Downhole Beam Pump Operation: Slippage and Buckling Forces Transmitted to the Rod String
Authors: Nickens H. , Lea J.F. , Cox J.C. , Bhagavatula R. , Garg D. 
Published: March 2010

Abstract
New results for downhole beam or rod pumps from fairly recent test data are in conflict with traditional relationships. Additional testing is in progress. A pump with large plunger/barrel clearance will cause high fluid slippage. A pump with smaller clearance will cause less fluid slippage, but a tighter fit will tend to increase rod buckling at the pump to a greater degree and may lead to advanced pump and rod wear rates. Therefore, it is important to be able to predict pump slippage and also related forces at the downhole pump. Considerations for pump leakage and example calculations are presented using the older and the new pump slippage relationships. A derivation to account for the pump velocity effects on slippage is also presented. The effect of pump clearances on possible rod buckling above the pump is also studied. Further additional possible causes of rod buckling are presented, discussed, and compared. The results will help the reader to decide on sizing pump clearances to provide leakage for pump lubrication without losing too much on pump efficiency. Several ideas on the sources of rod buckling, such as flow through the travelling valve, and the plunger-barrel interaction are presented and compared. A review of methods to combat rod buckling above the pump is presented.

Introduction
Pump slippage occurs primarily on the upstroke, occurs through the plunger-barrel interface, and serves to lubricate the plungerbarrel action. Usual industry minimum requirements are quoted to be in the range of 2 – 5% of production to provide lubrication. This figure could come under scrutiny when slippage becomes better defined. If the slippage is too large, then the system becomes inefficient. This can be due to a worn plunger-barrel, and/or travelling valve, or sizing the pump with an excessive clearance.
Recent tests(1–3) indicate that older equations(4, 5) used by industry for years may have over-predicted the slippage. If verified, then pumps can be sized with larger clearances, reducing plungerbarrel friction, and possibly eliminating some of the compression at the bottom of the rod string without allowing excessive leakage. In this paper, a derivation of the slippage equation is developed, which also gives a contribution to slippage due to plunger velocity.
Since buckling considerations may arise from pump clearance and other factors, rod buckling equations are presented and reviewed. Rods buckle due to outside forces acting up against the bottom of the rod string on the downstroke. It is well known that buoyancy forces do not contribute to buckling(6). Thus, only negative "effective" forces that exclude buoyancy contribute to buckling and "true forces" that include buoyancy should not be used when considering buckling. An example of how to calculate the rod projected area and buoyancy induced pressure forces is presented and examples of calculating "true forces" and "effective forces: are also presented.
Contributing factors to rod buckling include the force to slide the plunger in the barrel and also the pressure drop across the travelling valve as the pump travels downward.