An approach of optimal control is developed for predicting the behavior of sucker-rod pumping systems. Our method provides the error correction in prediction, and accurately generates polished rod and intermediate-depth work dynagraphs under any bottom-hole pump condition of vertical oil wells. From the prediction perspective, any normal or abnormal pumping condition of vertical oil wells can be simulated by our method. Our method can replace the conventional prediction methods and are definitely able to predict the complex pumping conditions which the conventional prediction methods cannot predict due to their technical constraints. The prediction results from our method will be of great values to improve the design, selection, installation, and operation of sucker-rod pumping systems. From the diagnostic point of view, a complete databank of surface work dynagraphs corresponding to all the downhole pump conditions of vertical oil wells can be generated by our method and can be used as an expert knowledge system for diagnostic of the sucker-rod pumping systems in the operation situations that only the surface work dynagraphs but not the pump dynagraphs are available. Our method is also a good tool to conveniently generate surface work dynagraphs for pump diagnostic emulators.

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