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Guo, Boyun / Computer Assited Petroleum Production Engg 0750682701_chap18 Final Proof page 271 4.1.2007 10:04pm Compositor Name: SJoearun




                                                                              PRODUCTION OPTIMIZATION  18/271
                                                                  N c
                       Gas expansion pressures for hydrate formation can be  X  X  z i
                                                                        N c
                       found from the chart prepared by Katz (1945) or Guo  x i ¼  n L þ k i n V  ¼ 1,  (18:11)
                       and Ghalambor (2005). Liquid and vapor phase densities  i¼1  i¼1
                       can be predicted by flash calculation.    where N c is the number of compounds in the fluid. Com-
                         Following the special requirement for construction of  bining Eqs. (18.1) and (18.8) also gives
                       low-temperature separation units, the pressure-reducing
                                                                    y i
                       choke is usually mounted directly on the inlet of the  z i ¼  n L þ y i n V ,  (18:12)
                       high-pressure separator. Hydrates form in the downstream  k i
                       of the choke because of the low gas temperature and fall to  which yields
                       the bottom settling section of the separator. They are
                       heated and melted by liquid heating coils located in the  y i ¼  z i k i  :  (18:13)
                       bottom of the separator.                     n L þ k i n V
                         Optimization of separation pressure is performed with
                       flash calculations. Based on the composition of well-  Mass balance applied to Eq. (18.13) requires
                       stream fluid, the quality of products from each stage of  X  X
                                                                       N c
                                                                  N c
                       separation can be predicted, assuming phase equilibriums  y i ¼  z i k i  ¼ 1:  (18:14)
                       are reached in the separators. This requires the knowledge  i¼1  i¼1  n L þ k i n V
                       of the equilibrium ratio defined as
                                                                 Subtracting Eq. (18.14) from Eq. (18.11) gives
                           y i
                       k i ¼  ,                            (18:1)
                                                                  N c
                                                                             N c
                           x i                                   X     z i   X   z i k i
                                                                                      ¼ 0,          (18:15)
                       where                                     i¼1  n L þ k i n V  i¼1  n L þ k i n V
                         k i ¼ liquid/vapor equilibrium ratio of compound i
                         y i ¼ mole fraction of compound i in the vapor phase  which can be rearranged to obtain
                         x i ¼ mole fraction of compound i in the liquid phase.  X  z i (1   k i )
                                                                  N c
                                                                           ¼ 0:                     (18:16)
                       Accurate determination of k i values requires computer  n L þ k i n V
                                                                 i¼1
                       simulators solving the Equation of State (EoS) for hydro-
                       carbon systems. Ahmed (1989) presented a detailed  Combining Eqs. (18.16) and (18.7) results in
                       procedure for solving the EoS. For pressures lower than
                                                                  N c
                       1,000 psia, a set of equations presented by Standing (1979)  X  z i (1   k i )
                                                                              ¼ 0:                  (18:17)
                       provide an easy and accurate means of determining k i  n V (k i   1) þ 1
                                                                 i¼1
                       values. According to Standing, k i can be calculated by
                                                                 This equation can be used to solve for the number of mole
                           1
                       k i ¼ 10 aþcF i  ,                  (18:2)  of fluid in the vapor phase n v . Then, x i and y i can be
                           p                                     calculated with Eqs. (18.10) and (18.13), respectively. The
                                                                 apparent molecular weights of liquid phase (MW) and
                       where
                                                                 vapor phase (MW) can be calculated by
                                     4
                                               9 2
                        a ¼ 1:2 þ 4:5   10 p þ 1:5   10 p  (18:3)       X
                                                                        N c
                                                                     L
                                      4
                                                8 2
                        c ¼ 0:89   1:7   10 p   3:5   10 p  (18:4)  MW ¼  x i MW i                  (18:18)
                                                                    a
                                                                        i¼1
                              1  1
                                                                        N c
                       F i ¼ b i                           (18:5)       X
                             T bi  T                             MW  V  ¼  y i MW i ,               (18:19)
                                                                    a
                              p ci                                      i¼1
                           log
                       b i ¼  14:7  ,                      (18:6)  where MW i is the molecular weight of compound i. With
                            1   1
                                                                 the apparent molecular weight of the vapor phase known,
                           T bi  T ci                            the specific gravity of the vapor phase can be determined,
                                                                                                  3
                       where                                     and the density of the vapor phase in lb m =ft can be
                         p c ¼ critical pressure, psia           calculated by
                         T b ¼ boiling point, 8R                     MW p
                                                                        V
                         T c ¼ critical temperature, 8R.         r V ¼  a  :                        (18:20)
                                                                      zRT
                                                                                        3
                       Consider 1 mol of fed-in fluid and the following equation  The liquid phase density in lb m =ft can be estimated by the
                       holds true on the basis of mass balance:  Standing method (1981), that is,
                       n L þ n V ¼ 1,                      (18:7)            62:4g oST þ 0:0136R s g g
                                                                 r L ¼          h  q ffiffiffiffi        i 1:175  ,
                       where                                                        g g  þ 1:25 T   460Þ
                                                                                          ð
                                                                     0:972 þ 0:000147 R s
                         n L ¼ number of mole of fluid in the liquid phase          g o
                         n V ¼ number of mole of fluid in the vapor phase.                          (18:21)
                                                                 where
                       For compound i,
                                                                   g oST ¼ specific gravity of stock-tank oil, water
                       z i ¼ x i n L þ y i n V ,           (18:8)   g g ¼ specific gravity of solution gas, air ¼ 1
                       where z i is the mole fraction of compound i in the fed-in  R s ¼ gas solubility of the oil, scf/stb.
                       fluid. Combining Eqs. (18.1) and (18.8) gives
                                                                 Then the specific volumes of vapor and liquid phases can
                       z i ¼ x i n L þ k i x i n V ,       (18:9)  be calculated by
                       which yields                                   zn V RT sc
                                                                 V Vsc ¼                            (18:22)
                             z i                                        p sc
                       x i ¼      :                       (18:10)
                           n L þ k i n V                              n L MW  L
                                                                  V L ¼    a  ,                     (18:23)
                       Mass balance applied to Eq. (18.10) requires       L
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