Page 85 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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2. CHARACTERIZATION AND PROPERTIES OF PURE HYDROCARBONS 65
Edmister method:
For T br ≤ 0.8(≤C 20 ∼ M ≤ 280)
1.3
ω = T br P c
− ln P c /1.01325 − 5.92714 + 6.09648/T br + 1.28862 ln T br − 0.169347T br 6 (2.109) ω = 0.5899 1 − T 1.3 × log 1.01325 − 1
15.2518 − 15.6875/T br − 13.4721 ln T br + 0.43577T br 6 br
(2.105) To compare this equation with the Edmister equation, the
factor (3/7), which is equivalent to 0.42857 in Eq. (2.108), has
where P c is in bar and T br is the reduced boiling point which been replaced by 0.58990 and the exponent of T br has been
is defined as changed from 1 to 1.3 in Eq. (2.109).
(2.106) T br = T b /T c One can realize that accuracy of these methods mainly de-
pends on the accuracy of the input parameters. However, for
and Kesler–Lee [12] proposed the following relation for T br > pure compounds in which experimental data on pure hydro-
0.8(∼>C 20 ∼ M > 280): carbons are available the Lee–Kesler method, Eq. (2.105),
2 gives an AAD of 1–1.3%, while the Edmister method gives
ω =−7.904 + 0.1352K W − 0.007465K + 8.359T br
W higher error of about 3–3.5%. The Korsten method is new
(2.107) + (1.408 − 0.01063K W )/T br and it has not been extensively evaluated for petroleum frac-
tions, but for pure hydrocarbons it seems that it is more ac-
in which K W is the Watson characterization factor defined by
Eq. (2.13). Equation (2.105) may also be used for compounds curate than the Edmister method but less accurate than the
heavier than C 20 (T br > 0.8) without major error as shown in Lee–Kesler method. Generally, the Edmister method is not
the example below recommended for pure hydrocarbons and is used to calcu-
late acentric factors of undefined petroleum fractions. For
2.5.4.2 Edmister Method petroleum fractions, the pseudocritical temperature and pres-
sure needed in Eqs. (2.105) and (2.108) must be estimated
The Edmister correlation [76] is developed on the same basis
as Eq. (2.105) but using a simpler two-parameter equation from methods discussed in this section. Usually, when the
for the vapor pressure derived from Clapeyron equation (see Cavett or Winn methods are used to estimate T c and P c ,
Eq. 7.15 in Chapter 7). the acentric factor is calculated by the Edmister method.
All other methods for the estimation of critical properties
3 T br P c use Eq. (2.105) for calculation of the acentric factor. Equa-

(2.108) ω = × × log 10 − 1
7 1 − T br 1.01325 tion (2.107) is applicable for heavy fractions and a detailed
evaluation of its accuracy is not available in the literature. Fur-
where log 10 is the logarithm base 10, T br is the reduced boiling ther evaluation of these methods is given in Section 2.9. The
point, and P c is the critical pressure in bar. As is clear from methods of calculation of the acentric factor for petroleum
Eqs. (2.105) and (2.108), these two methods require the same fractions are discussed in the next chapter.
three input parameters, namely, boiling point, critical temper-
ature, and critical pressure. Equations (2.105) and (2.108) are Example 2.8—Critical properties and acentric factor of
directly derived from vapor pressure correlations discussed in n-hexatriacontane (C 36 H 74 ) are given as by DIPPR [20] as
Chapter 7.
T b = 770.2K,SG = 0.8172, T c = 874.0K, P c = 6.8 bar, and ω =
2.5.4.3 Korsten Method 1.52596. Estimate the acentric factor of n-hexatriacontane us-
ing the following methods:
The Edmister method underestimates acentric factor for
heavy compounds and the error tends to increase with in- a. Kesler–Lee method with T c , P c from DIPPR
creasing molecular weight of compounds because the vapor b. Lee–Kesler method with T c , P c from DIPPR
pressure rapidly decreases. Most recently Korsten [77] mod- c. Edmister method with T c , P c from DIPPR
ified the Clapeyron equation for vapor pressure of hydro- d. Korsten method with T c , P c from DIPPR
carbon systems and derived an equation very similar to the e. Riazi–Sahhaf correlation, Eq. (2.42)
TABLE 2.12—Prediction of acentric factor of n-hexatriacontane from different
methods (Example 2.8).
Method for %
Part Method for ω T c & P c a T c, K P c, bar Calc. ω Rel. dev.
a Kesler–Lee DIPPR 874.0 6.8 1.351 −11.5
b Lee–Kesler DIPPR 874.0 6.8 1.869 22.4
c Edmister DIPPR 874.0 6.8 1.63 6.8
d Korsten DIPPR 874.0 6.8 1.731 13.5
e Riazi–Sahhaf not needed ··· ··· 1.487 −2.6
f Korsten R-D-80 885.8 7.3 1.539 0.9
g Lee–Kesler API 879.3 7.4 1.846 21.0
h Korsten Ext. RD 870.3 5.54 1.529 0.2
i Lee–Kesler R-S 871.8 5.93 1.487 −2.6
j Edmister Winn 889.5 7.6 1.422 −6.8
k Kesler–Lee L-K 935.1 5.15 0.970 −36.4
l Lee–Kesler Twu 882.1 6.03 1.475 −3.3
a R-D-80: Eqs. (2.63) and (2.64); API: Eqs. (2.65) and (2.66); Ext. RD: Eqs. (2.67) and (2.68);
R-S: Eqs. (2.42) and (2.43); Winn: Eqs. (2.94) and (2.95); L-K: Eqs. (2.69) and (2.70);
Twu: Eqs. (2.80) and (2.86).

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