Page 262 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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242 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS

C p −C p
TABLE 6.4—Values of 20:46 ig (0) for use in Eq. (6.57).
R
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 2.805 2.807 2.809 2.814 2.830 2.842 2.854 2.866 2.878 2.896 2.927 2.989 3.122 3.257 3.466
0.35 2.808 2.810 2.812 2.815 2.823 2.835 2.844 2.853 2.861 2.875 2.897 2.944 3.042 3.145 3.313
0.40 2.925 2.926 2.928 2.933 2.935 2.940 2.945 2.951 2.956 2.965 2.979 3.014 3.085 3.164 3.293
0.45 2.989 2.990 2.990 2.991 2.993 2.995 2.997 2.999 3.002 3.006 3.014 3.032 3.079 3.135 3.232
0.50 3.006 3.005 3.004 3.003 3.001 3.000 2.998 2.997 2.996 2.995 2.995 2.999 3.019 3.054 3.122
0.55 0.118 3.002 3.000 2.997 2.990 2.984 2.978 2.973 2.968 2.961 2.951 2.938 2.934 2.947 2.988
0.60 0.089 3.009 3.006 2.999 2.986 2.974 2.963 2.952 2.942 2.927 2.907 2.874 2.840 2.831 2.847
0.65 0.069 0.387 3.047 3.036 3.014 2.993 2.973 2.955 2.938 2.914 2.878 2.822 2.753 2.720 2.709
0.70 0.054 0.298 0.687 3.138 3.099 3.065 3.033 3.003 2.975 2.937 2.881 2.792 2.681 2.621 2.582
0.75 0.044 0.236 0.526 3.351 3.284 3.225 3.171 3.122 3.076 3.015 2.928 2.795 2.629 2.537 2.469
0.80 0.036 0.191 0.415 1.032 3.647 3.537 3.440 3.354 3.277 3.176 3.038 2.838 2.601 2.473 2.373
0.85 0.030 0.157 0.336 0.794 4.404 4.158 3.957 3.790 3.647 3.470 3.240 2.931 2.599 2.427 2.292
0.90 0.025 0.131 0.277 0.633 1.858 5.679 5.095 4.677 4.359 4.000 3.585 3.096 2.626 2.399 2.227
0.93 0.023 0.118 0.249 0.560 1.538 4.208 6.720 5.766 5.149 4.533 3.902 3.236 2.657 2.392 2.195
0.95 0.021 0.111 0.232 0.518 1.375 3.341 9.316 7.127 6.010 5.050 4.180 3.351 2.684 2.391 2.175
0.97 0.020 0.104 0.217 0.480 1.240 2.778 9.585 10.011 7.451 5.785 4.531 3.486 2.716 2.393 2.159
0.98 0.019 0.101 0.210 0.463 1.181 2.563 7.350 13.270 8.611 6.279 4.743 3.560 2.733 2.395 2.151
0.99 0.019 0.098 0.204 0.447 1.126 2.378 6.038 21.948 10.362 6.897 4.983 3.641 2.752 2.398 2.144
1.00 0.018 0.095 0.197 0.431 1.076 2.218 5.156 ∞ 13.182 7.686 5.255 3.729 2.773 2.401 2.138
1.01 0.018 0.092 0.191 0.417 1.029 2.076 4.516 22.295 18.967 8.708 5.569 3.821 2.794 2.405 2.131
1.02 0.017 0.089 0.185 0.403 0.986 1.951 4.025 13.183 31.353 10.062 5.923 3.920 2.816 2.408 2.125
1.05 0.016 0.082 0.169 0.365 0.872 1.648 3.047 6.458 20.234 16.457 7.296 4.259 2.891 2.425 2.110
1.10 0.014 0.071 0.147 0.313 0.724 1.297 2.168 3.649 6.510 13.256 9.787 4.927 3.033 2.462 2.093
1.15 0.012 0.063 0.128 0.271 0.612 1.058 1.670 2.553 3.885 6.985 9.094 5.535 3.186 2.508 2.083
1.20 0.011 0.055 0.113 0.237 0.525 0.885 1.345 1.951 2.758 4.430 6.911 5.710 3.326 2.555 2.079
1.30 0.009 0.044 0.089 0.185 0.400 0.651 0.946 1.297 1.711 2.458 3.850 4.793 3.452 2.628 2.077
1.40 0.007 0.036 0.072 0.149 0.315 0.502 0.711 0.946 1.208 1.650 2.462 3.573 3.282 2.626 2.068
1.50 0.006 0.029 0.060 0.122 0.255 0.399 0.557 0.728 0.912 1.211 1.747 2.647 2.917 2.525 2.038
1.60 0.005 0.025 0.050 0.101 0.210 0.326 0.449 0.580 0.719 0.938 1.321 2.016 2.508 2.347 1.978
1.70 0.004 0.021 0.042 0.086 0.176 0.271 0.371 0.475 0.583 0.752 1.043 1.586 2.128 2.130 1.889
1.80 0.004 0.018 0.036 0.073 0.150 0.229 0.311 0.397 0.484 0.619 0.848 1.282 1.805 1.907 1.778
1.90 0.003 0.016 0.031 0.063 0.129 0.196 0.265 0.336 0.409 0.519 0.706 1.060 1.538 1.696 1.656
2.00 0.003 0.014 0.027 0.055 0.112 0.170 0.229 0.289 0.350 0.443 0.598 0.893 1.320 1.505 1.531
2.20 0.002 0.011 0.021 0.043 0.086 0.131 0.175 0.220 0.265 0.334 0.446 0.661 0.998 1.191 1.292
2.40 0.002 0.009 0.017 0.034 0.069 0.104 0.138 0.173 0.208 0.261 0.347 0.510 0.779 0.956 1.086
2.60 0.001 0.007 0.014 0.028 0.056 0.084 0.112 0.140 0.168 0.210 0.278 0.407 0.624 0.780 0.917
2.80 0.001 0.006 0.012 0.023 0.046 0.070 0.093 0.116 0.138 0.172 0.227 0.332 0.512 0.647 0.779
3.00 0.001 0.005 0.010 0.020 0.039 0.058 0.078 0.097 0.116 0.144 0.190 0.277 0.427 0.545 0.668
3.50 0.001 0.003 0.007 0.013 0.027 0.040 0.053 0.066 0.079 0.098 0.128 0.187 0.289 0.374 0.472
4.00 0.000 0.002 0.005 0.010 0.019 0.029 0.038 0.048 0.057 0.071 0.093 0.135 0.209 0.272 0.350
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
ig
ig
contribution methods [4, 11]. Once C is known, C , H , and state of saturated liquid at 75 F at which H = 0. In steam ta-
◦
V
P
ig
S can be determined from the following relations: bles where properties of liquid water and steam are reported
[1] the reference state at which H = S = 0 is saturated liquid
ig ig
C V C P at 0.01 C. Therefore there is no need for the values of inte-
◦
2
3
(6.67) = − 1 = A − 1 + BT + CT + DT + ET 4
R R gration constants A H and A S in Eqs. (6.68) and (6.69) as they
B C D E cancel in the course of calculations. There are several other
2
4
3
ig
(6.68) H = A H + AT + T + T + T + T 5 ig
2 3 4 5 forms of Eq. (6.66) for C , as an example the following simple
P
C D E form is given for ideal gas heat capacity of water [1]:
ig
3
2
(6.69) S = A S + Aln T + BT + T + T + T 4
2 3 4 C ig −3 5 −2
P
ig
The relation for C is obtained through Eqs. (6.23) and (6.66), (6.70) R = 3.47 + 1.45 × 10 T + 0.121 × 10 T
V
ig
while relations for H and S have been obtained from Eqs. another relation for water is given by DIPPR [13]:
ig
(6.21) and (6.32), respectively. Constants A H and A S are ob-
ig
tained from integration of relations for dH and dS and can C ig = 4.0129 + 3.222 2610.5/T 2
ig
P
be determined based on the reference state for ideal gas en- R sinh (2610.5/T)
thalpy and entropy. These parameters are not necessary for 1169/T 2
calculation of H and Sas they are omitted during calculations (6.71) + 1.07
with respect to the arbitrary reference state chosen for H and cosh (1169/T)
ig
S. Usually the choice of reference state is on H and not on H . where in both equations T is in kelvin and they are valid up to
ig
For example, Lenoir and Hipkin [12] reported experimental 2000 C. A graphical comparison of C /R for water from Eqs.
◦
P
data on enthalpy of some petroleum fractions with reference (6.66), (6.70), and (6.71) is shown in Fig. 6.2. Equations (6.66)
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