Page 260 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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240 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS

TABLE 6.2—Values of − H−H 0 (0) for use in Eq. (6.56).
RT c
P r
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 6.045 6.043 6.040 6.034 6.022 6.011 5.999 5.987 5.975 5.957 5.927 5.868 5.748 5.628 5.446
0.35 5.906 5.904 5.901 5.895 5.882 5.870 5.858 5.845 5.833 5.814 5.783 5.721 5.595 5.469 5.278
0.40 5.763 5.761 5.757 5.751 5.738 5.726 5.713 5.700 5.687 5.668 5.636 5.572 5.442 5.311 5.113
0.45 5.615 5.612 5.609 5.603 5.590 5.577 5.564 5.551 5.538 5.519 5.486 5.421 5.288 5.154 5.950
0.50 5.465 5.469 5.459 5.453 5.440 5.427 5.414 5.401 5.388 5.369 5.336 5.270 5.135 4.999 4.791
0.55 0.032 5.312 5.309 5.303 5.290 5.278 5.265 5.252 5.239 5.220 5.187 5.121 4.986 4.849 4.638
0.60 0.027 5.162 5.159 5.153 5.141 5.129 5.116 5.104 5.091 5.073 5.041 4.976 4.842 4.704 4.492
0.65 0.023 0.118 5.008 5.002 4.991 4.980 4.968 4.956 4.945 4.927 4.896 4.833 4.702 4.565 4.353
0.70 0.020 0.101 0.213 4.848 4.838 4.828 4.818 4.808 4.797 4.781 4.752 4.693 4.566 4.432 4.221
0.75 0.017 0.088 0.183 4.687 4.679 4.672 4.664 4.655 4.646 4.632 4.607 4.554 4.434 4.303 4.095
0.80 0.015 0.078 0.160 0.345 4.507 4.504 4.499 4.494 4.488 4.478 4.459 4.413 4.303 4.178 3.974
0.85 0.014 0.069 0.141 0.300 4.309 4.313 4.316 4.316 4.316 4.312 4.302 4.269 4.173 4.056 3.857
0.90 0.012 0.062 0.126 0.264 0.596 4.074 4.094 4.108 4.118 4.127 4.132 4.119 4.043 3.935 3.744
0.93 0.011 0.058 0.118 0.246 0.545 0.960 3.920 3.953 3.976 4.000 4.020 4.024 3.963 3.863 3.678
0.95 0.011 0.056 0.113 0.235 0.516 0.885 3.763 3.825 3.865 3.904 3.940 3.958 3.910 3.815 3.634
0.97 0.011 0.054 0.109 0.225 0.490 0.824 1.356 3.658 3.732 3.796 3.853 3.890 3.856 3.767 3.591
0.98 0.010 0.053 0.107 0.221 0.478 0.797 1.273 3.544 3.652 3.736 3.806 3.854 3.829 3.743 3.569
0.99 0.010 0.052 0.105 0.216 0.466 0.773 1.206 3.376 3.558 3.670 3.758 3.818 3.801 3.719 3.548
1.00 0.010 0.052 0.105 0.216 0.466 0.773 1.206 2.593 3.558 3.670 3.758 3.818 3.801 3.719 3.548
1.01 0.010 0.051 0.103 0.212 0.455 0.750 1.151 1.796 3.441 3.598 3.706 3.782 3.774 3.695 3.526
1.02 0.010 0.049 0.099 0.203 0.434 0.708 1.060 1.627 3.039 3.422 3.595 3.705 3.718 3.647 3.484
1.05 0.009 0.046 0.094 0.192 0.407 0.654 0.955 1.359 2.034 3.030 3.398 3.583 3.632 3.575 3.420
1.10 0.008 0.042 0.086 0.175 0.367 0.581 0.827 1.120 1.487 2.203 2.965 3.353 3.484 3.453 3.315
1.15 0.008 0.039 0.079 0.160 0.334 0.523 0.732 0.968 1.239 1.719 2.479 3.091 3.329 3.329 3.211
1.20 0.007 0.036 0.073 0.148 0.305 0.474 0.657 0.857 1.076 1.443 2.079 2.807 3.166 3.202 3.107
1.30 0.006 0.031 0.063 0.127 0.259 0.399 0.545 0.698 0.860 1.116 1.560 2.274 2.825 2.942 2.899
1.40 0.005 0.027 0.055 0.110 0.224 0.341 0.463 0.588 0.716 0.915 1.253 1.857 2.486 2.679 2.692
1.50 0.005 0.024 0.048 0.097 0.196 0.297 0.400 0.505 0.611 0.774 1.046 1.549 2.175 2.421 2.486
1.60 0.004 0.021 0.043 0.086 0.173 0.261 0.350 0.440 0.531 0.667 0.894 1.318 1.904 2.177 2.285
1.70 0.004 0.019 0.038 0.076 0.153 0.231 0.309 0.387 0.446 0.583 0.777 1.139 1.672 1.953 2.091
1.80 0.003 0.017 0.034 0.068 0.137 0.206 0.275 0.344 0.413 0.515 0.683 0.996 1.476 1.751 1.908
1.90 0.003 0.015 0.031 0.062 0.123 0.185 0.246 0.307 0.368 0.458 0.606 0.880 1.309 1.571 1.736
2.00 0.003 0.014 0.028 0.056 0.111 0.167 0.222 0.276 0.330 0.411 0.541 0.782 1.167 1.411 1.577
2.20 0.002 0.012 0.023 0.046 0.092 0.137 0.182 0.226 0.269 0.334 0.437 0.629 0.937 1.143 1.295
2.40 0.002 0.010 0.019 0.038 0.076 0.114 0.150 0.187 0.222 0.275 0.359 0.513 0.761 0.929 1.058
2.60 0.002 0.008 0.016 0.032 0.064 0.095 0.125 0.155 0.185 0.228 0.297 0.422 0.621 0.756 0.858
2.80 0.001 0.007 0.014 0.027 0.054 0.080 0.105 0.130 0.154 0.190 0.246 0.348 0.508 0.614 0.689
3.00 0.001 0.006 0.011 0.023 0.045 0.067 0.088 0.109 0.129 0.159 0.205 0.288 0.415 0.495 0.545
3.50 0.001 0.004 0.007 0.015 0.029 0.043 0.056 0.069 0.081 0.099 0.127 0.174 0.239 0.270 0.264
4.00 0.000 0.002 0.005 0.009 0.017 0.026 0.033 0.041 0.048 0.058 0.072 0.095 0.116 0.110 0.061
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.
For low and moderate pressures where truncated virial may be used from Eq. (5.71), but corresponding derivatives
equation in the form of Eq. (5.113) is valid, the relation for must be used. The above equation may be applied at the same
fugacity coefficient can be derived from Eq. (6.53) as region that Eq. (5.75) or (5.114) were applicable, that is, V r >
2.0or T r > 0.686 + 0.439P r [2].
BP
(6.61) ln(φ) = For real gases that follow truncated virial equation with
RT three terms (coefficients D and higher assumed zero in
This relation may also be written as Eq. 5.76), the relations for C P and C V are givens as

P r BP c
(6.62) φ = exp
C P − C P T B (B − TB ) − C + TC − T C /2
T r RT c ig 2 2 2
where (BP c /RT c ) can be calculated from Eq. (5.71) or (5.72). R =− V − V 2
Similarly enthalpy departure based on the truncated virial (6.64)
equation is given as [1] C V − C ig 2TB + T B TC + T C /2
2
2

(6.65) V =− − 2
H − H ig dB (0) dB (1) R V V
(6.63) = P r B (0) − T r + ω B (1) − T r
RT c dT r dT r
where B and C are the first-order derivatives of B and C with

(0)
where B (0) and B (1) are given by Eq. (5.72) with dB /dT r = respect to temperature, while B and C are the second-order

(1)
0.675/T 2.6 and dB /dT r = 0.722/T 5.2 . Obviously B (0) and B (1) derivatives of B and C with respect to temperature.
r r

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