A progressing cavity pump (PCP) is a positive displacement pump with an eccentric screw movement, which is used as an artificial lift method in oil wells. Downhole PCP systems provide an efficient lifting method for heavy oil wells producing under cold production, with or without sand. Newer PCP designs are also being used to produce wells operating under thermal recovery. The objective of this study is to develop a set of theoretical operational, fluid property, and pump geometry dimensionless groups that govern fluid flow behavior in a PCP. A further objective is to correlate these dimensionless groups to develop a simple model to predict flow rate (or pressure drop) along a PCP. Four PCP dimensionless groups, namely, Euler number, inverse Reynolds number, specific capacity number, and Knudsen number were derived from continuity, Navier–Stokes equations, and appropriate boundary conditions. For simplification, the specific capacity and Knudsen dimensionless groups were combined in a new dimensionless group named the PCP number. Using the developed dimensionless groups, nonlinear regression modeling was carried out using large PCP experimental database to develop dimensionless empirical models of both single- and two-phase flow in a PCP. The developed single-phase model was validated against an independent single-phase experimental database. The validation study results show that the developed model is capable of predicting pressure drop across a PCP for different pump speeds with 85% accuracy.

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