Page 240 - Characterization and Properties of Petroleum Fractions - M.R. Riazi
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QC: IML/FFX
  P1: IML/FFX
            AT029-Manual
                                           August 16, 2007
  AT029-05
         220 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
                                  (0)
                                         (1)
                TABLE 5.11—Values of Z
                                           for use in Eq. (5.107) from the Lee–Kesler modification of BWR EOS—Eq. (5.109) [59].
                                     and Z
                                         (0)
                                        Z
         T r → P r P2: IML/FFX AT029-Manual-v7.cls  T1: IML  17:42                       Z (1)
         ↓             10          11          12         14          10           11           12           14
         0.30         2.851       3.131      3.411       3.967       −0.792       −0.869      −0.946       −1.100
         0.35         2.554       2.804      3.053       3.548       −0.886       −0.791      −1.056       −1.223
         0.40         2.321       2.547      2.772       3.219       −0.894       −0.978      −1.061       −1.225
         0.45         2.134       2.340      2.546       2.954       −0.861       −0.940      −1.019       −1.173
         0.50         1.980       2.171      2.360       2.735       −0.810       −0.883      −0.955       −1.097
         0.55         1.852       2.029      2.205       2.553       −0.752       −0.819      −0.885       −1.013
         0.60         1.744       1.909      2.073       2.398       −0.693       −0.753      −0.812       −0.928
         0.65         1.652       1.807      1.961       2.266       −0.635       −0.689      −0.742       −0.845
         0.70         1.573       1.720      1.865       2.152       −0.579       −0.627      −0.674       −0.766
         0.75         1.505       1.644      1.781       2.053       −0.525       −0.568      −0.610       −0.691
                      1.446       1.578      1.708       1.966       −0.474       −0.512      −0.549       −0.621
         0.85         1.394       1.520      1.645       1.890       −0.425       −0.459      −0.491       −0.555
         0.90         1.350       1.470      1.589       1.823       −0.379       −0.408      −0.437       −0.493
         0.95         1.311       1.426      1.540       1.763       −0.334       −0.360      −0.385       −0.434
         0.98         1.290       1.402      1.513       1.731       −0.308       −0.331      −0.355       −0.401
         0.99         1.284       1.395      1.504       1.721       −0.299       −0.322      −0.345       −0.390
         1.00         1.277       1.387      1.496       1.710       −0.290       −0.313      −0.335       −0.379
         1.01         1.271       1.380      1.488       1.701       −0.282       −0.304      −0.326       −0.368
         1.02         1.265       1.373      1.480       1.691       −0.273       −0.295      −0.316       −0.357
         1.03         1.259       1.367      1.473       1.682       −0.265       −0.286      −0.307       −0.347
         0.80 --`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
         1.04         1.254       1.360      1.465       1.672       −0.256       −0.277      −0.297       −0.337
         1.05         1.248       1.354      1.458       1.664       −0.248       −0.268      −0.288       −0.326
         1.06         1.243       1.348      1.451       1.655       −0.239       −0.259      −0.278       −0.316
         1.07         1.238       1.342      1.444       1.646       −0.231       −0.250      −0.269       −0.306
         1.08         1.233       1.336      1.438       1.638       −0.222       −0.241      −0.260       −0.296
         1.09         1.228       1.330      1.431       1.630       −0.214       −0.233      −0.251       −0.286
         1.10         1.223       1.325      1.425       1.622       −0.206       −0.224      −0.242       −0.276
         1.11         1.219       1.319      1.419       1.614       −0.197       −0.215      −0.233       −0.267
         1.12         1.214       1.314      1.413       1.606       −0.189       −0.207      −0.224       −0.257
         1.13         1.210       1.309      1.407       1.599       −0.181       −0.198      −0.215       −0.247
         1.15         1.202       1.299      1.395       1.585       −0.164       −0.181      −0.197       −0.228
         1.20         1.184       1.278      1.370       1.552       −0.123       −0.139      −0.154       −0.183
         1.25         1.170       1.259      1.348       1.522       −0.082       −0.098      −0.112       −0.139
         1.30         1.158       1.244      1.328       1.496       −0.042       −0.058      −0.072       −0.097
         1.40         1.142       1.220      1.298       1.453        0.035        0.019        0.005      −0.019
         1.50         1.134       1.205      1.276       1.419        0.106        0.090        0.076        0.052
         1.60         1.132       1.197      1.262       1.394        0.167        0.152        0.138        0.116
         1.70         1.134       1.193      1.253       1.374        0.218        0.204        0.192        0.171
         1.80         1.139       1.192      1.247       1.359        0.258        0.247        0.237        0.218
         2.00         1.152       1.196      1.243       1.339        0.310        0.305        0.300        0.290
         2.50         1.176       1.210      1.244       1.316        0.348        0.356        0.362        0.371
         3.00         1.185       1.213      1.241       1.300        0.338        0.353        0.365        0.385
         3.50         1.183       1.208      1.233       1.284        0.319        0.336        0.350        0.376
         4.00         1.177       1.200      1.222       1.268        0.299        0.316        0.332        0.360
         High Pressure Range: Value of Z (0)  and Z (1)  for 10 ≤ P r ≤ 14.
                                                                                                               ◦
         similar to the Kay’s mixing rule. Application of Kay’s mixing  Solution—For n-octane, from Example 5.2, T c = 295.55 C
         rule, expressed by Eq. (3.45), gives the following relations for  (568.7 K), P c = 24.9 bar, ω = 0.3996. T r = 0.972, and P r = 0.8.
         calculation of pseudocritical temperature and pressure:  From Table 5.9 it can be seen that the point (0.972 and 0.8) is
                                                              on the saturation line; therefore, there are both liquid and va-
                                                                                                         (1)
                                                              por phases at this condition and values of Z (0)  and Z are sep-
        (5.116)       T pc =  x i T ci  P pc =  x i P ci
                                        N !
                           N !
                          i=1           i=1                   arated by dotted lines. For the liquid phase at P r = 0.8, extrap-
                                                              olation of values of Z (0)  at T r = 0.90 and T r = 0.95 to T r = 0.972
         where T pc and P pc are the pseudocritical temperature and  gives Z (0)  = 0.141 + [(0.972 − 0.93)/(0.95 − 0.93)] × (0.141 −
         pressure, respectively. Generally for simplicity pseudocriti-  0.1359) = 0.1466, similarly we get Z (1)  =−0.056. Substitut-
         cal properties are calculated from Eqs. (5.116); however, use  ing Z (0)  and Z (1)  into Eq. (5.107) gives Z = 0.1466 + 0.3996 ×
                                                                                              L
         of Eqs. (5.115) for the LK correlations gives better property  (−0.056) = 0.1242. Similarly for the vapor phase, values of
         predictions [59].                                    Z (0)  and Z (1)  below the dotted line should be used. For this
                                                              case linear interpolations between the values for Z (0)  and
         Example 5.6—Repeat Example 5.2 using LK generalized cor-  Z (1)  at T r = 0.97 and T r = 0.98 for the gas phase give Z (0)  =
                                                                                                        V
                                  L
                            V
         relations to estimate V and V for n-octane at 279.5 C and  0.5642, Z (1)  =−0.1538. From Eq. (5.107) we get Z = 0.503.
                                                     ◦
                                                                                                     L
         19.9 bar.                                            From Eq. (5.15) corresponding volumes are V = 286.8 and








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