Page 261 - Formation Damage during Improved Oil Recovery Fundamentals and Applications
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232                                                       Xingru Wu







                                  r
                                      r












          Figure 5.8 Porous medium with cylindrical tubes after scale formation.
             The corresponding porosity ratio as follows:
                                       φ 1    2
                                       φ 2  5 X                       (5.12)

             Assuming two cases for the Carman-Kozeny equation: before scale
          formation shown by K 1; and, after scale formation shown by K 2 , then:
                                              3
                                         1   φ D 2
                                  K 1 5       1  s                    (5.13)
                                        72τ    12φ 1    2
                                              3
                                         1   φ D 2
                                  K 2 5       2  s                    (5.14)
                                        72τ    12φ    2
                                                 2
          where τ is tortuosity, D s is the representative diameter of rock, and φ 1
          and φ are porosities before and after scale deposition. Assuming that the
               2
          characteristic diameter and tortuosity remain the same, the ratio of per-
          meability contrast gives:

                                             φ 3
                                              2
                                               2
                                     K 2   ð 12φ 2Þ
                                        5                             (5.15)
                                     K 1     φ 3 1
                                               2
                                           ð 12φ 1Þ
                                   2
             Substituting φ with φ x to get Eq. (5.16):
                                 1
                          2
                                            12φ
                                                    2
                                 K 2    6       1
                                    5 X                               (5.16)
                                 K 1      12φ X  2
                                               1
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