Page 247 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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TABLE 5.17—Mixing rules for MRK EOS parameters (Eqs. (5.38)
TABLE 5.15—Evaluation of various EOS for prediction of liquid
density of heavy hydrocarbons [70]. 17:42 5. PVT RELATIONS AND EQUATIONS OF STATE 227
and (5.137)–(5.140)).
%AAD ! ! j x i x j T 2 /P cij 1/2
i
No. of T cm = ! ! cij T cij = T ci T c j 1 − k ij
Compound data points MRK RK SRK PR i j x i x j T cij /P cij
n-Heptane (n-C 7 ) 35 0.6 12.1 10.5 1.4 ! ! j x i x j T cij /P cij 8T cij
2
i
n-Nonane (n-C 9 ) 35 0.6 15.5 13.4 3.4 P cm = ! ! 2 P cij = (T cii /P cii ) 1/3 +(T c jj /P c jj) 1/3 3

n-Undecane (n-C 11 ) 35 1.7 18.0 15.5 5.4 i j x i x j T cij /P cij
n-Tridecane (n-C 13 ) 30 2.8 20.3 17.7 7.9 1/3 1/3 3

n-Heptadecane (n-C 17 ) 30 1.2 27.3 24.8 16.0 ! ! r ii +r jj
r m = i j x i x j r ij r ij = 8
n-Eicosane (n-C 20 ) 20 2.8 29.5 26.7 18.2
n-Triacontane (n-C 30 ) 20 0.6 41.4 39.4 32.5
n-Tetracontane (n-C 40 ) 20 4.1 50.9 49.4 44.4
Total 225 1.6 24.3 22.1 13.3 Predicted liquid densities from SRK and PR equations (Exam-
MRK: Eqs. (5.38), (5.138), and (5.141). Note none of these data were used ple 5.2) deviate from experimental data by +31.5 and 17.2%,
in development of Eq. (5.139). respectively. Advantage of MRK over other cubic equations
for liquid density is greater for heavier compounds as shown
interesting point about this equation is that it can be used up in Table 5.15.
to C 40 for density estimations. Obviously this equation is not
designed for VLE calculations as no VLE data were used to
develop Eq. (5.139). Prediction of Z c from MRK EOS is shown This modified version of RK EOS is developed only for den-
in Table 5.14. Evaluation of MRK with PR and SRK equations sity calculation of hydrocarbon systems and their mixtures.
for prediction of liquid density of heavy hydrocarbons is given It can be used directly to calculate density of petroleum frac-
in Table 5.15. Data sources for these compounds are given in tions, once M, d 20 , n 20 , T c , and P c are calculated from meth-
Table 5.14. Overall results for prediction of density for both ods discussed in Chapters 2 and 3. Moreover parameter r can
be accurately estimated for heavy fractions, while prediction
liquid and gaseous hydrocarbon compounds from C 1 to C 40
is shown in Table 5.15. The overall error for the MRK EOS of acentric factor for heavy compounds is not reliable (see
for more than 1700 data points is about 1.3% in comparison Figs. 2.20–2.22). The main characteristic of this equation is its
with 4.6 for PR and 7.3 for SRK equations. application to heavy hydrocarbons and undefined petroleum
To apply this EOS to defined mixtures a set of mixing rules fractions. The fact that Eq. (5.139) was developed based on
are given in Table 5.17 [70]. For petroleum fractions parame- data for hydrocarbons from C 2 to C 8 and it can well be used up
ters can be directly calculated for the mixture. For binary and to C 40 shows its extrapolation capability. The linear relation
that exists between 1/β and parameter r makes its extrapo-
ternary liquid mixtures containing compounds from C 1 to C 20
an average error of 1.8% was obtained for 200 data points [70]. lation to heavier hydrocarbons possible. In fact it was found
For the same dataset RK, SRK, and PR equations gave errors that by changing the functionality of 1/β with r, better pre-
of 15, 13, and 6%, respectively. Further characteristics and diction of density is possible but the relation would no longer
evaluations of this modified RK EOS are discussed by Riazi be linear and its extrapolation to heavier compounds would
and Roomi [71]. Application of this method in calculation of be less accurate. For example, for C 17 and C 18 , if the constant
density is shown in the following example. 0.02 in Eq. (5.139) is replaced by 0.018, the %AAD for these
compounds reduces from 2 to 0.5%.
Analysis of various EOS shows that use of refractive index
Example 5.9—Repeat Example 5.2 for prediction of liquid
and vapor density of n-octane using MRK EOS. in obtaining constants of an EOS is a promising approach.
Further work in this area should involve use of saturation
pressure in addition to liquid density data to obtain relations
Solution—The MRK EOS is to use Eq. (5.38) with parameters
obtained from Eqs. (5.139)–(5.141). The input data needed to for EOS parameters that would be suitable for both liquid
use MRK EOS are T c , P c , and r. From Example 5.2, T c = 568.7 density and VLE calculations.
K, P c = 24.9 bar, and T r = 0.9718 K. From Table 5.14 for
−4
n-C 8 , r = 5.608. From Eq. (5.139), β = 1.5001 × 10 . From
3 5.10 SUMMARY AND CONCLUSIONS
Eq. (5.139), b = 150.01 cm /mol and from Eq. (5.141), a =
2
7
6
3.837982 × 10 cm /mol . Solving Eq. (5.42) with u 1 = 1 and
u 2 = 0 (Table 5.1) and in a way similar to that performed in In this chapter the fundamental of PVT relations and math-
3
L
V
Example 5.2 we get V = 295.8 and V = 1151.7cm /mol. De- ematical EOS are presented. Once the PVT relation for a
viations of predicted values from experimental data are –2.7% fluid is known various physical and thermodynamic proper-
and –5.3% for liquid and vapor molar volume, respectively. ties can be determined as discussed in Chapters 6 and 7. In-
termolecular forces and their importance in property predic-
TABLE 5.16—Comparison of various EOSs for prediction of tions were discussed in this chapter. For light hydrocarbons
density of liquid and gaseous hydrocarbons. two-parameter potential energy relations such as LJ describes
%AAD
No. of the intermolecular forces and as a result two-parameter EOS
Compound data points MRK RK SRK PR are sufficient to describe the PVT relation for such fluids. It is
C 1 –C a 8 1520 1.3 4.9 5.1 3.3 shown that EOS parameters can be directly calculated from
C 7 –C b 225 1.6 24.3 22.1 13.3
40 the potential energy relations. Criteria for correct EOS are
Total 1745 1.33 7.38 7.28 4.59 given so that validity of any EOS can be analyzed. Three cat-
a These are the compounds that have been marked as bold in Table 5.14 and
are used in development of Eq. (5.139). egory of EOSs are presented in this chapter: (1) cubic type,
b These are the same compounds as in Table 5.15. (2) noncubic type, and (3) generalized correlations.
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