Rod String Research Articles

Denver Unit Well Surveillance and Pump-Off Control System

This paper describes a prototype system that demonstrates the technicalfeasibility of installing and operating an on-line, computer-based wellsurveillance and control system. This system provides a much higher levelof surveillance and control than possible with conventional equipment.Expansion of the system will include all wells and facilities in the DenverUnit of Wasson Field. Introduction Approval was obtained in Oct. 1974 to install a pilotcomputer production control (CPC) system to serve abattery (Battery 3) of the Denver Unit, Wasson Field.The test battery area contained 76 beam pumped wells, four satellite separation and test facilities, andtreating and storage facilities in the battery. The pump-off control portion of the system, whichmonitors and controls the individual wells, becameoperational in June 1976. Automatic well testing becameoperational in Feb. 1977. The system basically consistsof a small wellhead remote unit at each well, a largerremote unit at each satellite, and the battery. Thewellhead remote units take signals from the load andposition transducers on the pumping units and transmit position transducers on the pumping units and transmit the data to the pump-off control (POC) computer locatedin the production office at Denver City, TX. The largerbattery and satellite remote units communicate with adisc-based field computer located in the production office(see Fig.1). About 94,000 ft of six-pair cable was installed toconnect the wells, satellites, battery, and productionoffice. Microwave communication links the productionoffice with Shell computers located in Houston.Few problems have been encountered with this fieldcommunications network. Supervisory hardware, whichincludes all remote and computer interface units, alsohas performed satisfactorily. The first line amplifiers(repeaters) furnished by the hardware manufacturer wereunsatisfactory and had to be redesigned. The POCcomputer, which is a new model, had many problems earlier;however, recent changes seem to have improved itsreliability, Early problems also were experienced with loadcell transducers. The cables were constructed so that asmall strain on the cable caused it to tear out of the loadcell. This problem has been reduced substantially byusing a better method for connecting the cable to theload cell. Thus, the cable fails instead of damaging theload cell. The pump-off control technique has proven a reliablemethod for determining when a well is pumped off.The computer uses data from a well to calculate energy inputto the rod string during a certain portion of the stroke.When the energy drops below a specified limit, the well isconsidered pumped off. A limit can be set so that the wellshuts down for any degree of pump-off. The POC programalso checks for abnormal load conditions and eithershuts the well down or alerts the operator. To enhancewell surveillance, a sucker-rod diagnostic program wasimplemented in the field computer. Data can be transferredon request from the POC computer to the field computer foranalysis. Results normally are returned to the operator ina few seconds. From the results, the operator can determinehow the pump is performing and also detect any abnormal conditions that might be occurring in the well. The"on-line" combination of POC, automatic well testing, andsucker-rod diagnostics gives the field a powerful surveillancetool. JPT P. 1319

Wellsite Diagnosis of Pumping Problems Using Minicomputers

The truck-mounted computer system described here greatly enhances the efficiency of the sucker rod diagnosis technique. Using an example well, the paper shows how the method and the equipment can be used to increase production and decrease lifting costs. With this system, more definitive production and decrease lifting costs. With this system, more definitive and timely results can be obtained more efficiently, thus lowering the cost of applying the technique. Introduction The Sucker Rod Diagnostic Technique was perfected by Shell during the 1960's. Its concept was suggested by the work of British physicians who wanted to analyze human electrocardiograms more accurately and definitively. To do this, they subjected cardiograms to Fourier analysis, hoping to reveal subtle indications of heart disease that might be overlooked if only visual interpretations were made. Similarly the sucker rod method was designed to derive the maximum amount of information from a pumping-well dynamometer card and to make the analysis of the card a science rather than an art. This paper describes a portable computer system for implementing the sucker rod method. Brief Theoretical Review The basis for the diagnostic technique is a stress wave propagation problem based on the one-dimensional propagation problem based on the one-dimensional wave equation (1) The wave equation models the rod string and permits the use of surface data to deduce down-hole conditions in pumping wells. This is directly analogous to the human cardiogram where easy-to-measure surface data are used to infer conditions within the body. The boundary conditions measured at the surface are time histories of the load and position of the polished rod. These are expressed as truncated polished rod. These are expressed as truncated Fourier series of the following type: (2) (3) Solutions to the wave equation that satisfy the measured boundary conditions give operating conditions in a given well at a particular time in its producing life. The basic diagnostic solutions give producing life. The basic diagnostic solutions give displacement and load at arbitrary depths in the rod string. These are (4) and (5) The procedure for solving and generalizing for the case of tapered strings is detailed in Refs. 1 and 2. By cross-plotting the solution for displacement (Eq. 4) vs load (Eq. 5) at a given depth, a dynamometer card at that depth is obtained, This is equivalent to the card that would be measured with a dynamometer instrument placed at that depth. JPT P. 1319

Pumping Well Optimization Techniques

Abstract In recent years there have been a number of papers published dealing either with computer diagnosis of downhole pumping conditions (1,5) or with the results of optimization programs(13,14) based on computer analysis of pumping conditions. This paper can be considered a follow-up to previous papers inasmuch as it discusses techniques and presents guide lines which can be used when analyzing gear box and rod string loading situations, when attempting to establish connected horsepower requirements when reviewing mechanical pumping performance, and when calculating pump intake pressures and producing well capabilities. Consideration is given to the manner in which these inter-related factors affect optimization efforts. INTRODUCTION SURFACE LOADING CONDITIONS on a pumping installation can be determined from dynamometer measurements. Downhole conditions can be established using computer Programs(1) which mathematically simulate the pumping system. This paper discusses techniques and presents guidelines which can be used when analyzing wells for the purpose of obtaining optimum pumping performance. Optimization may be defined as those courses of action which result in minimum operating costs consistent with maximum production. Pumping well optimization recommendations should take into account the operating problems which are peculiar to any one pumping area. Consideration must be given to gearbox, motor and rod string loading. These loading situations are, however, quite often a direct result of the downhole conditions. It is therefore necessary to examine pump mechanical performance, and to establish the pump intake pressure and total well producing capability. Consideration must also be given to the interrelated manner in which each of the above factors contribute to tire performance of the pumping systems. DISCUSSION Torque Loading Torque Calculations Torque may be defined as "force acting at a distance." The loading on a gear box results from two forces, as shown on Figure 1; i.e. the well load and the counterbalance effect. The well load at any displacement position can readily be established from surface dynamometer measurements. The counterbalance effect is determined by either "clamping off" or "chaining off" at the polish rod with the crank arm in the horizontal position. Torque loading over a full pumping cycle can be calculated using the API recommended procedure(2). Manual torque calculations are time-consuming and consequently computer-calculated results are to be preferred. Example results showing the well load torque, counterbalance torque and net gear box torque are presented in Figure 2. Counterbalance Moment For a properly balanced condition the net torque, peaks should both be positive and be about equal in magnitude. As illustrated in Figure 3, when a pumping installation is either overbalanced or underbalanced a severe overload situation can occur. On pumping units the maximum counterbalance moment is often two to three times the gear box rating. Consequently, if a unit is overbalanced or underbalanced by 20 per cent the increase in gear box loading may be in the 40 to 60 per cent range. Gear Box Backlash Occasionally a severe "backlash" may be encountered.

High Volume Pumping with Sucker Rods

Abstract Recent studies have shown that often large fluid volumes can be lifted by sucker rods with great effectiveness from shallow to medium-depth wells. Wherever feasible, significant redaction in cost of elevating a barrel of fluid may be realized by the operator. The advent of longer stroke units with improved geometry, larger speed reducers and bottom-hole pumps, as well as the new high-strength sucker rods, make high volume rod pumping a practical and economical achievement. Past applications of this type generally have been considered only for bottom-hole centrifugal pumps. This paper reviews some field studies and emphasizes the practicality of high volume production with sucker rods. Introduction A century ago the almost universal mechanism for artificially lifting fluid in an oil well was the standard rig-front. A wooden walking beam drove a string of hickory sucker rods, often called "well poles", as many as ten 15-in.- strokes/minute with the maximum tensile stress of the rods about 12,800 psi. The bottom-hole pump was cast iron or brass with the barrel approximately 1 1/4-in. in diameter, and the well depth ranged from 500 to 1,000 ft. The torque capacity of the band wheel and flat-belt speed reducer ran only a few thousand inch-pounds, and the unit's structural capacity was from 1,000 to 1,500 lb. Today, the structure of a modern pumping unit with its 240-in. maximum stroke reaches higher than the wooden drilling and servicing derricks of those early days. Its structural capacity exceeds 47,000 lb, with a torque rating greater than 2.5 million in. lb. The plunger diameter of some bottom-hole pumps (casing-type) runs as high as 5 3/4 -in. Perhaps the greatest improvement is in the sucker rod, which now has a tensile stress of some 140,000 psi. Today practice sucker rod pumping approaches 13,000 ft, and capacities of 5,000 and 6,000 B/D from shallow to medium depths are handled with ease. Volumes as high as 9,500 B/D are entirely practical with modern sucker rod pumping equipment. Comparing the modern sucker-rod system with its counterpart of 100 years ago produces some startling figures. The structural capacity of the modern unit has increased nearly fifty-fold, the torque capacity perhaps a thousand-fold, the area of the bottom-hole pump over 20 times; the stroke length nearly twenty-fold; and maximum rod tensile stress nearly 12 times. With the increased stroke length, even the maximum rate of polished rod travel per minute has increased five or six times. Since all of these are compounding increases, the sucker-rod pumping unit of today has the capacity for producing massive fluid volumes from relatively great depths.

Investigation of the effect of a shock absorber on the delivery of a sucker rod pump (without calculating the self-oscillation of the rod string)

Investigation of the effect of a shock absorber on the delivery of a sucker rod pump (without calculating the self-oscillation of the rod string)

A Computer Technique for Analyzing Pumping Well Performance

Abstract A computerized analytical technique for investigating sucker rod pumping well performance develops load-position values (dynagraphs) at the pump, at desired points in the rod string and at the polished rod through use of a mathematical model of the sucker rod installation. Using the load-position diagrams of the pump, junction points and polished rod, quantitative deductions may be made regarding the mechanical condition and performance of the down-hole equipment (rod string, pump, tubing anchor, etc.) and the physical properties of the well itself (pump submergence, gas interference, fluid pound, etc.). Analysis of subsurface dynagraphs from several cave histories is discussed. Introduction Production men have recognized for years that a more complete knowledge of rod pumping performance would suggest means of lowering lifting costs, making more appropriate installation designs and increasing the proportion of oil economically recoverable by rod pumping. It was this need for knowledge that led to intensive studies from 1927 to 1943. During those years the polished rod dynamometer (1927), the bottom-hole pressure bomb (1929), the pump dynagraph (1936) and the sonic fluid-level sounder (1936) were developed. During that time many engineers used those tools to develop the theories on which our present knowledge of sucker rod pumping is based. Contributions made since 1943, in an effort to correlate data obtained from the various instruments, are mostly elaborations and refinements of the basic principles established during the preceding period. A notable exception is the Gibbs-Neely mathematical technique that analyzes pumping well performance with a digital computer. In effect, the technique yields all the information derived from these mechanical devices but has the added advantage of requiring only one series of measurements taken and recorded at the polished rod. Technique Procedure In application, polished rod data are recorded on the strip chart of a Delta II Dynamometer that consists of a dual-channel, carrier-amplifier recorder, a strain gauge-type load cell (for the polished rod loads) and a position transducer (for the instantaneous polished rod position). Eickmeier and Herbert described in detail the dynamometer, its components and its use. Polished rod data recorded at the well site, pertinent well data concerning down-hole equipment and known operating conditions are submitted to the computer for mathematical decoding. The computer output is plotted as load-position diagrams at the surface, at desired points in the rod string (i.e., junctions in tapered strings) and at the pump (similar to the Gilbert pump dynagraph). The loading information at junction points is extremely useful in analyzing sucker rod failures. Table I summarizes the various criteria evaluated by the computer technique and emphasizes its advantages over visual interpretation of a mechanical dynamometer card. Case Histories The pump cards and polished rod cards examined here are taken from some 1,000 well surveys run in the past 2 years throughout the United States, Canada, Colombia and Venezuela. They represent just a few of the downhole conditions detectable through the computer technique, and just a few of the cases where facts presented to the oil companies were acted upon to solve their problems. TABLE 1-CRITERIA EVALUATED BY COMPUTER Mechanical ComputerEvaluate Dynamometer Technique Surface loads and stresses Yes Yes Torsional analysis Yes Yes Pump dynagraph No Yes Maximum plunger stroke No Yes Effective plunger stroke No Yes Pump displacement No Yes Pump efficiency No Yes Plunger slippage No Yes Traveling-valve leak Possible Yes Standing-valve leak Possible Yes Gas interference Possible Yes Fluid pound Possible Yes Pump intake pressure No Yes Loads and stresses-tapered rod string No Yes Tubing movement No Yes Tubing anchor malfunction No Yes Packer malfunction No Yes JPT P. 243ˆ

Diagnostic Analysis of Dynamometer Cards

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

Applications of the Delta II Dynamometer Technique

Abstract The Delta II Dynamometer Technique provides a diagnostic method of evaluating downhole pumping performance. Surface dynamo meter cards are analyzed by computer to determine load displacement conditions at the pump and at intermediate points in the sucker rod string. The pump dynagraph card generated by the computer program permits a complete analysis of downhole pumping conditions. Pump intake pressures can be calculated from the pump dynagraph cards. A study of pump intake pressures at varying production rates and/or at different cumulative production provides essential information on well performance. Load conditions occurring 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 The Delta II Dynamometer is being used in production operations in the U.S.A. and Canada. Shell Canada first utilized the instrument in October, 1963.Since that time, approximately 800 cards have been obtained from more than 300 pumping wells in Western Canada and the instrument has become indispensable toproduction operation. The Delta II Dynamometer Technique provides a diagnostic method of evaluating downhole 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.With the Delta II Dynamometer Technique, however, the pump dynagraph card is calculated by computer analysis of the surface dynamometer card. The pumpdynagraph card accurately describes the downhole pumping conditions.Intermediate sucker rod stresses are also generated by the program. In essence, through the use of a mathematical solution of the sucker rod pumping system, the measured surface loads are "decoded" to determine the downhole loads.

Computer Diagnosis of Down-Hole Conditions In Sucker Rod Pumping Wells

Abstract Sucker rod equipment is the most widely used means for artificially lifting oil wells. Owing to this wide application, a large potential exists for increasing income through better methods for analyzing and trouble-shooting sucker rod installations. This paper describes a computer-oriented method whereby subsurface dynamometer cards can be determined from polished rod dynamometer data. The subsurface cards are useful in calculation of intermediate rod stress, estimation of pump intake pressures, detection of unanchored tubing and detection of leaking production strings and down-hole pumps. To date, this method has been used as a production engineering tool by Shell Oil Co. in over 500 wells in the United States, Canada and Venezuela. Introduction Through the years the polished rod dynamometer has been the principal tool for analyzing the operation of rod- pumped wells. The dynamometer is an instrument which records a curve of polished rod load vs displacement. The shape of this curve is affected by the down-hole operating conditions. Ideally, these conditions would be apparent from the dynamometer card by visual interpretation. Owing to the complex behavior of sucker rod systems and the diversity of card shapes, however, visual diagnosis of down-hole conditions is not always possible. Though much information can be gained from visual interpretation Of surface data, this information is qualitative in nature. Furthermore, the success in visual interpretation is directly linked with the skill and experience of the dynamometer analyst, and even the most experienced analysts are frequently misled into an incorrect diagnosis. The analytical technique described in this paper was developed to bridge the gap which arises when visual interpretation is inconclusive or when quantitative downhole data are needed. The method is based on a mathematical model of the pumping system which is virtually free from simplifying assumptions. The polished rod data are analyzed on a digital computer with a rigorous solution to the mathematical model. As a result, the technique provides a rational, quantitative method for calculating downhole conditions which is independent of the skill and experience of the analyst. It is no longer necessary to guess at down-hole pump conditions on the basis of recordings taken several thousands of feet above at the polished rod. By use of the analytical method, direct calculations of subsurface conditions can be made. The analytical method has been extensively used in field operations. Discussed in this paper are calculation of intermediate rod stresses, estimation of pump intake pressures, detection of unanchored tubing, detection of excessive rod friction, detection of leaking pumps and production strings, detection of gas separation problems and computation of gearbox torque. DEVELOPMENT OF EQUATIONS The theory underlying the analytical method is not particularly simple but the basic idea behind it is. It is helpful to think of the. sucker rod string as a transmission line. At the lower end of the transmission line, is a transmitter (the down-hole pump) and at the upper end is a receiver (an instrument installed at the polished rod). Information about down-hole pump conditions is transmitted along the sucker rod in the form of strain waves. These waves travel at the acoustical velocity in the rod material (about 16,000 ft/sec in steel). In its role as a transmission line, the sucker rod continually transmits information about downhole operations to the surface. But the information received at the surface is in code. Information received at the polished rod must be decoded so that quantitative deductions regarding down-hole operating conditions can be made. The technique of interpreting or decoding the information received at the polished rod is developed by solving a boundary value problem based on the wave equation.* The pertinent boundary conditions are the signals which are received at the polished rod, namely, time histories of polished rod load and displacement. To develop the basic equations, let z(x, t) be a complex variable in the wave equation: (1) Assume product solutions z(x, t)=X(x)T(t) and obtain the ordinary differential equations: (2) (3) JPT P. 91ˆ

Predicting the Behavior of Sucker-Rod Pumping Systems

Introduction Sucker-rod pumping systems are used in approximately 90 per cent of artificially lifted wells. In view of this wide application, it behooves the industry to have a fundamental understanding of the sucker-rod pumping process. Oddly enough, our understanding has been rather superficial. This is evidenced by the semi-empirical formulas which have been used as the basis for design and operation of sucker-rod installations. Though we have realized the limitations of our methods for many years, it has not been computationally feasible to use more refined techniques. With the advent and widespread use of digital computers, it is now possible to handle the mathematical problems associated with sucker-rod pumping. This paper summarizes a computer-oriented method which can provide greater insight into the sucker-rod pumping process. It is hoped that this technique, and techniques which may evolve from it, will prove to be the tool needed by industry to obtain the most efficient use of rod pumping equipment. THE MATHEMATICAL MODEL Prediction of sucker-rod system behavior involves the solution of a boundary value problem. Such a problem includes a differential equation and a set of boundary conditions. For the sucker-rod problem, the wave equation is used, together with boundary conditions which describe the initial stress and velocity of the sucker rods, the motion of the polished rod and the operation of the downhole pump. Of these items, the wave equation, the polished rod motion condition and the down-hole pump conditions are of primary importance. Discussion of the mathematical model centers about these factors. ROD STRING SIMULATION WITH THE WAVE EQUATION The one-dimensional wave equation with viscous damping, (1) is used in the sucker-rod boundary value problem to simulate the behavior of the rod string. This equation describes the longitudinal vibrations in a long slender rod and, hence, is ideal for the sucker-rod application. Its use incorporates into the mathematical model the phenomenon of force wave reflection, which is an important characteristic of real systems. The viscous damping effect postulated in Eq. 1 yields good solutions, even though nonvicous effect such as coulcomb friction and hysteresis loss in the rod material are present. Fortunately, the nonviscous effects are relatively small, so the viscous damping approximation used in the wave equation is adequate. The coefficient v is a dimensionless damping factor which is found in field measurements to vary over fairly narrow limits. For mathematical convenience the gravity term is omitted in Eq. 1. The effect of gravity on rod load and stretch can be treated separately, as will be noted later. Since Eq. 1 is linear, the legitimacy of this procedure is easy to demonstrate. POLISHED ROD MOTION SIMULATION The motion of the polished rod is determined by the geometry of the surface pumping unit and the torque- speed characteristics of its prime mover. By determining the motion of the polished rod, we formulate an important boundary condition. From trigonometrical considerations it can be shown that the position of the polished rod vs crank angle 0 is given by (see Fig. 1) (2) These equations are obtained from the general solution of the "four-bar" linkage problem and can be used to describe the kinematics of any modern beam pumping unit. If prime mover speed variations are disregarded, the angular velocity of the crank is constant, and Eq. 2 can be used to predict the position of the polished rod vs time. However, the constant-speed condition leading to constant crank angular velocity is only approached in practice: hence, it is better to make provisions for prime mover speed variations in the mathematical model. The speed at which the prime mover runs is determined by its torque-speed characteristics and the torque imposed upon it. The torque that the prime mover "feels" is the net torque arising from the polished rod load and the opposing torque from the counterbalance effect.

Calculation of Load and Stroke in Oil-Well Pump Rods

Abstract The sucker-rod pump as used in oil wells is treated as a problem in the longitudinal vibration of bars. Solutions are obtained for the forces and motions at both ends of the rod string, thus giving formulas for the calculation of polished-rod load and plunger travel. The results of the calculations are compared with test results.

The Sucker-rod Pump as a Problem in Elasticity

This paper is a progress report of a study the authors are making of thesucker-rod pump, considered as a vibrating system with one degree of freedom, with forced vibrations and with viscous damping. Dr. S. Timoshenko's formula isgiven, defining such a system. Each factor is considered in respect to theproblem of operating sucker rods, and the zone is pointed out in which themathematics do not apply to the sucker-rod pump, because of its variable mass.This general theory is interpreted in the light of nearly two years of testingwells in the field, and correlating the results of other tests. The motion of the pumping mechanism is a vibration. The string of sucker rodsvibrates with a natural frequency. The motion of the plunger is the result ofadding together these two vibrations, and is modified by a damping or frictionfactor. The controlling factor appears to be the ratio of the period of thenatural vibration of the rod string to the period of the vibration of the pump.The first conclusion is that a definite value of this ratio, which is belowresonance and is probably not greater than 0.5, should not be exceeded in orderto assure satisfactory performance from the sucker rods. The second conclusionis that the component parts of the pumping equipment should be selected to givethe smallest practical period of the natural vibration, and when this does notpermit operation at a safe speed and give the required plunger displacement, alonger polished-rod stroke should be used. While the quantitative results are but rough approximations, the qualitativeanalysis of pumping problems on this basis promises to be of considerable valuein diagnosing the cause of poor performance and prescribing suitableremedies. The trouble that results, whenever it becomes necessary to crowd the sucker-rodpump, to take potentials or to handle increasing volumes of water, isresponsible for the belief that this type of pump is not equal to present dayneeds, and that it is only a question of time before some other pumping devicewill take its place.