Page 81 - Characterization and Properties of Petroleum Fractions

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2. CHARACTERIZATION AND PROPERTIES OF PURE HYDROCARBONS 61
where T b and T c are in kelvin and P c is in bar. In these equa-
tions attempts were made to keep internal consistency among included in some references [49]. However, the Twu correla-
tions although based on the same format as the KLS or LC
T c and P c that at P c equal to 1 atm, T c is coincided with nor- require input parameters of T b and SG and are applicable to
mal boiling point, T b . The correlations were recommended hydrocarbons beyond C 20 . For heavy hydrocarbons similar
by the authors for the molecular range of 70–700 (∼C 5 –C 50 ). to the approach of Lee–Kesler [12], Twu [30] used the crit-
However, the values of T c and P c for compounds with carbon ical properties back calculated from vapor pressure data to
numbers greater than C 18 used to develop the above correla- expand his data bank on the critical constants of pure hydro-
tions were not based on experimental evidence. carbon compounds. For this reason the Twu correlations have
found a wider range of application. The Twu correlations for
2.5.1.4 Cavett Method the critical properties, specific gravity, and molecular weight
Cavett [26] developed empirical correlations for T c and P c in of n-alkanes are as follows:
terms of boiling point and API gravity, which are still available T = T b (0.533272 + 0.34383 × 10 −3
◦
in some process simulators as an option and in some cases c −7 2 × T b −10 3
give good estimates of T c and P c for light to middle distillate + 2.52617 × 10 × T − 1.658481 × 10 × T b
b
)
petroleum fractions. (2.73) + 4.60773 × 10 24 × T −13 −1
b
−1
T c = 426.7062278 + (9.5187183 × 10 )(1.8T b − 459.67) (2.74) α = 1 − T b /T ◦
−4
− (6.01889 × 10 )(1.8T b − 459.67) 2 c
−3
− (4.95625 × 10 )(API)(1.8T b − 459.67) ◦ 1/2
P = (1.00661 + 0.31412α + 9.16106α
c
−7
(2.71) + (2.160588 × 10 )(1.8T b − 459.67) 3 (2.75) + 9.5041α + 27.35886α )
4 2
2
−6
+ (2.949718 × 10 )(API)(1.8T b − 459.67) 2
−8
2
3
14 −8
+ (1.817311 × 10 )(API )(1.8T b − 459.67) 2 V = (0.34602 + 0.30171α + 0.93307α + 5655.414α )
◦
c
(2.76)
−4
log(P c ) = 1.6675956 + (9.412011 × 10 )(1.8T b − 459.67)
3
−6
◦
− (3.047475 × 10 )(1.8T b − 459.67) 2 SG = 0.843593 − 0.128624α − 3.36159α − 13749.5α 12
−5
− (2.087611 × 10 )(API)(1.8T b − 459.67) (2.77)
−9
(2.72) + (1.5184103 × 10 )(1.8T b − 459.67) 3
2
−8
+ (1.1047899 × 10 )(API)(1.8T b − 459.67) 2 T b = exp(5.12640 + 2.71579β − 0.286590β − 39.8544/β
2
2
−8
− (4.8271599 × 10 )(API )(1.8T b − 459.67) (2.78) − 0.122488/β ) − 13.7512β + 19.6197β 2
2
+ (1.3949619 × 10 −10 )(API )(1.8T b − 459.67) 2 where T b is the boiling point of hydrocarbons in kelvin and
β = ln(M ) in which M is the molecular weight n-alkane ref-
◦
◦
In these relations P c is in bar while T c and T b are in kelvin and erence compound. Critical pressure is in bar and critical vol-
the API gravity is defined in terms of specific gravity through ume is in cm /mol. Data on the properties of n-alkanes from
3
Eq. (2.4). Terms (1.8T b − 459.67) come from the fact that the C 1 to C 100 were used to obtain the constants in the above rela-
unit of T b in the original relations was in degrees fahrenheit.
tions. For heavy hydrocarbons beyond C 20 , the values of the
critical properties obtained from vapor pressure data were
2.5.1.5 Twu Method for T c ,P c ,V c , and M
used to obtain the constants. The author of these correla-
Twu [30] initially correlated critical properties (T c , P c , V c ), tions also indicates that there is internal consistency between
specific gravity (SG), and molecular weight (M)of n-alkanes T c and P c as the critical temperature approaches the boiling
to the boiling point (T b ). Then the difference between spe- point. Equation (2.78) is implicit in calculating M from T b .To
◦
cific gravity of a hydrocarbon from other groups (SG) and solve this equation by iteration a starting value can be found
specific gravity of n-alkane (SG ) was used as the second pa- from the following relation:
◦
rameter to correlate properties of hydrocarbons from differ-
ent groups. This type of correlation, known as a perturbation (2.79) M = T b /(5.8 − 0.0052T b )
◦
expansion, was first introduced by Kesler–Lee–Sandler (KLS)
[71] and later used by Lin and Chao [72] to correlate critical For other hydrocarbons and petroleum fractions the relation
properties of hydrocarbons using n-alkane as a reference fluid for the estimation of T c , P c , V c , and M are as follows:
and the specific gravity difference as the correlating param- Critical temperature
eter. However, KLS correlations did not find practical appli- ◦ 2
c
cation because they defined a new third parameter similar to (2.80) T c = T [(1 + 2 f T )/(1 − 2 f T )]
the acentric factor which is not available for petroleum mix-

f T = SG T − 0.27016/T 1/2
tures. Lin and Chao (LC) correlated T c , ln(P c ), ω, SG, and T b b
of n-alkanes from C 1 to C 20 to molecular weight, M. These (2.81) + 0.0398285 − 0.706691/T 1/2 SG T

properties for all other hydrocarbons in the same molecular b
weight were correlated to the difference in T b and SG of the ◦
substance of interest with that of n-alkane. Therefore, LC cor- (2.82) SG T = exp[5(SG − SG)] − 1
relations require three input parameters of T b , SG, and M for Critical volume
each property. Each correlation for each property contained
as many as 33 numerical constants. These correlations are (2.83) V c = V [(1 + 2 f V )/(1 − 2 f V )] 2
◦
c
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