Page 342 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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322 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
TABLE 7.8—Constants for estimation of heat capacity from refractive index (Eq. 7.46).
C P /R = (a 1 M + b 1 )[I/(1 − I)] + c 1 M + d 1
No. of
Group State Carbon range Temp. range, C a 1 b 1 c 1 d 1 data points AAD% MAD%
◦
n-Alkanes Liquid C 5 –C 20 −15–344 −0.9861 −43.692 0.6509 5.457 225 0.89 1.36
1-Alkenes Liquid C 5 –C 20 −60–330 −1.533 40.357 0.836 −21.683 210 1.5 5.93
n-Alkyl-cyclopentane Liquid C 5 –C 20 −75–340 −1.815 56.671 0.941 −28.884 225 1.05 2.7
n-Alkyl-cyclohexane Liquid C 6 –C 20 −100–290 −2.725 165.644 1.270 −68.186 225 1.93 2.3
n-Alkyl-benzene Liquid C 6 –C 20 −250–354 −1.149 4.357 0.692 −3.065 225 1.06 4.71
n-Alkanes Solid C 5 –C 20 −180–3 −1.288 −66.33 0.704 14.678 195 2.3 5.84
AAD%: Average absolute deviation percent. MAD%: Maximum absolute deviation percent. Coefficients are taken from Ref. [27]. Data source: DIPPR [10].
transferred to a system at constant pressure is the same as the on data generated from correlations provided in Ref. [10].
vap
enthalpy change. This amount of heat (Q) is called (latent) Specific value of H nbp (kJ/g) decreases as carbon number of
heat of phase change. hydrocarbon (or molecular weight) increases, while the molar
values (kJ/mol) increases with increase in the carbon number
Q (latent heat) = H (phase transition) vap
or molecular weight. In the API-TDB [9], H T for pure com-
(7.47) at constant T and P pounds is correlated to temperature in the following form:
The term latent is normally not used. Since during phase tran- (7.50) H vap = A (1 − T r) B+CT r
sition, temperature is also constant, thus the entropy change T
is given as where coefficients A, B, and C for a large number of com-
pounds are provided [9]. For most hydrocarbons coefficient
H (phase change)
S (phase change) = C is zero [9]. For some compounds values of A, B, and C are
T (phase change) given in Table 7.9 as provided in the API-TDB [9].
(7.48) at constant T and P The most approximate and simple rule to calculate H vap is
the Trouton’s rule, which assumes S vap at the normal boiling
Heat of fusion was discussed in Section 6.6.5 (Eq. 6.157) and point (T b ) is roughly 10.5R (∼87.5 J/mol · K) [22]. In some
is usually needed in calculations related to cloud point and references value of 87 or 88 is used instead or 87.5. Thus,
precipitation of solids in petroleum fluids (Section 9.3.3). In from Eq. (7.48)
this section calculation methods for heat of vaporization of
vap
petroleum fractions are discussed. (7.51) H nbp = 87.5T b
Heat of vaporization ( H vap ) can be calculated in the tem- vap
perature range from triple point to the critical point. Thermo- where H nbp is the heat of vaporization at the normal boil-
dynamically, H vap is defined by Eq. (6.98), which can be ing point in J/mol and T b is in K. This equation is not valid
rearranged as for certain compounds and temperature ranges. The accu-
racy of this equation can be improved substantially by taking
L
V
ig sat
ig sat
(7.49) H vap = (H − H ) − (H − H ) S vap as a function of T b , which gives the following relation for
nbp
vap
L
ig sat
ig sat
V
where (H − H ) and (H − H ) can be both calculated H nbp [22]:
from a generalized correlation or a cubic equation of state at (7.52) H vap = RT b (4.5 + ln T b)
T and corresponding P sat (i.e., see Example 7.7). At the criti- nbp
V
L
cal point where H and H become identical, H vap becomes where Ris 8.314 J/mol · K. This equation at T b = 400 K reduces
zero. For several compounds, variation of H vap versus tem- to Eq. (7.51). In general, H vap can be determined from a
perature is shown in Fig. 7.14. The figure is constructed based vapor pressure correlation through Eq. (6.99).
H vap dln P r sat
(7.53) = Z vap
500 −
RT c d (1/T r)
n-Pentane sat
n-Decane where P r is the reduced vapor (saturation) pressure at re-
Heat of Vaporization, kj/kg - 300 approximated as Z . Furthermore, at low pressure if the gas
400
vap
V
duced temperature of T r . Z
is the difference between Z
n-Butylbenzene
vap
V
L
L
can be
and Z where at low pressures Z Z and Z
V
= Z = 1. Under these condi-
is assumed ideal, then Z
vap
V
tions, use of Eq. (6.101) in the above equation would result in
200
= RB, where B is the coefficient in Eq. (6.101). Obvi-
vap
H
ously, because of the assumptions made to derive Eq. (6.101),
this method of calculation of H
100
vap
is very approximate. More
accurate predictive correlations for H vap can be obtained by
using a more accurate relation for the vapor pressure such as
0
Eqs. (7.17) and (7.18).
-200 -100 0 100 200 300 400 500
There are a number of generalized correlations for pre-
Temperature, C vap
diction of H based on the principle of corresponding
FIG. 7.14—Enthalpy of vaporization of several states theory. Pitzer correlated H vap /RT c to T r through acen-
hydrocarbons versus temperature. tric factor ω similar to Eq. (7.17). In such correlations,
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