A Review: Analyzing Beam-Pumped Wells
Authors: Tripp H.A. 
Published: December 2007

Introduction
Currently 85 to 90% of U.S. oil wells are produced by use of sucker rods with beam pumps. Perhaps 25% of these are large units, representing a significant investment in equipment, maintenance, and energy. The systems discussed in this paper monitor and calculate the surface and downhole performance of these large pumping units. For more than 60 years, the surface dynamometer card, which describes the polished-rod displacement vs. load for a pump cycle, has been used to analyze the performance of pump cycle, has been used to analyze the performance of beam-pumped wells. In sucker-rod strings that are more than 3,000 ft [915 m] long, however, stretching caused by fluid load and distortion from reflections of stress waves in the rod string cause significant differences between the surface and downhole pump cards. More than 25 years ago, Gibbs and Neely first used the damped-wave equation, which describes longitudinal vibration in long rods, to calculate the downhole pump card. With minimal changes, this algorithm is still used with the rodstring transmission characteristics and measured surface card to calculate load vs. position cards at the top of each taper and at the downhole pump. The downhole card has become invaluable for identifying subsurface problems and for calculating well production. production. System Description
Analysis systems calculations are based on polished-rod load and position measurements. Portable systems use a load cell mounted in series with the pumping-unit carrier bar and the polished rod and a spool-type variable resistor to measure the polished rod and a spool-type variable resistor to measure the polished-rod position. Some systems include either an amp polished-rod position. Some systems include either an amp probe or a three-phase power meter to measure motor power. probe or a three-phase power meter to measure motor power. Rod loads and displacements were originally recorded on a strip chart and manually transcribed for a remote mainframe computer. Modern portable diagnostic systems use van-mounted computers with data-acquisition systems that directly record 75 or more measurements from each transducer per pump cycle, while the computer monitor displays the real-time pump cycle, while the computer monitor displays the real-time surface card. The analysis, which requires less than one minute after setup, has three parts.

Surface Card.
The measured surface card represents the horsepower at the top of the rod string. Changes in the real-time surface-card shape result from well or system changes, such as the onset of fluid pound. Excessive gearbox torque, rod loads, or major downhole pump problems can frequently be inferred from rod loads and the card shape. In shallow wells, the surface and downhole cards are similar and no additional analysis is needed.

Downhole Card.
Calculating the shape of the downhole card simplifies problems of interpreting pump performance and minimizes the judgment problems of interpreting pump performance and minimizes the judgment required to diagnose subsurface problems. Fig. 1 shows a typical surface card and the calculated downhole pump card. Deviations from the rectangular downhole card shape indicate such problems as deep rod parts, unanchored tubing, improper pump spacing, or leaking pump valves and fluid pound (gas interference). pump valves and fluid pound (gas interference). The downhole card calculations include gross pump stroke, fluid load, and pump inlet pressure. The pumped fluid, calculated from the downhole stroke, is one of the more accurate methods of determining well production. Gross differences between this and the well test are a good indication of a tubing leak, pump malfunction, or bad well test.

Rod-String and Surface-Equipment Analysis.
Alternating rod loads at the surface and at the top of each rod taper are easily converted into stresses, which indicate the susceptibility to fatigue failure when used with a modified Goodman diagram. The maximum polished-rod load also represents pumping-unit beam load. polished-rod load also represents pumping-unit beam load. A complete system analysis includes three-phase power measurements of kilovolt-ampere, kilowatt, kilovar.
JPT
P. 457