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388                            Enhanced Oil Recovery in Shale and Tight Reservoirs























               Figure 12.49 Stabilized oil rate versus invasion depth in an oil-wet chip.

          decreased with invasion as shown in Fig. 12.49. Those preceding figures
          show that when the invasion depth was shallower, the flow back efficiency
          and stabilized oil rate for the water were higher than those for surfactants.
          This is because the surfactant reduced the capillary pressure gradient; but
          as the invasion depth became deeper, the surfactant-reduced IFT resulted
          in higher capillary numbers (in the order of 10  4  vs. 10  5  for water in
          the Tangirala and Sheng’s (2018) experiments), and the flow efficiency
          was improved compared with water.
             The preceding results and conclusions in oil-wet chips were verified by
          core flooding results (Tangirala et al., 2019). For the same fixed invasion
          depth, the remaining (residual) oil saturation (S w2 ) at the end of flow back,
          the flow back efficiency (flb), and the stabilized oil rate (Q o ) were compared
          for water flooding with and without a surfactant. The following parameters
          X, Y, and Z were defined:

                                   ðS w2 Þ   ðS w2 Þ
                                        water      surf
                             X ¼                                     (12.7)

                                   ðS w2 Þ water   ðS w2 Þ surf max
                                    ðflbÞ surf   ðflbÞ water
                              Y ¼                                    (12.8)
                                    ðflbÞ   ðflbÞ
                                       surf    water max
                                    ðQ o Þ    ðQ o Þ
                                        surf     water
                             Z ¼                                     (12.9)
                                    ðQ o Þ    ðQ o Þ
                                       surf     water max
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