Diagnostic Analysis of Dynamometer Cards
Authors: Eickmeier J.R. 
Published: December 2007

Abstract
A diagnostic method incorporating computer analysis of dynamometer cards is being used to determine load displacement conditions at the pump plunger and at intermediate points in the sucker rod string. Pump dynagraph cards generated by a computer program are evaluated to determine down-hole pumping conditions. Pump intake pressures calculated from the down-hole dynagraph cards provide essential information on well performance. Load conditions at the top of each rod string taper can be examined to determine maximum rod stresses and stress ranges. Rod strings can be altered to obtain balanced rod string loading where it is evident that designs are not satisfactory.

Introduction
A diagnostic method of analyzing dynamometer cards is being used in production operations in Venezuela, in the United States and in Canada. Shell Canada first utilized the diagnostic technique in Oct., 1963. To mid-year 1966 approximately 800 cards have been analyzed from more than 300 wells being pumped in western Canada and the diagnostic technique has become indispensable to production operations. The diagnostic technique provides a method of evaluating down-hole pumping performance. With conventionally obtained dynamometer cards, only a qualitative and somewhat dubious interpretation of pumping conditions can be inferred from visual inspection of the surface cards. However, with the diagnostic technique the pump dynagraph card is calculated by computer analysis of the surface dynamometer card. The pump dynagraph card accurately describes the down-hole pumping conditions. Intermediate sucker rod stresses are also generated by the program. In essence, through the use of mathematical solution of the sucker rod pumping system, the measured surface loads are decoded to determine the down-hole loads. Determination of bottom-hole pumping conditions by a production engineer utilizing the diagnostic technique is analogous to determination of a patient's heart condition by a doctor utilizing an electrocardiograph. In both cases, one is trying to determine conditions which cannot be readily determined from visual or surface inspection and in both cases recommendations for corrective action where necessary can be made based on both qualitative and quantitative interpretation of the results. The diagnostic method of analysis was developed by S. G. Gibbs and A. B. Neely who have published a paper on the subject. Included in their paper is the derivation of the equations giving the mathematical solution for the sucker rod pumping system. Pump dynagraph cards which were obtained using the diagnostic technique and which illustrate various pumping conditions are discussed in this paper. Also discussed are the applications of the technique in examining declines in producing well capability and in studying sucker rod string loading conditions.

DELTA II DYNAMOMETER
All surface dynamometer cards analyzed by means of the diagnostic technique were obtained using the Delta II Dynamometer. The dynamometer consists of a strain gauge load cell, a polished rod displacement transducer and a dual channel self-balancing recorder. The load cell is mounted in the conventional manner between the carrier bar and the polished rod clamp. Its electrical original is fed to one channel of the recorder. The displacement transducer consists of a potentiometer coil coupled to a constant torque retractable pulley on which a cable is wound. The free end of the cable is affixed to the polished rod. Vertical polished rod action is thus converted to rotary motion resulting in a change in resistance of the potentiometer. The output signal is fed to the other recorder channel. A typical strip chart record of load and displacement vs time is illustrated in Fig. 1. Component items of equipment comprising the Delta 11 Dynamometer are discussed in a paper by W. F. Herbert.

IDEAL DYNAGRAPH CARDS
Ideal pump dynagraph cards are shown in Fig. 2. The direction of the upstroke is indicated by arrows. During the upstroke the load is greater because of the static weight of fluid above the plunger. The pump dynagraph cards illustrate a pumping situation where complete fluid fill is occurring, where there is no gas compression or expansion during the stroke and where both traveling and standing valves are holding. Relative displacement is referenced to ground level in the mathematical solution of the sucker rod pumping system. Consequently, displacement shown on the pump dynagraph is relative to ground rather than to the tubing as was the case with the original pump dynagraph developed by W. E. Gilbert.'As shown in Fig. 2A, if there is no tubing movement the card has a rectangular shape. If tubing movement does occur the card has a parallelogram shape (Fig. 2B).
JPT
P. 97ˆ