Abstract: Aimed at the issue that the concave-S-shaped water cut rising law of water flooding oilfield is difficult to diagnose and the fitting effect is unsatisfactory,considering the circumstance that the S-shaped water cut rising curve deviates from the straight line in the high water cut stage,and the concave water cut rising curve strengthens or weakens the S-shaped water cut rising curve,the quadratic term,the logarithmic term related to water saturation and the morphological index n related to water cut are introduced,and the extended water flooding curve equation characterizing the "concave S-shaped" water cut rising law is established.The new equation integrates the characteristics and advantages of concave and S-shaped water cut rising curves,broadens the application scope of conventional water cut rising curves,and enhances the accuracy of the description of the water cut rising law.The research results are applied to WZ Oilfield.The outcomes reveal that the relevant parameters of the equation are acquired by employing the multiple regression analysis method,and the "concave-S shaped" water cut rising law is comprehensively characterized.The fitting effect is significantly enhanced,and the fitted R² reaches 0.977 8.In the actual application process,the coefficient of the extended waterflooding curve equation can be acquired through regression based on the existing production data,and the cumulative oil production at different water cuts can be predicted correspondingly,or the water cut at different cumulative oil production can be predicted.The research outcomes play a crucial role in accurately analyzing or predicting the law of water cut rise in oilfields.

Key words: concave-S shape water cut rising law, waterflooding curve, morphological index, characterization method, multiple regression