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Spontaneous imbibition                                       297


              what value of the diffusion coefficient is used. About 22% oil is recovered by
              w1.3 million days of imbibition, indicating diffusion is a very slow process.
              Reducing and increasing the diffusion coefficient by 10 and increasing it by
              100 times result in about (0.1e0.2)% difference in the oil recovery factor,
              showing the oil recovery is not sensitive to the diffusion coefficient. In other
              words, the diffusion cannot be a dominant mechanism.
                 When the IFT is 20 mN/m, the oil recovered is about 5% by 138 days of
              spontaneous imbibition, much higher than those when the IFT is
              0.008 mN/m. The discussion in this section shows that a high IFT is needed
              for the capillary pressure to help diffusion play the role. When the IFT is
              low, capillary pressure as a driving force will be low, leading to low diffusion.


                   10.7 Effect of gravity
                   When the rock permeability is high, the gravity force and the capillary
              pressure together determine the fluid distribution through imbibition. In the
              case of initial oil-wetness and the wettability is altered by a surfactant solu-
              tion, the imbibition rate and the oil recovery become higher as the IFT is
              lower. This has been verified by some experiments (e.g., Schechter et al.,
              1991) and by a numerical simulation study, as shown in Fig. 10.9 (Sheng,
              2013b). The figure shows that when the IFT is 0.049 mN/m, oil can barely
              be recovered by water imbibition because the core is initially oil-wet, and
              the capillary force is resistant to the surfactant solution imbibition into the
              core to displace oil out. When the IFT becomes lower (0.0323 or
              0.0088 mN/m), oil is driven out by gravity which overcomes the capillary





















              Figure 10.9 Effect of IFT on oil recovery by surfactant solution imbibition (Sheng,
              2013b).
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