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An Introduction to Enhanced Oil Recovery                                             23


                      For downstream minus upstream pressure
                                                           2σcosθ
                                                8μ L w v 1          8μ L o v 1
                                                   w
                                                                       o
                                      P A 2 P B 5       2         1
                                                   r 2 1     r 1       r 2 1
                                          μ 1 μ 5 μ and L w 1 L o 5 L; so
                                            o   w
                                                      8μLv 1
                                              ΔP AB 5       2 ΔP c1
                                                        r 1 2
                      For displacement of trapped oil fluid velocity in both pores must be positive;
                   therefore ΔP AB should be more than ΔP c1 and also more than ΔP c2 . Because of the
                   size structure of the pores, ΔP c1 is more than ΔP c2 .


                                                   ΔP AB . ΔP c1
                                               8μLv 1
                                                     2 ΔP c1 . ΔP c2
                                                 r 2
                                                 1
                      By applying capillary pressure equations, the required velocity to push oil in a big-
                   ger pore (for having positive velocity in a bigger pore) can be calculated as:

                                                   σcosθr 2    1  1
                                              v 1 .     1     2
                                                     μL    r 1  r 2





                        1.14 MICROSCOPIC DISPLACEMENT OF FLUIDS IN THE
                        RESERVOIR (ED)

                        An essential part of any EOR process consists of the ability of the injected fluids
                   to displace oil in the pore space at a microscopic scale. The microscopic displacement
                   efficiency, E D , has a significant impact on the success or failure of a project. For crude
                   oil, microscopic efficiency depends on the magnitude of residual oil (S or ) at the end of
                   the process where the displacing fluid is in contact with the displaced fluid.
                   Nonetheless, since the EOR processes are usually associated with the injection of
                   many slugs, the efficiency of each of the fluids is different in the porous environment
                   of the reservoir. Moreover, low efficiency leads to early fingering phenomenon and
                   consequently to poor performance in the injection process [1].
                      Capillary and viscous forces and viscosity of fluids and their mobility in porous
                   media are among the important parameters affecting the microscopic displacement
                   that are worth investigating as a research topic.

                   1.14.1 Macroscopic Displacement Efficiency
                   The oil efficiency in each displacement depends on the volume of the reservoir in
                   contact with the fluid injected. The Volumetric Sweep Efficiency is a measure that
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