Prediction of vapor pressures of pure compounds from knowledge of the normal boiling point temperature

Fluid Phase Equilibria 198 (2002) 81–93

Prediction of vapor pressures of pure compounds from knowledge of the normal boiling point temperature Epaminondas Voutsas∗ , Maria Lampadariou, Kostis Magoulas, Dimitrios Tassios Thermodynamics and Transport Phenomena Laboratory, Department of Chemical Engineering, National Technical University of Athens, 9, Heroon Polytechniou Street, Zographou Campus, Athens 157 80, Greece Received 11 June 2001; accepted 29 October 2001

Abstract A simple method for the prediction of vapor pressures of pure compounds from knowledge of the normal boiling point temperature is presented. Typical errors down to 10−5 bar (1 Pa) are below 20% and are off only by a factor of 2–3 down to 10−9 bar (10−4 Pa), which must be considered very satisfactory considering the simplicity of the method and the uncertainty in the very low vapor pressure data. For higher pressures, up to 5 bar, very satisfactory results are obtained with typical errors below 3% but somewhat higher for alcohols. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Vapor pressure; Pure; Prediction; Normal boiling point

1. Introduction Knowledge of vapor pressure values of pure compounds is essential in the separation of mixtures through distillation, stripping or supercritical extraction as well as for environmental purposes such as the determination of the amounts of pollutants transferred to the atmosphere. Vapor pressure values as a function of temperature for a variety of compounds is available in terms of correlations of existing experimental data in DIPPR [1]. The large number, however, of the compounds of practical interest—combined with the difficulty and high cost of the experimental determination of vapor pressures—renders prediction a valuable tool for providing such information. In this paper, we examine the possibility of predicting vapor pressure values (Ps ) from knowledge of the normal boiling point temperature (Tb ), which is available for a large number of compounds. For this purpose we consider first three available methods and identify the most promising one. We proceed next to evaluate the necessary empirical parameter Kf for each compound, by regressing experimental vapor pressure data from the melting point up to the normal boiling point, and then we develop predictive ∗

Corresponding author. Tel.: +301-772-3137; fax: +301-772-3155. E-mail address: [email protected] (E. Voutsas). 0378-3812/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 7 3 6 - 1

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Table 1 Vapor pressure database, correlation results using Kf,opt and prediction results using Kf,pred for different classes of compoundsa Chemical class

Reference Nc

Mw -range Tb -range (K)

AAE% (up to Tb )

AAE% (up to 5 bar)

AAE% (at Tm )

Using Kf,opt

Using Kf,opt

Using Kf,pred

Using Kf,opt

Using Kf,pred

1.7 1.9 1.8 0.9 7.8 4.3 1.9 4.8 2.7 1.8 1.8 2.6 1.6 4.1

2.0 2.2 2.5 1.1 7.8 4.9 3.0 3.9 3.3 1.6 1.7 1.9 1.1 3.5

22.9 43.5 30.6 35.2 15.9 34.7 4.6 15.1 10.6 10.2 14.6 38.7 24.3 31.4

26.6 41.1 31.7 37.6 21.2 24.0 9.8 22.9 26.2 21.2 20.7 43.8 30.0 36.1

1.7

1.7

31.8

36.4

1.1

1.3

25.5

32.6

Using Kf,pred

Alkanes [1] 20 44–282 231–617 4.4 6.6 Alkenes [1] 12 28–280 169–615 8.8 10.2 Alkynes–alkadienes [1] 11 40–110 238–400 5.8 9.5 Aromatics [1,7] 19 78–190 353–537 6.5 7.9 Alcohols [1,8] 16 60–242 355–587 11.0 11.9 Glycols [1] 4 76–118 460–516 6.0 12.7 Phenols [1] 6 94–206 455–564 1.4 4.3 Acids [1] 9 46–200 373–543 4.6 9.9 Amines [1] 11 31–171 266–515 3.2 8.4 Aldehydes [1] 8 44–170 321–506 3.1 5.1 Ketones [1] 9 42–142 223–467 3.2 5.6 Ethers [1] 10 58–168 278–558 7.5 13.3 Esters [1,9] 13 74–212 327–597 4.8 10.4 Nitrogen containing [1] 11 41–137 354–560 7.8 8.5 compounds Sulfur containing [1] 6 62–104 310–400 5.6 7.9 compounds Halogen containing [1] 14 78–204 311–462 4.8 8.3 compounds a Detailed results can be found in: http://ttpl.chemeng.ntua.gr/pdf/vp.pdf.

expressions for Kf as function of Tb and molecular mass (Mw ) for each class of compounds (alkanes, aromatics, ketones, alcohols, etc). Since several hydrocarbons cannot be strictly classified in one class, a general expression for hydrocarbons is developed. Finally, the prediction at pressures higher than 1 atm is investigated.

2. Database The database used is presented in Table 1. All data used with very few exceptions were obtained from the correlation of experimental data presented in DIPPR data compilation [1]. Table 1 also includes the molecular mass and normal boiling point range considered for each chemical class. All data obtained from DIPPR were selected such that the errors of the correlation from the experimental data used for its development do not exceed 5%.

3. Selection of the appropriate method Three methods, that require only the Tb value as input information, were derived and tested for the correlation and prediction of saturated liquid vapor pressures.

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83

3.1. Method I [2] The derivation of this method starts from the well-known Antoine equation: ln P s = A −

B T −C

(1)

Applying the boundary conditions:

and

ln P s |T =Tb = 0

(2)


d lnP s

Hvb =
dT T =Tb Zb RT2b

(3)

the following expressions for A and B are obtained: A=

B Tb − C

(4)

B=

Hvb (Tb − C)2 Zb RT2b

(5)

where Hvb is the heat of vaporization at the normal boiling point, Zb the difference in compressibility factors between the vapor and the liquid phase at the normal boiling point and C is a constant. Substituting A and B expressions into Eq. (1), the following equation for Ps is derived:   Hvb (Tb − C)2 1 1 ln P s = (6) − Tb − C T −C Zb RT2b where Ps is in atm. For the application of Eq. (6) at temperatures below Tb , Zb is assumed to have a constant value equal to 0.97 and Hvb is calculated by the following equation proposed by Fistine [3]: Hvb = Kf (8.75 + R ln Tb ) Tb

(7)

where Kf is a compound specific parameter. Finally, the parameter C is estimated via Thomson’s rule [4] as following: C = −18 + 0.19Tb Substituting in Eq. (6) the final expression for Method I is obtained:   Kf (8.75 + R ln Tb )(18 + 0.81Tb ) T − Tb s ln P = 0.97RTb T + 18 − 0.19Tb

(8)

(9)

3.2. Method II [2] In the derivation of Method I, it is assumed that the heat of vaporization (Hv ) is temperature independent and it was set equal to its value at the normal boiling point (Hvb ). In Method II, Hv is estimated

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using the correlation proposed by Watson [5]:   1 − (T /Tc ) m Hv = Hvb 1 − (Tb /Tc )

(10)

where Tc is the critical temperature and m is a constant. Using the approximation Tc = 3Tb /2, Eq. (10) yields: Hv = Hvb (3 − 2Trb )m

(11)

where T rb = T /T b . Substitution of Eq. (11) into the Clausius–Clapeyron equation and integration results to the following equation for Ps :   (3 − 2Trb )m Hvb s m−1 1− (12) − 2m(3 − 2Trb ) ln Trb ln P = Zb RTb Trb where Ps is in atm and m is set equal to 0.19 as proposed by Lyman [2]. The parameter Hvb /Tb is estimated from Eq. (7) and Zb is set for temperatures below Tb , as in Method I, equal to 0.97. Substituting in Eq. (12) the final expression for Method II is obtained:   Kf (8.75 + R ln Tb ) (3 − 2Trb )m s m−1 (13) − 2m(3 − 2Trb ) ln Trb ln P = 1− 0.97R Trb 3.3. Method III [6] The starting equation for the development of this method is the Clausius–Clapeyron equation. Assuming a linear temperature dependence of Hv over the temperature range from Tb to T, Hv can be expressed as: Hv (T ) = Hvb + Cpb (T − Tb )

(14)

In Eq. (14), Cpb is the difference between the vapor and liquid heat capacities at the normal boiling point. Substitution of Eq. (14) into the Clausius–Clapeyron equation and integration from 1 atm to Ps and from Tb to T yields:    Cpb Tb Svb Cpb Tb s − 1− − ln (15) ln P = R R T R T where Svb is the entropy of vaporization at Tb and that is equal to Hvb /Tb . Finally, assuming for the ratio of Cpb /Svb a constant value equal to −0.8 [6], the following equation for Ps is obtained:      Tb Svb Tb s 1.8 1 − + 0.8 ln (16) ln P = R T T In this study Svb is estimated through Eq. (7). Substituting in Eq. (16) the final expression for Method III is obtained:      Kf (8.75 + R ln Tb ) Tb Tb s 1.8 1 − ln P = + 0.8 ln (17) R T T

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85

Fig. 1. Experimental and calculated values, using the three different methods, vapor pressures of n-dodecane and isopropanol using optimum Kf values. For n-dodecane the optimum Kf value for Method I is 1.09, for Method II 1.11 and for Method III 1.11. For isopropanol the optimum Kf value for Method I is 1.34, for Method II 1.34 and for Method III 1.29. The temperature range is from the triple point up to the critical.

The common characteristic of the three methods is that they need as input information the normal boiling point of the compound (Tb ) and also they have a single, temperature independent, adjustable parameter (Kf ). For the selection of the most suitable method we considered a database consisting of both nonpolar compounds (different hydrocarbons) and polar ones (alcohols and acids). We tested the methods with respect to their performance in: (a) the correlation of vapor pressures for temperatures from the melting up to the normal boiling point; and (b) in the prediction of vapor pressures at higher temperatures up to the critical point. Two typical results are shown in Fig. 1. The following comments summarize our observations: 1. All three methods give similar correlation for temperatures from the melting up to the normal boiling point. Overall best results are obtained with Methods I and III. 2. Method II breaks down at high temperatures due to the assumption of T c = 3T b /2 as shown in Fig. 1. 3. Method I gives overall better prediction at temperatures above the normal boiling point and has been used in the remaining of this study. 4. Evaluation of optimum K f values The optimum Kf (Kf,opt ) values were determined using sixteen vapor pressure data for each compound in the range from the melting point up to the normal boiling point, covering the range in equal distances.

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Fig. 2. Average percent error (AE%) in Ps prediction as a function of the experimental Ps value for n-decyl cyclohexane. Kf,opt denotes results obtained using the optimum Kf value, Kf,pred results obtained using the predicted Kf from Eq. (18), Kf,HC results obtained using the predicted Kf from Eq. (20) and K f = 1 results using the Kf equal to one as proposed in [2]. The temperature range is from the triple point up to the critical.

Table 1 presents the average absolute percent error (AAE%) obtained in the range from Tm up to Tb and the AAE% at Tm . The latter represents the most difficult test of the proposed method since Ps at Tm has the lowest value and is more likely the one with the highest uncertainty. Typical results are also shown graphically in Figs. 2 and 3.

Fig. 3. AE% in Ps prediction as a function of the experimental Ps value for 1-decanol. Kf,opt and Kf,pred denote the same as in Fig. 2. The temperature range is from the triple point up to the critical.

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87

The obtained errors in Ps with the optimum Kf values are very satisfactory, considering especially the uncertainty in the data, with typical AAE% values in the range of 3–8%, and errors at Ps around 10−5 bar (1 Pa) typically below 20%. Slightly poorer results are obtained for alcohols (see, for example, Fig. 3) probably because of the strong hydrogen bonding involved. It is worth noticing that predictions at Tm are typically within a factor of 2–3 even down to the very low pressures of 10−9 bar (10−4 Pa).

5. Prediction of vapor pressures for separate classes of compounds The Kf,opt values determined by regressing the vapor pressure values up to 1 atm were used to develop expressions that can be used for prediction of Kf for each chemical class. Two types of expressions were considered: Kf = aMw + bTb + c

(18)

Kf = aMbw Tbc

(19)

Preliminary calculations indicated that both expressions provide an equally satisfactory correlation of the Kf values with a slight advantage for the first one (Eq. (18)), which we adopted in this study. The values of the parameters a, b, c for different classes of compounds are presented in Table 2 along with the correlation results for Kf . Table 2 also presents the maximum molecular mass and normal boiling point values involved. It is recommended that the Kf correlations should not be used much beyond these values. Prediction of vapor pressures using Kf values obtained from these correlations—referred to as Kf,pred , are presented in Table 1 and typical examples are shown in Figs. 2 and 3. The results must be

Table 2 The coefficients of Eq. (18) for the different classes of compounds Chemical class

Maximum Mw

Maximum Tb (K)

a

b

c

DKf

Alkanes Alkenes Alkynes–alkadienes Aromatics Alcohols Glycols Phenols Acids Amines Aldehydes Ketones Ethers Esters Nitrogen containing compounds Sulfur containing compounds Halogen containing compounds

282 280 110 190 242 118 206 200 171 170 142 168 212 137 104 204

617 615 400 537 587 516 564 543 515 506 467 558 597 560 400 462

8.910E−04 1.624E−03 1.423E−03 1.378E−03 3.750E−05 5.024E−03 −3.694E−04 4.270E−04 −1.359E−03 9.348E−05 1.670E−04 1.185E−03 1.555E−03 2.970E−04 −9.436E−04 −2.500E−04

−3.00E−05 −4.60E−04 −9.40E−04 −5.20E−04 −3.80E−04 −3.96E−04 −1.66E−04 9.18E−04 3.95E−04 1.95E−04 5.51E−05 −8.10E−04 −5.70E−04 −1.80E−04 6.59E−04 −8.95E−05

0.947232 1.035904 1.238489 1.082937 1.476083 1.080454 1.289163 0.768058 1.078792 0.995331 1.030682 1.214950 1.130594 1.084769 0.864638 1.077639

0.18 0.12 0.24 0.16 0.17 0.04 0.09 0.19 0.21 0.07 0.10 0.18 0.24 0.11 0.08 0.22

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considered very satisfactory with errors somewhat higher than those obtained using the optimum Kf value. It should be noted here that Kf values for several homologous series are given in [2] obtained from an old publication by Fistine [3]. These Kf values give, however, unreliable results. For example, the values given for n-alkanes from propane to n-eicosane are equal to one while the optimum values go up to 1.18. A typical example is shown in Fig. 2 for n-decyl cyclohexane.

6. A general expression for hydrocarbons Several hydrocarbons cannot be strictly classified in one class such, as for example, hexyl benzene. For this purpose a generalized expression for Kf of all hydrocarbons—referred to as Kf,HC , was developed by using all available Kf,opt values: Kf,HC = 1.455 × 10−3 Mw − 4.3 × 10−4 Tb + 1.040143

(20)

Eq. (20) provides practically the same results as the corresponding equations for each homologous series, as suggested by the results presented in Fig. 2, and can be used when there is a doubt as to which homologous series a compound belongs to.

7. Evaluation of the proposed correlations Prediction results for hydrocarbons not included in the development of the expressions for Kf,pred (Eq. (18)) and Kf,HC (Eq. (20)) are presented in Table 3. Comparison with experimental data of these hydrocarbons gives very satisfactory results. Table 4 presents results for several polar compounds that like those in Table 3 were not used in the development of the correlations. Typical results are shown graphically in Fig. 4. Very satisfactory results are obtained, with typical AAE% values for temperatures below Tb in the range of 5–20% and typical AE% at the lowest available Ps value are well below 50%. Notice that in most cases the lowest available Ps values are of the order of 10−5 bar (1 Pa). If a compound contains more than one functional group, e.g. diethanol amine or chloroacetic acid, then it must be characterized in the class which gives the highest Kf value as suggested by the results presented in Table 5 and the typical ones in Fig. 5. The quality of the obtained results in such cases is similar to the one obtained for compounds belonging to a single class (Table 4).

8. Prediction of vapor pressures higher than 1 atm Even though the correlations were developed for pressures up to 1 atm their performance at higher ones was also investigated. An upper pressure of 5 atm was arbitrarily set since, as suggested by the typical results presented in Figs. 3 and 4, large errors may be realized as the critical point was approached. Fifteen points in equal distances from 1 atm up to 5 bar were used. Prediction results are presented in Tables 1, 3, 4 and 5. Typical errors are below 3%, with the exception of alcohols where the errors are in the order of 10%.

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Table 4 Evaluation: prediction results for polar compounds not included in correlation development Compound

Mw

Tb

Reference

Class

P-range (bar)

Kf,pred

AAE%a

AAE%b

AE%c

Cyclohexanol 3-Octanol Octanoic acid Cyclohexanone Cyclopentanone 3-Hexanone Ethyl acrylate Diethyl carbonate Isoamyl acetate 1-Octanal 1-Dodecanal Benzaldehyde Furfural 2-Propen-1-amine Triethylene diamine n-Pentylamine Diethylamine o-Toluidine Aniline p-Nitrotoluene 4-Methyl pyridine Propionitrile Acrylonitrile Quinoline m-Cresol p-tert-Butyl phenol 2,4-Xylenol Ethyl propyl ether Dioxane Diphenyl ether Dibenzofuran Di-tert-butyl ether 1,1,1,3,3-Pentafluoropropane 1,1,1,2,3,3,3-Heptafluoropropane o-Dichlorobenzene Diethyldisulfide

100.16 130.23 144.21 98.15 84.12 100.16 100.12 118.00 130.00 128.21 198.00 106.12 96.08 59.11 112.18 87.17 76.00 107.16 93.13 137.14 93.13 55.08 53.06 129.16 108.14 150.22 122.17 88.15 88.11 170.21 168.00 130.23 134.00

434 447.85 512.85 428.9 403.8 396.65 372.65 399.95 415 447.15 523.15 451.9 434.85 326.45 447.15 377.65 328.6 473.55 457.6 511.65 418.5 370.5 350.5 510.75 464.15 512.88 490.07 337.01 374.47 531.46 557.86 380.4 287.53

[1] [8] [1] [1] [1] [1] [1] [1] [10] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [12]

Alcohol Alcohol Acid Ketone Ketone Ketone Ester Ester Ester Aldehyde Aldehyde Aldehyde Aldehyde Amine Amine Amine Amine Amine Amine Nitrogen Nitrogen Nitrogen Nitrogen Nitrogen Phenol Phenol Phenol Ether Ether Ether Ether Ether Halogen

8.9E–04–5 2.8E–01–5 1.8E−06–5 6.9E−05–5 2.8E−05–5 2.0E−05–5 1.6E−05–5 3.7E−05–5 1.21E−05–2 1.2E−05–5 5.48E−06–1 2.2E−05–5 1.5E−05–5 4.6E−05–5 6.97E−01–5 8.3E−05–5 3.74E−3–5 2.1E−06–5 3.4E−05–5 1.5E−04–5 1.95E−03–5 1.69E−06–5 3.7E−05–5 1.3E−06–5 4.4E−05–5 5.56E−03–5 1.3E−04–5 7.4E−09–5 2.5E−03–5 1.2E−04–5 2E−03–5 7.6E−06–5 1.26–5

1.31 1.31 1.30 1.07 1.07 1.06 1.07 1.05 1.09 1.08 1.1 1.09 1.08 1.13 1.1 1.11 1.11 1.18 1.20 1.03 1.04 1.03 1.04 1.11 1.17 1.15 1.16 1.05 1.02 0.98 0.96 1.06 1.04

8.39 9.2 13.7 19.7 11.3 2.0 1.8 27.2 4.8 3.2 9.8 14.6 5.6 4.7 1.3 10.5 10.3 24.5 19.1 10.3 1.5 10.8 12.6 23.3 11.4 1.5 1.3 18.5 6.5 7.7 14.1 20.8 5.3

5.77 – 6.0 6.4 6.1 0.5 1.7 0.8 1.1 1.4 – 1.1 4.4 1.8 0.5 1.8 4.4 9.6 13.1 3.5 0.6 0.5 1.3 4.8 3 3.5 3.7 2.1 4.0 2.2 0.7 6.1 5.3

10.7 19.0 52.3 39.8 15.3 4.8 3.8 42.9 19.3 4.2 7.5 53.1 34.2 25.1 1.8 35.1 15.3 49.2 24.8 68.7 2.1 52.9 43.0 0.0 51.5 5.5 1.0 46.3 16.7 41.2 80.0 31.0 1.0

172.00

256.71

[13]

Halogen

5.4E−01–5

1.03

3.3

3.3

3.1

147.00 122.25

453.57 427.13

[1] [1]

Halogen Sulfur

6.61E−05–5 2.2E−09–5

1.03 1.03

6.5 18.4

0.4 0.7

30.6 87.7

a

AAE% for pressures up to 1 atm. AAE% from 1 atm up to the highest pressure. c AE% at the lowest available pressure. b

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91

Fig. 4. Average percent error (AE%) in Ps prediction as a function of the experimental Ps value for p-tert-butyl phenol. Kf,pred denotes the same as in Fig. 2. The temperature range is from the triple point up to the critical.

Fig. 5. Average percent error (AE%) in Ps prediction as a function of the experimental Ps value for pentafluorophenol using Kf from phenols and halogen compounds, respectively (Table 5).

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Table 5 Prediction results for compounds containing more than one functional groups Compound

Mw

Tb

Reference

Class

P-range (bar)

Kf,pred

AAE%a

AAE%b

AE%c

Diethanol amine

108

542.04

[14]

Alcohol Amine Acid Halogen Phenol Halogen

2.7E−03–1.1E−01

1.27 1.05 1.24 1.07 1.19 1.05

16.3 126.6 0.8 44.3 3.6 19

– – 3.0 8.8 2.2 3.4

17.6 170.3 1.5 138.1 4.8 51.5

Chloroacetic acid

94.5

462.5

[1]

Pentafluorophenol

84

418.26

[9]

3.7E–03−5 2E–02−2.7

a

AAE% for pressures up to 1 atm. AAE% from 1 atm up to the highest pressure. c AE% at the lowest available pressure. b

9. Conclusions A simple method for the prediction of vapor pressures of pure compounds from knowledge of the normal boiling point temperature is presented. It uses a compound specific parameter, Kf , for which generalized expressions as a function of the normal boiling point and the molecular mass for several classes of compounds have been developed. For the vast majority of the compounds the overall average absolute percent errors in the range from the melting point up to the normal boiling point are well below 10%, while poorer results are obtained for alcohols. Typical errors at 10−5 bar (1 Pa) are around 20%, while predictions down to 10−9 bar (10−4 Pa) are only off by a factor of 2–3 in the worst case. Overall, the results must be considered satisfactory given the simplicity of the method along with the substantial uncertainty involved in the very low-pressure data. For pressures above 1 atm and up to 5 atm very satisfactory results are obtained with average absolute percent errors below 3% except for alcohols, where they are around 10%. At even higher pressures increased errors may be obtained. List of Symbols a, b, c parameters in Eq. (18),which are given in Table 2 AAE% average absolute percent error in vapor pressure defined as:  C NDP s,calc s,exp s,exp AAE% = 1/NC N − Pij /Pij | × 100 j =1 |Pij i=1 1/NDP AE% absolute percent error difference between the vapor and liquid heat capacities Cp  C i i DKf absolute deviation in the correlation of Kf defined as: DKf = 1/NC N i=1 |Kf,opt − Kf,pred | heat of vaporization Hv Kf empirical parameter in Eq. (7) m constant in Eq. (10) Mw molecular mass Nc number of compounds NDP number of data points Ps vapor pressure R gas constant

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Sv T Tb Tc Z

93

entropy of vaporization temperature normal boiling point temperature critical temperature difference in compressibility factors between the vapor and the liquid phase

Subscripts and superscripts b boiling point c critical property HC hydrocarbon opt optimum pred predicted r reduced s saturated v vaporization References [1] T.E. Daubert, R.P. Danner, Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation, Hemisphere, New York, 1994. [2] W.J. Lyman, W.F. Reehl, D.H. Resenblatt, Handbook of Chemical Property Estimation Methods, American Chemical Society, Washington, DC, 1990. [3] S.H. Fistine, Ind. Eng. Chem. 55 (1963) 47–56. [4] G.W. Thompson, in: A. Weissberger (Ed.), Techniques of Organic Chemistry, Interscience, New York, 1959. [5] K.M. Watson, Ind. Eng. Chem. 35 (1943) 398–406. [6] R.P. Schwarzenbach, P.M. Gschwend, D.M. Imboden, Environmental Organic Chemistry, Wiley, New York, 1993. [7] I. Mokbel, E. Rauzy, J.P. Meille, J. Jose, Fluid Phase Equilib. 147 (1998) 271–284. [8] J. N’Guimbi, C. Berro, I. Mokbel, E. Rauzy, J. Jose, Fluid Phase Equilib. 162 (1999) 143–158. [9] W.V. Steele, R.D. Chirico, S.E. Knipmeyer, A. Nguyen, J. Chem. Eng. Data 42 (1997) 1008–1020. [10] M.A. Espinosa Diaz, T. Guetachew, P. Landy, J. Jose, A. Voilley, Fluid Phase Equilib. 157 (1999) 257–270. [11] I. Mokbel, K. Ruzicka, V. Majer, V. Ruzicka, M. Ribeiro, J. Jose, M. Zabransky, Fluid Phase Equilib. 169 (2000) 191–207. [12] T. Sotani, H. Kubota, Fluid Phase Equilib. 161 (1999) 325–335. [13] L. Shi, Y.-Y. Duan, M.-S. Zhu, L.-Z. Han, X. Lei, Fluid Phase Equilib. 163 (1999) 109–117. [14] M.A. Abdi, A.J. Meisen, J. Chem. Eng. Data 43 (1998) 133–137.