z) ⎩ i=1

where zi represents the mole fraction of component i and N is the number of components in the mixture. The kij (T) parameter, whose choice is difficult even for the simplest systems, is the so-called binary interaction parameter (BIP) characterizing the molecular interactions between molecules i and j. Although the common practice is to fit kij to reproduce the vapor–liquid equilibrium data of the mixture under consideration, the predictive PPR78 model calculates the kij value, which is temperature-dependent, with a group contribution method using the following expression:

kij (T ) =

−(1/2)



Ng k=1

Ng l=1

(˛ik − ˛jk )(˛il − ˛jl )Akl · (298.15/T (K))



2((

explained by Jaubert et al. [9], the well-established Huron–Vidal mixing rules:

⎧ p ⎪ a(T, x) ai (T ) gE ⎪ ⎪ = xi − ⎪ ⎪ C b(x) b EoS i ⎪ ⎪ i=1 ⎨ p xi bi ⎪ ⎪ b(x) = ⎪ ⎪ i=1 ⎪ √ ⎪ √ ⎪ 2 ⎩ CEoS =

ln(1 +

2) for the PR EoS

are rigorously equivalent to the Van der Waals one-fluid mixing rules with temperature-dependent kij if a Van–Laar type excess function: E gVan –Laar

CEoS

1 = · 2

p p i=1

x x b b E (T ) j=1 i j i j ij

p

bx j=1 j j

(6)

is used in Eq. (5). The mathematical relation between kij (T) (Eq. (3)) and the interaction parameter of the Van–Laar gE model [Eij (T) in

((Bkl /Akl )−1)

ai (T ) · aj (T ))/(bi · bj ))

More information on Eq. (4) and an example of the kij calculation can be found in the paper by Jaubert and Mutelet [1].

2

(5)





− ((



ai (T )/bi ) − (

aj (T )/bj ))

2

(4)

214 Table 1 Group interaction parameters: (Akl = Alk )/MPa and (Bkl = Blk )/MPa. Only the last four lines of this table, relative to the alkenes and cycloalkenes groups (group 17 i.e. C2 H4 , group 18 i.e. CH2,alkenic or CHalkenic , group 19 i.e. Calkenic , group 20 i.e. CHcycloalkenic or Ccycloalkenic ), were determined in this study. The sixteen first lines of this table were determined in our previous papers [1–11]. CH3 (group 1) CH3 (group 1) CH2 (group 2) CH (group 3) C (group 4)

C2 H6 (group 6) CHaro (group 7) Caro (group 8) Cfused aromatic rings (group 9) CH2,cyclic (group 10) CHcyclic or Ccyclic (group 11) CO2 (group 12) N2 (group 13) H2 S (group 14) SH (group 15) H2 (group 16) C2 H4 (group 17) CH2,alkenic or CH alkenic (group 18) Calkenic (group 19) CHcycloalkenic or Ccycloalkenic (group 20)

= 74.81 = 165.7 = 261.5 = 388.8 = 396.7 = 804.3 = 32.94 = −35.00 = 8.579 = −29.51 = 90.25 = 146.1 = 62.80 = 41.86 = 62.80 = 41.86

CH (group 3)

C (group 4)

CH4 (group 5)

C2 H6 (group 6)

CHaro (group 7)

Caro (group 8)

Cfused aromatic rings (group 9)

CH2,cyclic (group 10)

–

–

–

–

–

–

–

–

–

0

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

0

–

–

A89 = 0.000 B89 = 0.000

0

–

A23 B23 A24 B24 A25 B25 A26 B26 A27 B27 A28 B28 A29 B29

= 51.47 = 79.61 = 88.53 = 315.0 = 36.72 = 108.4 = 31.23 = 84.76 = 29.78 = 58.17 = 3.775 = 144.8 = 3.775 = 144.8

0 A34 B34 A35 B35 A36 B36 A37 B37 A38 B38 A39 B39

= −305.7 = −250.8 = 145.2 = 301.6 = 174.3 = 352.1 = 103.3 = 191.8 = 6.177 = −33.97 = 6.177 = −33.97

A1–10 B1–10 A1–11 B1–11

= 40.38 = 95.90 = 98.48 = 231.6

A2–10 B2–10 A2–11 B2–11

= 12.78 = 28.37 = −54.90 = −319.5

A3–10 B3–10 A3–11 B3–11

A1–12 B1–12 A1–13 B1–13 A1–14 B1–14 A1–15 B1–15 A1–16 B1–16 A1–17 B1–17 A1–18 B1–18

= 164.0 = 269.0 = 52.74 = 87.19 = 158.4 = 241.2 = 799.9 = 2109 = 202.8 = 317.4 = 7.206 = 39.12 = 54.22 = 142.4

A2–12 B2–12 A2–13 B2–13 A2–14 B2–14 A2–15 B2–15 A2–16 B2–16 A2–17 B2–17 A2–18 B2–18

= 136.9 = 254.6 = 82.28 = 202.8 = 134.6 = 138.3 = 459.5 = 627.3 = 132.5 = 147.2 = 59.71 = 78.58 = 11.67 = 29.51

A3–12 = 184.3 B3–12 = 762.1 A2–16 = 132.5 B2–16 = 147.2 A3–14 = 193.9 B3–14 = 307.8 A3–15 = 425.5 B3–15 = 514.7 A3−16 = 415.2 B3–16 = 726.4 A3–17 = 176.7 B3–17 = 118.0 A3–18 = 118.4 B3–18 = 158.9

A1–19 B1–19 A1–20 B1–20

= 115.6 = 118.4 = 177.1 = 358.9

A2–19 B2–19 A2–20 B2–20

= 60.39 = 272.8 = 0.000 = −7.206

A3–19 B3–19 A3–20 B3–20

= 101.9 = −90.93 = −226.5 = −51.47

= 103.6 = 430.6 = 39.12 = 1038

0 A45 B45 A46 B46 A47 B47 A48 B48 A49 B49

= 263.9 = 531.5 = 333.2 = 203.8 = 158.9 = 613.2 = 79.61 = −326.0 = 79.61 = −326.0

0 A56 B56 A57 B57 A58 B58 A59 B59

= 13.04 = 6.863 = 67.26 = 167.5 = 139.3 = 464.3 = 139.3 = 464.3

0 A67 B67 A68 B68 A69 B69

= 41.18 = 50.79 = −3.088 = 13.04 = −3.088 = 13.04

0 A78 B78 A79 B79

= −13.38 = 20.25 = −13.38 = 20.25

A4–10 B4–10 A4–11 B4–11

= 177.1 = 601.9 = 17.84 = −109.5

A5–10 B5–10 A5–11 B5–11

= 36.37 = 26.42 = 40.15 = 255.3

A6–10 B6–10 A6–11 B6–11

= 8.579 = 76.86 = 10.29 = −52.84

A7–10 B7–10 A7–11 B7–11

= 29.17 = 69.32 = −26.42 = −789.2

A8−10 = 34.31 B8−10 = 95.39 A8–11 = −105.7 B8–11 = −286.5

A9–10 B9–10 A9–11 B9–11

= 34.31 = 95.39 = −105.7 = −286.5

A3–14 B3–14 A4–13 B4–13 A4–14 B4–14 A4–15 B4–15 A4–16 B4–16 A4–17 B4–17 A4–18 B4–18

= 193.9 = 307.8 = 263.9 = 772.6 = 305.1 = −143.1 = 682.9 = 1544 = 226.5 = 1812 = 319.5 = −248.1 = 50.79 = −284.5

A5–12 B5–12 A5–13 B5–13 A5–14 B5–14 A5–15 B5–15 A5–16 B5–16 A5–17 B5–17 A5–18 B5–18

= 137.3 = 194.2 = 37.90 = 37.20 = 181.2 = 288.90 = 704.2 = 1496 = 156.1 = 92.99 = 14.69 = 30.20 = 52.84 = 110.5

A6–12 B6–12 A6–13 B6–13 A6–14 B6–14

= 135.5 = 239.5 = 61.59 = 84.92 = 157.2 = 217.1

A7–12 B7–12 A7–13 B7–13 A7–14 B7–14 A7–15 B7–15 A7–16 B7–16 A7–17 B7–17 A7–18 B7–18

= 102.6 = 161.3 = 185.2 = 490.6 = 21.96 = 13.04 = 285.5 = 392.0 = 284.8 = 175.0 = 20.25 = 94.02 = 8.579 = −7.549

A8–12 B8–12 A8–13 B8–13 A8–14 B8–14 A8–15 B8–15 A8–16 B8–16 A8–17 B8–17 A8–18 B8–18

= 110.1 = 637.6 = 284.0 = 1892 = 1.029 = −8.579 = 1072 = 1094 = 377.5 = 1201 = 65.20 = 125.2 = −70.69 = 36.72

A2–17 B2–17 A9–13 B9–13 A9–14 B9–14 A9–15 B9–15 A9–16 B9–16 A9–17 B9–17

= 59.71 = 78.58 = 718.1 = 1892 = 1.029 = −8.579 = 1072 = 1094 = 549.0 = 1476 = 199.0 = 3820

A7–19 = 1.029 B7−19 = −16.81 A7–20 = 6.177 B7–20 = 5.490

A8–19 B8–19 A8–20 B8–20

= 217.5 = −170.2 = 3.431 = −37.75

N.A.a A6–16 B6–16 A6–17 B6–17 A6–18 B6–18

N.A.a

N.A.a

N.A.a

N.A.a

N.A.a

N.A.a

= 137.6 = 150.0 = 7.549 = 19.22 = 26.42 = 50.44

N.A.a N.A.a N.A.a

0 A10–11 = −50.10 B10–11 = −891.1 A10–12 = 130.1 B10–12 = 225.8 A10–13 = 179.5 B10–13 = 546.6 A10–14 = 120.8 B10–14 = 163.0 A10–15 = 446.1 B10–15 = 549.0 A10–16 = 232.0 B10–16 = 167.5 A10−17 = 35.34 B10–17 = 52.50 A10–18 = 27.11 B10–18 = 454.7 A10–19 B10–19 A10–20 B10–20

= −3.088 = −168.5 = 51.47 = 254.6

J.-W. Qian et al. / Fluid Phase Equilibria 354 (2013) 212–235

CH4 (group 5)

0 A12 B12 A13 B13 A14 B14 A15 B15 A16 B16 A17 B17 A18 B18 A19 B19

CH2 (group 2)

Table 1 (continued ).

CO2 (group 12) N2 (group 13) H2 S (group 14) SH (group 15) H2 (group 16) C2 H4 (group 17)

CO2 (group 12)

N2 (group 13)

H2 S (group 14)

SH (group 15)

H2 (group 16)

C2 H4 (group 17)

CH2,alkenic or CH alkenic (group 18)

C alkenic (group 19)

CH cycloalkenic or C cycloalkenic (group 20)

– – – – – – – – –

– – – – – – – – –

– – – – – – – – –

– – – – – – – – –

– – – – – – – – –

– – – – – – – – –

– – – – – – – – –

– – – – – – – – –

– – – – – – – – –

– – – – – – – – –

– 0

– –

– –

– –

– –

– –

– –

– –

– –

– –

–

–

–

–

–

–

–

–

0

–

–

–

–

–

–

–

–

–

–

–

–

–

0

–

–

–

–

–

N.A.a

0

–

–

–

–

0

–

–

–

A17–18 = 17.16 B17–18 = 36.72

0

–

–

A17–19 B17–19 A17–20 B17–20

A18–19 B18–19 A18–20 B18–20

0

–

A19–20 = −392.9 B19–20 = −197.3

0

A11–12 B11–12 A11–13 B11–13 A11–14 B11–14 A11–15 B11–15 A11–16 B11–16 A11–17 B11–17 a

CH2,alkenic or CH alkenic (group 18)

N.A.

Calkenic (group 19)

N.A.a

CHcycloalkenic or Ccycloalkenic (group 20) a

= 91.28 = 82.01 = 100.9 = 249.8 = −16.13 = −147.6 = 411.8 = −308.8 = −314.0 = −225.8 = −38.43 = −688.4

A11–20 = 37.75 B11–20 = 4173

0 A12–13 B12–13 A12–14 B12–14 A12–15 B12–15 A12–16 B12–16 A12–17 B12–17 A12–18 B12–18

= 98.42 = 221.4 = 134.9 = 201.4 = 469.6 = 899.6 = 265.9 = 268.3 = 73.09 = 115.3 = 59.71 = 210.3

A12–19 B12–19 A12–20 B12–20

= 23.68 = −186.0 = 87.85 = 94.37

A13–14 B13–14 A13–15 B13–15 A13–16 B13–16 A13–17 B13–17 A13–18 B13–18

= 319.5 = 550.1 = 1044 = 1872 = 65.20 = 70.10 = 88.53 = 109.1 = 125.2 = 285.5

A13–19 = 455.7 B13–19 = 30.54 N.A.a

0 A14–15 B14–15 A14–16 B14–16

= −77.21 = 156.1 = 145.8 = 823.5

N.A.a

N.A.a

a

a

N.A.

N.A.

N.A.a

N.A.a

N.A.a

N.A.a

A16–17 B16–17 A16–18 B16–18

= 151.3 = 165.1 = 163.0 = 322.2

A16–19 B16–19 A16–20 B16–20

= 630.0 = 573.1 = 483.1 = 2417

= 0.137 = 31.23 = −43.24 = 1798

= 21.62 = 134.9 = 119.8 = −72.06

J.-W. Qian et al. / Fluid Phase Equilibria 354 (2013) 212–235

CH3 (group 1) CH2 (group 2) CH (group 3) C (group 4) CH4 (group 5) C2 H6 (group 6) CHaro (group 7) Caro (group 8) Cfused aromatic rings (group 9) CH2,cyclic (group 10) CHcyclic or Ccyclic (group 11)

CHcyclic or Ccyclic (group 11)

N.A. = not available.

215

216

J.-W. Qian et al. / Fluid Phase Equilibria 354 (2013) 212–235 Table 2 List of the 76 pure components used in this study.

Eq. (6)] is: kij (T ) =

Eij (T ) − (ıi − ıj ) 2ıi ıj

√

2

with ıi =

ai bi

(7)

3. 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 , H2 S 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 [14–279] along with the temperature, pressure and composition ranges for each binary system. Most of the data available in the open literature (9324 bubble points + 6550 dew points + 182 mixture critical points) were collected. Our database includes VLE data for 198 binary systems. The 100 parameters (50 Akl and 50 Bkl ) determined in this study (see Table 1) were calculated by minimizing the following objective function: Fobj =

Fobj,bubble + Fobj,dew + Fobj,crit. comp + Fobj,crit. pressure n

+n

+n

+n

bubble dew crit crit ⎧     nbubble    ⎪   x x ⎪ ⎪ F = 100 0.5 + with x ⎪ obj,bubble ⎪ x1,exp x2,exp ⎪ ⎪ i=1 ⎪ i    ⎪ ⎪ = x1,exp − x1,cal  = x2,exp − x2,cal  ⎪ ⎪ ⎪ ⎪ ⎪ ⎪     ⎪ ndew ⎪ y y   ⎪ ⎪ ⎪ Fobj,dew = 100 0.5 + with y ⎪ ⎪ y y ⎪ 1,exp 2,exp ⎪ i=1 ⎪     i (8) ⎨ = y1,exp − y1,cal  = y2,exp − y2,cal  ⎪ ⎪     ⎪ ncrit ⎪ xc  xc    ⎪ ⎪ ⎪ Fobj,crit. comp = 100 0.5 + with xc  ⎪ ⎪ xc1,exp xc2,exp ⎪ ⎪ i=1 ⎪ i    ⎪ ⎪    = xc1,exp − xc1,cal = xc2,exp − xc2,cal  ⎪ ⎪ ⎪ ⎪ ⎪ ⎪   ⎪ ncrit ⎪ Pcm,exp − Pcm,cal  ⎪ ⎪ ⎪ ⎪ ⎩ Fobj,crit. pressure = 100 Pcm,exp i=1

i

where nbubble , ndew and ncrit are the number of bubble points, dew points and mixture critical points, respectively. The variable, x1 , is the mole fraction of the most volatile component in the liquid phase, and x2 is the mole fraction of the heaviest component (x2 = 1 − x1 ) at a fixed temperature and pressure. Similarly, y1 is the mole fraction of the most volatile component in the gas phase, and y2 is the mole fraction of the heaviest component (y2 = 1 − y1 ) at a fixed temperature and pressure. The xc1 variable is the critical mole fraction of the most volatile component, and xc2 is the critical mole fraction of the heaviest component at a fixed temperature. Pcm is the binary critical pressure at a fixed temperature. 4. Difficulties in predicting the phase behavior of alkene-containing mixtures 4.1. 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

Component

Short name

Methane Ethane Propane n-Butane n-Pentane n-Hexane n-Heptane n-Octane n-Nonane n-Decane n-Dodecane n-Tetradecane n-Hexadecane n-Eicosane 2-Methylpropane (isobutane) 2-Methylbutane 2,2,4-Trimethylpentane (isooctane) Benzene Methylbenzene (toluene) 1,3-Dimethylbenzene (m-xylene) 1,2-Dimethylbenzene (o-xylene) 1,4-Dimethylbenzene (Pxylene) Ethylbenzene 1,2,4-Trimethylbenzene 1-Metylethylbenzene (cumene) Propylbenzene Naphthalene 1-Methylnaphthalene Phenanthrene Cyclopentane Cyclohexane 1,2,3,4-Tetrahydronaphthalene (tetralin) trans-Decalin Carbon dioxide Nitrogen Hydrogen Ethylene Propene 1-Butene cis-2-Butene trans-2-Butene 1-Pentene 1-Hexene 1-Heptene 1-Octene cis-3-Octene trans-3-Octene cis-4-Octene trans-4-Octene 1-Decene 1-Undecene 1-Hexadecene 1-Octadecene 1,2-Propadiene 1,3-Butadiene 2-Methylpropene 2-Methyl-1-butene 2-Methyl-2-butene 3-Methyl-1-butene 2-Ethyl-1-butene 2-Methyl-1-pentene 4-Methyl-1-pentene 2-Methyl-1,3-butadiene Cyclopentene Cyclohexene 1-Methylcyclohexene Vinylbenzene (styrene) Alpha-methylstyrene 1,5-Cyclooctadiene Dicyclopentadiene p-Cymene Alpha-pinene Beta-pinene Myrcene Limonene (racemic mixture) Limonene (enantiomer R)

1 2 3 4 5 6 7 8 9 10 12 14 16 20 2m3 2m4 224m5 B mB 13mB 12mB 14mB eB 124mB iprB prB BB 1mBB Phe C5 C6 tet tCC6 CO2 N2 H2 a2 a3 1a4 c2a4 t2a4 1a5 1a6 1a7 1a8 c3a8 t3a8 c4a8 t4a8 1a10 1a11 1a16 1a18 aa3 13a4 2ma3 2m1a4 2m2a4 3m1a4 2e1a4 2m1a5 4m1a5 2m13a4 aC5 aC6 1maC6 Ba2 Bma2 15aC8 dicy pcy ap bp myr limRS limR

Table 3 Binary systems database. Binary system (1st compound–2nd compound)

1.40–40.53 13.79–67.02 53.90–80.76 2.79–95.65 0.81–108.42 15.00–95.00 2.78–30.89 20.27–58.01 1.01–91.19 10.35–76.12 4.90–244.40 10.10–65.76 6.20–90.00 0.10–60.80 0.06–52.01 0.84–118.55 0.98–128.68 3.95–9.83 2.77–31.09 1.82–12.77 2.45–14.71 7.50–303.98 15.29–38.67 69.90–311.30 0.66–113.28 3.55–7.53 7.32–69.17 2.68–110.38 2.00–5998.30 0.95–41.61 0.13–7.41 0.13–7.39 0.13–17.23 2.43–7.46 2.07–46.99 1.60–24.43 3.62–9.73 2.05–40.65 4.05–14.30 0.26–35.30 0.30–0.89 0.14–0.94 0.12–0.73 0.24–1.01 0.11–0.27 0.27–1.01 1.01–1.01 1.01–1.01 7.84–40.07 0.01–1.01 0.01–0.27 0.01–1.01 0.31–2.35

x1 range (1st compound liquid mole fraction) 0.0440–0.9950 0.0010–0.8250 0.2900–0.8650 0.0250–0.8550 0.0038–0.9699 0.1924–0.8897 0.0350–0.5620 0.2100–0.9560 0.0131–0.9500 0.5493–0.9280 0.0659–0.9520 0.0050–0.9490 0.3000–0.6030 0.0297–0.9851 0.0335–0.9861 0.0030–0.9244 0.0220–0.9693 0.0500–0.1770 0.0240–0.4820 0.0580–0.5100 0.0130–0.2010 0.2447–0.8300 – – 0.0040–0.8600 0.2012–0.9689 0.0200–0.9880 0.0132–0.9658 0.0043–0.7800 0.0370–0.9940 0.0282–0.7010 0.0171–0.6830 0.0282–0.9050 0.0990–0.6980 0.0170–0.9830 0.0430–0.9720 0.1000–0.9313 0.0210–0.9350 0.0930–0.7690 0.1420–0.8600 0.0050–0.9750 0.0494–0.9860 0.0500–0.9500 0.0830–0.9390 0.1000–0.9400 0.1050–0.9000 0.0152–0.8250 0.0182–0.9618 0.2160–0.9787 0.0690–0.8320 0.0580–0.9470 0.0100–0.8200 0.0474–0.9636

y1 range (1st compound gas mole fraction) 0.2608–0.9990 0.0065–0.8720 0.2900–0.8650 0.2002–0.9880 0.0622–0.9998 0.9605–0.9949 – 0.9984–0.9999 – 0.9440–1.0000 0.9350–1.0000 0.0080–0.9500 0.8890–0.9770 0.1873–0.9996 0.0500–0.9928 0.1000–0.9920 0.2530–0.9985 – – – – 0.7114–1.0000 0.9925–0.9997 0.9894–1.0000 0.6990–0.9910 – 0.0300–0.9640 0.1138–0.9994 0.0207–0.9997 0.0450–0.9950 – – – – 0.0480–0.9940 0.1600–0.9930 0.1140–0.9351 – 0.3220–0.9190 0.2102–0.7511 0.0070–0.9790 0.1490–0.9960 0.3060–0.9950 0.1240–0.9100 0.2940–0.9720 0.1170–0.9210 0.1317–0.9899 0.0471–0.9891 0.8000–0.9995 0.2940–0.9900 0.1140–0.9800 0.2050–0.9920 –

Number of bubble points (T,P,x) 101 31 0 137 364 20 12 16 62 10 118 36 12 193 462 163 84 10 29 16 20 33 0 0 50 9 301 87 304 621 25 40 46 9 67 25 58 49 5 50 84 49 11 51 11 40 19 34 21 45 65 75 14

Number of dew points (T,P,y) 91 31 0 41 202 20 0 8 0 24 49 35 14 218 279 60 16 0 0 0 0 240 7 49 24 0 301 132 309 534 0 0 0 0 48 25 58 0 5 9 62 43 11 14 11 20 19 34 21 45 65 75 0

Number of binary critical points (Tcm ,Pcm ,xc ) 0 4 6 12 14 0 0 0 0 0 5 5 0 0 2 9 5 0 0 0 0 7 0 0 0 0 4 0 23 0 0 0 0 0 3 0 0 0 0 3 0 0 0 0 0 0 0 0 2 0 0 0 0

References

[14–18] [19] [20] [20–25] [20,22,26–30] [31] [22] [32,33] [28,34] [33,35] [36–40] [21,41,42] [43,44] [17,45–49] [17,48,50–57] [22,24,27,43,44,58–67] [22,33,43,68–71] [72] [22,72] [72] [62,72] [73–80] [35] [75,81,82] [24,27,66] [66] [83–91] [17,92–94] [95–98,49,99] [53,100–110] [22,111] [22,27,111] [111–114] [22] [115] [116] [117,118] [29] [119] [120,121] [122–125] [126–128] [123] [129–131] [131] [132,133] [134] [134] [135] [136] [137,138] [139] [140]

217

199.83–283.15 322.04–388.71 333.15–443.15 293.15–491.28 212.30–535.40 318.15–338.15 293.15–333.15 283.65–353.15 263.95–348.15 283.65–448.15 295.00–573.15 292.95–393.15 346.65–346.65 103.94–248.15 140.00–293.15 210.00–552.75 228.05–563.15 283.15–303.15 243.15–333.15 223.15–293.15 273.15–423.15 285.15–540.15 348.15–448.15 298.15–343.15 180.00–423.15 195.00–235.00 223.15–298.15 120.00–260.00 112.00–281.70 228.65–360.93 238.15–333.15 238.15–333.15 238.15–343.15 293.15–333.15 277.59–410.93 273.20–333.20 310.93–344.26 353.15–443.15 373.60–373.60 273.15–468.50 302.92–333.15 313.15–365.72 328.15–328.15 328.15–371.00 328.15–328.15 352.97–398.43 348.52–438.51 400.03–442.37 472.10–572.50 368.95–544.25 396.75–502.15 374.95–576.95 273.15–293.15

Pressure range (bar)

J.-W. Qian et al. / Fluid Phase Equilibria 354 (2013) 212–235

a2-3 a2-4 a2-5 a2-6 a2-7 a2-8 a2-9 a2-10 a2-12 a2-16 a2-20 a2-2m3 a2-224m5 1-a2 a2-2 a2-B a2-mB a2-14mB a2-12mB a2-13mB a2-eB a2-BB a2-1mBB a2-Phe a2-C6 a2-tCC6 a2-CO2 N2 -a2 H2 -a2 a3-3 a3-6 a3-7 a3-8 a3-9 a3-1a4 a3-13a4 1a4-4 1a4-7 1a4-1a6 1a5-5 1a6-6 1a6-7 1a6-8 1a7-7 1a7-8 1a8-8 6-1a10 8-1a10 6-1a16 12-1a16 14-1a16 12-1a18 13a4-5

Temperature range (K)

218

Table 3 (Continued) Binary system (1st compound–2nd compound)

233.15–413.15 233.15–413.15 233.15–413.15 278.15–338.15 278.15–318.15 273.15–293.15 278.15–338.71 388.35–398.48 388.01–398.54 387.52–398.54 374.47–398.55 278.15–358.15 298.15–338.15 277.00–416.00 278.00–338.00 323.15–423.15 313.15–365.23 289.20–330.20 100.00–273.15 134.80–134.80 295.00–295.00 197.85–344.26 298.15–318.15 293.15–555.95 298.15–298.15 298.15–413.15 283.15–348.80 328.15–328.15 283.15–323.15 283.15–323.15 238.15–333.15 233.15–413.15 283.15–381.30 328.15–328.15 243.15–363.15 312.35–413.25 337.27–414.60 293.15–353.15 337.36–408.23 323.15–323.15 337.53–403.55 394.95–408.45 324.38–370.15 293.15–353.15 293.15–614.55 441.95–497.05 364.85–572.25 298.15–318.15 298.15–298.15 303.15–413.15 313.15–313.15 313.15–313.15 273.15–293.15 229.65–355.15

Pressure range (bar) 0.03–33.44 0.03–33.44 0.03–33.44 1.10–7.83 1.20–4.96 0.39–2.29 1.30–8.36 0.80–1.01 0.80–1.01 0.80–1.01 0.53–1.01 1.14–11.21 2.19–6.99 1.61–38.50 1.66–9.65 1.32–32.51 0.14–0.94 1.01–1.01 0.04–42.28 0.72–4.68 69.90–173.30 0.32–49.78 3.03–52.77 0.63–67.40 0.41–1.02 0.25–33.44 0.07–0.94 0.29–0.43 0.02–0.33 0.09–0.86 0.13–7.34 0.03–33.44 0.04–1.01 0.16–0.27 0.10–4.55 0.07–1.01 1.01–1.01 2.03–5.07 1.01–1.01 0.03–0.04 1.01–1.01 1.01–1.01 0.05–0.27 2.03–5.07 2.03–80.40 0.27–0.27 0.01–1.01 0.32–1.27 0.41–1.02 0.25–33.44 0.26–0.44 0.10–0.24 1.13–9.97 1.31–71.80

x1 range (1st compound liquid mole fraction) 0.0380–0.9620 0.0400–0.9760 0.0220–0.9720 0.0882–0.7498 0.0529–0.9515 0.0702–0.9283 0.0944–0.9000 0.1540–0.8860 0.1260–0.8990 0.1030–0.8990 0.0990–0.8940 0.2642–0.8937 0.2755–0.8870 0.2464–0.8420 0.2525–0.7522 0.0848–0.9703 0.0470–0.9550 0.0601–0.2031 0.0260–0.9940 0.0725–0.8710 0.2883–0.5701 0.0140–0.9770 0.0972–0.9853 0.0310–0.9509 0.0660–0.2450 0.0376–0.9740 0.0320–0.9616 0.0500–0.9500 0.1650–0.8870 0.1050–0.9140 0.0200–0.5980 0.0280–0.9820 0.0222–0.9715 0.0500–0.9500 0.0023–0.8110 0.0654–0.9000 0.0094–0.9792 0.0300–0.4470 0.0195–0.9779 0.0233–0.9465 0.0290–0.9703 0.0410–0.9470 0.0390–0.9780 0.0520–0.4000 0.0520–0.8950 0.0630–0.9620 0.0330–0.9200 0.0132–0.0714 0.0830–0.2870 0.0200–0.9820 0.0323–0.9584 0.2236–0.9834 0.1114–0.9822 0.0140–0.9490

y1 range (1st compound gas mole fraction) 0.1560–0.9997 0.2800–0.9997 0.2840–0.9999 – – – 0.1172–0.9061 0.1660–0.8930 0.1370–0.9060 0.1130–0.9070 0.1090–0.9010 – – 0.4000–0.8420 – – – – 0.1666–0.9999 – – 0.0450–0.9968 – 0.0792–0.9981 – 0.2600–0.9995 0.0910–0.9620 0.1000–0.9540 – – – 0.2500–0.9999 0.0881–0.9920 0.1180–0.9600 0.3780–0.9995 0.1806–0.9677 0.0830–0.9983 – 0.1171–0.9977 0.0309–0.9603 0.1666–0.9966 0.0720–0.9610 0.0550–0.9840 – 0.2160–0.8950 0.2470–0.9900 0.3060–0.9940 – – 0.1480–0.9980 – – – 0.1190–0.9620

Number of bubble points (T,P,x) 60 61 65 16 15 12 58 15 15 15 20 20 12 12 12 90 39 7 109 12 4 168 30 78 4 41 90 11 24 24 44 64 63 11 27 19 21 16 20 25 20 16 65 16 16 8 56 12 4 36 29 12 31 157

Number of dew points (T,P,y) 60 61 65 0 0 0 9 10 10 10 10 0 0 0 0 0 0 0 55 0 0 194 0 42 0 41 38 11 0 0 0 64 21 11 17 19 21 0 20 25 20 16 65 0 0 8 56 0 0 36 0 0 0 154

Number of binary critical points (Tcm ,Pcm ,xc ) 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 2 0 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 6

References

[141,142] [141,142] [141,142] [143] [143] [144] [117,143] [132] [132] [132] [132] [143] [143] [145,146] [146] [147,148] [149,150] [151] [17,53,152–154] [155] [156] [17,53,157–160] [161] [22,162–166] [167] [141,168] [169–173] [123] [171] [171] [22,111,174] [141,142] [149,171,175] [123] [176,177] [178,179] [175] [164] [175] [180] [175] [181] [182,183] [164] [164,165] [138] [184] [27] [167] [141] [169,185] [186] [108] [86,87,90,160,187,188]

J.-W. Qian et al. / Fluid Phase Equilibria 354 (2013) 212–235

13a4-6 13a4-7 13a4-8 13a4-c2a4 13a4-t2a4 13a4-1a5 13a4-4 t3a8-8 c3a8-8 t4a8-8 c4a8-8 4-c2a4 t2a4-c2a4 2m3-1a4 2m3-13a4 1a4-4m1a5 1a6-224m5 a3-224m5 1-a3 1-1a6 1-1a8 2-a3 2-1a11 a3-B 1a4-B 13a4-B 1a6-B B-1a7 B-1a8 4m1a5-B a3-mB 13a4-mB 1a6-mB 1a7-mB 13a4-Ba2 mB-Ba2 1a6-12mB a3-13mB 1a6-13mB 14mB-Ba2 1a6-eB 1a8-eB eB-Ba2 a3-124mB a3-iprB BB-1a16 BB-1a18 a3-C6 1a4-C6 13a4-C6 1a6-C6 C6-1a8 a3-tet CO2 -a3

Temperature range (K)

273.15–318.15 303.00–333.00 303.15–328.60 303.15–393.15 303.15–343.15 333.15–333.15 308.00–393.20 314.20–531.30 194.65–295.65 273.15–293.15 173.15–364.70 313.20–453.20 333.15–473.15 295.00–463.15 233.15–357.95 273.14–393.15 293.20–373.60 293.15–423.15 303.00–342.40 253.15–353.15 283.15–298.15 298.15–313.10 278.15–298.15 307.66–341.05 273.15–340.34 313.94–340.58 298.15–343.15 273.15–293.15 293.15–298.15 318.55–367.55 298.15–311.70 293.15–293.15 278.15–311.58 217.17–253.15 321.48–412.04 277.59–344.26 358.15–368.15 368.15–388.15 277.59–346.43 301.60–313.15 302.53–308.80 294.55–305.35 278.15–298.15 283.15–323.15 419.05–437.15 305.90–380.26 308.41–375.65 311.61–377.72 293.15–313.15 420.25–437.55 278.15–298.15 343.15–358.15

3.14–75.07 6.00–79.30 13.50–84.30 9.95–120.90 10.10–73.15 12.17–102.39 14.39–162.40 9.85–51.40 1.19–214.45 4.05–11.15 17.23–551.21 40.53–303.98 40.53–303.98 40.53–303.98 1.67–55.69 2.05–66.40 7.70–87.80 3.43–85.10 10.00–89.70 1.83–31.49 0.40–0.81 0.71–1.25 0.27–0.68 1.01–1.01 0.09–1.01 1.01–1.01 1.01–8.53 0.39–2.30 0.65–0.85 5.07–10.30 0.64–1.14 0.62–0.67 0.28–1.01 0.01–1.01 13.79–41.37 1.32–9.69 0.10–0.91 0.13–0.84 1.65–10.96 0.90–1.52 1.01–1.01 1.01–1.01 0.08–0.68 0.07–0.66 1.01–1.01 1.01–1.01 1.01–1.01 1.01–1.01 0.01–0.08 1.01–1.01 0.11–0.69 0.05–1.10

0.0246–0.9400 0.0320–0.9080 0.1462–0.9300 0.0820–0.9769 0.0740–0.8030 0.1019–0.9607 0.0820–0.9908 0.0463–0.5050 0.0090–0.4882 0.0025–0.0125 0.0044–0.4625 0.0400–0.4140 0.0280–0.3530 0.0240–0.3410 0.0200–0.9840 0.0230–0.9610 0.0810–0.9440 0.0143–0.8670 0.1170–0.9090 0.0009–0.9459 0.1507–0.8001 0.0950–0.9500 0.1501–0.8002 0.0120–0.8450 0.0207–0.9817 0.0260–0.8817 0.1840–0.9375 0.1264–0.9469 0.0680–0.9560 0.0340–0.9778 0.0050–0.9950 0.1080–0.8849 0.0109–0.9005 0.0060–0.9340 0.0860–0.8530 0.2500–0.7500 0.0140–0.9790 0.0300–0.9830 0.1000–0.9000 0.0369–0.9472 0.1840–0.7760 0.0597–0.9140 0.0860–0.8930 0.0450–0.9340 0.0500–0.9000 0.0105–0.9300 0.0344–0.9510 0.0249–0.9994 0.1202–0.8901 0.0400–0.9000 0.1460–0.8810 0.0020–0.9580

0.2188–0.9850 0.2450–0.9660 0.8390–0.9826 0.8140–0.9929 0.9560–0.9950 0.9607–0.9607 0.8608–0.9989 0.9383–0.9806 0.2320–0.9920 – 0.0288–0.9970 0.6415–0.9977 – 0.8740–0.9997 0.0640–0.9890 0.1331–0.9980 0.7730–0.9858 0.6300–0.9870 0.9651–0.9962 – – – – 0.0358–0.9520 0.0575–0.9925 0.0555–0.9522 – – – 0.0880–0.9900 0.0060–0.9957 – 0.0131–0.7350 – 0.1250–0.9030 – 0.1550–0.9970 0.1510–0.9970 0.1059–0.9052 – – 0.1130–0.9510 – – – 0.0919–0.9955 0.2075–0.9895 0.1681–0.9999 – – – 0.0560–0.9980

53 73 37 154 24 10 111 15 39 12 46 60 12 65 152 141 18 47 10 38 24 37 25 12 76 13 23 13 17 26 96 7 46 29 29 30 25 23 39 23 5 12 45 24 10 13 11 18 40 11 59 23

48 76 37 94 24 0 108 5 69 0 42 48 0 48 178 84 18 23 10 0 0 0 0 12 14 13 0 0 0 26 75 0 11 0 29 0 25 23 9 0 0 9 0 0 0 13 11 18 0 0 0 23

2 0 0 5 0 1 7 0 0 0 16 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

[90,189] [190] [191] [192–195] [194] [196] [197–202] [203] [17,93,204] [205] [95,99,206] [207,208] [207] [156,207,208] [14,17,86,160,209,210] [148,209,211–213] [212] [119,148] [212] [214] [120] [120,215] [120] [216] [120,217,218] [219] [112] [220] [120] [221,222] [120,223–233] [120] [120,229] [234] [235] [236] [237] [237] [236,238] [230,239] [230] [226,230] [120] [171] [240] [216] [216] [216] [241] [240] [120] [237]

J.-W. Qian et al. / Fluid Phase Equilibria 354 (2013) 212–235

CO2 -1a4 CO2 -13a4 CO2 -1a5 CO2 -1a6 CO2 -1a7 CO2 -1a8 CO2 -Ba2 CO2 -1a16 N2 -a3 N2 -13a4 H2 -a3 H2 -1a6 H2 -1a7 H2 -1a8 a2-a3 a2-1a4 a2-1a6 a2-4m1a5 a2-1a8 3-aa3 2m1a4-5 2m13a4-5 5-2m2a4 2m1a4-6 2m13a4-6 2m2a4-6 2ma3-8 13a4-2m13a4 1a5-2m13a4 2ma3-2m13a4 2m13a4-2m2a4 2m1a4-2m13a4 2m1a4-2m2a4 aa3-8 3-2ma3 2ma3-4 7-bP 1a8-bP 2m3-2ma3 2m4-2m13a4 2m4-2m2a4 3m1a4-2m13a4 2m13a4-B 2m1a5-B 12mB-Bma2 2m1a4-mB 2m13a4-mB 2m2a4-mB mB-Bma2 Ba2-Bma2 2m13a4-C6 C6-bP

219

220

Table 3 (Continued) Binary system (1st compound–2nd compound)

Total number of points:

303.15–343.15 308.00–393.10 313.15–373.15 323.15–323.15 273.15–293.15 287.95–373.15 288.15–308.15 278.15–298.15 278.15–298.15 372.05–381.65 283.15–337.37 324.15–353.50 353.84–355.94 293.45–333.75 343.15–358.15 313.10–323.10 338.15–353.15 358.15–368.15 348.15–354.65 278.15–351.76 356.65–372.25 329.05–405.75 271.25–396.65 278.65–398.65 313.85–336.15 429.95–448.05 315.45–347.25 293.32–348.12 295.85–335.25 315.00–323.20 303.15–373.15 288.15–308.15 288.15–308.15 307.50–312.80 310.87–313.00 313.10–323.10 429.50–450.00 439.35–449.45 315.37–397.59

Pressure range (bar) 10.20–74.30 29.80–180.90 24.30–115.50 70.40–94.60 4.05–11.15 1.01–130.00 43.73–74.99 0.09–0.60 0.05–0.19 1.01–1.01 0.12–1.01 1.01–1.01 1.01–1.01 0.12–1.57 0.11–1.06 0.10–1.44 0.10–0.79 0.14–0.91 0.81–1.02 0.07–1.01 1.01–1.01 0.40–0.99 0.13–1.01 0.13–1.01 0.08–0.08 1.01–1.01 19.53–112.06 8.30–129.35 32.50–109.30 3.00–100.50 6.89–68.95 44.71–73.69 40.67–77.97 1.01–1.01 1.01–1.01 0.09–1.52 1.01–1.01 1.01–1.01 13.79–41.37

x1 range (1st compound liquid mole fraction) 0.0830–0.8480 0.1894–0.9257 0.2250–0.9770 0.5142–0.8560 0.0023–0.0126 0.0000–0.0407 0.7228–0.9933 0.1440–0.8420 0.0860–0.8680 0.0890–0.9320 0.0600–0.9650 0.0467–0.9171 0.0240–0.9420 0.1680–0.8640 0.0250–0.9820 0.0500–0.9000 0.0520–0.8140 0.0440–0.9880 0.0680–0.9430 0.0272–0.8100 0.5466–0.9361 0.0280–0.9350 0.0370–0.9480 0.0480–0.8960 0.1000–0.9000 0.0427–0.9041 0.1604–0.9554 0.0732–0.9966 0.3007–0.9896 0.0281–0.9540 0.0024–0.0397 0.7471–0.9950 0.5864–0.9935 0.0500–0.9500 0.0500–0.9500 0.0490–0.9000 0.0207–0.9843 0.0752–0.9712 0.0650–0.8990

y1 range (1st compound gas mole fraction) 0.8820–0.9930 0.9430–0.9988 0.8220–0.9770 0.9680–0.9972 – – 0.9512–0.9986 – – 0.1500–0.9440 0.2050–0.4152 0.1216–0.9679 0.0270–0.9440 – 0.2810–0.9960 – 0.3770–0.9990 0.2690–0.9960 0.0820–0.9380 0.0607–0.4556 0.9358–0.9946 0.1840–0.9900 0.3260–0.9980 0.5430–0.9980 0.4000–0.9750 0.0948–0.9492 0.9410–0.9889 0.9562–0.9998 0.9718–0.9988 0.9670–0.9998 – 0.9572–0.9980 0.9742–0.9961 0.0650–0.9560 0.0615–0.9440 – 0.0334–0.9905 0.1033–0.9759 0.1180–0.9350

Number of bubble points (T,P,x)

Number of dew points (T,P,y)

Number of binary critical points (Tcm ,Pcm ,xc )

24 67 30 6 12 33 49 40 40 17 13 16 19 18 31 46 18 30 42 30 8 30 18 17 9 17 45 100 64 53 10 52 32 27 18 25 47 16 33

24 60 0 6 0 0 17 0 0 17 2 16 19 0 31 0 18 30 42 6 8 30 18 17 9 17 45 135 148 37 0 17 6 20 18 0 47 16 33

0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0

9324

6550

182

References

[194] [198,242] [192] [243] [205] [244–246] [247] [120] [120] [248] [120,249] [250] [125] [251] [237] [215] [237] [237] [252–254] [120,249] [255] [256] [257] [257] [258] [259] [260] [261–269] [261,270,271] [272–274] [245] [247] [275] [227,231,276] [227,231] [215] [259,277] [278] [279]

J.-W. Qian et al. / Fluid Phase Equilibria 354 (2013) 212–235

CO2 -2m1a5 CO2 -Bma2 CO2 -2e1a4 CO2 -myr N2 -2ma3 H2 -Bma2 a2-bP 5-aC6 6-aC6 7-1maC6 13aC5-6 C5-aC6 C6-aC6 13aC5-dicy aC6-aP 5-dicy C6-aP 7-aP B-aC6 13aC5-B B-dicy aC6-13mB aC5-eB aC5-iprB mB-15aC8 aP-pcy CO2 -aC6 CO2 -limRS CO2 -aP CO2 -limR H2 -aC6 a2-aP a2-limR 2m13a4-13aC5 2m2a4-13aC5 2m13a4-dicy aP-limRS bP-limRS a3-2m3

Temperature range (K)

J.-W. Qian et al. / Fluid Phase Equilibria 354 (2013) 212–235

221

Fig. 1. Prediction of isothermal phase diagrams for the three binary systems: (1-butene(1) + n-butane(2)), (1,3-butadiene(1) + n-butane(2)) and (1-butene(1) + 1,3butadiene(2)) using the PPR78 model. (+) experimental bubble points, ( ) experimental dew points, () experimental pure component vapor pressure, () pure component vapor pressure as predicted by the PR EoS. Solid line: predicted phase diagram with the PPR78 model. (a) (1-Butene(1) + n-butane(2)) at T = 310.93 K (kij = 0.0043) (red), (1,3butadiene(1) + n-butane(2)) at T = 310.93 K (kij = 0.0156) (bright green), (1-butene(1) + 1,3-butadiene(2)) at T = 310.93 K (kij = 0.0035) (blue). (b) (1-butene(1) + n-butane(2)) at T = 324.82 K (kij = 0.0040) (red), (1,3-butadiene(1) + n-butane(2)) at T = 324.82 K (kij = 0.0144) (bright green), (1-butene(1) + 1,3-butadiene(2)) at T = 324.82 K (kij = 0.0032) (blue). (c) (1-butene(1) + n-butane(2)) at T = 338.71 K (kij = 0.0037) (red), (1,3-butadiene(1) + n-butane(2)) at T = 338.71 K (kij = 0.0133) (bright green), (1-butene(1) + 1,3-butadiene(2)) at T = 338.71 K (kij = 0.0029) (blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

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 narrow (for a given temperature and pressure, the liquid- and

gas-phase compositions are very similar), and the two components have very close vapor pressures. The key to being able to satisfactorily predict the phase behavior of these binary systems is perfectly estimating the

Fig. 2. Prediction of isothermal phase diagrams for the two binary systems: (ethylene(1) + n-butane(2)) and (1,3-butadiene(1) + n-hexane(2)). (+) experimental bubble points, ( ) experimental dew points, () experimental critical points. (a) System (ethylene(1) + n-butane(2)) at T = 338.71 K. Calculations were performed with two different kij values: kij(1) = 0.0000 (red) and kij(2) = 0.3000 (bright green). (b) System (1,3-butadiene(1) + n-hexane(2)) at T = 233.15 K. Calculations were performed with two different kij values: kij(1) = −0.0058 (red) and kij(2) = −0.3829 (bright green). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

222

J.-W. Qian et al. / Fluid Phase Equilibria 354 (2013) 212–235

Fig. 3. Prediction of isothermal Pxy phase diagrams in the sub-critical and super-critical regions for six binary systems using the PPR78 model. (+) experimental bubble points, ( ) experimental dew points, () experimental critical points. Solid line: predicted phase diagram with the PPR78 model. (a) System (methane(1) + ethylene(2)) at five different temperatures: T1 = 150.00 K (kij = 0.0265) (red), T2 = 160.00 K (kij = 0.0248) (bright green), T3 = 170.00 K (kij = 0.0234) (blue), T4 = 180.00 K (kij = 0.0221), T5 = 190.00 K (kij = 0.0210) (violet). (b) System (1,3-butadiene(1) + n-octane(2)) at four different temperatures: T1 = 303.15 K (kij = 0.0009) (red), T2 = 343.15 K (kij = −0.0018) (bright green), T3 = 383.15 K (kij = −0.0038) (blue), T4 = 413.15 K (kij = −0.0051). (c) System (ethylene(1) + n-butane(2)) at four different temperatures: T1 = 322.04 K (kij = 0.0209) (red), T2 = 344.26 K (kij = 0.0218) (bright green), T3 = 366.48 K (kij = 0.0228) (blue), T4 = 388.71 K (kij = 0.0240). (d) System (n-hexane(1) + 1-hexadecene(2)) at three different temperatures: T1 = 472.10 K (kij = −0.0057) (red), T2 = 524.70 K (kij = −0.0071) (bright green), T3 = 572.50 K (kij = −0.0083) (blue). (e) System (n-pentane(1) + cyclohexene(2)) at five different temperatures: T1 = 278.15 K (kij = −0.0022) (red), T2 = 283.15 K (kij = −0.0027) (bright green), T3 = 288.15 K (kij = −0.0028) (blue), T4 = 293.15 K (kij = −0.0025), T5 = 298.15 K (kij = −0.0021) (violet). (f) System (n-hexane(1) + cyclohexene(2)) at five different temperatures: T1 = 278.15 K (kij = −0.0090) (red), T2 = 283.15 K (kij = −0.0097) (bright green), T3 = 288.15 K (kij = −0.0099) (blue), T4 = 293.15 K (kij = −0.0097), T5 = 298.15 K (kij = −0.0094) (violet). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

vapor pressures of the pure components. Unfortunately, although very precise in most cases, the PR EoS is not always able to calculate these pressures with sufficient accuracy. In order to illustrate this difficulty, the measurements by Laurance et al. [117] on three binary systems composed of C4 hydrocarbons,

1-butene + n-butane, 1,3-butadiene + n-butane and 1-butene + 1,3butadiene, are considered. At T = 310.93 K (see Fig. 1a), the calculated vapor pressures of n-butane, 1-butene and 1,3butadiene (solid black squares) are slightly underestimated compared to the experimental values (black hollow squares), and

J.-W. Qian et al. / Fluid Phase Equilibria 354 (2013) 212–235

223

Fig. 4. Prediction of isothermal or isobaric phase diagrams for binary systems that contain components of similar or very different volatility, using the PPR78 model. (+) experimental bubble points, ( ) experimental dew points. Solid line: predicted phase diagram with the PPR78 model. (a) System (propene(1) + propane(2)) at six different temperatures: T1 = 280.00 K (kij = 0.0087) (red), T2 = 290.00 K (kij = 0.0082) (bright green), T3 = 300.00 K (kij = 0.0078) (blue), T4 = 310.00 K (kij = 0.0073), T5 = 320.00 K (kij = 0.0069) (violet), T6 = 330.32 K (kij = 0.0065) (turquoise). (b) System (1-octene(1) + n-octane(2)) at four different pressures: P1 = 0.267 bar (red), P2 = 0.533 bar (bright green), P3 = 0.800 bar (blue), P4 = 1.013 bar. (c) System (propane(1) + 1,2-propadiene(2)) at five different temperatures: T1 = 253.15 K (kij = 0.0401) (red), T2 = 278.15 K (kij = 0.0398) (bright green), T3 = 303.15 K (kij = 0.0392) (blue), T4 = 328.15 K (kij = 0.0386), T5 = 353.15 K (kij = 0.0382) (violet). (d) System (2-methyl-1,3-butadiene(1) + n-pentane(2)) at three different temperatures: T1 = 298.15 K (kij = 0.0141) (red), T2 = 303.12 K (kij = 0.0137) (bright green), T3 = 313.10 K (kij = 0.0131) (blue). (e) System (ethane(1) + 1-undecene(2)) at two different temperatures: T1 = 298.15 K (kij = 0.0220) (red), T2 = 318.15 K (kij = 0.0201) (bright green). (f) System (ethylene(1) + n-eicosane(2)) at five different temperatures: T1 = 323.15 K (kij = 0.0430) (red), T2 = 348.15 K (kij = 0.0445) (bright green), T3 = 373.15 K (kij = 0.0461) (blue), T4 = 398.15 K (kij = 0.0479), T5 = 423.15 K (kij = 0.0498) (violet). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

224

J.-W. Qian et al. / Fluid Phase Equilibria 354 (2013) 212–235

Fig. 5. (a–d) Predictions of the critical locus for fifteen binary systems using the PPR78 model. () experimental critical points, (䊉) critical points of the pure compounds, () Upper critical end point (UCEP), () Lower critical end point (LCEP). Solid line: predicted phase diagram with the PPR78 model. Dashed line: vaporization curve of a pure compound.

the resulting Pxy phase diagrams calculated using the PPR78 model are thus shifted to lower pressures than the experimentally determined ones. On the other hand, at T = 324.82 K (see Fig. 1b), the pure-component vapor pressures are somewhat overestimated, and the predicted phase diagrams are shifted to higher pressures than the experimental pressures. At T = 338.71 K (see Fig. 1c), however, the pure-component vapor pressures are correctly predicted, and the PPR78 model yields calculated fluid-phase compositions that are in good agreement with the experimental data. The phase diagrams plotted in Fig. 1a and b cannot be improved by changing the kij value because this parameter has no influence on the pure-component vapor pressures. The previous examples also demonstrate that an accuracy of better than 0.2 % for the vapor pressures is necessary to properly predict the phase behavior of these systems. The PR EoS is generally able to predict these vapor pressures accurately, i.e., with less than a 1 % deviation, but this level of accuracy is not sufficient for systems containing isomers. From our experience, it is extremely difficult – if not impossible – to find out an alpha function (see Eq. (2)) that gives a 0.2 % accuracy regardless of the temperature. Consequently, for these systems, only the experimental data points at T = 338.71 K were considered in our data-fitting procedure. The deviation in the 1,3-butadiene vapor pressure still observed at this temperature, however, artificially increases the objective function.

ethylene(1) + n-butane(2), at T = 338.71 K (see Fig. 2a). A null kij allows the PR EoS to reproduce the critical pressure accurately, while the kij value needed to obtain the correct critical composition is kij = 0.3000. It is therefore impossible to reproduce both the critical pressure and the critical composition with the same kij value. (2) For all the binary systems containing 1,3-butadiene, the isothermal bubble and dew curves cannot be simultaneously reproduced with a single kij value. This behavior is illustrated in Fig. 2b for the 1,3-butadiene(1) + n-hexane(2) system at T = 233.15 K. The bubble curve can be accurately captured when kij = −0.0058, while a significantly more negative value (kij = −0.3829) is needed to reproduce the dew curve. 4.3. Impact of low solubility on the objective function Several binary mixtures, especially those containing 1,3butadiene, exhibit a mole fraction of the light component in the vapor phase close to one (see Fig. 2b). This type of behavior inevitably increases the objective function. For example, if y1,exp = 0.999 and y1,cal = 0.998, the model might seem extremely accurate; however, for this data point, the corresponding objective function (Fobj,dew defined by Eq. (8)) is 50 % (y1 % = 0.1, but y2 % = 100).

4.2. Difficulties in optimizing the temperature dependency of kij 5. Results and discussion (1) For some of the studied alkene-containing mixtures, it is very difficult to reproduce both the critical pressure and the critical composition. Let us consider, e.g., the binary system,

For all the data points included in our database, the objective function defined by Eq. (8) is Fobj = 9.06%.

J.-W. Qian et al. / Fluid Phase Equilibria 354 (2013) 212–235 312.0

314.0

(a)

225

(b)

T/K

T/K

2m13a4(1)-2m2a4(2)

308.0

312.0

2m1a4(1)-2m2a4(2)

x1,y1

x1,y1 310.0 0.0

304.0 0.0

25.0

0.5

1.0

(c)

0.5

1.0

(d)

P/bar

395.0

T/K

20.0

375.0 15.0

355.0 10.0

335.0

5.0 x1,y1 0.0 0.0

60.0

0.5

x1,y1 315.0 0.0

1.0

80.0

(e)

P/bar

0.5

1.0

(f)

P/bar

40.0

40.0

20.0

x1,y1 0.0

x1,y1 0.0

0.0

0.5

1.0

0.0

0.5

1.0

Fig. 6. Prediction of isothermal or isobaric phase diagrams for seven binary systems that contain two ethylenic components using the PPR78 model. (+) experimental bubble points, ( ) experimental dew points. Solid line: predicted phase diagram with the PPR78 model. (a) System (2-methyl-1,3-butadiene(1) + 2-methyl-2-butene(2)) at P = 1.013 bar (red), system (2-methyl-1-butene(1) + 2-methyl-2-butene(2)) at P = 1.013 bar (bright green). (b) System (2-methyl-2-butene(1) + 1,3-cyclopentadiene(2)) at P = 1.013 bar. (c) System (propene(1) + 1,3-butadiene(2)) at four different temperatures: T1 = 273.20 K (kij = 0.0083) (red), T2 = 293.20 K (kij = 0.0076) (bright green), T3 = 313.20 K (kij = 0.0071) (blue), T4 = 333.20 K (kij = 0.0066). (d) System (2-methylpropene(1) + 2-methyl-1,3-butadiene(2)) at two different pressures: P1 = 5.066 bar (red), P2 = 10.300 bar (bright green). (e) System (ethylene(1) + propene(2)) at seven different temperatures: T1 = 233.15 K (kij = 0.0048) (red), T2 = 263.07 K (kij = 0.0030) (bright green), T3 = 283.15 K (kij = 0.0024) (blue), T4 = 298.15 K (kij = 0.0021), T5 = 323.15 K (kij = 0.0018) (violet), T6 = 348.15 K (kij = 0.0017) (turquoise), T7 = 357.95 K (kij = 0.0017) (light orange). (f) System (ethylene(1) + beta-pinene(2)) at three different temperatures: T1 = 288.15 K (kij = −0.0183) (red), T2 = 298.15 K (kij = −0.0103) (bright green), T3 = 308.15 K (kij = −0.0061) (blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

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Fig. 7. Prediction of isothermal or isobaric phase diagrams for six binary systems using the PPR78 model. (+) experimental bubble points, ( ) experimental dew points. Solid line: predicted phase diagram with the PPR78 model. (a) System (1-hexene(1) + benzene(2)) at five different temperatures: T1 = 283.15 K (kij = −0.0006) (red), T2 = 298.15 K (kij = −0.0004) (bright green), T3 = 303.15 K (kij = −0.0004) (blue), T4 = 313.15 K (kij = −0.0003), T5 = 323.15 K (kij = −0.0002) (violet). (b) System (cyclohexane(1) + betapinene(2)) at two different temperatures: T1 = 343.15 K (kij = −0.0158) (red), T2 = 358.15 K (kij = −0.0150) (bright green). (c) System (1,3-butadiene(1) + cyclohexane(2)) at four different temperatures: T1 = 303.15 K (kij = 0.0244) (red), T2 = 343.15 K (kij = 0.0029) (bright green), T3 = 383.15 K (kij = −0.0003) (blue), T4 = 413.15 K (kij = −0.0010). (d) System (naphthalene(1) + 1-octadecene(2)) at four different pressures: P1 = 0.013 bar (red), P2 = 0.067 bar (bright green), P3 = 0.267 bar (blue), P4 = 1.013 bar. (e) System (ethylene(1) + cyclohexane(2)) at six different temperatures: T1 = 303.15 K (kij = 0.0410) (red), T2 = 323.15 K (kij = 0.0409) (bright green), T3 = 348.15 K (kij = 0.0408) (blue), T4 = 373.15 K (kij = 0.0408), T5 = 398.15 K (kij = 0.0408) (violet), T6 = 423.15 K (kij = 0.0408) (turquoise). (f) System (ethylene(1) + naphthalene(2)) at five different temperatures: T1 = 285.15 K (kij = 0.1098) (red), T2 = 308.15 K (kij = 0.0300) (bright green), T3 = 332.10 K (kij = 0.0077) (blue), T4 = 341.85 K (kij = 0.0038), T5 = 352.00 K (kij = 0.0011) (violet). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

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227

Fig. 8. Prediction of isothermal or isobaric phase diagrams for four binary systems that contain two components of very similar volatility, and predictions of critical locus for five binary systems using the PPR78 model. (+) experimental bubble points, ( ) experimental dew points, () experimental critical points, (䊉) critical points of the pure compounds. Solid line: predicted phase diagram with the PPR78 model, dashed line: vaporization curve of the pure compounds. (a) System (benzene(1) + cyclohexene(2)) at two different temperatures: T1 = 348.15 K (kij = 0.0109) (red), T2 = 353.15 K (kij = 0.0110) (bright green). (b) System (ethylbenzene(1) + styrene(2)) at five different pressures: P1 = 0.050 bar (red), P2 = 0.067 bar (bright green), P3 = 0.133 bar (blue), P4 = 0.150 bar, P5 = 0.267 bar (violet). (c) System (benzene(1) + cyclohexene(2)) at P = 0.987 bar (red), system (cyclohexane(1) + cyclohexene(2)) at P = 1.013 bar (bright green). (d) Prediction of the critical locus for five binary systems. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

The average overall deviation in the liquid-phase composition is:

nbubble i=1

x1 =

(|x1,exp − x1,cal |)i nbubble

= 0.023. Moreover,

Fobj,bubble nbubble

= 8.06%.

The average overall deviation in the gas-phase composition is:

ndew y1 =

i=1

(|y1,exp − y1,cal |)i ndew

= 0.016. Moreover,

Fobj,dew ndew

= 10.66%.

The average overall deviation in the critical composition is:

ncrit xc1 =

i=1

(|xc1,exp − xc1,cal |)i ncrit

= 0.025. Moreover,

Fobj,crit. comp ncrit

= 9.33%.

The average overall deviation in the binary critical pressure is: Pc % =

Fobj,crit. pressure ncrit

ncrit

=

100

i=1

((Pcm,exp − Pcm,cal )/Pcm,exp )i ncrit

= 3.79%.

The value of the objective function indicates that the PPR78 model provides a reasonable representation of the systems studied in this work. The results are, however, not as accurate as those obtained for mixtures containing saturated hydrocarbons. This higher objective function value can be explained by the following factors.

(1) Some of the experimental data reported in the literature are generally inconsistent and scattered. (2) As previously discussed, the PR78 EoS is not able to predict the vapor pressures of several pure components with sufficient accuracy.

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(3) Very narrow phase diagrams and phase diagrams exhibiting azeotropy are common in this study. (4) A number of the dew-point compositions are close to one. Accordingly, the absolute deviation in the gas-phase composition (y1 = 0.016) is smaller than the absolute deviation in the liquid-phase composition (x1 = 0.023), while the percent deviation in the gas-phase composition (10.7%) is higher than that in the liquid-phase composition (8.1%). In order to illustrate the accuracy and the limitations of the PPR78 model, several families of binary systems were defined to provide a fair representation of the whole database. 5.1. Results for mixtures of an alkene (or cycloalkene) + n-alkane (or branched alkane) In this family, 4335 bubble points, 2676 dew points and 60 mixture critical points were collected for 75 binary systems. It is therefore impossible to graphically show all the results, and it was thus decided to discuss the quality of the PPR78 model based on the characteristics of the phase diagrams in several figures (see Figs. 3–5). Fig. 3 shows the isothermal phase diagrams in the subcritical and supercritical regions for six binary systems. For the mixtures of methane(1) + ethylene(2) and 1,3-butadiene(1) + n-octane(2) (see Fig. 3a and b, respectively), the isothermal bubble curves are nearly linear, thus demonstrating that the liquid phases behave as ideal solutions. A significant difference between the liquid- and gasphase compositions is also observed (the phase diagrams are not as narrow as those observed for mixtures of isomers). The kij (T) value is close to zero and slightly decreases with temperature. It is observed that the dew curve of the 1,3-butadiene(1) + n-octane(2) system deviates considerably from the experimental data. As discussed in Section 4, it is indeed difficult to accurately predict both the bubble and dew curves for systems containing 1,3-butadiene. Fig. 3c and d shows the isothermal phase diagrams in the supercritical region for two binary systems. The prediction of the whole phase diagram (bubble curve + dew curve + critical region) for the ethylene(1) + n-butane(2) system is not very accurate (see Fig. 3c), owing to the fact that the critical pressure and the critical composition cannot be simultaneously predicted as discussed in Section 4. For this system, after minimization of the objective function, the critical pressures are found to be predicted more accurately than the critical compositions. On the other hand, very accurate results are obtained for the n-hexane(1) + 1hexadecene(2) system (see Fig. 3d) in which the influence of the double bond is much weaker. Fig. 3e and f shows the isothermal phase diagrams at low pressures for two different binary systems containing a cycloalkene: n-pentane(1) + cyclohexene(2) and nhexane(1) + cyclohexene(2). For both systems, the BIPs are negative (with increasing temperature, they first decrease, reach a minimum and then increase), and accurate predictions are obtained with the PPR78 model. Fig. 4a–d shows the isothermal or isobaric phase diagrams for four binary systems that contain two components of very similar volatility. These phase diagrams are so narrow that it is difficult to reproduce with high accuracy the liquid- and gas-phase compositions at a fixed temperature and pressure and the objective function increases accordingly. The value of kij is always nearly zero, and it is interesting to note that for each of these 4 systems, it slightly decreases with increasing temperature. Fig. 4e and f shows the isothermal phase diagrams for two size-asymmetric binary systems for which the critical locus and the bubble and dew curves are simultaneously in good agreement with the experimental data. It is thus possible to conclude that the PPR78 model is accurate for all chain lengths of the n-alkanes and/or the n-alkenes.

Of these 75 binary mixtures of an alkene (or cycloalkene) + nalkane (or branched alkane), the experimental critical points are only available for 13 systems. The predictions of the critical loci are shown in Fig. 5. All these systems except ethylene(1) + neicosane(2) exhibit a continuous vapor–liquid critical curve between the critical points of the two pure components, which corresponds to Type I or Type II behavior according to the classification of Van Konynenburg and Scott [280,281]. Generally, these types of critical loci are accurately predicted by the PPR78 model. We should mention that obvious scatter in the data can be observed for several systems. In particular, the experimental critical points of the ethylene(1) + n-octane(2) system on the right-hand side of the pressure maximum of the critical curve overlap with the experimental critical locus of the ethylene(1) + n-heptane(2) system (see Fig. 5b). We suggest that the experimental critical pressures of the ethylene(1) + n-octane(2) system at high temperatures are too low and are thus overestimated by the PPR78 model. Type IV phase behavior is exhibited by the ethylene(1) + n-eicosane(2) system (see Fig. 5c); the mixture critical line extending between the critical point of n-eicosane and the LCEP (lower critical end point) is accurately predicted, whereas the one extending between the critical point of pure ethylene and the UCEP (upper critical end point) cannot be experimentally confirmed. 5.2. Results for mixtures of an alkene (or cycloalkene) + alkene (or cycloalkene) Fig. 6a and b shows the isobaric phase diagrams for three binary systems that contain two ethylenic components of very similar volatility. A general overview of the results shows that the nearly ideal phase behaviors as well as the azeotropic behaviors are predicted accurately regardless of the uncertainty in the purecomponent vapor pressures and the scatter in the experimental data points. In addition, the Pxy and Txy phase diagrams in the subcritical area for two different binary systems are shown in panels c and d of Fig. 6. It can be observed that the PPR78 model is able to perfectly capture these data. Fig. 6e and f shows the isothermal phase diagrams in both the subcritical and supercritical regions for two binary systems. All the experimental VLE data for the ethylene(1) + propene(2) system are predicted with excellent accuracy over a wide range of temperatures. When the structure of the alkene mixed with ethylene becomes more complex, e.g., beta-pinene, the mixture becomes highly asymmetric, and as a consequence, the results are less satisfactory (see Fig. 6f). The accurate predictions of the critical loci for two binary systems in this family, ethylene(1) + propene(2) and propene(1) + 1butene(2), are shown in Fig. 5d. In conclusion, accurate results are obtained for the various binary systems belonging to this family. 5.3. Results for mixtures of an alkene (or cycloalkene) + aromatic compound and an alkene (or cycloalkene) + naphthenic compound Fig. 7a and b shows the isothermal phase diagrams at very low pressures for two binary systems. Very good results are obtained for these systems, including the cyclohexane(1) + beta-pinene(2) system, which contains a more complex compound. Fig. 7c and d shows isothermal or isobaric phase diagrams in the subcritical region for two systems. From the isothermal Pxy diagram (Fig. 7c), it can be concluded that the bubble and dew curves of the 1,3-butadiene(1) + cyclohexane(2) system cannot be reproduced simultaneously as discussed in Section 4. The isobaric Txy diagram (Fig. 7d) indicates that the PPR78 model can accurately

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Fig. 9. Prediction of isothermal or isobaric phase diagrams and prediction of the critical locus for the binary system: (ethylene(1) + carbon dioxide(2)) using the PPR78 model. (+) experimental bubble points, ( ) experimental dew points, () experimental critical points, (♦) experimental azeotropic points (䊉) critical points of the pure compounds, () Upper critical end point (UCEP). Solid line: predicted phase diagram with the PPR78 model. Dashed line: predicted azeotropic lines (Pxy and Txy diagrams) and vaporization curves of the pure compounds (PT diagram). (a) System (ethylene(1) + carbon dioxide(2)) at three different temperatures: T1 = 223.15 K (kij = 0.0535) (red), T2 = 231.55 K (kij = 0.0538) (bright green), T3 = 243.15 K (kij = 0.0543) (blue). (b) System (ethylene(1) + carbon dioxide(2)) at four different temperatures: T1 = 252.95 K (kij = 0.0548) (red), T2 = 258.15 K (kij = 0.0551) (bright green), T3 = 263.14 K (kij = 0.0553) (blue), T4 = 273.16 K (kij = 0.0560). (c) System (ethylene(1) + carbon dioxide(2)) at five different temperatures: T1 = 276.65 K (kij = 0.0561) (red), T2 = 281.15 K (kij = 0.0564) (bright green), T3 = 283.16 K (kij = 0.0565) (blue), T4 = 288.15 K (kij = 0.0568), T5 = 293.15 K (kij = 0.0572) (violet). (d) System (ethylene(1) + carbon dioxide(2)) at three different pressures: P1 = 50.663 bar (red), P2 = 55.729 bar (bright green), P3 = 60.795 bar (blue). (e) Prediction of the critical locus for the (ethylene(1) + carbon dioxide(2)) binary system. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

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Fig. 10. Prediction of isothermal phase diagrams for five binary systems, and prediction of the critical locus for five binary systems using the PPR78 model. (+) experimental bubble points, ( ) experimental dew points, () experimental critical points, (䊉) critical points of the pure compounds. Solid line: predicted phase diagram with the PPR78 model. Dashed line: vaporization curve of the pure compound. (a) System (carbon dioxide(1) + 2-ethyl-1-butene(2)) at three different temperatures: T1 = 313.15 K (kij = 0.0724) (red), T2 = 348.15 K (kij = 0.0870) (bright green), T3 = 373.15 K (kij = 0.1075) (blue). (b) System (carbon dioxide(1) + 1,3-butadiene(2)) at three different temperatures: T1 = 303.00 K (kij = 0.0463) (red), T2 = 313.00 K (kij = 0.0432) (bright green), T3 = 333.00 K (kij = 0.0380) (blue). (c) System (carbon dioxide(1) + 1-hexadecene(2)) at three different temperatures: T1 = 314.20 K (kij = 0.0784) (red), T2 = 394.10 K (kij = 0.0787) (bright green), T3 = 531.30 K (kij = 0.0929) (blue). (d) System (carbon dioxide(1) + alphamethylstyrene(2)) at three different temperatures: T1 = 323.00 K (kij = 0.0767) (red), T2 = 353.20 K (kij = 0.0813) (bright green), T3 = 393.10 K (kij = 0.0965) (blue). (e) System (carbon dioxide(1) + (R + S)-limonene(2)) at three different temperatures: T1 = 323.00 K (kij = 0.0821) (red), T2 = 323.15 K (kij = 0.0822) (bright green), T3 = 323.20 K (kij = 0.0822) (blue). (f) Prediction of the critical locus for five binary systems. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

predict the complete phase diagrams for systems containing a polyaromatic and a long-chain alkene. Fig. 7e and f shows the isothermal phase diagrams in the supercritical region for two binary systems. As shown in Fig. 7e, very good results are obtained for the ethylene(1) + cyclohexane(2) system. Unfortunately, the results for the ethylene(1) + naphthalene(2)

system (Fig. 7f) are in poor agreement with the experimental data as demonstrated by an objective function of 18.35 %, the highest found in this study, calculated on 33 bubble points, 240 dew points and 7 critical points. For this system, most of the experimental data are dew points, and most of the vapor-phase compositions are close to one, which inevitably results in an increase of the

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Fig. 11. Prediction of isothermal phase diagrams for two binary systems using the PPR78 model. (+) experimental bubble points, ( ) experimental dew points. Solid line: predicted phase diagram with the PPR78 model. (a) System (nitrogen(1) + ethylene(2)) at five different temperatures: T1 = 134.00 K (kij = 0.0849) (red), T2 = 160.00 K (kij = 0.0841) (bright green), T3 = 200.00 K (kij = 0.0837) (blue), T4 = 240.00 K (kij = 0.0841), T5 = 260.00 K (kij = 0.0845) (violet). (b) System (nitrogen(1) + propene(2)) at four different temperatures: T1 = 194.65 K (kij = 0.1463) (red), T2 = 218.45 K (kij = 0.1246) (bright green), T3 = 260.00 K (kij = 0.0940) (blue), T4 = 290.00 K (kij = 0.0757). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

objective function. Furthermore, by fitting the kij value for each temperature, it is found that no kij value is able to exactly reproduce the complete phase diagram (bubble curve + dew curve + critical region), thus highlighting the limitations of the mixing rules used in the PPR78 model for this complex system. By examining the predicted isothermal Pxy phase diagrams in Fig. 7f, we can, however, conclude that reasonable results are obtained for the ethylene(1) + naphthalene(2) system, except at T = 308.15 K. Moreover, it is surprising that for this system, the kij value varies much more significantly with temperature (it decreases from 0.1098 to 0.0011 as the temperature increases from 285.15 K to 352.00 K) than those for the other systems investigated. Fig. 8 shows the isothermal or isobaric phase diagrams for four binary systems that contain two components of very similar volatility and the predictions of critical loci for five different binary systems. Two phase diagrams exhibiting azeotropy for the benzene(1) + cyclohexene(2) system, the nearly ideal phase behavior of the ethylbenzene(1) + styrene(2) system and two Txy phase diagrams for the cyclohexane(1) + cyclohexene(2) and benzene(1) + cyclohexene(2) systems are shown in Fig. 8a–c, respectively. Once again, the PPR78 model is able to accurately predict these kinds of phase behavior. Regarding the critical loci (see Fig. 8d), it is observed that the experimental critical points of the ethylene(1) + benzene(2), ethylene(1) + toluene(2), propene(1) + benzene(2) and propene(1) + isopropylbenzene(2) systems are predicted satisfactorily. However, for the ethylene(1) + naphthalene(2) system, the critical curve shows a pressure minimum and maximum, and the slope of the critical curve at low temperature is very steep (a small change in temperature induces a large change in pressure). Such Type III systems are very difficult to model using a cubic EoS as demonstrated in our previous papers [3,4]. For this reason, the predicted Pxy diagram of the ethylene(1) + naphthalene(2) system does not capture the experimental diagram well (see Fig. 7f).

The ethylene(1) + CO2 (2) system exhibits absolute positive azeotropy (see Fig. 9) like the CO2 (1) + ethane(2) system [4], but the critical locus (see Fig. 9e) does not have a temperature minimum. The BIP varies from 0.0535 to 0.0572 as the temperature increases from 223.15 K to 293.15 K, and very accurate results are obtained. The PPR78 model is still able to provide an accurate reproduction of the experimental data in both the subcritical and supercritical areas for branched alkenes and even dienes (see Fig. 10a and b). The accuracy of the model is the same regardless of the alkene chain length (e.g., 1-hexadecene) as shown in Fig. 10c. Moreover, the predicted phase diagrams of the CO2 (1) + alpha-methylstyrene(2) system are in good agreement with the experimental data (see Fig. 10d). As the cycloalkene becomes more complex (limonene), the bubble pressures are slightly underestimated by the PPR78 model. Note that for the CO2 (1) + (R + S)-limonene(2) system (see Fig. 10e), a great deal of scatter is observed (as an example, the difference in the bubble pressure measured by two different authors at the same composition can be as high as 15 bar). Fig. 10f shows the prediction quality of the critical loci for five different binary mixtures in this family. They all exhibit Type II phase behavior according to the classification scheme of Van Konynenburg and Scott [280,281]. For the mixtures containing alkene + N2 , experimental data points are only available for four binary systems. The bubble points of the N2 (1) + 1,3-butadiene(2) and N2 (1) + 2-methylpropene(2) systems (see Table 3) only illustrate the low solubility of N2 in alkenes at low temperatures and have thus not been plotted here. Fig. 11a and b shows several isothermal phase diagrams predicted by the PPR78 model for two binary systems: N2 (1) + ethylene(2) and N2 (1) + propene(2). The objective function is Fobj = 5.38 %, which demonstrates that the PPR78 model is able to accurately predict the phase behavior of these mixtures over a wide range of temperatures despite the overestimation of the critical pressures at intermediate temperatures. 5.5. Results for mixtures of an alkene + hydrogen

5.4. Results for mixtures of an alkene (or cycloalkene) + CO2 (or N2 ) VLE measurements of binary systems containing an alkene (or a cycloalkene) and CO2 were extensively performed by several investigators. However, experimental data for binary mixtures containing an alkene and N2 are scarce; they are only available for 4 systems and do not contain any critical points. Furthermore, no experimental VLE data points for alkene + H2 S systems are available in the open literature.

According to our database, VLE data have only been obtained for six binary systems in this family. The data-fitting procedure performs well for the H2 (1) + ethylene(2) binary mixture for which many experimental data points, including 20 critical points, have been collected. Fig. 12a and b shows 14 isothermal phase diagrams for this system. As typically observed in hydrogen-containing systems [11], the critical pressures are overestimated at low temperatures (see e.g., T = 166.15 K and T = 175.15 K in Fig. 12b). Note that the LLE at low temperatures and the VLE in the vicinity of

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Fig. 12. Prediction of isothermal phase diagrams for five binary systems, and prediction of the critical locus for two binary systems using the PPR78 model. (+) experimental bubble points, ( ) experimental dew points, () experimental critical points, (䊉) critical points of the pure compounds. Solid line: predicted phase diagram with the PPR78 model. Dashed line: vaporization curve of the pure compounds. (a) System (hydrogen(1) + ethylene(2)) at seven different temperatures: T1 = 112.00 K (kij = −0.0389) (red), T2 = 149.70 K (kij = 0.0040) (bright green), T3 = 173.05 K (kij = 0.0278) (blue), T4 = 199.85 K (kij = 0.0562), T5 = 227.55 K (kij = 0.0833) (violet), T6 = 241.45 K (kij = 0.0965) (turquoise), T7 = 255.35 K (kij = 0.1095) (light orange). (b) System (hydrogen(1) + ethylene(2)) at seven different temperatures: T1 = 166.15 K (kij = 0.0216) (red), T2 = 175.15 K (kij = 0.0311) (bright green), T3 = 189.55 K (kij = 0.0458) (blue), T4 = 205.15 K (kij = 0.0615), T5 = 220.15 K (kij = 0.0761) (violet), T6 = 235.15 K (kij = 0.0905) (turquoise), T7 = 247.15 K (kij = 0.1019) (light orange). (c) System (hydrogen(1) + propene(2)) at five different temperatures: T1 = 199.85 K (kij = 0.1917) (red), T2 = 227.55 K (kij = 0.1749) (bright green), T3 = 255.35 K (kij = 0.1640) (blue), T4 = 283.15 K (kij = 0.1573), T5 = 297.05 K (kij = 0.1551) (violet). (d) System (hydrogen(1) + 1-hexene(2)) at four different temperatures: T1 = 313.20 K (kij = 0.1945) (red), T2 = 353.20 K (kij = 0.2081) (bright green), T3 = 393.20 K (kij = 0.2228) (blue), T4 = 433.20 K (kij = 0.2383). (e) System (hydrogen(1) + alphamethylstyrene(2)) at three different temperatures: T1 = 308.00 K (kij = 0.4833) (red), T2 = 333.15 K (kij = 0.5051) (bright green), T3 = 373.15 K (kij = 0.5390) (blue). (f) System (hydrogen(1) + cyclohexene(2)) at two different temperatures: T1 = 303.15 K (kij = 0.3722) (red), T2 = 373.15 K (kij = 0.2659) (bright green). (g) Prediction of the critical locus for two binary systems: (hydrogen(1) + ethylene(2)) and (hydrogen(1) + propene(2)). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

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the critical point of ethylene are described accurately by the PPR78 model. The prediction of the critical locus of this mixture is shown in Fig. 12g. For the binary mixtures consisting of H2 and a linear alkene, critical points are only available for the H2 (1) + propene(2) system, and all the experimental VLE (or LLE) points were measured at low to moderate pressures. As shown in Fig. 12c, the Pxy phase diagrams of the H2 (1) + propene(2) system at five different temperatures are reproduced accurately as are the 16 critical points in the vicinity of the critical point of pure propene (Fig. 12g). In Fig. 12d, four predicted isothermal phase diagrams of the H2 (1) + 1-hexene(2) system are plotted together with the experimental data points published by Vasil’eva et al. [208]. These authors have demonstrated that the solubility of 1-hexene in the H2 -rich liquid phase at P = 300 bar has little temperature dependence, which is not easy to predict with the PPR78 model. The group interaction parameters between group 19 (branched alkene) and group 16 (H2 ) were determined based on 26 experimental data points available for the H2 (1) + alphamethylstyrene(2) system. Similarly, only 10 experimental points (for the H2 (1) + cyclohexene(2) system) were available to fit the interaction parameters between group 20 (cycloalkene) and group 16 (H2 ). These experimental data are accurately captured by the PPR78 model (see Fig. 12e and f); however, these parameters might not be generally applicable. 6. 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 higher accuracy than Type III, IV or V phase behaviors. The kij value is often low (especially when alkenes are mixed with other hydrocarbons) but strongly depends on temperature. Unfortunately (see Table 3), due to a lack of experimental data, some interactions (e.g., between ethylenic groups and H2 S or SH) were not determined. By combining the proposed group contribution method with the one developed by Avaullée et al. [282] to determine the critical parameters and the acentric factor of heavy hydrocarbons, it becomes possible to use the PPR78 model to predict the phase behavior of petroleum fluids. To conclude, let us stress that following the theory developed by Jaubert and Privat [283,284], the Akl and Bkl values published in this paper or those developed for fatty acid esters [285,286] can be used to predict the kij values for any other cubic EoS, such as the SRK EoS. Acknowledgments The French Petroleum Company TOTAL and more particularly Dr. Pierre Duchet-Suchaux (expert in thermodynamics) are gratefully acknowledged for sponsoring this research. References [1] J.-N. Jaubert, F. Mutelet, Fluid Phase Equilib. 224 (2004) 285–304. [2] J.-N. Jaubert, S. Vitu, F. Mutelet, J.-P. Corriou, Fluid Phase Equilib. 237 (2005) 193–211. [3] S. Vitu, J.-N. Jaubert, F. Mutelet, Fluid Phase Equilib. 243 (2006) 9–28. [4] S. Vitu, R. Privat, J.N. Jaubert, F. Mutelet, J. Supercrit. Fluids 45 (2008) 1–26. [5] R. Privat, J.-N. Jaubert, F. Mutelet, Ind. Eng. Chem. Res. 47 (2008) 2033–2048. [6] R. Privat, F. Mutelet, J.-N. Jaubert, Ind. Eng. Chem. Res. 47 (2008) 10041–10052.

[7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]

[20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69]

233

R. Privat, J.-N. Jaubert, F. Mutelet, J. Chem. Thermodyn. 40 (2008) 1331–1341. R. Privat, J.-N. Jaubert, F. Mutelet, Ind. Eng. Chem. Res. 47 (2008) 7483–7489. J.-N. Jaubert, R. Privat, F. Mutelet, AIChE J. 56 (2010) 3225–3235. R. Privat, J.-N. Jaubert, Fluid Phase Equilib. 334 (2012) 197–203. J.-W. Qian, J.-N. Jaubert, R. Privat, J. Supercrit. Fluids 75 (2013) 58–71. D.B. Robinson, D.Y. Peng, GPA Research Report RR-28, 1978, pp. 1–36. B.E. Poling, J.M. Prausnitz, J.P. O’Connell, The Properties of Gases and Liquids, 5th ed., McGraw-Hill, New York, 2000. Confidential Company Research Report, 1982. I.M. Elshayal, B.C.Y. Lu, Can. J. Chem. Eng. 53 (1975) 83–87. V. Machat, T. Boublik, Fluid Phase Equilib. 21 (1985) 11–24. M.S. Rozhnov, V.G. Kozya, V.I. Zhdanov, Khim. Prom-st. (Moscow) (1988) 674–675. P. Smith, Ph.D. thesis, University of Wisconsin, 1974. B. Williams, Pressure-Volume-Temperature Relationships and Phase Equilibria in the System Ethylene-Normal Butane, Ph.D. thesis, University of Michigan, 1947. M.T. Raetzsch, W. Soell, Z. Phys. Chem. (Leipzig) 256 (1975) 815–828. Confidential Company Research Report, 1979. B.I. Konobeev, V.V. Lyapin, Khim. Prom-st. (Moscow) 43 (1967) 114–116. I. Nagy, R.A. Krenz, R.A. Heidemann, L.T.W. de, J. Chem. Eng. Data 50 (2005) 1492–1495. T.P. Zhuze, A.S. Zhurba, Bull. Acad. Sci. USSR Div. Chem. Sci. 9 (1960) 335–337. T.P. Zhuze, A.S. Zhurba, E.A. Esakov, Bull. Acad. Sci. USSR Div. Chem. Sci. 9 (1960) 331–334. W.B. Kay, J. Ind. Eng. Chem. (Washington, D.C.) 40 (1948) 1459–1464. C.R.N. Pacheco, J.P. Ferreira Filho, A.M.C. Uller, World Congress III of Chemical Engineering, Tokyo, 1986, pp. 104–107. A. Sahgal, H.M. La, W. Hayduk, Can. J. Chem. Eng. 56 (1978) 354–357. I. Thoedtmann, H. Preuss, D. Pape, FIZ Report, 1989, pp. 12011. V.S. Zernov, V.B. Kogan, O.G. Egudina, V.M. Kobyakov, T.V. Babayants, L.I. Kalichava, J. Appl. Chem. USSR 63 (1990) 1469–1472. W.L. Weng, M.J. Lee, J. Chem. Eng. Data 37 (1992) 213–215. G.W. Nederbragt, Appl. Sci. Res. A A1 (1948) 237–248. D.B. Todd, J.C. Elgin, AIChE J. 1 (1955) 20–27. J.V. Ribeiro, A.A. Susu, J.P. Kohn, J. Chem. Eng. Data 17 (1972) 279–280. B.K. Kaul, Solubilities and Dew-Point Temperature in Hydrocarbon and Coal Processing, Ph.D. thesis, University of California, Berkeley, 1977, pp. 1–128. J.S. Chou, K.C. Chao, J. Chem. Eng. Data 34 (1989) 68–70. T.W. De Loos, W. Poot, R.N. Lichtenthaler, Ber. Bunsen-Ges. Phys. Chem. 88 (1984) 855–859. J. Gregorowicz, J. Supercrit. Fluids 26 (2003) 95–113. J. Gregorowicz, Fluid Phase Equilib. 240 (2006) 29–39. J.P. Kohn, E.S. Andrle, K.D. Luks, J.D. Colmenares, J. Chem. Eng. Data 25 (1980) 348–350. A.A. Naumova, T.N. Tyvina, Zh. Prikl. Khim. (Leningrad) 54 (1981) 1416–1417. A.A. Naumova, T.N. Tyvina, J. Appl. Chem. USSR 54 (1981) 2440–2441. F.H. Fallaha, Phase Equilibria at high Pressures with Application to Vapor Phase Extraction, Ph.D. thesis, University of Birmingham, 1974. M.B. King, D.A. Alderson, F.H. Fallah, D.M. Kassim, K.M. Kassim, J.R. Sheldon, R.S. Mahmud, Chem. Eng. Supercrit. Fluid Cond. (1983) 31–80. J.C.G. Calado, V.A.M. Soares, J. Chem. Soc. Faraday Trans. 1 (73) (1977) 1271–1280. C. Hsi, B.C.Y. Lu, Can. J. Chem. Eng. 49 (1971) 140–143. R.C. Miller, A.J. Kidnay, M.J. Hiza, J. Chem. Thermodyn. 9 (1977) 167–178. D.W. Moran, Low temperature equilibria in binary systems, including the solid phases, Ph.D. thesis, University of London, 1959, pp. 1–192. H. Sagara, Y. Arai, S. Saito, J. Chem. Eng. Jpn. 5 (1972) 339–348. D.A. Barclay, J.L. Flebbe, D.B. Manley, J. Chem. Eng. Data 27 (1982) 135–142. J.C.G. Calado, d.A.E.J.S. Gomes, P. Clancy, K.E. Gubbins, J. Chem. Soc. Faraday Trans. 1 (79) (1983) 2657–2667. A.M. Clark, F. Din, Discuss. Faraday Soc. 15 (1953) 202–207. P.T. Eubank, M.A. Barrufet, H. Duarte-Garza, L. Yurttas, Fluid Phase Equilib. 52 (1989) 219–227. A. Fredenslund, J. Mollerup, K.R. Hall, J. Chem. Eng. Data 21 (1976) 301–304. G.H. Hanson, R.J. Hogan, F.N. Ruehlen, M.R. Cines, Chem. Eng. Prog. Symp. Ser. 49 (1953) 37–44. F.F. Kharakhorin, For. Petrol. Technol. 9 (1941) 411–422. J.L. McCurdy, D.L. Katz, J. Ind. Eng. Chem. (Washington, D.C.) 36 (1944) 674–680. C.R. Coan, A.D. King Jr., J. Chromatogr. 44 (1969) 429–436. S.R.M. Ellis, R.L. Valteris, G.J. Harris, Chem. Eng. Progr. Symp. Ser. 64 (1968) 16–21. H. Hiraoka, Rev. Phys. Chem. Jpn. 28 (1958) 64–66. G.A. Holder, D. Macauley, J. Chem. Eng. Data 37 (1992) 100–104. Y.I. Kozorezov, A.P. Rusakov, N.M. Pikalo, Khim. Prom. (Moscow) 45 (1969) 343–345. T. Liu, J.-Y. Fu, K. Wang, Y. Gao, W.-K. Yuan, J. Chem. Eng. Data 46 (2001) 809–812. S.G. Lyubetskii, J. Appl. Chem. USSR 35 (1962) 125–129. S.G. Lyubetskii, Zh. Prikl Khim, S. Peterburg, Russ. Fed. 35 (1962) 141–147. D.L. Tiffin, J.P. Kohn, K.D. Luks, J. Chem. Eng. Data 24 (1979) 96–98. A.S. Zhurba, T.P. Zhuze, Izv. Vyssh. Uchebn. Zaved. Neft Gaz. 1 (1960) 93–106. L.-S. Lee, H.-j. Ou, H.-l. Hsu, Fluid Phase Equilib. 231 (2005) 221–230. E.R. Shenderei, Y.D. Zel’venskii, F.P. Ivanoskii, Zh. Fiz. Khim. 36 (1962) 801–807.

234

J.-W. Qian et al. / Fluid Phase Equilibria 354 (2013) 212–235

[70] E.R. Shenderei, Y.D. Zel’venskii, F.P. Ivanovskii, Russ. J. Phys. Chem. 36 (1962) 415–419. [71] T.N. Tyvina, A.A. Naumova, S.A. Polyakov, J. Appl. Chem. USSR 52 (1979) 910–913. [72] E. Nakamura, K. Koguchi, T. Amemiya, Kogyo Kagaku Zasshi 69 (1966) 1940–1944. [73] G.A.M. Diepen, F.E.C. Scheffer, J. Am. Chem. Soc. 70 (1948) 4085–4089. [74] G.A.M. Diepen, F.E.C. Scheffer, J. Phys. Chem. 57 (1953) 575–577. [75] K.P. Johnston, C.A. Eckert, AIChE J. 27 (1981) 773–779. [76] S. Seiichi, O. Kazunari, K. Takashi, J. Supercrit. Fluids 1 (1988) 1–6. [77] Y.V. Tsekhanskaya, M.B. Iomtev, E.V. Mushkina, Russ. J. Phys. Chem. 38 (1964) 1173–1176. [78] G.S.A. van Welie, G.A.M. Diepen, Recl. Trav. Chim. Pays Bas 80 (1961) 659–665. [79] G.S.A. van Welie, G.A.M. Diepen, Recl. Trav. Chim. Pays Bas 80 (1961) 673–680. [80] G.S.A. van Welie, G.A.M. Diepen, Recl. Trav. Chim. Pays Bas 80 (1961) 666–672. [81] K.P. Johnston, D.H. Ziger, C.A. Eckert, Ind. Eng. Chem. Fundam. 21 (1982) 191–197. [82] R.T. Kurnik, S.J. Holla, R.C. Reid, J. Chem. Eng. Data 26 (1981) 47–51. [83] H.K. Bae, K. Nagahama, M. Hirata, J. Chem. Eng. Data 27 (1982) 25–27. [84] D. Cook, H.C. Longuet-Higgins, Proc. R. Soc. London Ser. A 209 (1951) 28–38. [85] T. Hakuta, K. Nagahama, S. Suda, Kagaku Kogaku 33 (1969) 904–907. [86] G.G. Haselden, F.A. Holland, M.B. King, R.F. Strickland-Constable, Proc. R. Soc. London Ser. A 240 (1957) 1–28. [87] G.G. Haselden, D.M. Newitt, S.M. Shah, Proc. R. Soc. London Ser. A 209 (1951) 1–14. [88] N.E. Khazanova, E.E. Sominskaya, A.V. Zakharova, M.B. Rozovskii, N.L. Nechitailo, Zh. Fiz. Khim. 53 (1979) 1594–1597. [89] J. Mollerup, J. Chem. Soc. Faraday Trans. 1 (71) (1975) 2351–2360. [90] K. Nagahama, H. Konishi, D. Hoshino, M. Hirata, J. Chem. Eng. Jpn. 7 (1974) 323–328. [91] J.S. Rowlinson, J.R. Sutton, F. Weston, Proceedings International Conference Thermodynamics and Transport Properties Fluids, vol. 1957, 1957, pp. 3–7. [92] K.A.M. Gasem, M.J. Hiza, A.J. Kidnay, Fluid Phase Equilib. 6 (1981) 181–189. [93] L. Grauso, A. Fredenslund, J. Mollerup, Fluid Phase Equilib. 1 (1977) 13–26. [94] S. Zeck, H. Knapp, Fluid Phase Equilib. 26 (1986) 37–58. [95] Z.-h. Chen, Z. Yao, F.-j. Zhu, K. Cao, Y. Li, Z.-m. Huang, J. Chem. Eng. Data 55 (2010) 2004–2007. [96] A. Heintz, W.B. Streett, Ber. Bunsen-Ges. Phys. Chem. 87 (1983) 298–303. [97] M.J. Hiza, C.K. Heck, A.J. Kidnay, Chem. Eng. Progr. Symp. Ser. 64 (1968) 57–65. [98] A.I. Likhter, N.P. Tikhonovich, Zh. Tekh. Fiz. 9 (1939) 1916–1922. [99] R.B. Williams, D.L. Katz, J. Ind. Eng. Chem. (Washington, D.C.) 46 (1954) 2512–2520. [100] T. Hakuta, K. Nagahama, M. Hirata, Bull. Jpn. Petrol. Inst. 11 (1969) 10–15. [101] G.H. Hanson, R.J. Hogan, W.T. Nelson, M.R. Cines, J. Ind. Eng. Chem. (Washington, D.C.) 44 (1952) 604–609. [102] A. Harmens, J. Chem. Eng. Data 30 (1985) 230–233. [103] M. Hirata, T. Hakuta, Mem. Fac. Technol. Tokyo Metropol. Univ. 18 (1968) 1595–1606. [104] M. Hirata, T. Hakuta, T. Onoda, Int. Chem. Eng. 8 (1968) 175–179. [105] Q.N. Ho, K.S. Yoo, B.G. Lee, J.S. Lim, Fluid Phase Equilib. 245 (2006) 63–70. [106] D.R. Laurance, G.W. Swift, J. Chem. Eng. Data 17 (1972) 333–337. [107] D.B. Manley, G.W. Swift, J. Chem. Eng. Data 16 (1971) 301–307. [108] K. Noda, M. Sakai, K. Ishida, J. Chem. Eng. Data 27 (1982) 32–34. [109] U. Onken, W. Arlt, Monograph. The Institution of Chemical Engineers, Rugby, Warwickshire, 1990, pp. 1–61. [110] H.H. Reamer, B.H. Sage, J. Ind. Eng. Chem. (Washington, D.C.) 43 (1951) 1628–1634. [111] E.R. Shenderei, Y.D. Zel’venskii, F.P. Ivanovskii, Tr. Gos. Nauchno Issled. Proektn. Inst. Azotn. Promst. Prod. Org. Sin. 15 (1963) 161–175. [112] H. Asatani, W. Hayduk, World Congress III of Chemical Engineering, Tokyo, 1986. [113] W. Hayduk, H. Asatani, Y. Miyano, Can. J. Chem. Eng. 66 (1988) 466–473. [114] W. Hayduk, H. Asatani, Y. Miyano, Can. J. Chem. Eng. 69 (1991) 1197–1203. [115] G.H. Goff, P.S. Farrington, B.H. Sage, J. Ind. Eng. Chem. (Washington, D.C.) 42 (1950) 735–743. [116] J.L. Oscarson, S.O. Lundell, J.R. Cunningham, AIChE Symp. Ser. 83 (1987) 1–17. [117] D.R. Laurance, G.W. Swift, J. Chem. Eng. Data 19 (1974) 61–67. [118] B.H. Sage, W.N. Lacey, J. Ind. Eng. Chem. (Washington, D.C.) 40 (1948) 1299–1301. [119] S. Laugier, D. Richon, J. Chem. Eng. Data 41 (1996) 282–284. [120] H.J. Gumpert, H. Koehler, W. Schiller, H.J. Bittrich, Z. Wiss Tech, Hochsch. Chem. Carl Schorlemmer Leuna-Merseburg 15 (1973) 179–187. [121] D. Wolfe, W.B. Kay, A.S. Teja, J. Chem. Eng. Data 28 (1983) 322–324. [122] D.O. Hanson, W.M. Van, J. Chem. Eng. Data 12 (1967) 319–325. [123] H. Kirss, L.S. Kudryavtseva, O. Eisen, Eesti NSV Tead. Akad. Toim., Keem. Geol. 24 (1975) 15–22. [124] L.M. Lozano, E.A. Montero, M.M.C.M.A. Villamanan, Fluid Phase Equilib. 133 (1997) 155–162. [125] B. Marrufo, A. Aucejo, M. Sanchotello, S. Loras, Fluid Phase Equilib. 279 (2009) 11–16. [126] C.R. Chamorro, J.J. Segovia, M.C. Martin, M.A. Villamanan, J. Chem. Eng. Data 46 (2001) 1574–1579. [127] J.J. Segovia, M.C. Martin, C.R. Chamorro, E.A. Montero, M.A. Villamanan, Fluid Phase Equilib. 152 (1998) 265–276. [128] H. Segura, J. Wisniak, G. Galindo, R. Reich, Phys. Chem. Liq. 40 (2002) 67–81.

[129] H.J. Bittrich, G. Zimmermann, E. Schaar, Z. Phys. Chem. (Leipzig) 260 (1979) 1005–1008. [130] L.S. Kudryavtseva, M. Toome, E. Otsa, Eesti NSV Tead. Akad. Toim. Keem. 30 (1981) 147–149. [131] L.S. Kudryavtseva, H. Viit, O. Eisen, Eesti NSV Tead. Akad. Toim. Keem. Geol. 20 (1971) 292–296. [132] M. Kuus, M. Toome, L.S. Kudryavtseva, O. Eisen, Eesti NSV Tead. Akad. Toim. Keem. 29 (1980) 32–37. [133] V. Mikhelson, H. Kirss, L.S. Kudryavtseva, O.G. Eizen, Fluid Phase Equilib. 1 (1977) 201–209. [134] A.H. Jalili, M. Sina, J. Chem. Eng. Data 53 (2008) 398–402. [135] P.C. Joyce, B.E. Leggett, M.C. Thies, Fluid Phase Equilib. 158–160 (1999) 723–731. [136] J.R. Keistler, W.M. Van, J. Ind. Eng. Chem. (Washington, D.C.) 44 (1952) 622–624. [137] R.R. Rasmussen, W.M. Van, J. Ind. Eng. Chem. (Washington D.C.) 42 (1950) 2121–2124. [138] S.H. Ward, W.M. Van, J. Ind. Eng. Chem. (Washington, D.C.) 46 (1954) 338–350. [139] B.T. Jordan Jr., W.M. Van, J. Ind. Eng. Chem. (Washington, D.C.) 43 (1951) 2908–2912. [140] K.E. Doering, H. Preuss, FIZ Report, 1967, pp. 3061. [141] M.S. Rozhnov, Khim. Prom-st. (Moscow) 43 (1967) 288–290. [142] M.S. Rozhnov, G.D. Efremova, Khim. Prom. Ukr. 6 (1970) 33–35. [143] J.L. Flebbe, D.A. Barclay, D.B. Manley, J. Chem. Eng. Data 27 (1982) 405–412. [144] K.E. Doering, H. Preuss, FIZ Report, 1967, pp. 4141. [145] J. Li, Z. Qin, G. Wang, M. Dong, J. Wang, J. Chem. Eng. Data 52 (2007) 1736–1740. [146] K. Steele, B.E. Poling, D.B. Manley, J. Chem. Eng. Data 21 (1976) 399–403. [147] I. Thoedtmann, H. Preuss, D. Pape, FIZ Report, 1989, pp. 9151. [148] C. Wohlfarth, U. Finck, R. Schultz, T. Heuer, Angew. Makromol. Chem. 198 (1992) 91–110. [149] C.R. Chamorro, M.C. Martin, M.A. Villamanan, J.J. Segovia, Fluid Phase Equilib. 220 (2004) 103–110. [150] H. Segura, J. Wisniak, G. Galindo, R. Reich, J. Chem. Eng. Data 46 (2001) 511–515. [151] R. Popescu, L. Stanescu, D. Sandulescu, Rev. Roum. Chim. 37 (1992) 1117–1124. [152] Y.P. Blagoi, N.A. Orobinskii, Russ. J. Phys. Chem. 40 (1966) 1625–1629. [153] N.A. Orobinskii, Y.P. Blagoi, E.L. Semyannikova, L.N. V’yunnik, Fiz. Khim. Rastvorov. (1972) 233–238. [154] F. Steckel, Sven. Kem. Tidskr. 57 (1945) 209–216. [155] V. Sandri, Corsi Semin. Chim. 5 (1967) 63–71. [156] S. Peramanu, B.B. Pruden, Can. J. Chem. Eng. 75 (1997) 535–543. [157] M. Hirata, S. Suda, T. Hakuta, K. Nagahama, Mem. Fac. Technol. Tokyo Metrop. Univ. 19 (1969) 103–122. [158] H. Lu, D.M. Newitt, M. Ruhemann, Proc. R. Soc. London Ser. A 178 (1941) 506–525. [159] R.A. McKay, H.H. Reamer, B.H. Sage, W.N. Lacey, J. Ind. Eng. Chem. (Washington, D.C.) 43 (1951) 2112–2117. [160] K. Ohgaki, S. Nakai, S. Nitta, T. Katayama, Fluid Phase Equilib. 8 (1982) 113–122. [161] S.S. Estrera, M.M. Arbuckle, K.D. Luks, Fluid Phase Equilib. 35 (1987) 291–307. [162] J. Guo, T. Liu, Y.-C. Dai, W.-K. Yuan, J. Chem. Eng. Data 46 (2001) 668–670. [163] O.Y. Guzechak, V.N. Sarancha, I.M. Romanyuk, O.M. Yavorskaya, G.P. Churik, J. Appl. Chem. USSR 57 (1984) 1662–1665. [164] Y.I. Kozorezov, T.S. Novozhilova, Sov. Chem. Ind. Engl. Transl. 47 (1971) 399–401. [165] G. Wang, Z. Qin, J. Liu, Z. Tian, X. Hou, J. Wang, Ind. Eng. Chem. Res. 42 (2003) 6531–6535. [166] H. Yamamoto, K. Ohgaki, T. Katayama, Fluid Phase Equilib. 46 (1989) 53–58. [167] Y. Miyano, K. Nakanishi, J. Chem. Thermodyn. 35 (2003) 519–528. [168] K.F. Wong, C.A. Eckert, J. Chem. Eng. Data 14 (1969) 432–436. [169] C.R. Chamorro, J.J. Segovia, M.C. Martin, M.A. Villamanan, J. Chem. Eng. Data 47 (2002) 316–321. [170] J. Dojcansky, J. Heinrich, J. Surovy, Chem. Zvesti. 21 (1967) 713–717. [171] J.M. Prausnitz, J.H. Vera, J. Chem. Eng. Data 16 (1971) 149–154. [172] J.J. Segovia, M.C. Martin, C.R. Chamorro, M.A. Villamanan, J. Chem. Eng. Data 43 (1998) 1014–1020. [173] H. Segura, J. Wisniak, G. Galindo, R. Reich, J. Chem. Eng. Data 46 (2001) 506–510. [174] C. Dariva, H. Lovisi, L.C.S. Mariac, F.M.B. Coutinho, J.V. Oliveira, J.C. Pinto, Can. J. Chem. Eng. 81 (2003) 147–152. [175] C. Diaz, A. Dominguez, J. Tojo, J. Chem. Eng. Data 47 (2002) 867–871. [176] B.C.Y. Lu, L.-W. Ni, M. Taylor, J. Chem. Eng. Data 41 (1996) 287–291. [177] R.H. Wilhelm, D.W. Collier, J. Ind. Eng. Chem. (Washington, D.C.) 40 (1948) 2350–2353. [178] N.S. Laevskaya, I.V. Bagrov, L.L. Dobroserdov, Deposited Doc. VINITI (1977) 1–7. [179] R.S. Martirosyan, V.V. Beregovykh, Z.A. Pluzhnikova, G.A. Kolyuchkina, S.V. L’vov, L.A. Serafimov, Tr. Mosk. Inst. Tonkoi Khim. Tekhnol. 4 (1974) 122–125. [180] Confidential Company Research Report, 1977. [181] J.H. Weber, J. Ind. Eng. Chem. (Washington, D.C.) 48 (1956) 134–136. [182] A. Aucejo, S. Loras, V. Martinez-Soria, N. Becht, R.G. Del, J. Chem. Eng. Data 51 (2006) 1051–1055. [183] P. Chaiyavech, W.M. Van, J. Chem. Eng. Data 4 (1959) 53–56. [184] W.L. Martin, W.M. Van, J. Ind. Eng. Chem. (Washington, D.C.) 46 (1954) 1477–1481.

J.-W. Qian et al. / Fluid Phase Equilibria 354 (2013) 212–235 [185] J.J. Segovia, M.C. Martin, C.R. Chamorro, M.A. Villamanan, J. Chem. Eng. Data 43 (1998) 1021–1026. [186] K.L. Young, R.A. Mentzer, R.A. Greenkorn, K.C. Chao, J. Chem. Thermodyn. 9 (1977) 979–985. [187] J. Ke, B. Han, M.W. George, H. Yan, M. Poliakoff, J. Am. Chem. Soc. 123 (2001) 3661–3670. [188] M. Yorizane, S. Yoshimura, H. Masuoka, Kagaku Kogaku 30 (1966) 1093–1096. [189] P.K. Behrens, S.I. Sandler, J. Chem. Eng. Data 28 (1983) 52–56. [190] K.D. Wagner, J. Zappe, A. Reeps, N. Dahmen, E. Dinjus, Fluid Phase Equilib. 153 (1998) 135–142. [191] G. Wu, N. Zhang, X. Zheng, H. Kubota, T. Makita, J. Chem. Eng. Jpn. 21 (1988) 25–29. [192] H.-S. Byun, T.-H. Choi, Korean J. Chem. Eng. 21 (2004) 1032–1037. [193] D.W. Jennings, A.S. Teja, J. Chem. Eng. Data 34 (1989) 305–309. [194] J.H. Vera, H. Orbey, J. Chem. Eng. Data 29 (1984) 269–272. [195] Z. Wagner, I. Wichterle, Fluid Phase Equilib. 33 (1987) 109–123. [196] W. Ren, B. Rutz, A.M. Scurto, J. Supercrit. Fluids 51 (2009) 142–147. [197] M. Akgun, D. Emel, N. Baran, N.A. Akgun, S. Deniz, S. Dincer, J. Supercrit. Fluids 31 (2004) 27–32. [198] A. Bamberger, J.u. Schmelzer, D. Walther, G. Maurer, Fluid Phase Equilib. 97 (1994) 167–189. [199] G.J. Suppes, M.A. McHugh, J. Chem. Eng. Data 34 (1989) 310–312. [200] C.S. Tan, S.J. Yarn, J.H. Hsu, J. Chem. Eng. Data 36 (1991) 23–25. [201] B. Wang, J. He, D. Sun, R. Zhang, B. Han, Fluid Phase Equilib. 239 (2006) 63–68. [202] J. Zhang, L. Gao, X. Zhang, B. Zong, T. Jiang, B. Han, J. Chem. Eng. Data 50 (2005) 1818–1822. [203] H. Kim, H.M. Lin, K.C. Chao, AIChE Symp. Ser. 81 (1985) 86–89. [204] M. Yorizane, S. Sadamoto, S. Yoshimura, H. Masuoka, N. Shiki, T. Kimura, A. Toyama, Kagaku Kogaku 32 (1968) 257–264. [205] H.G. Steinbach, M. Steinbrecher, Chem. Tech. (Leipzig) 18 (1966) 633. [206] H. Sagara, S. Mihara, Y. Arai, S. Saito, J. Chem. Eng. Jpn. 8 (1975) 98–104. [207] V.I. Sokolov, A.A. Polyakov, J. Appl. Chem. USSR 50 (1977) 1347–1349. [208] I.I. Vasil’eva, A.A. Naumova, A.A. Polyakov, T.N. Tyvina, V.V. Fokina, J. Appl. Chem. USSR 59 (1986) 1180–1183. [209] H.K. Bae, K. Nagahama, M. Hirata, J. Chem. Eng. Jpn. 14 (1981) 1–6. [210] H. Kubota, H. Inatome, Y. Tanaka, T. Makita, J. Chem. Eng. Jpn. 16 (1983) 99–103. [211] Confidential Company Research Report, 1981. [212] S. Laugier, D. Richon, H. Renon, J. Chem. Eng. Data 39 (1994) 388–391. [213] H. Preuss, K. Moerke, FIZ Report, 1984, pp. 9261. [214] A.F. Burcham, M.D. Trampe, B.E. Poling, D.B. Manley, ACS Symp. Ser. 300 (1986) 86–107. [215] C.S. Howat, G.W. Swift, Fluid Phase Equilib. 21 (1985) 113–134. [216] A.V. Kozhenkov, Y.I. Malenko, S.N. Nikolaev, D.M. Sobolev, Promst. Sint. Kauch. Shin. Rezinotekh. Izdel. 7 (1988) 2–3. [217] A.V. Kozhenkov, Y.I. Malenko, S.N. Nikolaev, D.M. Sobolev, Promst. Sint. Kauch. Shin. Rezinotekh. Izdel. 1 (1987) 3–4. [218] T. Roscher, FIZ Report, 1970, pp. 12281. [219] A.V. Kozhenkov, S.N. Nikolaev, D.M. Sobolev, Y.I. Malenko, Promst. Sint. Kauch. Shin. Rezinotekh. Izdel. 11 (1987) 4–5. [220] K.E. Doering, H. Preuss, FIZ Report, 1967, pp. 2041. [221] Z. Mervart, Collect. Czech. Chem. Commun. 24 (1959) 4034–4036. [222] Z. Wu, Z. Chen, Z. Shou, S. Zhu, Huagong Xuebao (Chinese Edition) 38 (1987) 406–415. [223] K.E. Doering, H. Preuss, FIZ Report, 1968, pp. 7091. [224] Z. Dolejsek, O. Grubner, E. Hala, V. Hanus, I. Kossler, Chem. Prum. 11 (1961) 361–363. [225] J.N. Ezekwe, C.S. Howat III, G.W. Swift, Fluid Phase Equilib. 7 (1981) 75–85. [226] A.F. Frolov, V.N. Korotkova, Khim. Promst. Moscow (1961) 376–378. [227] V.N. Korotkova, S.Y. Pavlov, L.L. Karpacheva, L.S. Kofman, L.A. Serafimov, Promst. Sint. Kauch. (1971) 1–4. [228] A.V. Kozhenkov, S.N. Nikolaev, L.I. Reshetova, Y.I. Malenko, Proizvod. Ispolz. Elastom. (1991) 8–12. [229] Z.U. Lianzhou, Research Inst. of Chem. machinery, Huaxue Gongcheng 3 (1973) 110–120. [230] S.K. Ogorodnikov, V.B. Kogan, M.S. Nemtsov, J. Appl. Chem. USSR 33 (1960) 1581–1587. [231] L.A. Shestakova, L.S. Kofman, T.N. Matveeva, T.N. Savel’eva, Prom. Sin. Kauch. Nauch. -Tekh. Sb. 11 (1970) 10–13. [232] L.R.I.o.C.I. Tianjin University, Huaxue Gongcheng 5 (1978) 74–92. [233] V.N. Vostrikova, T.P. Moiseeva, A.A. Grinfeld, Z.V. Markhovskaya, Promst. Sint. Kauch. Shin. Rezinotekh. Izdel. 12 (1986) 2–4. [234] E.R. Shenderei, Khim. Promst. Moscow 41 (1965) 580–585. [235] H.W. Scheeline, E.R. Gilliland, J. Ind. Eng. Chem. (Washington, D.C.) 31 (1939) 1050–1057.

235

[236] J.A. Martinez-Ortiz, D.B. Manley, J. Chem. Eng. Data 23 (1978) 165–167. [237] R. Reich, V. Sanhueza, Fluid Phase Equilib. 77 (1992) 313–325. [238] M. Hirata, S. Suda, T. Hakuta, K. Nagahama, Sekiyu Gakkai Shi 12 (1969) 773–777. [239] K.E. Doering, H. Preuss, FIZ Report, 1968, pp. 1221. [240] S.I. Prikhodko, L.F. Komarova, O.M. Gorelova, N.N. Gorlova, V.G. Bondaletov, Zh. Prikl. Khim. (Leningrad) 78 (2005) 403–407. [241] V.T. Bui, A. Hamdouni, J. Leonard, Can. J. Chem. Eng. 70 (1992) 153–158. [242] H.-S. Phiong, F.P. Lucien, J. Supercrit. Fluids 25 (2003) 99–107. [243] E. Bogel-Lukasik, A. Szudarska, R. Bogel-Lukasik, d.P.M. Nunes, Fluid Phase Equilib. 282 (2009) 25–30. [244] M. Herskowitz, S. Morita, J.M. Smith, J. Chem. Eng. Data 23 (1978) 227– 228. [245] M. Herskowitz, J. Wisniak, L. Skladman, J. Chem. Eng. Data 28 (1983) 164– 166. [246] H.-S. Phiong, F.P. Lucien, J. Chem. Eng. Data 47 (2002) 474–477. [247] M.A.M. Costa, H.A.S. Matos, d.P.M. Nunes, d.A.E.J.S. Gomes, J. Chem. Eng. Data 41 (1996) 1104–1110. [248] B.F. Ruiz, T.M.J. Fernandez, ELDATA: Int. Electron. J. Phys. Chem. Data 5 (1999) 143–148. [249] V.N. Vostrikova, E.V. Ambrozaitis, L.A. Savostina, S.A. Reshetov, J. Appl. Chem. USSR 55 (1982) 1178–1179. [250] D.S. Jan, Y.C. Xie, F.N. Tsai, J. Chem. Eng. Data 38 (1993) 383–385. [251] S. Stoeck, FIZ Report, 1975, pp. 12011. [252] J. Dojcansky, J. Heinrich, J. Surovy, Chem. Zvesti. 22 (1968) 514–520. [253] J.M. Harrison, L. Berg, J. Ind. Eng. Chem. (Washington, D.C.) 38 (1946) 117– 120. [254] A. Sander, H.G. Wagner, Private Communication, 1987. [255] V.N. Vostrikova, T.V. Komarova, M.E. Aerov, A.V. Sidorkova, L.A. Savostina, J. Appl. Chem. USSR 48 (1975) 960–961. [256] F. Comelli, R. Francesconi, Can. J. Chem. Eng. 63 (1985) 344–347. [257] V.V. Afanas’ev, A.E. Demidov, A.V. Grishunin, Deposited Doc. Oniitekhim. (1984) 1–16. [258] N.V. Karaseva, A.P. Karavaeva, T.N. Antonova, E.M. Chabutkina, G.N. Koshel, Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 40 (1997) 18–20. [259] M.G. Bernardo-Gil, M.A. Ribeiro, Fluid Phase Equilib. 53 (1989) 15–22. [260] P.G. Bendale, R.M. Enick, Fluid Phase Equilib. 94 (1994) 227–253. [261] M. Akgun, N.A. Akgun, S. Dincer, J. Supercrit. Fluids 15 (1999) 117–125. [262] A. Berna, A. Chafer, J.B. Monton, J. Chem. Eng. Data 45 (2000) 724–727. [263] C.-M.J. Chang, C.-C. Chen, Fluid Phase Equilib. 163 (1999) 119–126. [264] G.G. Di, V. Brandani, R.G. Del, V. Mucciante, Fluid Phase Equilib. 52 (1989) 405–411. [265] T. Gamse, R. Marr, Fluid Phase Equilib. 171 (2000) 165–174. [266] Y. Iwai, T. Morotomi, K. Sakamoto, Y. Koga, Y. Arai, J. Chem. Eng. Data 41 (1996) 951–952. [267] P. Marteau, J. Obriot, R. Tufeu, J. Supercrit. Fluids 8 (1995) 20–24. [268] S. Raeissi, C.J. Peters, J. Supercrit. Fluids 35 (2005) 10–17. [269] S.A.B. Vieira de Melo, P. Pallado, G.B. Guarise, A. Bertucco, Braz. J. Chem. Eng. 16 (1999) 7–17. [270] J. Pavlicek, M. Richter, Fluid Phase Equilib. 90 (1993) 125–133. [271] M. Richter, H. Sovova, Fluid Phase Equilib. 85 (1993) 285–300. [272] F. Benvenuti, F. Gironi, J. Chem. Eng. Data 46 (2001) 795–799. [273] G.A. Leeke, R. Santos, M.B. King, J. Chem. Eng. Data 46 (2001) 541–545. [274] H.A. Matos, d.A.E. Gomes, P.C. Simoes, M.T. Carrondo, d.P.M. Nunes, Fluid Phase Equilib. 52 (1989) 357–364. [275] E. Gomes de Azevedo, H.A. Matos, d.P.M. Nunes, Fluid Phase Equilib. 83 (1993) 193–202. [276] T.M. Lesteva, S.K. Ogorodnikov, A.I. Morozova, J. Appl. Chem. USSR 40 (1967) 853–856. [277] F. Farelo, F. Santos, L. Serrano, Can. J. Chem. Eng. 69 (1991) 794–799. [278] M.G. Bernardo-Gil, A. Ribeiro, Fluid Phase Equilib. 85 (1993) 153–160. [279] E.R. Gilliland, H.W. Scheeline, J. Ind. Eng. Chem. (Washington, D.C.) 32 (1940) 48–54. [280] P.H. Van Konynenburg, R.L. Scott, Philos. Trans. R. Soc. London Ser. A 298 (1980) 495–540. [281] R. Privat, J.-N. Jaubert, Classification of global fluid-phase equilibrium behaviors in binary systems, Chem. Eng. Res. Des. (2013), http://dx.doi.org/10.1016/j.cherd.2013.06.026. [282] L. Avaullée, L. Trassy, E. Neau, J.-N. Jaubert, Fluid Phase Equilib. 139 (1997) 155–170. [283] J.-N. Jaubert, R. Privat, Fluid Phase Equilib. 295 (2010) 26–37. [284] J.-N. Jaubert, J. Qian, R. Privat, C.F. Leibovici, Fluid Phase Equilib. 338 (2013) 23–29. [285] J.-N. Jaubert, L. Coniglio, Ind. Eng. Chem. Res. 38 (1999) 5011–5018. [286] J.-N. Jaubert, L. Coniglio, F. Denet, Ind. Eng. Chem. Res. 38 (1999) 3162–3171.