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298                            Enhanced Oil Recovery in Shale and Tight Reservoirs


















             Figure 10.10 Effect of gravity on incremental recovery factor (Sheng, 2013b).

          resistance. Fig. 10.10 shows as the density difference between oil and water
                 3
          (1 g/cm ) is large, the incremental oil recovery due to gravity effect is
          higher. The incremental oil recovery is the oil recovered over that recovered
          when the oil density is equal to the water density.
             When the gravity dominates an imbibition process, Cuiec et al. (1994)
          proposed a scaled or normalized time which is defined as the real imbibition
          time divided by the reference time (t g ):
                                          L c m o
                                     t g ¼                          (10.20)
                                         kðDrÞg
          where t g is the ratio of viscous force to gravity force, m o is the oil viscosity, k is
          the permeability, L c is the characteristic length, and Dr is the density dif-
          ference between water and oil. When the normalized time is used to plot the
          oil recovery factors from the simulation models of different scales (different
          L c ), the recovery factor curves overlap each other, as shown in Fig. 10.11
          (Sheng, 2013b). This indicates that the gravity is the dominant mechanism.
             In a practical case, both capillary force and gravity force act in the imbi-
          bition process. To define the relative importance of the two forces, the Bond
          number is defined:
                                          kðDrÞg
                                    N B ¼                           (10.21)
                                            s
             A higher Bond number represents a higher gravity force. Morrow and
          Songkran’s (1981) data showed that as the Bond number was increased
          (higher dip angle), the trapped oil saturation became lower (higher oil re-
          covery) (See Fig. 10.12). A higher Bond number can also be achieved by
          lower IFT, higher permeability, and high density-difference. In the case
          of ultralow IFT, the flow is dominated by gravity segregation. The flow is
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