This study presents a transient inflow-performance relationship (IPR) model using the steady-state solution to the diffusivity equation on a periodic varying well-flowing pressure. A wellbore model can be coupled to accurately depict the deliverability from wells with an artificial-lift system (ALS), such as gas lift and plunger lift. The commercial simulators allowed verification of model results and field data validated the solution approach.

For verification of this simplified IPR modeling approach, we first attempted to replicate two-step rate flow and shut-in periods, such as those associated with a transient flow test. Our model successfully reproduced those transient pressure profiles obtained from a rigorous superposition approach, generated with an analytical model using a commercial software package. Thereafter, we replicated the results of a coupled wellbore/reservoir model for a gas-lift well, using a numerical simulator. The difference between the results of rigorous simulators and our simplified transient-IPR model turned out to be well within engineering accuracy.

Field data from two plunger lift operations validated the transient-IPR model presented in this study. One important aspect to note is that a smaller period of oscillation translates into a more significant error between the traditional steady-state IPR model and the actual transient-IPR model. This finding suggested the need for the accuracy of the transient-IPR model in ALS to express the realistic rates and pressures. By capturing the essence of transient behavior, it is possible to combat downhole tool failures due to large pressure fluctuations or issues with surface metering due to higher than expected rates.

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