This study presents a 3D analytical model to analyze the transient flow into perforated vertical wells. The model considers arbitrary phasing angle, non-uniform perforation size and length, and formation damage around perforations. The characteristics of transient pressure and derivative responses of perforated wells are investigated and the flow regimes are documented. Asymptotic approximations for each flow regime are provided. A sensitivity study is carried out to identify the impact of various reservoir and completion parameters on the transient pressure and derivative responses as well as the productivity of the well. It is observed that convergent flow into perforations significantly influences the early-time and intermediate-time pressure responses. A pseudoskin expression to be used to estimate the inflow performance of perforated vertical wells is also presented.

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