Page 260 - Formation Damage during Improved Oil Recovery Fundamentals and Applications
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Formation Damage by Inorganic Deposition                     231


              5.3.3 Formation damage from scale deposition
              Field operations have observed scale-dropout issues, both in the reservoir
              and near wellbore, and recognized that they can have a significant impact
              on well performance and operations (Paulo et al., 2001, Sorbie and
              Mackay, 2000). However, there is no accepted model in practice to quan-
              tify the relationship between the amount of deposition and changes on
              reservoir properties. Some efforts to establish such a relationship are based
              on many assumptions of idealized models. Assuming the reservoir rock
              can be represented by a bundle of tubes of different radii, the modified
              Carman-Kozeny model can be used to understand the relationship
              (Hajirezaie et al., 2017).
                 Eq. (5.9) can be used to calculate the change in porosity resulting
              from mineral dissolution/precipitation:
                                                        !
                                           n m  N β   N 0
                                  ^
                                           X

                                  φ 5 φ 2          2   β                  (5.9)
                                                ρ     ρ
                                           β51   β     β
                     ^
              where, φ is the reference porosity when dissolution/precipitation is

              included, φ is the reference porosity without mineral dissolution/precip-
              itation and ρ is the molar density of mineral β.
                         β
                 If there are n cylindrical tubes in the medium, the corresponding
              porosity is calculated based on the following equation:
                                             P    2 0
                                                πr l
                                        φ 5    n                         (5.10)
                                         1
                                               BV
                 Here, BV stands for bulk volume, r denotes the pore radius, and l’ is
              the length of tubes. Assuming that scale formation has occurred as shown
              in Fig. 5.8 with the same thickness of scale in each pore, the correspond-
              ing porosity is calculated based on the new radius of the tubes r’ using
              Eq. (5.11):

                                                πr l
                                            P
                                                  02 0
                                       φ 5     n                         (5.11)
                                         2
                                               BV
                 Defining,
                                           r 0
                                             5 X
                                           r
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