Page 88 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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68 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
of −0.0004 in Eq. (2.118)) as a function of n 20 rather than
a constant. Another approach to estimate refractive index determined the atomic HC ratio can be calculated from their
definitions as described in Section 2.1.18:
at temperatures other than 20 C is to assume that specific
◦
refraction is constant for a given hydrocarbon: (2.122) HC (atomic ratio) = 11.9147
CH(weight ratio)
I T I 20
(2.119) Specific refraction = = = constant
d T d 20 Example 2.9—Estimate the values of CH (weight) and HC
where I 20 is the refractive index parameter at 20 C and I T is its (atomic) ratios for n-tetradecylbenzene (C 20 H 34 ) from Eqs.
◦
value at temperature T. Similarly d T is density at temperature (2.120) and (2.121) and compare with the actual value. Also
T. In fact the value of specific refraction is the same at all tem- draw a graph of CH values from C 6 to C 50 for the three homol-
peratures [38]. If I 20 , d 20 , and d T are known, then I T can be esti- ogous hydrocarbon groups from paraffins, naphthenes, and
mated from the above equation. Value of n T can be calculated aromatics based on Eq. (2.121) and actual values.
from I T and Eq. (2.114). Equation (2.119) has the same accu-
racy as Eq. (2.118), but at the temperatures far from the refer- Solution—The actual values of CH weight and HC
ence temperature of 20 C accuracy of both methods decrease. atomic ratios are calculated from the chemical formula
◦
Because of simplicity, Eq. (2.118) is recommended for calcu- and Eq. (2.122) as CH = (20 × 12.011)/(34 × 1.008) = 7.01,
lation of refractive index at different temperatures. It is obvi- HC (atomic) = 34/20 = 1.7. From Table 2.1, for n-tetradecyl-
ous that the reference temperature in both Eqs. (2.118) and benzene (C 20 H 34 ), T b = 627 K and SG = 0.8587. Substitut-
(2.119) can be changed to any desired temperature in which ing these values into Eq. (2.120) gives CH = 7.000, and from
refractive index is available. Refractive index is also related to Eq. (2.122) atomic HC ratio = 1.702. The error from
another property called dielectric constant, ε, which for non- Eq. (2.134) is %D = 0.12%. Equation (2.121) gives CH =
2
polar compounds at any temperature is ε = n . For example, 6.998, which is nearly the same as the value obtained from --`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
at temperature of 20 C, a paraffinic oil has dielectric constant Eq. (2.120) with the same error. Similarly CH values are cal-
◦
2
of 2.195 and refractive index of 1.481 (n = 2.193). Dielectric culated by Eq. (2.121) for hydrocarbons ranging from C 6 to
constants of petroleum products may be used to indicate the C 50 in three homologous hydrocarbon groups and are shown
presence of various constituents such as asphaltenes, resins, with actual values in Fig. 2.10.
etc. [11]. However, for more complex and polar molecules
such as multiring aromatics, this simple relation between ε 2.6.4 Prediction of Freezing/Melting Point
2
and n is not valid and they are related through dipole mo-
ment. Further discussion on the methods of estimation of For pure compounds, the normal freezing point is the same
refractive index is given by Riazi and Roomi [37]. as the melting point, T M . Melting point is mainly a param-
eter that is needed for predicting solid–liquid phase behav-
ior, especially for the waxy oils as shown in Chapter 9. All
2.6.3 Prediction of CH Weight Ratio
attempts to develop a generalized correlation for T M in the
Carbon-to-hydrogen weight ratio as defined in Section 2.1.18 form of Eq. (2.38) have failed. However, Eq. (2.42) developed
is indicative of the quality and type of hydrocarbons present by Riazi and Sahhaf for various homologous hydrocarbon
in a fuel. As will be shown in Chapter 3 from the knowledge groups can be used to estimate melting or freezing point of
of CH value, composition of petroleum fractions may be es- pure hydrocarbons from C 7 to C 40 with good accuracy (error
timated. CH value is also related to carbon residues as it is of 1–1.5%) for practical calculations [31]. Using this equation
discussed in the next chapter. For hydrocarbons with molec- with appropriate constants in Table 2.6 gives the following
ular weight in the range of 70–300, the relations to estimate equations for predicting the freezing point of n-alkanes (P),
CH values are given through Eq. (2.40) and Table 2.5. In terms n-alkycyclopentanes (N), and n-alkybenzenes (A) from molec-
of T b and SG the relation is also given by Eq. (2.120) which ular weight.
is also recommended for use in prediction of composition of 0.47
petroleum fractions [78]. (2.123) T MP = 397 − exp(6.5096 − 0.14187M )
−2
CH = 3.4707 exp 1.485 × 10 T b + 16.94SG 2/3

(2.124) T MN = 370 − exp(6.52504 − 0.04945M )
−2
(2.120) −1.2492 × 10 T b SG T −2.725 SG −6.798
b
where T b is in kelvin. The above equation was used to extend (2.125) T MA = 395 − exp(6.53599 − 0.04912M 2/3 )
its application for hydrocarbons from C 6 to C 50 .
where T M is in kelvin. These equations are valid in the car-
−3
CH = 8.7743 × 10 −10
exp 7.176 × 10 T b + 30.06242SG bon ranges of C 5 –C 40 ,C 7 –C 40 , and C 9 –C 40 for the P, N, and

−3
(2.121) −7.35 × 10 T b SG T −0.98445 SG −18.2753 A groups, respectively. In fact in wax precipitation linear
b hydrocarbons from C 1 to C 15 as well as aromatics are ab-
where T b is in kelvin. Although this equation was developed sent, therefore there is no need for the melting point of very
based on data in the range of C 20 –C 50 , it can also be used light hydrocarbons [64]. Equation (2.124) is for the melt-
for lower hydrocarbons and it gives AAD of 2% for hydrocar- ing point of n-alkylcyclopentanes. A similar correlation for
bons from C 20 to C 50 . Most of the data used in the develop- n-alkylcyclohexanes is given by Eq. (2.42) with constants in
ment of this equation are from n-alkanes and n-alkyl mono- Table 2.6. In Chapter 3, these correlations will be used to es-
cyclic naphthenic and aromatic compounds. Estimation of timate freezing point of petroleum fractions.
CH weight ratio from other input parameters is possible Won [79] and Pan et al. [63] also proposed correlations
through Eq. (2.40) and Table 2.5. Once CH weight ratio is for the freezing points of hydrocarbon groups. The Won

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