PCP Axial Load: Theory and Lab Results

Abstract

Abstract Accurate estimation of pump axial load in Progressing Cavity Pump (PCP) applications is an important aspect of the installation design. It affects the calculation of rod stresses, and therefore the determination of the rod string torque capacity. In deviated wells, it also directly affects the calculated rod-tubing contact loads, and therefore the evaluation of wear related issues. This paper discusses the current theory related to the calculation of axial load in PCP applications, in light of laboratory test results obtained with 25 different pump models. The axial load is normally estimated by multiplying the differential pressure across the pump by an effective pump cross sectional area. However, given the complexity of the pump geometry, it is not straightforward how to properly calculate this effective area. In the paper, it is shown that intuitive choices, such as the circle defined by the rotor minor diameter, the circle defined by the rotor major diameter, or the pump cavity area, do not yield adequate results. A new method is suggested that not only matches quite well the extensive laboratory data for single-lobe pumps but also matches reasonably well the limited data available for multi-lobe pumps. Introduction In a PCP application, the dominant load affecting stresses in the rod string is torque. Axial load does exist, however, both due to rod weight and due to a load generated at the downhole pump, and it can be significant in many cases. Other design considerations affected by the rod string axial load are pump space-out and, in deviated wells, rod-tubing wear and rod fatigue life. It is therefore quite important to be able to accurately calculate the axial load in many PCP applications. Calculation of Pump Axial Load The axial load generated at the pump is normally estimated based on the pressure forces acting on the pump rotor, which is connected to the rod string, as illustrated in Figure 1. Note that, for a downhole-driven PCP, the formulation would be slightly different. The pump axial load is therefore determined by multiplying the differential pressure across the pump by an effective pump cross sectional area, and applying a small correction to account for the cross sectional area of the rod string:Equation 1 whereEquation 2 The geometry of a PCP pump is somehow complex; so, it is not immediately obvious what value for the cross-sectional area (Aeff) area one should use. A few approaches have been suggested in the literature1,2,3, and the formulas most commonly used in the industry, for single-lobe pumps, are listed below.