Page 261 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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6. THERMODYNAMIC RELATIONS FOR PROPERTY ESTIMATIONS 241

TABLE 6.3—Values of − H−H ig (1) 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 11.098 11.096 11.095 11.091 11.083 11.076 11.069 11.062 11.055 11.044 11.027 10.992 10.935 10.872 10.781
0.35 10.656 10.655 10.654 10.653 10.650 10.646 10.643 10.640 10.637 10.632 10.624 10.609 10.581 10.554 10.529
0.40 10.121 10.121 10.121 10.121 10.121 10.121 10.121 10.121 10.121 10.121 10.122 10.123 10.128 10.135 10.150
0.45 9.515 9.515 9.516 9.516 9.519 9.521 9.523 9.525 9.527 9.531 9.537 9.549 9.576 9.611 9.663
0.50 8.868 8.869 8.870 8.870 8.876 8.880 8.884 8.888 8.892 8.899 8.909 8.932 8.978 9.030 9.111
0.55 0.080 8.211 8.212 8.215 8.221 8.226 8.232 8.238 8.243 8.252 8.267 8.298 8.360 8.425 8.531
0.60 0.059 7.568 7.570 7.573 7.579 7.585 7.591 7.596 7.603 7.614 7.632 7.669 7.745 7.824 7.950
0.65 0.045 0.247 6.949 6.952 6.959 6.966 6.973 6.980 6.987 6.997 7.017 7.059 7.147 7.239 7.381
0.70 0.034 0.185 0.415 6.360 6.367 6.373 6.381 6.388 6.395 6.407 6.429 6.475 6.574 6.677 6.837
0.75 0.027 0.142 0.306 5.796 5.802 5.809 5.816 5.824 5.832 5.845 5.868 5.918 6.027 6.142 6.318
0.80 0.021 0.110 0.234 0.542 5.266 5.271 5.278 5.285 5.293 5.306 5.330 5.385 5.506 5.632 5.824
0.85 0.017 0.087 0.182 0.401 4.753 4.754 4.758 4.763 4.771 4.784 4.810 4.872 5.008 5.149 5.358
0.90 0.014 0.070 0.144 0.308 0.751 4.254 4.248 4.249 4.255 4.268 4.298 4.371 4.530 4.688 4.916
0.93 0.012 0.061 0.126 0.265 0.612 1.236 3.942 3.934 3.937 3.951 3.987 4.073 4.251 4.422 4.662
0.95 0.011 0.056 0.115 0.241 0.542 0.994 3.737 3.712 3.713 3.730 3.773 3.873 4.068 4.248 4.497
0.97 0.010 0.052 0.105 0.219 0.483 0.837 1.616 3.470 3.467 3.492 3.551 3.670 3.885 4.077 4.336
0.98 0.010 0.050 0.101 0.209 0.457 0.776 1.324 3.332 3.327 3.363 3.434 3.568 3.795 3.992 4.257
0.99 0.009 0.048 0.097 0.200 0.433 0.722 1.154 3.164 3.164 3.223 3.313 3.464 3.705 3.909 4.178
1.00 0.009 0.046 0.093 0.191 0.410 0.675 1.034 2.348 2.952 3.065 3.186 3.358 3.615 3.825 4.100
1.01 0.009 0.044 0.089 0.183 0.389 0.632 0.940 1.375 2.595 2.880 3.051 3.251 3.525 3.742 4.023
1.02 0.008 0.042 0.085 0.175 0.370 0.594 0.863 1.180 1.723 2.650 2.906 3.142 3.435 3.661 3.947
1.05 0.007 0.037 0.075 0.153 0.318 0.498 0.691 0.877 0.878 1.496 2.381 2.800 3.167 3.418 3.722
1.10 0.006 0.030 0.061 0.123 0.251 0.381 0.507 0.617 0.673 0.617 1.261 2.167 2.720 3.023 3.362
1.15 0.005 0.025 0.050 0.099 0.199 0.296 0.385 0.459 0.503 0.487 0.604 1.497 2.275 2.641 3.019
1.20 0.004 00.020 0.040 0.080 0.158 0.232 0.297 0.349 0.381 0.381 0.361 0.934 1.840 2.273 2.692
1.30 0.003 0.013 0.026 0.052 0.100 0.142 0.177 0.203 0.218 0.218 0.178 0.300 1.066 1.592 2.086
1.40 0.002 0.008 0.016 0.032 0.060 0.083 0.100 0.111 0.115 0.108 0.070 0.044 0.504 1.012 1.547
1.50 0.001 0.005 0.009 0.018 0.032 0.042 0.048 0.049 0.046 0.032 −0.008 −0.078 0.142 0.556 1.080
1.60 0.000 0.002 0.004 0.007 0.012 0.013 0.011 0.005 −0.004 −0.023 −0.065 −0.151 −0.082 0.217 0.689
1.70 0.000 0.000 0.000 0.000 −0.003 −0.009 −0.017 −0.027 −0.040 −0.063 −0.109 −0.202 −0.223 −0.028 0.369
1.80 −0.000 −0.001 −0.003 −0.006 −0.015 −0.025 −0.037 −0.051 −0.067 −0.094 −0.143 −0.241 −0.317 −0.203 0.112
1.90 −0.001 −0.003 −0.005 −0.011 −0.023 −0.037 −0.053 −0.070 −0.088 −0.117 −0.169 −0.271 −0.381 −0.330 −0.092
2.00 −0.001 −0.003 −0.007 −0.015 −0.030 −0.047 −0.065 −0.085 −0.105 −0.136 −0.190 −0.295 −0.428 −0.424 −0.255
2.20 −0.001 −0.005 −0.010 −0.020 −0.040 −0.062 −0.083 −0.106 −0.128 −0.163 −0.221 −0.331 −0.493 −0.551 −0.489
2.40 −0.001 −0.006 −0.012 −0.023 −0.047 −0.071 −0.095 −0.120 −0.144 −0.181 −0.242 −0.356 −0.535 −0.631 −0.645
2.60 −0.001 −0.006 −0.013 −0.026 −0.052 −0.078 −0.104 −0.130 −0.156 −0.194 −0.257 −0.376 −0.567 −0.687 −0.754
2.80 −0.001 −0.007 −0.014 −0.028 −0.055 −0.082 −0.110 −0.137 −0.164 −0.204 −0.269 −0.391 −0.591 −0.729 −0.836
3.00 −0.001 −0.007 −0.014 −0.029 −0.058 −0.086 −0.114 −0.142 −0.170 −0.211 −0.278 −0.403 −0.611 −0.763 −0.899
3.50 −0.002 −0.008 −0.016 −0.031 −0.062 −0.092 −0.122 −0.152 −0.181 −0.224 −0.294 −0.425 −0.650 −0.827 −1.015
4.00 −0.002 −0.008 −0.016 −0.032 −0.064 −0.096 −0.127 −0.158 −0.188 −0.233 −0.306 −0.442 −0.680 −0.874 −1.097
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.
6.3 PROPERTIES OF IDEAL GASES change with temperature appreciably. As the number of
atoms in a molecule increases, dependency of ideal gas prop-
Calculation of thermodynamic properties through the meth- erties to temperature also increases. Data on properties of
ods outlined above requires properties of ideal gases. Based ideal gases for a large number of hydrocarbons have been
ig
ig
on definition of ideal gases, U , H , and C ig are functions reported by the API-TDB [5]. These data for ideal gas heat ca-
P
of only temperature. Kinetic theory shows that the mo- pacity have been correlated to temperature in the following
lar translational energy of a monoatomic ideal gas is 3 2 RT, form [5]:
where R is the universal gas constant and T is the abso- ig
lute temperature [10]. Since for ideal gases the internal en- (6.66) C P = A + BT + CT + DT + ET 4
2
3
3
ig
ergy is independent of pressure thus U = RT. This leads R
2 ig
ig 5 ig 5 ig 3 C P 5 ig
to H = RT, C = R, C = R, and γ = ig = = 1.667. where R is the gas constant (Section 1.7.24), C is the molar
V
P
2 2 2 C 3 P
V
Ideal gas heat capacity of monoatomic gases such as ar- heat capacity in the same unit as R, and T is the absolute
gon, helium, etc. are constant with respect to temperature temperature in kelvin. Values of the constants for a number
[10]. Similarly for diatomic gases such as N 2 ,O 2 , air, etc., of nonhydrocarbon gases as well as some selected hydrocar-
ig 7 ig 7 ig 5
H = RT, which leads to C = R, C = R, and γ = 7/5 = bons are given in Table 6.8. The temperature range at which
2 P 2 V 2
1.4. In fact variation of heat capacities of ideal diatomic these constants can be used is also given for each compound
gases with temperature is very moderate. For multiatomic in Table 6.8. For a compound with known chemical struc-
molecules such as hydrocarbons, ideal gas properties do ture, ideal gas heat capacity is usually predicted from group

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