Page 133 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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3. CHARACTERIZATION OF PETROLEUM FRACTIONS 113
distribution model that reduces the mixture into a number of
The values of T ◦ and SG o determined from regression of
pseudocomponents with known characterization parameters data through Eq. (3.35) do not match well with the exper-
will be discussed in detail in Chapter 4. However, a simpler imental initial values. This is due to the maximizing value
approach based on the use of TBP curve is outlined in Ref. of RS with data used in the regression analysis. Actually
[32]. In this approach the mixture property is calculated from one can imagine that the actual initial values are lower than
the following relation: experimentally measured values due to the difficulty in such
measurements. However, these initial values do not affect
subsequent calculations. Predicted values at all other points
1
(3.39) θ = θ(x)dx from 5 up to 95% are consistent with the experimental values.
0 From calculated values of SG ◦ , A, and B for the SG curve,
in which θ is the physical property of mixture and θ(x) is the one can determine the mixture SG for the whole fraction
value of property at point x on the distillation curve. This through use of Eqs. (3.37) and (3.38). For SG, B = 7.1957 and
approach may be applied to any physical property. The in- from Eq. (3.38), (1 + 1/ B) = 0.9355. From Eq. (3.37) we
1

0.07161 1/7.1957
tegration should be carried out by a numerical method. The get SG ∗ av = 7.1957 1 + 7.1957 = 0.5269 × 0.9355 =
fraction is first divided into a number of pseudocomponents 0.493. Therefore, for the mixture: SG av = 0.5(1 + 0.493) =
along the entire range of distillation curve with known boiling 0.746. Comparing with experimental value of 0.74, the
points and specific gravity. Then for each component physi- percent relative deviation (%D) with experimental value is
cal properties are calculated from methods of Chapter 2 and 0.8%. In Chapter 4 another method based on a distribution
finally the mixture properties are calculated through a sim- function is introduced that gives slightly better prediction
ple mixing rule. The procedure is outlined in the following for the density of wide boiling range fractions and crude
example. oils.
To calculate a mixture property such as molecular weight,
the mixture is divided to some narrow pseudocomponents,
Example 3.8—For a low boiling naphtha, TBP curve is pro-
vided along with the density at 20 C as tabulated below [32]. N P . If the mixture is not very wide such as in this exam-
◦
ple, even N P = 5 is sufficient, but for wider fractions the mix-
Estimate specific gravity and molecular weight of this fraction ture may be divided to even larger number of pseudocompo-
using the wide boiling range approach. Compare the calcu-
lated results with the experimental values reported by Lenior nents (10, 20, etc.). If N P = 5, then values of T and SG at x =
0, 0.2, 0.4, 0.6, 0.8, and 0.99 are evaluated through Eq. (3.35)
and Hipkin and others [1, 11, 32] as SG = 0.74 and M = 120.
and parameters determined above. Value of x = 0.99 is used
instead of x = 1 for the end point as Eq. (3.35) is not defined
vol% 0 (IBP) 5 10 20 30 50 70 90 95 at x = 1. At every point, molecular weight, M, is determined
TBP, K 283.2 324.8 348.7 369.3 380.9 410.4 436.5 467.6 478.7 from methods of Chapter 2. In this example, Eq. (2.50) is quite
d 20 , g/cm 3 ... 0.654 0.689 0.719 0.739 0.765 0.775 0.775 0.785
accurate and may be used to calculate M since all compo-
nents in the mixture have M < 300 (∼N C < 20) and are within
Solution—For this fraction the 10–90% slope based on TPB the range of application of this method. Equation (2.50) is
curve is about 1.49 C/%. This value is slightly above the slope M = 1.6604 × 10 T 2.1962 SG −1.0164 . Calculations are summa-
◦
−4
b
based on the ASTM D 86 curve but still indicates how wide rized in the following table.
the fraction is. For this sample based on the ASTM distilla-
tion data [1], the 10–90% slope is 1.35 C/%, which is above
◦
the value of 0.8 specified for narrow fractions. To use the x T b ,K SG M
method by Riazi–Daubert [32] for this relatively wide frac- 0 0.2 240.0 0.500 56.7
99.8
367.1
0.718
tion, first distribution functions for both boiling point and 0.4 396.4 0.744 114.0
specific gravity should be determined. We use Eqs. (3.35)– 0.6 421.0 0.764 126.7
(3.38) to determine the distribution functions for both prop- 0.8 448.4 0.785 141.6
erties. The molecular weight, M, is estimated for all points on 0.99 511.2 0.828 178.7
the curve through appropriate relations in Chapter 2 devel-
oped for pure hydrocarbons. The value of M for the mixture The trapezoidal rule for integration is quite accurate to
then may be estimated from a simple integration over the en-
1 estimate the molecular weight of the mixture. M av = (1/5) ×

tire range of x as given by Eq. (3.39): M av = M(x)dx, where
0 [(56.7 + 178.7)/2 + (99.8 + 114 + 126.7 + 141.6 + 178.7)] =
M(x) is the value of M at point x determined from T b (x) and 119.96 = 120. This is exactly the same as the experimental
∼
SG(x). M av is the average molecular weight of the mixture. value of molecular weight for this fraction [1, 11].
For this fraction values of densities given along the distilla- If the whole mixture is considered as a single pseudocom-
tion curve are at 20 C and should be converted to specific ponent, Eq. (2.50) should be applied directly to the mixture
◦
gravity at 15.5 C (60 F) through use of Eq. (2.112) in Chap- using the MeABP and SG of the mixture. For this fraction
◦
◦
ter 2: SG = 0.9915d 20 + 0.01044. Parameters of Eq. (3.35) for the Watson K is given as 12.1 [1]. From Eq. (3.13) using
both temperature and specific gravity have been determined experimental value of SG, average boiling point is calcu-
and are given as following. lated as T b = (12.1 × 0.74) /1.8 = 398.8 K. From Eq. (2.50),
3
the mixture molecular weight is 116.1, which is equivalent to
Parameters in Eq. (3.35) T ◦ ,K SG ◦ A B RS %D =−3.25%. For this sample, the difference between 1 and
TBP curve 240 1.41285 3.9927 0.996 5 pseudocomponents is not significant, but for wider fraction
SG curve 0.5 0.07161 7.1957 0.911 the improvement of the proposed method is much larger.
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