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214                            Enhanced Oil Recovery in Shale and Tight Reservoirs


          include the EOR mechanisms of wettability alteration and IFT reduction,
          formulation of these two functions, IFT reduction versus wettability alter-
          ation, surfactants used to alter wettability, determination of wettability, and
          conversion of wetting angles.


               9.2 Mechanisms of interfacial tension (IFT) reduction

               To understand mechanisms of interfacial tension reduction, first review
          the concept of capillary number. The dimensionless capillary number, N C ,is
          defined by the ratio of the viscous to capillary force:

                                        F v   vm
                                   N C ¼   ¼                           (9.1)
                                        F c  scosq
          where F v and F c are viscous and capillary forces, respectively, m is the displacing
          fluid viscosity, v is the pore flow velocity of the displacing fluid, s is the
          interfacial tension (IFT) between the displacing and displaced phases, and q is
          the contacting angle defined by the displacing fluid. A set of consistent units
          are used so that the dimensionless group is dimensionless. For example, v is in
          m/s, m in mPa$s, s in mN/m or dyne/cm.
             Let us first use the above equation to calculate the waterflooding capil-
          lary number in a conventional reservoir. A typical injection velocity may
                                 6
          be 1 ft/day (3.528   10  m/s), the water viscosity is close to 1 mPa$s,
          the oil-water interfacial tension is assumed to be 30 mN/m, and the
          contact angle is assumed zero. Then the corresponding capillary number is
                                           6
                          um    3:528   10  m=s ð1 mPa$sÞ      7
                     N C ¼   ¼                           z10
                           s           ð30 mN=mÞ
             It has been established that as the capillary number is increased, the residual
          oil saturationis decreased, thus the oil recovery will beimproved. The relation-
          ship between the capillary number and the residual oil saturation is the capillary
          desaturation curve (CDC), as shown in the solid curve and square points in
          Fig. 9.1. It is also known that as the capillary number is increased, the residual
          water saturation and residual microemulsion saturation are also decreased.
          The CDCs for them are also presented in this figure. In the figure, the discrete
          data points are experimental data and the smooth curves are fitted curves.
             The presented CDC curves show that when the capillary number is less
          than 0.00,001, even though it is increased from 0.000,001 to 0.00,001, the
          residual oil saturations are barely decreased. It means that for a residual satu-
          ration to be decreased, a minimum capillary number is required; in this case
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