Page 264 - Characterization and Properties of Petroleum Fractions - M.R. Riazi
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244 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
(0)
TABLE 6.6—Values of φ
P r for use in Eq. (6.59).
T r 0.01 0.05 0.1 0.2 0.4 0.6 0.8 1 1.2 1.5 2 3 5 7 10
0.30 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.35 0.0094 0.0007 0.0009 0.0002 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.40 0.0272 0.0055 0.0028 0.0014 0.0007 0.0005 0.0004 0.0003 0.0003 0.0003 0.0002 0.0002 0.0002 0.0002 0.0003
0.45 0.1921 0.0266 0.0195 0.0069 0.0096 0.0025 0.0020 0.0016 0.0014 0.0012 0.0010 0.0008 0.0008 0.0009 0.0012
0.50 0.4529 0.0912 0.0461 0.0295 0.0122 0.0085 0.0067 0.0055 0.0048 0.0041 0.0034 0.0028 0.0025 0.0027 0.0034
0.55 0.9817 0.2492 0.1227 0.0625 0.0925 0.0225 0.0176 0.0146 0.0127 0.0107 0.0089 0.0072 0.0063 0.0066 0.0080
0.60 0.9840 0.5989 0.2716 0.1984 0.0718 0.0497 0.0986 0.0321 0.0277 0.0234 0.0193 0.0154 0.0132 0.0135 0.0160
0.65 0.9886 0.9419 0.5212 0.2655 0.1974 0.0948 0.0798 0.0611 0.0527 0.0445 0.0364 0.0289 0.0244 0.0245 0.0282
0.70 0.9908 0.9528 0.9057 0.4560 0.2960 0.1626 0.1262 0.1045 0.0902 0.0759 0.0619 0.0488 0.0406 0.0402 0.0453
0.75 0.9931 0.9616 0.9226 0.7178 0.3715 0.2559 0.1982 0.1641 0.1413 0.1188 0.0966 0.0757 0.0625 0.0610 0.0673
0.80 0.9931 0.9683 0.9354 0.8730 0.5445 0.9750 0.2904 0.2404 0.2065 0.1738 0.1409 0.1102 0.0899 0.0867 0.0942
0.85 0.9954 0.9727 0.9462 0.8933 0.7594 0.5188 0.4018 0.3319 0.2858 0.2399 0.1945 0.1517 0.1227 0.1175 0.1256
0.90 0.9954 0.9772 0.9550 0.9099 0.8204 0.6829 0.5297 0.4375 0.3767 0.3162 0.2564 0.1995 0.1607 0.1524 0.1611
0.95 0.9954 0.9817 0.9616 0.9226 0.8472 0.7709 0.6668 0.5521 0.4764 0.3999 0.3251 0.2523 0.2028 0.1910 0.2000
1.00 0.9977 0.9840 0.9661 0.9333 0.8690 0.8035 0.7379 0.6668 0.5781 0.8750 0.3972 0.3097 0.2483 0.2328 0.2415
1.05 0.9977 0.9863 0.9705 0.9441 0.8872 0.8318 0.7762 0.7194 0.6607 0.5728 0.4710 0.3690 0.2958 0.2773 0.2844
1.10 0.9977 0.9886 0.9750 0.9506 0.9016 0.8531 0.8072 0.7586 0.7112 0.6412 0.5408 0.4285 0.3451 0.3228 0.3296
1.15 0.9977 0.9886 0.9795 0.9572 0.9141 0.8730 0.8318 0.7907 0.7499 0.6918 0.6026 0.4875 0.3954 0.3690 0.3750
1.20 0.9977 0.9908 0.9817 0.9616 0.9247 0.8892 0.8531 0.8166 0.7834 0.7328 0.6546 0.5420 0.4446 0.4150 0.4198
1.30 0.9977 0.9931 0.9863 0.9705 0.9419 0.9141 0.8872 0.8590 0.8318 0.7943 0.7345 0.6383 0.5383 0.5058 0.5093
1.40 0.9977 0.9931 0.9886 0.9772 0.9550 0.9333 0.9120 0.8892 0.8690 0.8395 0.7925 0.7145 0.6237 0.5902 0.5943
1.50 1.0000 0.9954 0.9908 0.9817 0.9638 0.9462 0.9290 0.9141 0.8974 0.8730 0.8375 0.7745 0.6966 0.6668 0.6714
1.60 1.0000 0.9954 0.9931 0.9863 0.9727 0.9572 0.9441 0.9311 0.9183 0.8995 0.8710 0.8222 0.7586 0.7328 0.7430
1.70 1.0000 0.9977 0.9954 0.9886 0.9772 0.9661 0.9550 0.9462 0.9354 0.9204 0.8995 0.8610 0.8091 0.7907 0.8054
1.80 1.0000 0.9977 0.9954 0.9908 0.9817 0.9727 0.9661 0.9572 0.9484 0.9376 0.9204 0.8913 0.8531 0.8414 0.8590
1.90 1.0000 0.9977 0.9954 0.9931 0.9863 0.9795 0.9727 0.9661 0.9594 0.9506 0.9376 0.9162 0.8872 0.8831 0.9057
2.00 1.0000 0.9977 0.9977 0.9954 0.9886 0.9840 0.9795 0.9727 0.9683 0.9616 0.9528 0.9354 0.9183 0.9183 0.9462
2.20 1.0000 1.0000 0.9977 0.9977 0.9931 0.9908 0.9886 0.9840 0.9817 0.9795 0.9727 0.9661 0.9616 0.9727 1.0093
2.40 1.0000 1.0000 1.0000 0.9977 0.9977 0.9954 0.9931 0.9931 0.9908 0.9908 0.9886 0.9863 0.9931 1.0116 1.0568
2.60 1.0000 1.0000 1.0000 1.0000 1.0000 0.9977 0.9977 0.9977 0.9977 0.9977 0.9977 1.0023 1.0162 1.0399 1.0889
2.80 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0023 1.0023 1.0023 1.0046 1.0069 1.0116 1.0328 1.0593 1.1117
3.00 1.0000 1.0000 1.0000 1.0000 1.0023 1.0023 1.0046 1.0046 1.0069 1.0069 1.0116 1.0209 1.0423 1.0740 1.1298
3.50 1.0000 1.0000 1.0000 1.0023 1.0023 1.0046 1.0069 1.0093 1.0116 1.0139 1.0186 1.0304 1.0593 1.0914 1.1508
4.00 1.0000 1.0000 1.0000 1.0023 1.0046 1.0069 1.0093 1.0116 1.0139 1.0162 1.0233 1.0375 1.0666 1.0990 1.1588
Taken with permission from Ref. [9]. The value at the critical point (T r = P r = 1) is taken from the API-TDB [5]. Bold numbers indicate liquid region.
ig
g
g 2
g
of C = A + BT + C(SG ) + D(SG ) + E[T(SG )], where T is range of 16–60. The average deviation for this equation for
P
g
g
temperature and SG is gas specific gravity (M /29). Although these ranges is 5%; however, when it is applied in the tem-
ig
the equation is very useful for calculation of C of undefined perature range of 200–1000 K and molecular weight range
P
natural gases but using the reported coefficients we could not of 16–50, the error reduces to 2.5%. Use of this equation is
ig
obtain reliable values for C . In another correlation, ideal recommended for undefined light hydrocarbon gas mixtures
P g g
heat capacities of hydrocarbons (N C > C 5 ) were related to when gas specific gravity (SG ) is known (M = 29 × SG ). For
boiling point and specific gravity in the form of Eq. (2.38) defined hydrocarbon mixtures of known composition the fol-
at three temperatures of 0 F(∼255 K), 600 F(∼589 K), lowing relation may be used to calculate mixture ideal gas
◦
◦
and 1200 F (922 K) [18]. For light gases based on the data heat capacity:
--`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
◦
generated through Eq. (6.66) for compounds from C 1 to C ig C ig
C 5 with H 2 S, CO 2 , and N 2 the following relation has been (6.74) P,mix = y i Pi
determined: R i R
C ig 2 where C ig is the molar ideal heat capacity of component i
Pi
(6.73) P = (A i + B i M)T i (with mole fraction y i ) and may be calculated from Eq. (6.66).
R
i=0
for natural and light gases with 16 ≤ M ≤ 60 Example 6.2—Calculate C P for saturated liquid benzene at
where 450 K and 9.69 bar using generalized correlation and SRK
A 0 = 3.3224 B 0 =−2.5379 × 10 −2 EOS and compare with the value of 2.2 kJ/kg · K as given
A 1 =−7.3308 × 10 −3 B 1 = 7.5939 × 10 −4 in Ref. [6]. Also calculate heat capacity at constant volume,
ig
A 2 = 4.3235 × 10 −6 B 2 =−2.6565 × 10 −7 heat capacity ratio, and residual enthalpy (H − H ) from both
SRK EOS and generalized correlations of LK.
in which T is the absolute temperature in kelvin. This equa-
tion is based on more than 500 data points generated in Solution—From Table 2.1 for benzene we have T c = 562 K,
the temperature range of 50–1500 K and molecular weight P c = 49 bar, ω = 0.21, M = 78.1, and K W = 9.72 and from
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