Page 82 - Characterization and Properties of Petroleum Fractions

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62 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
f V = SG V 0.347776/T

b 1/2 August 16, 2007 16:6 (2.94) ln T c =−0.58779 + 4.2009T b 0.08615 SG 0.04614
(2.84) + − 0.182421 + 2.248896/T 1/2 7 −2.3177 2.4853

b SG V (2.95) P c = 6.148341 × 10 T SG
b
2
◦2
(2.85) SG V = exp[4(SG − SG )] − 1 where T b and T c are in kelvin and P c is in bar. Comparing
values estimated from these correlations with the values from
Critical pressure
the original figures gives AAD of 2, 1, and 1.5% for M, T c , and
P c , respectively, as reported in Ref. [36]. In the literature these
(2.86) P c = P (T c /T ) × (V /V c )[(1 + 2 f P )/(1 − 2 f P )] 2 equations are usually referred as Winn or Sim–Daubert and
◦
◦
◦
c
c
c
are included in some process simulators. The original Winn

f P = SG P 2.53262 − 34.4321/T b 1/2 − 2.30193T b /1000 nomograph for molecular weight and some other properties
is given in Section 2.8.

+ − 11.4277 + 187.934/T 1/2
b + 4.11963T b /1000 SG P
(2.87) 2.5.1.7 Tsonopoulos Correlations
Based on the critical properties of aromatic compounds,
(2.88) SG P = exp[0.5(SG − SG)] − 1 Tsonopoulos et al. [34] proposed the following correlations
◦
for estimation of T c and P c for coal liquids and aromatic-rich
Molecular weight
fractions.
(2.89) ln(M) = (ln M )[(1 + 2 f M )/(1 − 2 f M )] 2
◦
log T c = 1.20016 + 0.61954(log T b )
10
10

f M = SG M χ + − 0.0175691 + 0.143979/T 1/2 SG M (2.96) + 0.48262(log SG) + 0.67365(log SG) 2

10
10
b
(2.90) log 10 P c = 7.37498 − 2.15833(log T b )
10

(2.91) χ = 0.012342 − 0.244541/T 1/2

(2.97) + 3.35417(log SG) + 5.64019(log SG) 2
10
10

b
where T b and T c are in kelvin and P c is in bar. These correla-
(2.92) SG M = exp[5(SG − SG)] − 1 tions are mainly recommended for coal liquid fractions and
◦
3
In the above relations T b and T c are in kelvin, V c is in cm /mol, they give average errors of 0.7 and 3.5% for the estimation of
and P c is in bar. One can see that these correlations should critical temperature and pressure of aromatic hydrocarbons.
be solved simultaneously because they are highly interrelated
to each other and for this reason relations for estimation of 2.5.2 Prediction of Critical Volume
M and V c based on this method are also presented in this part.
Critical volume, V c , is the third critical property that is not
directly used in EOS calculations, but is indirectly used to
Example 2.6—Estimate the molecular weight of n-eicosane
(C 20 H 42 ) from its normal boiling point using Eq. (2.49) and estimate interaction parameters (k ij ) needed for calculation
the Twu correlations. of mixture pseudocritical properties or EOS parameters as
will be discussed in Chapter 5. In some corresponding state
correlations developed to estimate transport properties of flu-
Solution—n-Eicosane is a normal paraffin whose molecular
weight and boiling point are given in Table 2.1 as M = 282.55 ids at elevated pressure, reduced density (V c /V) is used as the
correlating parameter and values of V c are required as shown
and T b = 616.93 K. Substituting T b in Eq. (2.49) gives M = --`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
282.59 (%AD = 0.01%). Using the Twu method, first an initial in Chapter 8. Critical volume is also used to calculate critical
guess is calculated through Eq. (2.79) as M = 238 and from compressibility factor, Z c , as shown by Eq. (2.8).
◦
iteration the final value of M calculated from Eq. (2.78) is 2.5.2.1 Riazi–Daubert Methods
◦
281.2 (%AD = 0.48%). Twu method for estimation of proper-
ties of hydrocarbons from other groups is shown later in the A simplified equation to calculate V c of hydrocarbons in the
next example. range of C 5 –C 20 is given by Eq. (2.38) as follows.
−4
(2.98) V c = 1.7842 × 10 T b 2.3829 SG −1.683
2.5.1.6 Winn–Mobil Method
3
in which V c is in cm /mol and T b is in kelvin. When evalu-
Winn [25] developed a convenient nomograph to estimate var- ated against more than 100 pure hydrocarbons in the carbon
ious physical properties including molecular weight and the range of C 5 –C 20 an average error of 2.9% was observed. This
pseudocritical pressure for petroleum fractions. Mobil [73] equation may be used up to C 35 with reasonable accuracy. For
proposed a similar nomograph for the estimation of pseudo- heavier hydrocarbons, V c is given by Eq. (2.46a) and in terms
critical temperature. The input data in both nomographs are of T b and SG is given as
boiling point (or K W ) and the specific gravity (or API gravity). 10 −3
As part of the API project to computerize the graphical meth- V c = 6.2 × 10 [exp(−7.58 × 10 T b − 28.5524SG
−2
ods for estimation of physical properties, these nomographs (2.99) + 1.172 × 10 T b SG)]T b 1.20493 SG 17.2074
were reduced to equation forms for computer applications by where V c is in cm /mol. Although this equation is recom-
3
Riazi [36] and were later reported by Sim and Daubert [74]. mended for hydrocarbons heavier than C 20 it may be used, if
These empirically developed correlations have forms similar necessary, for the range of C 5 –C 50 in which the AAD is about
to Eq. (2.38) and for M, T c , and P c are as follows.
2.5%. To calculate V c from other input parameters, Eqs. (2.40)
−5
(2.93) M = 2.70579 × 10 T 2.4966 SG −1.174 and (2.46b) with Tables 2.5 and 2.9 may be used.
b
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