Page 238 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

T1: IML
P2: IML/FFX
QC: IML/FFX
P1: IML/FFX
AT029-05
August 16, 2007
17:42
218 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
(0)
TABLE 5.9—Values of Z
1.2
1
1.5
0.1
0.4
3
0.6
2
0.8
0.01
5
0.2
T r → AT029-Manual 0.05 AT029-Manual-v7.cls for use in Eq. (5.107) from the Lee-Kesler modification of BWR EOS (Eq. 5.109) [58]. 7 10
0.30 0.0029 0.0145 0.0290 0.0579 0.1158 0.1737 0.2315 0.2892 0.3479 0.4335 0.5775 0.8648 1.4366 2.0048 2.8507
0.35 0.0026 0.0130 0.0261 0.0522 0.1043 0.1564 0.2084 0.2604 0.3123 0.3901 0.5195 0.7775 1.2902 1.7987 2.5539
0.40 0.0024 0.0119 0.0239 0.0477 0.0953 0.1429 0.1904 0.2379 0.2853 0.3563 0.4744 0.7095 1.1758 1.6373 2.3211 --`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
0.45 0.0022 0.0110 0.0221 0.0442 0.0882 0.1322 0.1762 0.2200 0.2638 0.3294 0.4384 0.6551 1.0841 1.5077 2.1338
0.50 0.0021 0.0103 0.0207 0.0413 0.0825 0.1236 0.1647 0.2056 0.2465 0.3077 0.4092 0.6110 1.0094 1.4017 1.9801
0.55 0.9804 0.0098 0.0195 0.0390 0.0778 0.1166 0.1553 0.1939 0.2323 0.2899 0.3853 0.5747 0.9475 1.3137 1.8520
0.60 0.9849 0.0093 0.0186 0.0371 0.0741 0.1109 0.1476 0.1842 0.2207 0.2753 0.3657 0.5446 0.8959 1.2398 1.7440
0.65 0.9881 0.9377 0.0178 0.0356 0.0710 0.1063 0.1415 0.1765 0.2113 0.2634 0.3495 0.5197 0.8526 1.1773 1.6519
0.70 0.9904 0.9504 0.8958 0.0344 0.0687 0.1027 0.1366 0.1703 0.2038 0.2538 0.3364 0.4991 0.8161 1.1341 1.5729
0.75 0.9922 0.9598 0.9165 0.0336 0.0670 0.1001 0.1330 0.1656 0.1981 0.2464 0.3260 0.4823 0.7854 1.0787 1.5047
0.80 0.9935 0.9669 0.9319 0.8539 0.0661 0.0985 0.1307 0.1626 0.1942 0.2411 0.3182 0.4690 0.7598 1.0400 1.4456
0.85 0.9946 0.9725 0.9436 0.8810 0.0661 0.0983 0.1301 0.1614 0.1924 0.2382 0.3132 0.4591 0.7388 1.0071 1.3943
0.90 0.9954 0.9768 0.9528 0.9015 0.7800 0.1006 0.1321 0.1630 0.1935 0.2383 0.3114 0.4527 0.7220 0.9793 1.3496
0.93 0.9959 0.9790 0.9573 0.9115 0.8059 0.6635 0.1359 0.1664 0.1963 0.2405 0.3122 0.4507 0.7138 0.9648 1.3257
0.95 0.9961 0.9803 0.9600 0.9174 0.8206 0.6967 0.1410 0.1705 0.1998 0.2432 0.3138 0.4501 0.7092 0.9561 1.3108
0.97 0.9963 0.9815 0.9625 0.9227 0.8338 0.7240 0.5580 0.1779 0.2055 0.2474 0.3164 0.4504 0.7052 0.9480 1.2968
0.98 0.9965 0.9821 0.9637 0.9253 0.8398 0.7360 0.5887 0.1844 0.2097 0.2503 0.3182 0.4508 0.7035 0.9442 1.2901
0.99 0.9966 0.9826 0.9648 0.9277 0.8455 0.7471 0.6138 0.1959 0.2154 0.2538 0.3204 0.4514 0.7018 0.9406 1.2835
1.00 0.9967 0.9832 0.9659 0.9300 0.8509 0.7574 0.6355 0.2901 0.2237 0.2583 0.3229 0.4522 0.7004 0.9372 1.2772
1.01 0.9968 0.9837 0.9669 0.9322 0.8561 0.7671 0.6542 0.4648 0.2370 0.2640 0.3260 0.4533 0.6991 0.9339 1.2710
1.02 0.9969 0.9842 0.9679 0.9343 0.8610 0.7761 0.6710 0.5146 0.2629 0.2715 0.3297 0.4547 0.6980 0.9307 1.2650
1.05 0.9971 0.9855 0.9707 0.9401 0.8743 0.8002 0.7130 0.6026 0.4437 0.3131 0.3452 0.4604 0.6956 0.9222 1.2481
1.10 0.9975 0.9874 0.9747 0.9485 0.8930 0.8323 0.7649 0.6880 0.5984 0.4580 0.3953 0.4770 0.6950 0.9110 1.2232
1.15 0.9978 0.9891 0.9780 0.9554 0.9081 0.8576 0.8032 0.7443 0.6803 0.5798 0.4760 0.5042 0.6987 0.9033 1.2021
1.20 0.9981 0.9904 0.9808 0.9611 0.9205 0.8779 0.8330 0.7858 0.7363 0.6605 0.5605 0.5425 0.7069 0.8990 1.1844
1.30 0.9985 0.9926 0.9852 0.9702 0.9396 0.9083 0.8764 0.8438 0.8111 0.7624 0.6908 0.6344 0.7358 0.8998 1.1580
1.40 0.9988 0.9942 0.9884 0.9768 0.9534 0.9298 0.9062 0.8827 0.8595 0.8256 0.7753 0.7202 0.7761 0.9112 1.1419
1.50 0.9991 0.9954 0.9909 0.9818 0.9636 0.9456 0.9278 0.9103 0.8933 0.8689 0.8328 0.7887 0.8200 0.9297 1.1339
1.60 0.9993 0.9964 0.9928 0.9856 0.9714 0.9575 0.9439 0.9308 0.9180 0.9000 0.8738 0.8410 0.8617 0.9518 1.1320
1.70 0.9994 0.9971 0.9943 0.9886 0.9775 0.9667 0.9563 0.9463 0.9367 0.9234 0.9043 0.8809 0.8984 0.9745 1.1343
1.80 0.9995 0.9977 0.9955 0.9910 0.9823 0.9739 0.9659 0.9583 0.9511 0.9413 0.9275 0.9118 0.9297 0.9961 1.1391
1.90 0.9996 0.9982 0.9964 0.9929 0.9861 0.9796 0.9735 0.9678 0.9624 0.9552 0.9456 0.9359 0.9557 1.0157 1.1452
2.00 0.9997 0.9986 0.9972 0.9944 0.9892 0.9842 0.9796 0.9754 0.9715 0.9664 0.9599 0.9550 0.9772 1.0328 1.1516
2.20 0.9998 0.9992 0.9983 0.9967 0.9937 0.9910 0.9886 0.9865 0.9847 0.9826 0.9806 0.9827 1.0094 1.0600 1.1635
2.40 0.9999 0.9996 0.9991 0.9983 0.9969 0.9957 0.9948 0.9941 0.9936 0.9935 0.9945 1.0011 1.0313 1.0793 1.1728
2.60 1.0000 0.9998 0.9997 0.9994 0.9991 0.9990 0.9990 0.9993 0.9998 1.0010 1.0040 1.0137 1.0463 1.0926 1.1792
2.80 1.0000 1.0000 1.0001 1.0002 1.0007 1.0013 1.0021 1.0031 1.0042 1.0063 1.0106 1.0223 1.0565 1.1016 1.1830
3.00 1.0000 1.0002 1.0004 1.0008 1.0018 1.0030 1.0043 1.0057 1.0074 1.0101 1.0153 1.0284 1.0635 1.1075 1.1848
3.50 1.0001 1.0004 1.0008 1.0017 1.0035 1.0055 1.0075 1.0097 1.0120 1.0156 1.0221 1.0368 1.0723 1.1138 1.1834
4.00 1.0001 1.0005 1.0010 1.0021 1.0043 1.0066 1.0090 1.0115 1.0140 1.0179 1.0249 1.0401 1.0747 1.1136 1.1773
where BP c /RT c can be estimated from Eq. (5.71) or (5.72) These equations are equivalent to the following equations as
provided by the API-TDB [59].
through T r and ω. Equation (5.114) may be used at low P r
and V r > 2or T r > 0.686 + 0.439P r [60] instead of complex
Eqs. (5.108)–(5.111). The API-TDB [59] also recommends
V ci = Z ci RT ci /P ci
the following relation, proposed by Pitzer et al. [56], for
calculation of Z for gases at P r ≤ 0.2. Z ci = 0.2905 − 0.085ω i
N N N
1 1/3 2/3
P r −1 V mc = x i V ci + 3 x i V ci x i V ci
Z = 1 + (0.1445 + 0.073ω) − (0.33 − 0.46ω)T r 4 i=1 i=1 i=1
T r
N N N
− (0.1385 + 0.5ω)T −2 − (0.0121 + 0.097ω)T −3 1
r r 1/3 2/3
T mc = x i V ci T ci + 3 x i V ci T ci x i V ci T ci
(5.114) − 0.0073ωT −8 4V mc i=1 i=1 i=1
r
N

Obviously neither Eq. (5.113) nor (5.114) can be applied to ω m = x i ω i
liquids. i=1
The LK corresponding states correlations expressed by P mc = Z mc RT mc /V mc = (0.2905 − 0.085ω m )RT mc /V mc
Eq. (5.107) and Tables 5.9–5.11 can also be applied to mix-
tures. Such correlations are sensitive to the input data for (5.115)
the pseudocritical properties. The mixing rules used to cal-
culate mixture critical temperature and pressure may greatly where x i is the mole fraction of component i, N is the number
affect calculated properties specially when the mixture con- of compounds in the mixture, and T mc , P mc , and V mc are the
tains dissimilar compounds. Lee and Kesler proposed special mixture pseudocritical temperature, pressure, and volume re-
set of equations for mixtures for use with their correlations. spectively. ω m is the mixture acentric factor and it is calculated

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