An Expression for Ratio of Critical Temperature to Critical Pressure

Jan 29, 2009 - In this paper, a new correlation for prediction of the ratio of critical temperature to critical pressure has been developed in terms o...
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J. Chem. Eng. Data 2009, 54, 690–700

Correlations An Expression for Ratio of Critical Temperature to Critical Pressure with the Heat Capacity for Low to Medium Molecular Weight Compounds Mohammad Hasan Khademi, Ali Zeinolabedini Hezave, Abdolhossein Jahanmiri,* and Jamshid Fathikaljahi Chemical and Petroleum Engineering Department, School of Engineering, Shiraz University, Shiraz 71345, Iran

In this paper, a new correlation for prediction of the ratio of critical temperature to critical pressure has been developed in terms of heat capacity at 298.15 K, which is readily available for many compounds. The correlation has been applied for more than 100 low to medium size compounds. The results of these estimations validate the generalization of this correlation. The comparison between predicted and available experimental data shows an absolute relative error of 4.69 %. The results show that the accuracy of the proposed correlation is similar to the methods of Constantinou and Gani,7 Ambrose,2,3 and Joback5 for various types of compounds.

Introduction

[ ( ∑∆ ) ] ) M[0.339 + ∑ ∆ ] -1

TC ) TB 1 + 1.242 +

In the application of thermodynamic equations of state, one must have knowledge of critical temperature and critical pressure. The critical constants are key parameters in the prediction of thermodynamic and transfer properties via the principle of the corresponding state. They are also of importance in equation of state calculations and in the design of processes for supercritical fluid extraction. They are often used in composition-dependent mixing rules for the parameters to describe mixtures. Critical temperature and pressure are widely used in estimation of pure component constants. Many of the estimation methods are based on the group contribution concept and require knowledge of the boiling point and structure of the substance. Examples of such methods include those of Lydersen,1 Ambrose,2,3 Fedors,4 Joback,5 Somayajulu,6 and Constantinou and Gani.7 One of the first successful group contribution methods to estimate critical properties was developed by Lydersen.1 Joback5 suggested a modification of Lydersen’s1 method. This method depends on the group contribution method. Joback5 reevaluated Lydersen’s1 scheme, added several functional groups, and determined the new values of the group contributions. His proposed relations are

∑ ∆T - (∑ ∆T) ] -2 PC ) (0.113 + 0.0032nA - ∑ ∆P)

[

TC ) TB 0.584 + 0.965

2 -1

PC

T

-2

P

(3) (4)

where TC and PC are, respectively, in Kelvin and bar. In employment of correlations, the normal boiling point TB (at 1 atm) and molecular weight M are needed. The Joback5 and Ambrose2,3 methods perform well for low-to-medium molecular weight compounds. Their validity for high molecular weight and/or structurally complex compounds is not yet clear.8 The estimation of the critical properties with the methods of Lydersen,1 Ambrose2,3 (see Reid et al.9), and Joback and Reid10 (and others, e.g., Klincewicz and Reid;11 Somayajulu6) requires accurate values for the normal boiling point, which is usually not available for high molecular weight compounds. The recent group contribution method by Constantinou and Gani7 is more general in the sense that the critical temperature (and pressure) is estimated only from the structure of the compound. Constantinou and Gani7 developed an advanced group contribution method based on the UNIFAC groups. It is more accurate than the methods of Klincewicz and Reid11 and Lydersen.1 They suggested the following correlations

(5) ∑ i Nitc1i + ∑ j Mjtc2j (PC - 1.3705)-0.5 - 0.100220 ) ∑ i Nipc1i + ∑ j Mj pc2j exp(TC ⁄ 181.128) )

(6) (1) (2)

The units employed for TC and PC are, respectively, Kelvin and bar. nA is the number of atoms in the molecule. The ∆ quantities are evaluated by summing contributions for various atoms or groups of atoms. Ambrose2,3 suggested another estimated method including a group contribution technique using the following correlations * Corresponding author. Tel.: +98 711 2303071. Fax: +98 711 6287294. E-mail: [email protected].

where TC and PC are, respectively, in Kelvin and bar. In these equations, Ni and Mj are number of occurrences of the type-i first-order group and the type-j second-order group in a compound, respectively. tc1i, tc2j and pc1i, pc2j are contributions of the type-i and type-j for estimation of the critical temperature and critical pressure, respectively. In the group contribution method proposed by Constantinou and Gani7sexcept from the classical UNIFAC main and subgroups which are called firstorder groupsssecond-order groups have been incorporated for the differences of the physical properties among the isomers to be captured. Unlike the methods proposed by Joback and Reid10 and Ambrose2,3 (see Reid et al.9), Constantinou and Gani7 gave some emphasis on the proper extrapolation of the critical

10.1021/je8003996 CCC: $40.75  2009 American Chemical Society Published on Web 01/29/2009

Journal of Chemical & Engineering Data, Vol. 54, No. 3, 2009 691 Table 1. Absolute Deviation between Experimental and Predicted Critical Temperature (K) and Critical Pressure (bar) by Various Group Contribution Methods Constantinou and Gani

Ambrose

Joback

compound

ref

∆TC

∆PC

∆TC

∆PC

∆TC

∆PC

nC48

12

0.00

a

24

a

349

a

a

Lack of experimental data.

properties at high molecular weight; thus, their method may be more useful for high molecular weight compounds (see in Table 1). This point is not confirmed yet by literature evidence based on thorough evaluation/comparison of the above estimation methods for heavy/complex compounds.8 Elhassan et al.13 developed a correlation for n-alkanes which is based on the fact that the quantities of TC/PC are proportional to the molecular weight for each homologous series. The proposed relation is

ln(TC ⁄ PC) ) -3.70171 + 1.38315 ln(M + 25.3538) (7) Kontogeorgis et al.8 suggested that the ratio TC:PC can be expressed in terms of the van der Waals surface area that is estimated using the group increments given by Bondi14 and are readily available in all UNIFAC tables (e.g., Fredeslund et al.15) for any compounds. The method is suitable for medium to high molecular weight compounds. The proposed relation is

Qw1.3 + Qw1.95

TC ⁄ PC ) 9.0673 + 0.43309(

)

(8)

where TC is in K; PC is in bar; and Qw is the van der Waals surface area. Due to deficiencies and problems of available group contribution estimation methods for the critical properties, we suggest a correlation that tackles the problem of estimating the critical properties in a different and simpler way. We observed that, unlike the critical properties alone, the ratio TC:PC follows a regular trend with the ratio of heat capacity at 298.15 K to the universal gas constant for low-to-medium molecular weight compounds. The rest of the paper is organized as follows. The correlation of TC:PC with the heat capacity of real gas at 298.15 K is presented, and an application of proposed correlation and comparison with other methods is given. We end with discussion of our results and the conclusions.

New Correlation According to the above correlations, the critical temperature and pressure are dependent on the molecular structure of components. To propose a more general and simple correlation, a term that corresponds to the molecular structure can be used. The heat capacity could be related to the structure of the compounds.16-21 Joback5 suggested a group contribution method for the polynomial coefficient of heat capacity of ideal gases as follows

(∑ n ∆ - 37.93) + (∑ n ∆ + 0.210)T + (∑ n ∆ - 3.91 · 10 )T + (∑ n ∆ + 2.06 · 10 )T

Cp(T) )

j

a

j

j

-4

j

j

b

j

-7

2

c

j

d

3

(9)

j

where nj is the number of groups of the jth type and the ∆ contributions are for the jth atomic or molecules group. The temperature T is in Kelvin, and CP is in J · mol-1 · K-1. Yoneda9 modified a group contribution technique for ideal heat capacity that was originally proposed by Anderson et al.9,16 In this method, one begins with a base molecule and sequentially

Table 2. Variety of Number of Data Points Used in This Study compound type

no. of data points

hydrocarbons oxygenated hydrocarbons nitrogenated hydrocarbons hydrocarbon sulfide and mercaptanes halogenated hydrocarbons inorganic total

79 61 11 7 8 12 178

modifies the structure by substituting other groups to arrive at the final structure. Each substitution has a group contribution value, and values are summed to arrive at the final value of the heat capacity.

Cp(T) )

T T ∑ nj∆a + (∑ nj∆b)( 1000 ) + (∑ nj∆c)( 1000 )

2

j

j

j

(10) ∆ is the contribution, and nj is the number of times the contribution is required. T is in Kelvin, and CP is in J · mol-1 · K-1. A group contribution method for estimating the ideal gas heat capacity just for hydrocarbons is employed by Thinh et al.17,18 as the following equation

Cp(T) )

[

( )

∑ nj A + B1 exp

-C1 T

n1

( )]

- B2 exp

-C2 T n2

(11)

where T is in Kelvin; CP is in J · mol-1 · K-1; and A, B1, B2, C1, C2, n1, and n2 are constants for all hydrocarbon groups. This equation is a modified form suggested earlier by Yuan and Mok.19 It is sometimes inconvenient to use because it can not be integrated analytically, and numerical techniques must be employed. For the estimation of ideal gas heat capacity, an accurate group contribution method was developed by Benson20,21 and his colleagues. Contributions are given only for atoms with valences greater than unity. For each group, the key atom is given but followed by a notation specifying other atoms bonded to the key atom. The heat capacity is obtained by summing the necessary group contributions at the system temperature. Using the aforementioned subjects, the heat capacity (CP) is dependent on the molecular structure of each compound. Also, since the TC:PC ratio is dependent on the molecular structure, one can relate the TC:PC ratio to the heat capacity. An appropriate correlation for the ratio of the critical temperature to the critical pressure can be introduced in the form of

TC ⁄ PC ) εCP ⁄ R

(12)

In this correlation, TC is the critical temperature in Kelvin; PC is the critical pressure in atm; R is the universal gas constant; CP is the heat capacity of real gases at 298.15 K; and ε is the equation coefficient in K · atm-1. Note that the ratio of the heat capacity to the universal gas constant is dimensionless. In this study, to obtain the equation coefficient (ε), an extensive database of critical temperature and pressure data together with heat capacities of real gases for low-to-medium molecular weight compounds is used.22,23 Table 2 represents the variety of number of compounds used in this study. Values of RTC/PCCP have been determined for the data training set which consist of 178 compounds (see Table 3). The data training set includes hydrocarbons (i.e., alkane, alkene, alkyne, and cyclo compounds), halogenated hydrocarbons, oxygenated hydrocarbons (i.e., ether, ketone, ester, alcohol, aldehyde, and carboxylic acid), nitrogenated hydrocarbons, hydrocarbon sulfide, mercaptanes, and inorganic compounds. As one can see in this table,

chemical special

Methane Ethane Propane n-Butane n-Pentane n-Octane n-Nonane n-Decane 1-undecene n-Undecane n-Dodecane n-Tridecane n-Pentadecane 2-Methylpropane 2-Methylbutane 2,3-Dimethylbutane 2-Methylpentane 2,2-dimethylbutane 2,3-Dimethylpentane 2,4-Dimethylpentane 2-methylhexane 3-methylhexane 3-ethylpentane 2,2,3-trimethylbutane 2-methylheptane 4-methylheptane 3-ethylhexane 2,2-dimethylhexane 2,3-dimethylhexane 2,4-dimethylhexane 2,5-dimethylhexane 3,3-dimethylhexane 3-ethyl-2-methylpentane 2,2,3-trimethylpentane 2,3,4-trimethylpentane 2,3,3-Trimethylpentane 2,2,4-Trimethylpentane 2-Methyloctane 2,2-Dimethylheptane 2,2,5-Trimethylhexane 2,2,3,4-Tetramethylpentane 2,3,3,4-Tetramethylpentane 3,3,5-Trimethylheptane Ethylene 1-Butene cis-2-Butene trans-2-Butene 1-Pentene 1-Heptene 1-Octene 1-Nonene 1-Decene 2-Methylpropene 2-Methyl-2-butene 1,2-Butadiene

compd no.

1 2 3 4 5 6 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

CH4 C2H6 C3H8 C4H10 C5H12 C8H18 C9H20 C10H22 C11H22 C11H24 C12H26 C13H28 C15H32 C4H10 C5H12 C6H14 C6H14 C6H14 C7H16 C7H16 C7H16 C7H16 C7H16 C7H16 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C9H20 C9H20 C9H20 C9H20 C9H20 C10H22 C2H4 C4H8 C4H8 C4H8 C5H10 C7H14 C8H16 C9H18 C10H20 C4H8 C5H10 C4H6

chemical formula 0.9802 1.0121 1.0072 0.9658 0.9829 1.0368 1.0349 1.0719 1.0559 1.0733 1.0874 1.1243 1.1707 0.9841 0.9699 0.9715 0.9819 0.9322 0.9829 0.9235 0.9813 0.9679 0.9366 0.9165 1.0019 0.9830 0.9498 0.9594 0.9674 0.9347 0.9900 0.9237 0.9091 0.9242 0.9001 0.9251 0.9562 0.9963 0.9674 0.9769 0.9395 0.8659 0.9383 1.1009 1.0248 1.0813 1.0134 1.0178 1.0468 1.0558 1.0801 1.0488 1.0051 1.1176 1.0998

K · atm-1

(RTC/PCCP)

4.2067 6.3787 8.9010 11.425 14.164 23.329 26.081 29.946 31.369 33.203 36.632 40.710 48.801 11.424 13.843 16.185 16.691 16.073 18.905 19.213 19.669 19.293 18.945 18.237 22.857 22.401 21.944 22.013 21.700 21.902 22.375 21.483 21.273 20.905 21.013 20.679 21.530 25.741 24.906 24.772 23.731 23.033 26.617 5.6875 10.532 10.409 10.644 13.228 19.305 22.340 25.798 28.261 10.639 14.119 10.504

Exp. 4.3959 6.6443 9.2725 12.157 14.530 22.021 24.785 27.847 30.005 31.596 35.486 39.494 49.964 11.950 14.405 16.565 16.871 17.092 18.913 20.382 19.666 19.562 19.838 19.530 22.330 22.305 22.620 22.461 21.952 22.950 22.120 22.774 22.917 22.138 22.862 21.876 22.036 25.470 25.370 24.952 24.847 26.313 28.357 5.3939 10.684 10.052 10.901 13.239 18.184 20.720 23.410 26.702 10.980 12.904 9.9784

predicted by eq 13 6.0042 8.5763 11.021 13.891 22.750 24.964 28.390 31.692 33.391 36.139 42.013 50.345 11.002 14.074 16.018 16.273 14.947 19.343 18.592 18.621 18.714 18.798 17.437 22.267 22.271 22.318 21.733 22.136 21.784 22.257 22.027 22.139 21.957 22.003 21.663 21.297 25.616 25.053 24.994 25.046 25.757 28.632 5.3854 10.262 10.595 10.325 13.096 18.886 21.747 25.374 28.510 10.392 13.218 9.9733

Joback5 6.5584 8.9226 11.613 14.442 23.305 26.508 28.224 31.151 33.103 36.455 39.901 47.055 11.510 13.835 16.619 16.698 15.916 18.755 19.167 19.683 19.781 19.870 18.934 22.783 22.787 22.835 21.886 22.667 22.307 22.288 22.182 22.670 22.068 22.549 20.710 21.507 25.977 25.047 26.601 25.083 25.791 28.216 10.544 10.939 10.804 13.420 19.333 22.205 25.785 28.644 10.637 13.632 10.201

10.675a 10.500a 10.490a 13.298 19.410a 22.375a 25.044 29.198a 10.825 13.847 9.9857a

Ambrose2,3

6.3461 7.7471 10.781 13.678 22.974 26.346 29.689 31.591 33.551a 37.386 41.918 49.792 9.9074a 13.194 15.449a 16.097a 15.414 19.170a 18.854 19.291 19.291 19.291 18.066 22.535 22.535 22.535 21.733 22.126 22.126 22.126 21.733 22.126 21.316 21.694 20.882a 21.366a 25.868a 25.038a 23.398a 24.525a 24.525a 28.207

Cons. & Gani7

(TC/PC)/K · atm-1

13.432 13.429 13.429 15.096 19.159 21.551 24.180 27.042 13.780 15.485 13.285

11.288 12.544 14.055 15.816 22.555 25.276 28.229 29.740 31.413 34.827 38.468 46.427 14.043 15.803 17.791 17.807 18.120 20.035 20.030 20.047 20.047 20.047 20.383 22.530 22.530 22.530 24.052 22.511 22.511 22.511 24.052 22.511 22.899 22.492 22.904 22.904 25.248 25.671 25.650 25.628 25.628 28.633

Kontogeorgis et al.8 4.4977 4.1633 4.1732 6.4105 2.5865 5.6049 4.9672 7.0081 4.3482 4.8379 3.1285 2.9855 2.3845 4.6072 4.0612 2.3482 1.0829 6.3413 0.0435 6.0879 0.0143 1.3966 4.7148 7.0923 2.3023 0.4255 3.0810 2.0352 1.1650 4.7859 1.1391 6.0108 7.7321 5.9003 8.8017 5.7893 2.3523 1.0526 1.8659 0.7291 4.7032 14.240 6.5391 5.1624 1.4467 3.4261 2.4221 0.0861 5.8020 7.2499 9.2547 5.5140 3.2067 8.6023 5.0041

predicted by eq 13 6.3193 3.8352 3.5353 1.9890 2.4805 4.5326 5.5519 1.0270 0.5715 1.3827 3.1416 3.1635 3.8815 1.6615 1.0310 2.6054 7.0051 2.2933 3.2340 5.3312 3.0021 0.7779 4.3830 2.5810 0.5819 1.7047 1.2709 2.0085 0.5374 0.5292 2.5325 4.0719 5.0321 4.7113 4.6008 1.1043 0.4856 0.5885 0.8929 5.5423 11.827 7.5723 5.6831 2.6685 1.7824 2.9969 1.0243 2.2483 2.7644 1.6922 0.8837 2.3999 6.3779 5.0523

Joback5

1.3541 0.8756 1.4468 0.5310 0.5469 0.1559 2.9230 3.3187 1.7529 1.9242 4.9343

0.5109 12.963 5.6432 3.4274 1.5216 1.0172 0.8590 0.7052 1.0494 2.0558 2.9657 2.0311 13.275 4.6881 4.5449 3.5600 4.0984 1.4046 1.8690 1.9240 0.0120 1.8259 0.9370 1.4110 0.5969 2.6926 1.2709 1.9652 1.0263 1.1105 1.1670 4.0142 1.9677 3.2400 0.9784 0.7604 0.4950 0.5291 5.5483 3.3465 6.4781 5.9724

Cons. & Gani7

0.1170 5.0905 1.5031 1.4478 0.1480 0.6063 0.0493 1.3576 0.0184 3.4442 2.8846

2.8185 0.2427 1.6454 1.9662 0.1040 1.6365 5.7516 0.6945 0.3007 0.4833 1.9871 3.5763 0.7576 0.0550 2.6864 0.0396 0.9712 0.7927 0.2414 0.0679 2.5301 4.8811 3.8231 0.3235 1.7219 4.0618 0.5775 4.4580 1.8509 0.3870 3.2530 6.5709 5.5622 7.3136 0.1508 0.1053 0.9149 0.5665 7.3824 5.6964 11.973 6.0085

Ambrose2,3

100 RE

27.529 29.010 26.157 14.116 0.7530 3.5314 6.2730 4.3122 29.520 9.6700 26.472

76.977 40.928 23.017 11.666 3.3160 3.0873 5.7330 5.1900 5.3902 4.9300 5.5090 4.8645 22.930 14.153 9.9200 6.6839 12.737 5.9780 4.2510 1.9219 3.9089 5.8190 11.765 1.4305 0.5770 2.6723 9.2608 3.7372 2.7820 0.6080 11.958 5.8219 9.5361 7.0393 10.760 6.3800 1.9141 3.0694 3.5410 7.9955 11.268 7.5746

Kontogeorgis et al.8

Table 3. Value of RTC/PCCP and the Ratio TC/PC for 178 Components (Training Data Set) Based on Experimental Data, Estimated by Correlation (Equation 13) and Various Group Contribution Methods, Together with Values for Relative Errors, RE ) ((TC/PC)exp - (TC/PC)calc)/((TC/PC)exp)

692 Journal of Chemical & Engineering Data, Vol. 54, No. 3, 2009

chemical special

1,3-Butadiene 2-Methyl-1,3-butadiene Acetylene 1-Pentyne 2-Pentyne 1-Hexyne 2-Hexyne 3-Hexyne Vinylacetylene Methylcyclopentane Ethylcyclopentane cis-1,3-Dimethylcyclopentane trans-1,3-Dimethylcyclopentane Cyclooctane 1,1-Dimethylcyclohexane Ethylcyclohexane 1-Methylcyclopentene Cyclohexene Propylbenzene 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene Isopropylbenzene Biphenyl Styrene 2-Butanol 2-Propanol 2-Methyl-1-propanol 2-Methyl-2-propanol 1-Pentanol 2-Methyl-1-butanol 2-Methyl-2-butanol 3-Methyl-1-butanol 1-Hexanol Phenol m-Cresol p-Cresol 2-Ethylphenol 3-Ethylphenol 4-Ethylphenol 3,5-Dimethylphenol 1-Decanol Dimethyl ether Methyl n-propyl ether Methyl isopropyl ether Methyl isobutyl ether Diethyl ether Ethyl propyl ether Methyl phenyl ether 1-Propanal 1-Pentanal 1-Heptanal 1-Octanal 1-Nonanal Methyl ethyl ketone 2-Pentanone

compd no.

56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110

Table 3 Continued

C4H6 C5H8 C2H2 C5H8 C5H8 C6H10 C6H10 C6H10 C4H4 C6H12 C7H14 C7H14 C7H14 C8H16 C8H16 C8H16 C6H10 C6H10 C9H12 C9H12 C9H12 C9H12 C12H10 C8H8 C4H10O C3H8O C4H10O C4H10O C5H12O C5H12O C5H12O C5H12O C6H14O C6H6O C7H8O C7H8O C8H10O C8H10O C8H10O C8H10O C10H22O C2H6O C4H10O C4H10O C5H12O C4H10O C5H12O C7H8O C3H6O C5H10O C7H14O C8H16O C9H18O C4H8O C5H10O

chemical formula 1.0982 1.0325b 0.9610 0.9154 1.1060 0.9272b 1.0764b 1.0917b 1.0682b 1.0853 1.0601 1.0017 1.0053 1.0310 1.0957b 1.0617b 1.1013 1.0636 1.0967 1.0341 1.0919 1.1185 1.0441b 1.1475b 0.9466 0.9961 0.9372 0.9414 0.9777 0.9280 0.9078 0.9432 0.9716 0.9234 1.0597 0.9223 0.8992 0.9694 0.9881 0.9433 0.9847 0.9726 0.9455b 0.9050b 0.9352b 0.9253 0.9234b 1.1332 1.0710b 0.9551b 0.9547b 0.9342b 0.9341 1.0611 1.0557

K · atm-1

(RTC/PCCP)

10.018 12.738 5.0798 11.692 13.081 14.369 15.758 15.570 9.4073 14.281 16.972 16.416 16.476 18.364 20.373 20.303 13.297 12.934 20.211 19.539 20.237 20.108 20.718 16.869 12.932 10.752 12.904 12.855 15.346 14.792 14.566 14.996 17.903 11.608 15.823 13.863 16.561 17.545 17.918 17.552 29.253 7.6926 12.801 12.099 14.767 12.991 15.040 15.319 10.387 14.448 19.659 21.769 24.332 13.169 15.323

Exp. 9.5558 12.630 5.5280 13.033 12.155 15.514 14.738 14.395 9.2418 13.388 15.977 16.319 16.320 17.609 18.323 18.810 12.385 12.466 18.173 18.600 18.269 17.760 19.478 14.793 13.848 11.179 13.946 13.842 15.694 15.914 16.009 15.877 18.170 12.846 15.002 15.092 18.162 17.871 17.903 18.336 30.005 8.3335 13.736 13.581 15.779 14.193 16.228 13.717 10.122 15.179 20.181 22.819 25.701 12.698 14.624

predicted by eq 13 10.014 12.595 5.2812 11.643 12.477 12.463 13.296 14.823 9.1993 13.541 17.824 17.086 17.048 21.899 18.259 21.161 13.395 13.225 19.873 21.293 20.953 24.734 22.970 16.339 12.206 10.325 12.478 12.442 15.023 14.634 13.579 14.700 17.317 11.472 14.290 14.473 16.776 17.264 17.249 17.691 28.996 8.1921 12.611 12.665 14.822 12.665 14.915 13.040 10.302 14.840 19.376 22.231 25.480 12.725 15.298

Joback5 10.048 12.686 12.407 12.365 14.600 15.745 15.628 11.180 10.955 17.985 17.888 17.845 18.631 19.439 21.105 8.2904 11.174 20.261 22.066 19.178 20.300 24.320 17.752 12.280 10.597 12.508 11.479 15.304 15.029 13.762 15.027 17.842 11.464 14.235 14.418 16.867 17.349 18.039 17.444 29.223 7.9337 12.761 12.137 15.439 12.816 15.235 10.037 9.0305 14.260 19.114 22.795 25.220 12.989 15.337

10.082a 13.574a 12.056 12.364a 14.651 15.450 14.897a 8.8659a 14.054a 17.695a 16.417a 16.417 19.932 19.502a 20.626a 14.523a 13.978a 21.485a 21.428a 20.577 25.645a 27.493a 18.386 12.057a 10.457a 13.204 11.987 16.043 16.010 15.128 16.010 18.784 14.073 14.246 19.275 20.219a 20.219a 22.236a 31.398 7.4037 12.429 11.317 14.315a 12.756a 13.964a 15.939a 9.2644a 15.158 20.739 24.598 26.299 13.046 15.659

Ambrose2,3

Cons. & Gani7

(TC/PC)/K · atm-1

14.807 14.820 16.678 16.693 16.693 12.616 15.540 17.510 17.490 17.490 19.734 20.075 19.722 13.815 14.843 18.594 19.221 18.825 18.578 19.396 15.417 17.082 15.162 17.077 17.387 19.260 19.244 19.579 19.244 21.663 13.768 15.581 15.581 17.977 17.977 17.977 18.524 33.604 11.814 14.807 14.795 16.961 14.807 16.678 15.445 12.804 16.170 20.512 23.041 25.805 14.363 16.170

12.847 14.794

Kontogeorgis et al.8 4.6133 0.8469 8.8237 11.469 7.0768 7.9712 6.4715 7.5421 1.7593 6.2519 5.8593 0.5883 0.9448 4.1067 10.058 7.3491 6.8551 3.6171 10.083 4.8035 9.7246 11.672 5.9825 12.303 7.0880 3.9800 8.0782 7.6844 2.2680 7.5864 9.9114 5.8783 1.4949 10.671 5.1836 8.8703 9.6706 1.8602 0.0821 4.4678 2.5711 8.3320 7.3083 12.250 6.8541 9.2560 7.9029 10.452 2.5434 5.0653 2.6568 4.8248 5.6299 3.5733 4.5562

predicted by eq 13 0.0426 1.1442 3.9651 0.4264 4.9074 15.497 15.875 5.1052 2.2907 5.5416 5.0242 4.0831 3.4756 19.250 11.730 4.1077 0.7398 2.2331 1.7224 8.9741 3.4622 18.948 9.9353 3.2870 6.0225 4.1928 3.3032 3.3578 2.0987 1.0937 6.7768 2.0368 3.4299 1.1961 10.867 4.2670 1.2985 1.5992 3.7328 0.7958 0.8764 6.1787 1.4804 4.5325 0.3758 2.6050 0.8506 17.709 0.8148 2.6745 1.4807 2.1069 4.5627 3.5414 0.1688

Joback5

11.055 2.7592 16.390 15.239 12.839 26.690 7.3344 3.7550 2.9068 6.4638 3.0651 1.8045 7.1517 4.0430 10.814 4.9131 5.4918 12.996 8.0841 0.9397 2.1908

3.1139 5.4792 1.9656 1.9526 4.3217 5.7543 1.5899 4.2583 0.0067 0.3553 8.5394 4.2751 1.5928 9.2241 8.0740 6.2994 9.6683 1.6788 27.532 32.703 8.9984 6.7620 2.7414 2.3267 6.7467 4.5432 8.2310 3.8532 6.7645 4.9237

0.6386 6.5697 6.1132 5.4761 1.6130 0.0762 0.3700 18.846 23.291 5.9669 8.9659 8.3137 1.4556 4.5830 3.9488 37.653 13.609 0.2434 12.930 5.2359 0.9592 17.385 5.2306 5.0383 1.4386 3.0704 10.699 0.2711 1.6059 5.5236 0.2116 0.3397 1.2330 10.035 4.0017 1.8490 1.1194 0.6710 0.6146 0.1007 3.1351 0.3060 0.3195 4.5507 1.3613 1.3016 34.480 13.059 1.3002 2.7697 4.7114 3.6496 1.3659 0.0917

0.2988 0.4014

Ambrose2,3

100 RE Cons. & Gani7

26.650 13.296 16.070 5.9327 7.2100 34.110 8.8140 3.1710 6.5445 6.1587 7.4621 1.4870 2.8606 3.8983 14.759 7.9990 1.6252 6.9785 7.6110 6.3778 8.6070 32.089 41.015 32.338 35.255 25.505 30.090 34.414 28.327 21.000 18.610 1.5262 12.391 8.5480 2.4589 0.3250 5.5417 14.875 53.583 15.674 22.281 14.854 13.980 10.893 0.8170 23.267 11.916 4.3402 5.8440 6.0522 9.0610 5.5230

28.234 16.148

Kontogeorgis et al.8

Journal of Chemical & Engineering Data, Vol. 54, No. 3, 2009 693

chemical special

Methyl isopropyl ketone Methyl isobutyl ketone 3-Methyl-2-pantanone Ethyl propyl ketone Ethyl isopropyl ketone Diisopropyl ketone n-Butyric acid 2-Methylpropanoic acid Methyl formate Methyl acetate Methyl propanoate Methyl n-butyrate Methyl 2methylpropanoate Ethyl propionate Ethyl n-butyrate n-Propyl formate n-Propyl acetate n-Butyl acetate Propyl propanoate Ethyl 2-methyl propanoate 2-Methylpropyl ethanoate Pentyl methanoate 3-Methylbutyl methanoate Vinyl acetate Ethyl 3-methylbutanoate Propyl butanoate 2-Methylpropyl propanoate 3-Methylbutyl butanoate Ethylene oxide Furan Methyl amine Trimethyl amine Ethylamine Butyl amine Diethyl amine Isobutyl amine Triethyl amine n-Propylamine Di-n-propylamine Isopropylamine N-Methylaniline Methyl mercaptan Ethyl mercaptan Isobutyl mercaptan sec-Butyl mercaptan Dimethyl sulfide Methyl ethyl sulfide Diethyl sulfide Chloroethane Bromoethane 1-Chloropropane 2-Chloropropane 1,1-Dichloropropane 1,2-Dichloropropane 1-Chloropentane Fluorobenzene

compd no.

111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166

Table 3 Continued

C5H10O C6H12O C6H12O C6H12O C6H12O C7H14O C4H8O2 C4H8O2 C2H4O2 C3H6O2 C4H8O2 C5H10O2 C5H10O2 C5H10O2 C6H12O2 C4H8O2 C5H10O2 C6H12O2 C6H12O2 C6H12O2 C6H12O2 C6H12O2 C6H12O2 C4H6O2 C7H14O2 C7H14O2 C7H14O2 C9H18O2 C2H4O C4H4O CH5N C3H9N C2H7N C4H11N C4H11N C4H11N C6H15N C3H9N C6H15N C3H9N C7H9N CH4S C2H6S C4H10S C4H10S C2H6S C3H8S C4H10S C2H5Cl C2H5Br C3H7Cl C3H7Cl C3H6Cl2 C3H6Cl2 C5H11Cl C6H5F

chemical formula 1.0813 0.9973 1.0738b 0.9569 0.9874 1.0556b 1.1041b 1.1376b 1.0421b 1.0712 0.9915 0.9964 0.9930 1.0346 1.0491b 1.0201 1.0105b 1.0262b 1.0157 0.9724b 0.9565b 0.9921b 0.9854b 1.1219b 1.0174 1.0206 1.0043 0.9976 1.1366b 1.1387 0.9227 0.9695 0.9449 0.9518 0.9845 0.9334 0.9209 0.9220 0.9413 0.8987b 0.9087b 1.0896 1.0490 0.9764b 0.9609b 1.0351 1.1089b 1.0123 1.1372 1.0520 1.0914 1.0473b 1.1270 1.1586 1.0586 1.0996b

K · atm-1

(RTC/PCCP)

14.591 17.705 17.487 17.782 17.201 19.072 15.328 16.563 8.2551 10.943 13.340 16.145 15.971 16.563 19.679 13.526 16.528 18.868 18.948 18.247 17.983 18.883 18.706 13.384 21.818 21.863 21.966 26.911 6.5477 8.9485 5.8505 10.707 8.2682 13.209 13.710 13.317 17.836 10.623 17.919 10.530 13.696 6.5861 9.2125 13.950 13.826 9.2171 12.677 14.255 8.5430 8.1157 11.131 10.545 13.382 13.701 16.842 12.500

Exp. 13.695 17.556 16.226 18.314 17.254 17.842 14.050 14.665 8.3461 10.625 13.659 16.152 16.044 15.976 18.474 13.480 16.290 18.134 18.380 18.481 18.514 18.728 18.681 12.251 20.994 20.971 21.406 26.736 6.0544 8.2814 6.6854 11.417 9.1854 14.046 14.089 14.400 19.037 11.868 18.731 12.051 15.130 6.3647 9.2173 14.418 14.510 9.3395 11.784 14.231 7.9241 8.1333 10.608 10.483 12.198 12.153 15.887 11.723

predicted by eq 13 14.746 17.429 15.283 17.512 17.491 19.853 14.415 14.257 8.7635 11.714 12.884 16.026 15.556 16.080 18.436 14.242 16.187 18.884 18.465 17.392 18.161 19.366 19.051 13.077 20.716 20.189 20.812 27.417 7.4061 9.7340 6.8946 10.051 8.5622 12.673 13.082 12.338 16.720 10.457 17.682 9.8918 16.324 7.3608 9.1608 13.456 12.953 9.9383 11.975 14.307 9.7018 9.0591 12.041 11.484 13.253 14.298 17.348 12.981

Joback5

10.344 8.4064 14.283 13.103 12.484 17.366 10.461a 18.596a 10.415a 16.396 6.8911 8.7757a 13.003 15.045 9.2103 11.412a 15.045 9.2334 8.2207 11.243 10.740a 13.516 12.883a 16.316 12.417

15.813 12.961 8.3898a 10.660 12.778a 15.889 15.293 16.442 18.716 13.034 15.568 18.691 18.668 18.351 18.351 18.668 18.351 10.498 21.362 21.669 21.362 27.876 6.5163

14.411 17.467 17.521 18.939 17.790a

Cons. & Gani7

(TC/PC)/K · atm-1

15.055 17.904 17.998 16.828 18.040 20.582 15.455 16.263 8.0030 11.076 13.508 15.609 15.637 16.168 18.702 13.577 16.117 18.879 18.706 18.104 18.422 19.080 18.779 12.501 21.048 21.519 21.166 27.223 5.3603 11.364 5.9977 10.492 8.1961 12.992 12.487 12.764 18.495 10.453 18.487 10.426 17.656 6.8583 9.1952 12.403 14.318 9.2111 11.765 14.316 9.1395 7.8942 11.014 11.956 13.259 14.041 17.405 12.790

Ambrose2,3

12.492 13.995 15.747 12.232 12.503 13.686 13.674 14.990 14.964 17.336 9.9595

10.982 11.484 12.164 15.292 15.323 15.891 19.464 13.604 17.264 13.593 15.985 11.247 12.492 15.733

15.255 15.305 12.048 13.466 15.135 17.051 17.032 17.051 19.210 15.135 17.051 19.210 19.205 19.188 19.188 19.205 19.188 14.450 21.583 21.602 21.583 25.777

16.155 20.854 18.205 18.216 18.205

Kontogeorgis et al.8 6.1376 0.8402 7.2091 2.9923 0.3091 6.4453 8.3346 11.454 1.1028 2.9054 2.3932 0.0459 0.4584 3.5386 6.1195 0.3346 1.4363 3.8902 2.9960 1.2831 2.9535 0.8201 0.1289 8.4651 3.7768 4.0766 2.5475 0.6489 7.5341 7.4545 14.271 6.6352 11.093 6.3368 2.7696 8.1345 6.7352 11.726 4.5314 14.453 10.469 3.3609 0.0520 3.3579 4.9511 1.3278 7.0415 0.1635 7.2447 0.2166 4.6912 0.5876 8.8407 11.294 5.6697 6.2098

predicted by eq 13 1.0594 1.6040 14.613 1.5192 1.6874 4.0966 5.9500 13.922 6.1589 6.6640 3.4182 0.7509 2.6016 3.0457 6.8318 5.0895 2.1368 0.0810 2.5500 4.6832 0.9879 2.5599 1.8449 2.3814 5.0519 7.6556 5.2534 1.8771 13.110 8.7791 17.846 6.1268 3.4802 4.0553 4.8678 7.3539 6.7639 1.6017 1.3576 6.0600 16.312 11.762 0.5715 3.7266 6.8237 7.3538 5.9383 0.3664 13.565 10.552 8.1788 8.9046 0.9873 4.2266 3.0006 3.7567

Joback5

3.3847 1.6721 8.1313 4.4287 6.2532 2.6374 1.5180 3.7782 1.0841 19.711 4.6309 4.7404 6.7892 8.8195 0.0729 9.9801 5.5358 8.0823 1.2941 1.0031 1.8492 1.0035 5.9707 3.1215 0.6622

3.1683 21.747 1.6321 2.5874 4.2128 1.5816 4.2450 0.7343 4.8898 3.6402 5.8083 0.9295 1.4760 0.5723 2.0447 1.1335 1.8980 21.559 2.0911 0.8845 2.7526 3.5834 0.4790

1.2318 1.3449 0.1992 6.5078 3.4273

2.5161 2.0080 0.8719 1.6388 8.9220 4.1538 3.6947 1.5943 3.1732 0.9925 28.916 4.1329 0.1869 11.093 3.5649 0.0642 7.1907 0.4283 6.9828 2.7282 1.0540 13.466 0.9196 2.4819 3.3446 2.3252

3.1817 1.1221 2.9187 5.3650 4.8825 7.9189 0.8339 1.8112 3.0529 1.2162 1.2652 3.3151 2.0949 2.3872 4.9633 0.3790 2.4883 0.0585 1.2766 0.7838 2.4378 1.0444 0.3882 6.5972 3.5309 1.5707 3.6417 1.1578 18.133

Ambrose2,3

100 RE Cons. & Gani7

35.541 10.393 10.462 43.191 54.061 22.951 27.976 12.015 9.2150 2.9338 20.324

87.726 7.2581 47.124 15.771 11.761 19.330 9.1270 28.066 3.6500 29.077 16.712 70.775 35.608 12.784

0.4710 7.5950 45.956 23.051 13.455 5.6170 6.6423 2.9459 2.3810 11.895 3.1660 1.8092 1.3552 5.1596 6.6991 1.7075 2.5776 7.9670 1.0757 1.1935 1.7440 4.2143

10.718 17.785 4.1029 2.4427 5.8381

Kontogeorgis et al.8

694 Journal of Chemical & Engineering Data, Vol. 54, No. 3, 2009

2.6066 12.136 8.0538 20.393 11.645 6.2131 10.093 10.601 11.804 0.4193 26.518 5.7617

Figure 1. Correlation of RTC/PCCP for 178 compounds

Estimated by the second-order group contribution method. b In column 4, is obtained from ref 22 and other values from ref 23. a

3.4487 3.4988 3.4682 4.3792 4.8105 7.2499 3.4696 4.6133 3.4703 4.1877 1.8759 6.4226 3.5410 3.1201 3.7720 3.6374 4.3087 6.8258 3.8591 4.1711 3.9348 4.2053 2.5529 6.0727 1.0153b 0.8840 1.0765 0.8504 0.9263 0.9937b 1.1010 0.9311 1.1224 1.0225 1.1569 0.9959 O2 N2 NH3 N2O C2N2 CO CO2 HCl H2S SO2 SO3 Air Oxygen Nitrogen Ammonia Nitrous oxide Cyanogen Carbon monoxide Carbon dioxide Hydrogen chloride Hydrogen sulfide Sulfur dioxide Sulfur trioxide 167 168 169 170 171 172 173 174 175 176 177 178

Exp. chemical special compd no.

K · atm-1

Joback5

Cons. & Gani7 predicted by eq 13 chemical formula

Table 3 Continued

(RTC/PCCP)

(TC/PC)/K · atm-1

Ambrose2,3

Kontogeorgis et al.8

predicted by eq 13

Joback5

100 RE

Cons. & Gani7

Ambrose2,3

Kontogeorgis et al.8

Journal of Chemical & Engineering Data, Vol. 54, No. 3, 2009 695

Figure 2. Correlation of experimental TC/PC versus TC/PC calculated from eq 13 for the training data set. Table 4. Variety of Number of Test Data Used in This Study compound type

no. of data points

hydrocarbons oxygenated hydrocarbons nitrogenated hydrocarbons hydrocarbon sulfide and mercaptanes halogenated hydrocarbons total

23 18 3 2 3 49

the values of RTC/PCCP for all of the compounds used are nearly close to one. The mean absolute relative error between values of RTC/PCCP and one is less than 5.89 %. Therefore, the equation coefficient (ε) in eq 12 is considered equal to one.

Results and Discussion Figure 1 shows the value of RTC/PCCP for 178 compounds. It can be seen that the proposed correlation works well for the light and medium organic compounds, but there are considerable errors for some organic and inorganic compounds. Although high molecular weight compounds have a high error, this error is not necessarily for high molecular weight compounds. The value of RTC/PCCP for some of the light compounds deviates from unity similar to the high molecular weight compounds. It

1 2 3 4 5 6 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

C6H14 C7H16 C5H12 C6H14 C8H18 C8H18 C8H18 C9H20 C10H22 C3H6 C6H12 C5H10 C12H24 C14H30 C3H4 C4H6 C7H12 C8H14 C4H8 C6H12 C7H14 C5H8 C8H10 C2H6O C3H8O C4H10O C6H12O C7H8O C9H20O C5H12O C5H12O C4H8O C6H12O C6H12O C5H10O C5H10O2 C3H6O2 C4H8O2 C7H14O2 C7H14O2 C7H14O2 C2H7N C6H7N C4H11N C3H8S C5H12S CH3Br C2H5F C4H9Cl

chemical formula

b

0.9914 1.0174 0.9331 0.9593 0.9889 0.9641 0.9099 0.8787 0.9697 1.0279 1.0347 1.0318 1.0284 1.1482 0.9940 1.0497 0.9937b 1.0040b 1.0861 1.0622 1.0249 1.0962 1.0719 1.0861 1.0334 1.0128 1.0118 0.9123 0.9559 0.9809b 0.9603b 1.0146 0.9686 1.0073 0.9842 1.0742b 1.0162 1.0074 0.9614 1.0250 1.0214 0.9889b 0.9920 0.9518 1.0291b 1.0082 1.1570b 1.0658 1.0658

K · atm-1 16.918 20.123 13.735 16.376 22.389 21.419 20.843 22.463 27.081 8.0003 16.264 13.656 33.411 44.725 7.2548 9.8654 18.096 21.019 9.3381 13.680 16.660 10.680 17.077 8.5087 10.622 13.145 15.496 13.968 23.033 15.612 14.770 12.600 17.307 17.970 15.361 18.194 10.937 13.772 20.770 21.855 21.593 8.4219 13.238 13.209 11.743 17.481 5.9148 7.5905 14.314

exp. 16.931 19.418 14.810 16.937 22.159 21.742 22.423 25.174 27.835 8.2040 15.714 13.458 33.728 44.412 7.7016 9.8285 17.973 20.506 9.0324 13.131 16.199 10.166 15.906 8.2564 10.685 13.223 15.349 15.345 23.626 15.892 15.409 12.705 17.661 17.635 15.614 16.816 11.149 13.857 21.147 20.876 20.702 8.9505 13.558 14.046 11.764 17.180 5.3331 7.5165 13.637

predicted by eq 13

17.476 15.287 17.057 11.932 12.786 20.322 20.751 19.567 9.1774 14.358 12.673 11.649 15.906 7.1621 7.8913 14.148

16.552 19.568 12.593 16.243 22.340 21.766 22.387 25.106 28.303 7.9079 15.913 13.429 40.874 45.180 7.5041 10.291 16.449 22.281 9.3160 14.530 16.729 10.773 17.834 9.1288 10.580 12.593 14.137 14.138 25.757 15.426 14.835 12.283

Joback5

13.327

16.658 19.749a 12.386 16.171 22.535 22.126 21.733 25.924a 28.207 7.1336a 16.302a 14.172 30.087 45.505 7.6520 10.124 17.391 20.573 9.8103 15.026a 17.695a 11.531a 16.332 7.9023a 11.130 13.493 14.692a 14.248 24.525 15.518 14.654a 12.756a 17.078 18.439 16.546 15.609 10.645 13.016a 21.669 21.362 21.066 7.6932 13.297a 14.283 11.409 16.074 6.3936

Cons. & Gani7

(TC/PC)/K · atm-1

18.441 15.365 18.562 10.872 12.845 21.661 21.104 21.448 8.6329 13.998 12.992 12.632 20.808 5.6813 8.1090 14.029

17.128 20.186 12.243 16.619 22.858 22.791 22.544 25.254 27.892 7.9834 16.340 12.949 34.757 42.995 7.7615 10.398 17.799 19.890 9.5546 13.648 16.936 10.641 17.324 8.3536 10.540 12.825 13.197 14.316 25.791 15.756 15.089 11.623

Ambrose2,3

Estimated by the second-order group contribution method. In column 4: obtained from ref 22 and other values from ref 23.

n-Hexane n-Heptane 2,2-Dimethylpropane 3-Methylpentane 3-Methylheptane 3,4-Dimethylhexane 3-Ethyl-3-methylpentane 2,2,3,3-Tetramethylpentane 2,2,5-Trimethylheptane Propylene 1-Hexene 2-Methyl-1-butene 1-Dodecene n-Tetradecane Methylacetylene Dimethylacetylene 1-Heptyne 1-Octyne Cyclobutane Cyclohexane Methylcyclohexane Cyclopentene o-Xylene Ethanol 1-Propanol 1-Butanol Cyclohexanol o-Cresol 1-Nonanol Methyl n-butyl ether Methyl tert-butyl ether 1-Butanal 1-Hexanal 2-Hexanone 3-Pentanone Pentanoic acid Ethyl formate Ethyl acetate Ethyl pentanoate Propyl 2-methylpropanoate 3-Methylbutyl ethanoate Dimethyl amine Aniline Butyl amine n-Propyl mercaptan Isopentyl mercaptan Bromomethane Fluoroethane 2-Chlorobutane

compd no.

a

chemical special

(RTC/PCCP)

15.373

17.823 20.070 16.080 18.400 22.530 22.511 24.052 26.077 28.633 12.020 17.006 15.499 33.020 42.335 11.814 13.195 18.792 21.145 12.348 15.554 17.510 13.215 16.604 13.500 15.175 17.097 18.925 15.581 25.628 16.678 16.961 14.363 18.221 18.221 16.170 17.047 13.466 15.135 21.602 21.583 21.583 12.183 14.177 15.292 13.995 17.724 11.255

Kontogeorgis et al.8 0.0803 3.4994 7.8334 3.4261 1.0274 1.5090 7.5829 12.070 2.7859 2.5456 3.3791 1.4470 0.9487 0.6992 6.1586 0.3736 0.6768 2.4368 3.2732 4.0130 2.7652 4.8117 6.8523 2.9649 0.6014 0.5935 0.9426 9.8642 2.5784 1.7986 4.3263 0.8399 2.0456 1.8627 1.6480 7.5733 1.9469 0.6181 1.8157 4.4795 4.1241 6.2769 2.4241 6.3368 0.1828 1.7216 9.8338 0.9748 4.7281

predicted by eq 13

2.8653 0.4886 6.2501 8.4562 7.8140 2.1537 5.0502 9.3837 8.3416 7.9056 4.0553 0.8187 9.0109 21.087 3.9628 1.1577

2.1633 2.8708 8.3089 0.8152 0.2162 1.6174 7.4081 11.765 4.5149 1.1546 2.2372 1.7121 22.338 1.0223 3.3669 4.1914 9.1014 5.7387 0.2364 5.9215 0.4223 0.8814 4.3007 7.3000 0.4041 4.4428 8.7642 1.2192 11.827 1.2158 0.4381 2.6101

Joback5

6.8901

1.5368 3.1426 9.8201 1.2525 0.6524 3.3015 4.2719 15.408 4.1576 10.833 0.2313 3.7744 9.9478 1.7444 0.1942 2.6215 3.8958 2.1237 5.0573 9.8359 6.2133 7.9739 4.3630 7.1260 4.7744 2.6472 5.1922 2.0072 6.4781 0.6003 0.7867 1.2392 1.3223 2.6086 7.7122 14.209 2.6703 5.4896 4.3319 2.2576 2.4426 8.6518 0.4489 8.1313 2.8439 8.0477 8.0954

Cons. & Gani7

100 RE

2.6187 0.0314 2.0227 0.5933 6.7329 4.2938 3.4349 0.6731 2.5055 5.7377 1.6388 7.5705 19.033 3.9475 6.8317 1.9893

1.2412 0.3112 10.859 1.4808 2.0957 6.4039 8.1629 12.427 2.9954 0.2109 0.4637 5.1799 4.0297 3.8672 5.4474 5.4029 1.6412 5.3728 2.3182 0.2309 1.6592 0.3652 1.4505 1.8218 0.7721 2.4346 14.836 2.4925 11.973 0.9248 2.6677 7.7537

Ambrose2,3

7.3996

5.3400 0.2628 17.075 12.359 0.6325 5.0967 15.395 16.088 5.7324 50.190 4.5815 13.492 1.1600 5.3420 62.851 33.758 3.8481 0.6000 32.236 13.693 5.1056 23.736 2.7645 58.669 42.859 30.062 22.124 11.551 11.268 6.8321 14.830 13.993 5.2810 1.3950 5.2630 6.3030 23.125 9.9010 4.0066 1.2440 0.0469 44.670 7.0930 15.771 19.177 1.3901 90.296

Kontogeorgis et al.8

Table 5. Value of RTC/PCCP and Comparison of the Estimated Ratio TC/PC by Equation 13 with the Experimental Data and Various Group Contribution Methods, Together with Values for Relative Errors RE ) ((TC/PC)exp - (TC/PC)calc)/((TC/PC)exp) for 49 Compounds (Test Data Set)

696 Journal of Chemical & Engineering Data, Vol. 54, No. 3, 2009

Journal of Chemical & Engineering Data, Vol. 54, No. 3, 2009 697

Figure 3. Correlation of experimental TC/PC versus of TC/PC calculated from eq 13 for the test data set.

can be described that the characterizations and properties of the compounds are extremely dependent on the structure of the compounds. For example, the compounds which have double or triple bonds will deviate more from unity because these bonds affect the properties of compounds. In addition, some of the groups such as O, N, and Cl will influence the electronegativity of compounds and so change the compounds’ properties. Therefore, not only deviation from unity for some compounds is dependent on the molecular weight but also it is affected by the molecular structure. Consequently, to improve the accuracy of the previous correlation (eq 12), a cubic polynomial function is considered as follows

( ) ( ) ( )

TC CP 3 CP 2 CP )a +b +c +d PC R R R

(13)

By optimizing the relative error between experimental data and predicted values, it is found that the optimal constants of this equation are: a ) 0.0006314, b ) -0.03017, c ) 1.384, d ) -1.038. The linear regression, R-value, and RMSE between the desired and the predicted values from the correlation (13) are 0.9818 and 0.9852, respectively. The predicted values for TC/ PC given by this new correlation, together with the values for various group contribution methods and relative errors (RE) for 178 components, are given in Table 3. Figure 2 shows the closeness of the correlation between the predicted results from eq 13 and the experimental training data set. A perfect fit (experimental equal to predicted data) is indicated by the solid line. The close proximity of the best linear fit to the perfect fit, as observed in Figure 2, shows a good correlation among predictions and experimental data. Also, the performance of the proposed correlation was tested using another set of 49 experimental data (Table 5) that were not previously used for training of the correlation. Table 4 provides information on the type and number of different compounds that comprised the test data set used in this study. The results indicate that the mean relative error (MRE) of the proposed correlation is less than 3.33 % for the test data set. Figure 3 indicates there is good correlation between predicted and experimental test data of the TC:PC ratio. In this figure, the correlation outputs are plotted versus the experimental data as stars. A perfect fit (experimental equal to predicted data) is indicated by the solid line. The slope and the y-intercept of the best linear regression relating experimental to predicted data

are, respectively, 0.9661 and 0.4614 which nearly overlaps the perfect linear fit. The correlation coefficient (R-value) between the predictions and the experimental test data is 0.9896. This shows a very good correlation among the training and test data. The results obtained using the proposed simple new correlation (eq 13) were compared with the experimental TC:PC test data and the values predicted using the methods of Joback,5 Ambrose,2,3 Constantinou and Gani,7 and also Kontogeorgis8 in Table 5. Also, in this table, results for the 49 compounds including the values of RTC/PCCP and relative errors (RE) are shown. The mean relative error between values of RTC/PCCP and one is less than 4.24 %. Also, the mean relative errors (MRE) between all the predictive methods and experimental data for this data set are: proposed correlation 3.33 %; Ambrose2,3 method 4.15 %; Constantinou and Gani7 method 4.78 %; Joback5 method 4.99 %; and Kontogeorgis8 method 16.37 %. The results show a good agreement between the proposed correlation and the experimental data. Also, the MRE of the proposed correlation is less than the previous methods for the test data set. One of the advantages of the proposed correlation is in its ability to predict the TC:PC ratio for organic and inorganic compounds. It should be noted (as can be seen at the end of Table 3) that the proposed correlation is the only applicable method to predict the TC:PC ratio for inorganic compounds. The other methods are unable to predict the TC:PC ratio for inorganic compounds since there are not enough group contributions for these compounds. This limitation could be considered as a weakness for the other methods. According to Table 3, one of the disadvantages of the Constantinou and Gani7 and Kontogeorgis8 methods appears when these are used to evaluate the TC:PC ratio for isomers of compounds such as octane. Critical temperature and pressure estimation by these methods is independent of any properties of the compounds such as boiling point temperature, molecular weight, or atom numbers in the molecule, so the estimation of TC and PC is only dependent on group contributions. Since isomers of one compound have the same group contributions, then the methods developed based on group contribution are not able to accurately predict values for TC and PC. Tables 3 and 5 show the Kontogeorgis8 method strongly depends on the molecular weight of the compounds. The evaluated TC:PC ratio by the Kontogeorgis8 method would be more accurate for high molecular weight compounds. So, it could be better to use this method only for medium-to-high molecular weight compounds. Although these methods have some disadvantages, it should mentioned that the Constantinou and Gani7 method requires no compound properties to be measured but only the structural formula of a compound. This shows the generality of this method. A major benefit of using the Ambrose,2,3 Constantinou and Gani,7 and Joback5 methods is the ability of these methods to predict both critical temperature and critical pressure while the proposed correlation can be used to estimate one of the two critical properties whenever only the other one is available. It is considerable that these methods are relatively complex because they need to be familiar with the molecular structure which in some cases is really time consuming, but the proposed correlation is simple and just needs the heat capacity to predict the TC:PC ratio. In addition, the calculation of critical temperature and pressure by these methods may be impossible because the group contributions of some compounds such as methane, ethylene, and acetylene are not available.

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Figure 4. Mean relative errors of proposed correlation and various methods used in prediction of TC/PC for all types of compounds. (a) Hydrocarbons. (b) Oxygenated hydrocarbons. (c) Nitrogenated hydrocarbons. (d) Hydrocarbon sulfide and mercaptanes. (e) Halogenated hydrocarbons.

Figure 4 shows the mean relative errors corresponding to the proposed correlation and Joback,5 Constantinou and Gani,7 Ambrose,2,3 and Kontogeorgis8 methods for hydrocarbons, oxygenated hydrocarbons, nitrogenated hydrocarbons, hydrocarbon sulfide and mercaptanes, and halogenated hydrocarbons. This figure illustrates that the Kontogeorgis8 method is the least accurate method in prediction of the TC:PC ratio for various types of compounds used with errors of 11.79 % for hydrocarbons, 13.30 % for oxygenated hydrocarbons, 24.51 % for nitrogenated hydrocarbons, 24.52 % for hydrocarbon sulfide and mercaptanes, and 29.04 % for halogenated hydrocarbons. According to Figure 4a, b, and c, almost all methods except the Kontogeorgis8 method result in similar errors when they are used for

hydrocarbons, oxygenated and nitrogenated hydrocarbons. Furthermore, it should be noted that the proposed correlation requires just one basic property (i.e., heat capacity), whereas in the Joback5 method, normal boiling point and number of atoms in the molecule, and in the Ambrose2,3 method, molecular weight and normal boiling point, in addition to group contributions are also required. Figure 4d presents that the proposed correlation is the best accurate method in prediction of the TC:PC ratio for hydrocarbon sulfide and mercaptanes with an error of 2.46 %, while the Ambrose2,3 method has an error of 5.91 %, Joback5 method 5.15 %, and Constantinou and Gani7 method 5.71 %. As can be seen in Figure 4e, it seems that the Constantinou and Gani7 and

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nA nj Ni pc1i pc2j PC Qw R tc1i tc2j TB TC SG Figure 5. Overall performance of proposed correlation and various methods in the prediction of TC/PC for all types of compounds

Ambrose2,3 methods are the best for halogenated hydrocarbons with errors of 3.80 % and 4.19 %, respectively. The proposed correlation is the next most accurate approach with an error of 5.48 %. Figure 5 shows the overall performance of proposed correlation and various methods in prediction of the TC:PC ratio for all types of compounds. The correlation of Ambrose2,3 yields the best result, with a typical error less than 3.99 %. The overall performance of the Joback5 method is rather good with an error of around 4.45 %. The proposed correlation is equally good with respect to Constantinou and Gani,7 with an error of 4.69 %, but the proposed correlation is more general. The Kontogeorgis8 method is the least accurate method with an error less than 14.50 %. It seems that the accuracy of the proposed correlation is similar to the methods of Constantinou and Gani,7 Ambrose,2,3 and Joback,5 for various types of compounds. However, the important point is that the proposed correlation is simple and general to predict critical temperature to critical pressure ratio for low to medium molecular weight compounds.

Conclusions It was shown in this study that, unlike the critical properties alone, a simple correlation of the TC:PC ratio with the heat capacity at 298.15 K can be developed for low to medium molecular weight compounds. The proposed correlation can be used to estimate one of the two critical properties whenever only the other one is available. It is important to note that the proposed correlation just requires one basic property (i.e., heat capacity), whereas the other methods need two basic properties in addition to group contributions. The proposed correlation is simple and general to predict critical temperature to critical pressure ratio for low to medium molecular weight compounds. This proposed correlation is applicable to predict the TC:PC ratio for organic and inorganic compounds, while the other methods just predict this ratio for organic compounds. Appendix Nomenclature

CP M Mj

Heat capacity Molecular weight Number of occurrences of the type-j second-order group in a compound

∆ ∆P ∆T

Number of atoms in the molecule Number of groups of the jth type Number of occurrences of the type-i first-order group in a compound Contribution of the type-i first-order group for estimation of the critical pressure Contribution of the type-j second-order group for estimation of the critical pressure Critical pressure van der Waals surface area Universal gas constant Contribution of the type-i first-order group for estimation of the critical temperature Contribution of the type-j second-order group for estimation of the critical temperature Normal boiling point at 1 atm Critical temperature Specific gravity of liquid hydrocarbons at 60 °F relative to water at the same temperature Contributions for the jth atomic or molecules group Group contribution for PC Group contribution for TC

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