Page 343 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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7. APPLICATIONS: ESTIMATION OF THERMOPHYSICAL PROPERTIES 323
TABLE 7.9—Coefficients of Eq. 7.50 for calculation of enthalpy of vaporization of pure compounds versus temperature [9].
vap
H [kJ/kg] = A(1 − T r ) B+CT r
T
Compound A B C Compound A B C
Water 2612.982 −0.0577 0.3870 Methylcyclopentane 527.6931 0.3967 0.0000
Ammonia 1644.157 −0.017 0.3739 Ethylcyclopentane 502.1246 0.3912 0.0000
H 2 S 754.073 0.3736 0.0000 Pentylcyclopentane 442.0789 0.3800 0.0000
CO 2 346.1986 −0.6692 0.9386 Decylcyclopentane 397.8670 0.3800 0.0000
N 2 228.9177 −0.1137 0.4281 Pentadecylcyclopentane 372.6050 0.3800 0.0000
CH 4 570.8220 −0.1119 0.4127 Cyclohexane 534.5225 0.3974 0.0000
C 2 H 6 588.1554 0.0045 0.3236 Methylcyclohexane 503.9656 0.4152 0.0000
C 3 H 8 610.2175 0.3649 0.0000 Ethylene 679.2083 0.3746 0.0000
n-C 4 H 10 568.6540 0.3769 0.0000 Propylene 539.9479 0.0169 0.0000
n-C 5 H 12 540.6440 0.3838 0.0000 Benzene 651.8210 0.6775 −0.2695
n-C 6 H 14 515.2685 0.3861 0.0000 Toluene 544.7929 0.3859 0.0000
n-C 7 H 16 497.0039 0.3834 0.0000 Ethylbenzene 515.2839 0.3922 0.0000
n-C 8 H 18 489.0450 0.4004 0.0000 o-Xylene 521.7788 0.3771 0.0000
n-C 10 H 22 461.4396 0.3909 0.0000 Propylbenzene 500.4582 0.3967 0.0000
n-C 15 H 32 431.6786 0.4185 0.0000 n-Butylbenzene 470.0009 0.3808 0.0000
n-C 20 H 42 407.3617 0.4089 0.0000 n-Octylbenzene 456.0581 0.4281 0.0000
Cyclopentane 517.7318 0.1808 0.1706 Naphthalene 371.4852 −0.3910 0.0000
vap
f (0) (T r ) and f (1) (T r ) are correlated to (1 − T r ), where as T r → 1, meters. Once the value of H nbp is calculated, it should be
H vap /RT c → 0. However, more accurate predictive methods divided by M to convert its unit from kJ/kmol to kJ/kg.
are developed in two steps. In the first step heat of vaporiza- Equation (7.56) with coefficients given in Table 7.10 can be
tion at normal boiling point, H vap , is calculated and then
nbp used for fractions with molecular weight range of 70–300 (∼T b
corrected to the desired temperature by a second correla- of 300–600 K) with accuracy of about 2% when tested against
tion. One of the most successful correlations for prediction 138 pure hydrocarbons. Application of the equation can be
vap vap
of H was proposed by Riedel [12]: extended up to 700 K with reasonable accuracy. Once H
nbp nbp
is determined, the Watson relation can be used to calculate
(7.54) H vap = 1.093RT c T br ln P c − 1.013 H vap at the desired temperature (T).
nbp
0.93 − T br
0.38

vap
where T br is the reduced boiling point (T b /T c ) and P c is the (7.57) H vap = H nbp 1 − T r
critical pressure in bars. The unit of H vap depends on the 1 − T br
nbp
units of R and T c . Later Chen and Vetere developed similar where T r and T br are the reduced temperature and reduced
correlations for calculation of H vap in terms of P c and T br boiling point, respectively. The same equation can be used to
nbp
[12]. For example, Chen correlation is in the following form: calculate H vap at any temperature when its value at one tem-
perature is available. As it was shown in Example 7.5, use of
(7.55) H vap 3.978T br − 3.958 + 1.555 ln P c Eqs. (7.54) and (7.57) predicts H vap of petroleum fractions
nbp = RT c T br --`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
1.07 − T br with good accuracy. Tsonopoulos et al. [18] modified the orig-
Although for certain pure compounds the Chen correlation inal Lee–Kesler correlation for calculation of heat of vapor-
is slightly superior to the Riedel method, but for practical ization of coal liquids and aromatics in the following form:
applications especially for petroleum fractions in which T c (7.58) ( H vap ) T r =0.8 = RT c (4.0439 + 5.3826ω)
and P c are calculated values, the Riedel equation is reasonably
vap
accurate. A more direct calculation of H for petroleum where R is 8.314 J/mol · K, T c is the critical temperature in
nbp vap
fractions is use of fraction’s bulk properties such as T b and kelvin, ω is the acentric factor, and H is the heat of va-
SG or other available parameters in an equation similar to porization at T = 0.8T c in J/mol. Equation (7.57) can be used
Eq. (2.38) [28]: to calculate H vap at temperatures other than T r = 0.8. An
vap
evaluation of various methods for estimation of H nbp of sev-
b c
(7.56) H vap = aθ θ
nbp 1 2 eral coal liquid samples is shown in Tables 7.11 and 7.12.
where H vap is in J/mol (or kJ/kmol) and constants a, b, and Basic calculated parameters are given in Table 7.11, while es-
nbp timated values of H vap from Riedel, Vetere, Riazi–Daubert,
c are given in Table 7.10 for a number of different input para- nbp
and Lee–Kesler are given in Table 7.12. In Table 7.11, M is
calculated from Eq. (2.51), which is recommended for heavy
TABLE 7.10—Coefficients of Eq. (7.56) for estimation of heat of fractions. If Eq. (2.50) were used to estimate M, the %AAD
vaporization of petroleum fractions at the normal boiling point [28]. for the four methods increase to 4.5, 3.2, 4.9, and 2.3, re-
vap b c spectively. Equation (2.50) is not applicable to heavy fractions
(7.56) H = aθ θ
nbp 1 2 (M > 300), which shows the importance of the characteriza-
vap
H nbp , J/mol θ 1 θ 2 A b c tion method used to calculate molecular weight of hydrocar-
vap
H T b , K SG 37.32315 1.14086 9.77089 × 10 −3
1,nbp bon fractions. Evaluations shown in Table 7.12 indicate that
H vap T b ,K I 39.7655 1.13529 0.024139 both the Riedel method and Eq. (7.56) predict heats of va-
2,nbp
H vap M I 5238.3846 0.5379 0.48021 porization with good accuracy despite their simplicity. For a
3,nbp coal liquid sample 5HC in Table 7.11, experimental data on

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