Page 263 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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6. THERMODYNAMIC RELATIONS FOR PROPERTY ESTIMATIONS 243
TABLE 6.5—Values of C p −C p ig (1) 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 8.462 8.445 8.424 8.381 8.281 8.192 8.102 8.011 7.921 7.785 7.558 7.103 6.270 5.372 4.020
0.35 9.775 9.762 9.746 9.713 9.646 9.568 9.499 9.430 9.360 9.256 9.080 8.728 8.013 7.290 6.285
0.40 11.494 11.484 11.471 11.438 11.394 11.343 11.291 11.240 11.188 11.110 10.980 10.709 10.170 9.625 8.803
0.45 12.651 12.643 12.633 12.613 12.573 12.532 12.492 12.451 12.409 12.347 12.243 12.029 11.592 11.183 10.533
0.50 13.111 13.106 13.099 13.084 13.055 13.025 12.995 12.964 12.933 12.886 12.805 12.639 12.288 11.946 11.419
0.55 0.511 13.035 13.030 13.021 13.002 25.981 12.961 12.939 12.917 12.882 12.823 12.695 12.407 12.103 11.673
0.60 0.345 12.679 12.675 12.668 12.653 12.637 12.620 12.589 12.574 12.550 12.506 12.407 12.165 11.905 11.526
0.65 0.242 1.518 12.148 12.145 12.137 12.128 12.117 12.105 12.092 12.060 12.026 11.943 11.728 11.494 11.141
0.70 0.174 1.026 2.698 11.557 11.564 11.563 11.559 11.553 11.536 11.524 11.495 11.416 11.208 10.985 10.661
0.75 0.129 0.726 1.747 10.967 10.995 11.011 11.019 11.024 11.022 11.013 10.986 10.898 10.677 10.448 10.132
0.80 0.097 0.532 1.212 3.511 10.490 10.536 10.566 10.583 10.590 10.587 10.556 10.446 10.176 9.917 9.591
0.85 0.075 0.399 0.879 2.247 9.999 10.153 10.245 10.297 10.321 10.324 10.278 10.111 9.740 9.433 9.075
0.90 0.058 0.306 0.658 1.563 5.486 9.793 10.180 10.349 10.409 10.401 10.279 9.940 9.389 8.999 8.592
0.93 0.050 0.263 0.560 1.289 3.890 ... 10.285 10.769 10.875 10.801 10.523 9.965 9.225 8.766 8.322
0.95 0.046 0.239 0.505 1.142 3.215 9.389 9.993 11.420 11.607 11.387 10.865 10.055 9.136 8.621 8.152
0.97 0.042 0.217 0.456 1.018 2.712 6.588 ... 13.001 ... 12.498 11.445 10.215 9.061 8.485 7.986
0.98 0.040 0.207 0.434 0.962 2.506 5.711 20.918 14.884 14.882 13.420 11.856 10.323 9.037 8.420 7.905
0.99 0.038 0.198 0.414 0.863 2.324 5.027 ... ... ... ... 12.388 10.457 9.011 8.359 7.826
1.00 0.037 0.189 0.394 0.863 2.162 4.477 10.511 ∞ 25.650 16.895 13.081 10.617 8.990 8.293 7.747
1.01 0.035 0.181 0.376 0.819 2.016 4.026 8.437 ... ... ... ... 10.805 8.973 8.236 7.670
1.02 0.034 0.173 0.359 0.778 1.884 3.648 7.044 15.109 115.101 26.192 15.095 11.024 8.960 8.182 7.595
1.05 0.30 0.152 0.313 0.669 1.559 2.812 4.679 7.173 2.277 ... ... 11.852 8.939 8.018 7.377
1.10 0.024 0.123 0.252 0.528 1.174 1.968 2.919 3.877 4.002 3.927 ... ... 8.933 7.759 7.031 --`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
1.15 0.020 0.101 0.205 0.424 0.910 1.460 2.048 2.587 2.844 2.236 7.716 12.812 8.849 7.504 6.702
1.20 0.016 0.083 0.168 0.345 0.722 1.123 1.527 1.881 2.095 1.962 2.965 9.494 8.508 7.206 6.384
1.30 0.012 0.058 0.118 0.235 0.476 0.715 0.938 1.129 1.264 1.327 1.288 3.855 6.758 6.365 5.735
1.40 0.008 0.042 0.083 0.166 0.329 0.484 0.624 0.743 0.833 0.904 0.905 1.652 4.524 5.193 5.035
1.50 0.006 0.030 0.061 0.120 0.235 0.342 0.437 0.517 0.580 0.639 0.666 0.907 2.823 3.944 4.289
1.60 0.005 0.023 0.045 0.089 0.173 0.249 0.317 0.374 0.419 0.466 0.499 0.601 1.755 2.871 3.545
1.70 0.003 0.017 0.034 0.068 0.130 0.187 0.236 0.278 0.312 0.349 0.380 0.439 1.129 2.060 2.867
1.80 0.003 0.013 0.027 0.052 0.100 0.143 0.180 0.212 0.238 0.267 0.296 0.337 0.764 1.483 2.287
1.90 0.002 0.011 0.021 0.041 0.078 0.111 0.140 0.164 0.185 0.209 0.234 0.267 0.545 1.085 1.817
2.00 0.002 0.008 0.017 0.032 0.062 0.088 0.110 0.130 0.146 0.166 0.187 0.217 0.407 0.812 1.446
2.20 0.001 0.005 0.011 0.021 0.042 0.057 0.072 0.085 0.096 0.110 0.126 0.150 0.256 0.492 0.941
2.40 0.001 0.004 0.007 0.014 0.028 0.039 0.049 0.058 0.066 0.076 0.089 0.109 0.180 0.329 0.644
2.60 0.001 0.003 0.005 0.010 0.020 0.028 0.035 0.042 0.048 0.056 0.066 0.084 0.137 0.239 0.466
2.80 0.000 0.002 0.004 0.008 0.014 0.021 0.026 0.031 0.036 0.042 0.051 0.067 0.110 0.187 0.356
3.00 0.000 0.001 0.003 0.006 0.011 0.016 0.020 0.024 0.028 0.033 0.041 0.055 0.092 0.153 0.285
3.50 0.000 0.001 0.002 0.003 0.006 0.009 0.012 0.015 0.017 0.021 0.026 0.038 0.067 0.108 0.190
4.00 0.000 0.001 0.001 0.002 0.004 0.006 0.008 0.010 0.012 0.015 0.019 0.029 0.054 0.085 0.146
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
and (6.71) are almost identical and Eq. (6.70) is not valid at where C is in J/mol · K, M is the molecular weight (g/mol), T
P
very low temperatures. The most accurate formulation and is in kelvin, K W is defined by Eq. (2.13), and ω may be deter-
tabulation of properties of water and steam is made by IAPWS mined from Eq. (2.10). Tsonopoulos et al. [16] suggested that
[14]. the correction term C in the above equation should equal to
To calculate ideal gas properties of petroleum fractions, the zero when K W is less than 10 or greater than 12.8. But our
pseudocomponent method discussed in Section 3.3.4 may be evaluations show that the equation in its original form pre-
used. Kesler and Lee [15] provide an equation for direct cal- dicts values of C ig for hydrocarbons in this range of K W very
P
culation of ideal gas heat capacity of petroleum fractions in close to those reported by DIPPR [13]. This equation may
terms of Watson K W , and acentric factor, ω: also be applied to pure hydrocarbons with carbon number
ig 2 2 greater than or equal to C 5 . Ideal gas heat capacities of sev-
C = M A 0 + A 1 T + A 2 T − C B 0 + B 1 T + B 2 T eral hydrocarbons from paraffinic group predicted from Eqs.
P
A 0 =−1.41779 + 0.11828K W (6.66) and (6.72) are shown in Fig. 6.3. As expected heat capac-
A 1 =− 6.99724 − 8.69326K W + 0.27715K 2 × 10 −4 ity and enthalpy increase with carbon number or molecular

W ig
A 2 =−2.2582 × 10 −6 weight. Equation (6.72) generally predicts C of pure hydro-
P
(6.72) B 0 = 1.09223 − 2.48245ω carbons with errors of 1–2% as evaluated by Kesler and Lee
B 1 =− (3.434 − 7.14ω) × 10 −3 [15] and can be used in the temperature range of 255–922 K
(0–1200 F). There are similar other correlations for estima-
◦
B 2 =− (7.2661 − 9.2561ω) × 10 −7 tion of ideal gas heat capacity of natural gases and petroleum
2
(12.8 − K W) × (10 − K W) fractions [17, 18]. The relation reported by Firoozabadi [17]

C =
10ω for calculation of heat capacity of natural gases is in the form

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