Plunger leakage and viscous drag for beam pump systems
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Abstract
Many pump slippage formulas have been developed over the years. Most of these formulas over predict the pump slippage and a more accurate formula is needed. A slippage formula is required for plunger lubrication, pump efficiency and plunger pump production calculations to maximize production. Historical models are discussed and compared, which include Robinson (1935), Davis and Steams (1944), Robinson and Reekstin (1960), Davis, Steams, and Reekstin (1960), and the ARCOHarbinson Fisher (2000). A new method for calculating slippage is introduced. This method involves calculating a velocity profile for an annulus with the inner wall moving parallel to the outer wall. An average velocity is determined for the annular fluid flow, which in turn is used to calculate the fluid slippage. Eccentricity is also considered in the slippage calculation method. The method is compared to the historical formulas. A formula to calculate viscous drag on the pump plunger, which takes into account eccentricity, is also derived from the velocity profile.