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Spontaneous imbibition                                       301



                   10.8 Effect of viscosity ratio
                   Generally, the wetting phase viscosity (m w ) is used and the nonwetting
              phase viscosity is ignored. Ma et al. (1997) included the effect of nonwetting
                                            p
              phase (oil) viscosity (m nw )by using  m m . However, many experimental
                                             ffiffiffiffiffiffiffiffiffiffiffiffiffi
                                               w nw
              studies (Behbahani and Blunt, 2005; Fischer and Morrow, 2006; Fischer
              et al., 2006) and numerical results (Behbahani and Blunt, 2005) did not
              support that such treatment could be general. Wang et al. (2015b) observed
              in laboratory that as the oil viscosity was lower, the oil recovery from spon-
              taneous imbibition was higher. Makhanov et al. (2014) found that the imbi-
              bition rate of xanthan gum solution was significant despite its high viscosity.
              This suggests that water uptake is mainly controlled through preferential
              adsorption of water molecules by the clay particles, and high viscosity of
              the solution can only partly reduce the imbibition rate.


                   10.9 Effect of initial water content
                   If the initial water saturation S wi is higher than the connate (immobile)
              water saturation S wc , the capillary pressure will be lower but the water (wet-
              ting) phase mobility will be higher. They affect the imbibition in different
              directions. Most of experiments were done at S wc or S wi ¼ 0 so far.


                   10.10 Countercurrent flow versus cocurrent flow

                   In a case of water-wet core which has a high initial oil saturation, the
              space between the outside core and the wall of the imbibition cell is full of
              water. The water and oil phase pressures in the imbibition cell is the same,
              but the oil phase pressure inside the core is higher because the capillary pres-
              sure is positive. Then oil will flow from the inside of the core to the outside.
              Meanwhile the water outside the core will flow toward the inside. Thus
              countercurrent flow occurs by the capillary force. In laboratory, oil can be
              seen to flow out of the core from all the faces of the core.
                 In the above system, if chemicals, a surfactant as an example, are added in
              the water so that the water-oil interfacial tension is reduced, the water-oil
              capillary pressure is significantly reduced, and the gravity force can over-
              come the capillary force. Then water will push oil from the bottom of
              the core. Both oil and water will flow out of the top face of the core in
              the same vertical direction. This flow is called cocurrent flow.
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