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    USMS026278 A New Technique for Data Retrieval from ConventionalDynamometer CardsGabor Takacs, U. of Miskolc

    COPYRIGHT ; ' 7 ' ~ ~ SOCIETY OF PETROLEUM ENGINEERSThis manuscript was provided to the Society of Petroleum Engineers fordistribution and possible publication in an SPE journal. The contents of thispaper (1) are subject to correction by the author(s) and (2) have not undergoneSPE peer review for technical accuracy. Thus, SPE makes no claim about thecontents of the work. Permission to copy or use is restricted to an abstract ofnot more than 300 words. Write SPE Book Order Dept., Library Technician, P.O.Box 833836, Richardson, TX 75083-3836 U.S.A. Telex 730989 SPEDAL.

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    ABSTRACT

    UNSOLICITEDA New Technique for Data Retrieval

    from Conventional Dynamometer Cardsby

    Gabor Takacs, Ph.D.Petroleum Engineering Department

    The University of MiskolcHungary

    MAR 18 1993c26t( 7.1

    A conventional dynamometer (the most common type ofmeasuring device in rodpumping well analysis) records polished rod loads versus rod displacement during thepumping cycle on a plot called dynamometer card. Calculations requiring rod loads anddisplacements as input variables must rely on information retrieved from these cards.There are many conditions that prevent the pumping analyst from getting the righttype, and the desired amount of reliable measurement data from dynamometer cards.These include: (a) the card's small physical size, (b) visual reading of the card can beinsufficient, and (c) additional information not readily available from the card may be

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    INTRODUCTIONImportance of Dynamometry

    In analyzing the perfonnance of a pumping system the most valuable tool is the dy-namometer which records the loads occurring in the rod string. These loads aremeasured either at the surface with a conventional polished rod dynamometer or atpump setting depth with a special downhole measuring device. In both cases, loads arerecorded in the function of rod displacement or pumping time, during one or morepumping cycles, producing the familiar dynamometer "card". Since the variation of rodloads is a result of all the forces acting along the rod string, and since it reflects theoperation of the pump as well as the surface pumping unit, an evaluation of themeasured loads reveals valuable infonnation on downhole and surface conditions.Accordingly, performance analyses of the downhole and surface equipment are usuallyconducted by running a dynamometer survey on the well.

    The first surface dynamometers were used in the early 1920s. Since then, both thehardware and the analysis methods have considerably been improved. Thus the early,mostly qualitative interpretationswhich heavily relied on the analyst's skill and previousexperience, have evolved into the sophisticated, highly reliable analysis methods oftoday.

    The proper use of dynamometry techniques and the correct interpretation of thecards taken are of utmost importance for the production engineer when he tries toincrease the profitability of sucker rod pumping. It is the interpretation ofdynamometer surveys that helps accomplish the following basic tasks: Reducing lifting costs Detection and prevention of equipment failures Improving the selection and application ofpumping equipment, and Increasing well production rates.The correct interpretation of surface and downhole dynamometer cards reveals a

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    Use of Conventional Dynamometer CardsThe predominantly used conventional dynamometers, working on mechanical or

    hydraulic principles, record the loads at the polished rod as a function of polished roddisplacement. Such "conventional" dynamometer cards are taken on a daily basis in alloil producing areas of the world and are the basic information available for pumpingwell analysis. The usual interpretation of such cards by visual means is a task for highlyspecialized analysts. Due to the many interactions of influencing parameters and thegreat number of possible pumping problems, an infinite number of dynamometer cardshapes can exist, making the analysis of surface dynamometer cards more an art thanan exact science. A proper analysis of these cards, therefore, heavily relies on theanalyst's expertise and skill.

    To ease the qualitative analysis of cards taken in the field the American PetroleumInstitute published API Bul l1L21, where dynamometer cards for ideal pumpingconditions (perfect fillage and no gas interference in the pump, pump in perfectmechanical conditions, etc.) are given. The published cards, obtained from an analogcomputer specifically built for the purpose, are classified according to the values oftwo dimensionless parameters: NINo' and Fo/S/kr, also used in the API RP 11L2procedure. The use of API Bul l1L2 involves the calculation of these dimensionlessparameters and then the selection of the analog card closest to these conditions fromthe collection. I f the shape of the measured card closely resembles the analog card justfound, no apparent problems are present, otherwise further expert analysis is required.

    If a quantitative analysis of dynamometer survey data is required and numericalvalues of the polished rod load have to be determined, most frequently the analyst mustrely on visual reading of the dynamometer card. This approach works fine as long asthe necessary number of polished rod loads is limited to a few values, e.g. whenmaximum and minimum loads, or pump valve test data are only needed. In such cases,visual reading of the card is easily accomplished and the required few load values arefound with due consideration to the load scale of the dynamometer. But when a more

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    overcomes these problems and allows the determination of the right type and numberof information from conventional dynamometer cards.PREVIOUS DATA RETRIEVAL TECHNIQUES

    The traditional analysis of dynamometer cards involves the visual reading of alimited number of points from the card. This fairly time-consuming manual procedurecan be accelerated with the use of special rulers with appropriate load scales or othersimple devices. But its main drawbacks, the relative low accuracy and the poorreliability cannot be eliminated.

    Basically the same manual data retrieval technique is described in the appendices ofAPI Spec. IIE3, where a procedure is recommended for the calculation of torsionalloads on pumping unit speed reducers. Although the recommended technique allowsthe determination of several points' of the polished rod load vs. polished roddisplacement function, the general accuracy of dynamometer card processing did notimprove. Also, the number of points that can be read from the card is still limited.The use of digitizers in processing dynamometer cards has become standardpractice and has also increased the reliability of card analysis. Gray4 reports on asimple procedure that can be used to read the coordinates of several points into acomputer for further calculations. His digitizing procedure, however, does not permitfinding of polished rod loads at equidistant crank angles, a very desirable feature whensolving the damped wave equation. Since the most powerful application ofdynamometer card data is the calculation of downhole cards through the solution ofthe wave equation, the method ofGray can find limited use in rod pumping analysis.

    PROPOSED METHODObjectives

    As shown above, most available data retrieval procedures for dynamometer card

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    angle function. The polished rod displacement vs. crank angle function, based on anexact kinematic analysis of the pumping unit's motion and given in the API Spec. IlE3is ideally suited for this purpose and will be used in developing the calculation model.As stated in Spec. lIE, the non-dimensional form of the polished rod displacement isfound from the basic formula:

    PR(O) = (1)where: PR( f:J) dimensionless polished rod position (Position ofRods),

    ocrank angle, and'If" , '1ft extreme values of angle 'If .

    The definition of angle 'If for conventional pumping units is given in Fig. 1,showing the geometrical arrangement of the driving mechanism of those units. Angles'If" , '1ft represent the two extreme values of this angle valid at the bottom and at thetop of the polished rod's stroke. The formulae to be used for the calculation of theseangles are given in API Spec. IIE.3

    By utilizing the PR( f:J) function the polished rod load vs. crank angle values areobtained from the dynamometer card by using the following procedure, also given inAPI Spec. lIE:

    Begin with the crank angle 0, valid at the start of the upstroke. Calculate PR( f:J) and, based on its value, find the polished rod displacement. From the card, determine the polished rod load belonging to the displacementjust calculated. Increase the crank angle by a constant increment and repeat the calculationsuntil the full pumping cycle is covered.

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    time-proven conventional dynamometer survey can readily be utilized for the analysisof downhole pumping problems. According to experiences gained by a major oilcompany on thousands of rod pumped wells, this approach gives practically identicalresults to those achieved when the more expensive electronic dynamometers are used,except when the pumping unit is driven by a fully loaded high slip motor.7,8

    As seen, one of the objectives of this paper can be met by the application of thetheory detailed above which ensures that data retrieved from conventional cards can beused in different kinds ofpumping analysis. The remaining objectives i.e. increasing thenumber and accuracy of the data received from the card, will be reached by thecomputerized technique presented in the following.Details of the Calculation Procedure

    Hardware RequirementsBasically, two methods are available for entering information from dynamometer

    cards into computers: either a digitizer tablet or a graphics plotter with digitizing capability can be used. The digitizer tablet, at least in the author's opinion, is not an idealdevice for this purpose since its hand-held cursor moves in two directions on thetablet's surface, thus increasing the chances of input errors. An additional and muchmore serious disadvantage is that there is no direct way to ensure that points at aconstant crank angle increment apart are digitized on the card. Therefore, the idea ofusing a digitizer tablet was discarded as unsuitable for achieving the goals set forthearlier.

    Many graphics plotters possess digitizing capabilities and this feature can be veryadvantageously utilized for the special conditions of data retrieval from dynamometercards. Since the movement of the plotter pen, or in our case the digitizing sight, can becontrolled from a computer, the plotter can simultaneously be used for moving thesight on the card and for digitizing some selected points. This potential feature ofgraphics plotters was utilized by the author to develop the special digitizing program

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    First digitize two points (DI and D2) on the zero load line of the card. Thisestablishes the relative rotation of the two coordinate systems, a.

    Next, the start of the upstroke on the card, point D3 is digitized, then the startof the downstroke, D4. The distances between coordinate origins Xo and Yo,and the load and displacement scales on the axes can thus be determined.

    These preliminary operations form the basis of transforming the points read in theplotter coordinate system into the coordinate system of the card, i.e. finding thecorresponding load and displacement values. Given the plotter coordinates X and Y ofone point on the card, the transposed coordinates X' and Y' are calculated as:

    X'=X-XoY'=Y - Yo (2)(3)Now the X' - Y' coordinates must be rotated to find the coordinates in the card'ssystem:

    S = X' cos a + Y' sin aF = Y' cos a - XI sin a

    (4)(5)

    Since all the above coordinates are in length units, the polished rod load anddisplacement values are calculated by applying the force and displacement scales of thecard axes found before:PR = S / Smax (6)Load = F Fscale (7)

    The use of the above equations allows the determination of polished rod load anddisplacement values from the digitized plotter coordinates of any point on thedynamometer card.

    Automated Digitizing ProcessThe main objective of the digitizing process is to retrieve from the dynamometer

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    that belong to each value of the crank angle senes are calculated and stored incomputer memory based on Eq. 1.After these data preparations the actual digitizing of the dynamometer cardfollows. Since the card has two loads for any polished rod position, one on the

    upstroke, and one on the downstroke, the actual case must always be determined bycomparing the actual crank angle to the crank angles at the polished rod's extremepositions (see Table 1). The digitizing procedure is illustrated on the flowchart givenin Fig. 3, valid for any crank angle on the upstroke portion of the dynamometer card.

    At the start of the procedure, the polished rod position in card units, S is calculatedbased on the precalculated PR value valid at the actual crank angle. Now a sufficientlylarge polished rod load, LStart is assumed and its card coordinate, F is found. After theplotter coordinates X and Y, corresponding to these card coordinates are determined,the digitizing sight is moved to this position in a "pen down" state. The computer thengives an audible signal and the user visually checks whether the sight is still above thedynamometer card's upper portion. I f so, no user signal is given and the assumedpolished rod load is decreased by Dload1. Another pair of plotter coordinates iscalculated and the digitizing sight is moved to the new point and the above processrepeats. Thus the sight travels along a PR = const. line towards the upper portion ofthe dynamometer card while its current state (either "pen up" or "pen down") iscontinuously monitored by the computer program. As soon as the user detects that thesight has just crossed the upper part of the card, he/she signals to the computer bypressing the "pen up" button on the plotter's front panel.

    Now the digitizing sight's direction ofmovement is reversed and at the same timethe magnitude of its movement in each step is substantially reduced by using a loadstep, Dload2 much less than the previous Dloadl. The above detailed process is usedbut the sight, in the "pen down" state, now approaches the upstroke part of the cardfrom below. By using an appropriate load increment, Dload2, it can be ensured thatduring its upward travel the sight once will lie exactly over one point of the upperportion of the dynamometer card. At this moment, the user signals to the computer by

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    SAMPLE APPLICATIONSIn the following some example problems are presented with the use of the

    computer programs described in the author's recently published book9 on sucker rodpumping. The dynamometer card digitizing process introduced in this paper is utilizedin the computer program CARDIGIT. This program not only enables one to retrievethe necessary load and displacement data from the card but it is also stores in a datafile all relevant data for use in a number of different analyses to be performed later.Two such methods are covered here: the analysis of gearbox torques and thecalculation of downhole and pump cards.

    An input data sheet of the program CARDIGIT is shown in Fig. 4 for an examplecase. In order that the output file contains a complete set of data, all relevant well andequipment data are recorded for future use. The card is digitized, in the given case, bytaking 75 points on the card which represents a crank angle increment of about5 degrees. If compared to a manual analysis of the card or to the data retrievaltechnique of API Spec lIE it is clearly seen that a much finer resolution can beachieved with the digitizing process presented here.

    The data file prepared by the program CARDIGIT is used in the analysis ofgearbox torques for the example case. Fig. 5 is a part of the output from the computerprogram TORQANAL and shows the dynamometer card with the permissible loadssuperimposed on the card. It is widely known that the total number of digitized pointshas a great impact on the reliability of torque calculations because a low number ofpoints usually means that the peak values of net gearbox torque are undetected. Sincethe digitizing process discussed in this paper allows a great number of points to beretrieved from the dynamometer card, the accuracy and reliability of torquecalculations based on the data thus received can be improved considerably.Another important field of application for dynamometer card data is the downholeanalysis involving the calculation of pump cards. Such analyses require polished rodload and displacement data in the function of time. As discussed before, the program

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    The digitizing process is simple and requires little effort from the user ascompared to previous methods.

    Simple, universally available equipment is used.Acknowledgment

    The financial support of the National Scientific Research Foundation (Hungary) infunding the Project OTKA-2388 is gratefully acknowledged.REFERENCES1. "Catalog of Analog Computer Dynamometer Cards." API BulllL2, 1st Ed.,

    American Petroleum Institute, Dallas Texas, December 19692. "Recommended Practice for Design Calculations for SuckerRod Pumping Systems

    (Conventional Units)." API RP IlL 4th Ed. American Petroleum Institute,Washington D.C. 19883. "Specification for Pumping Units." API Spec. lIE, 15th Ed., American Petroleum

    Institute, Washington D.C. 19884. Gray, C. R: "Dynamometer Analysis Using a Digitizer and an IBM PC." PaperSPE 15288 presented at the Symposium on Petroleum Application of Mi

    crocomputers of the SPE in Silver Creek, Colorado, June 18-20, 19865. Takacs, G.: "Torque Analysis ofPumping Units Using Dynamometer Cards." Proc.

    36th Annual Southwestern Petroleum Short Course, Lubbock Texas, 1989 p. 36676

    6. Takacs, G. - Papp, 1.: "Dynamometer Card Analysis Using Minicomputers."(in Hungarian) Koolaj es Foldgaz, March 1978, p. 65-73

    7. Ford, W. H. - Svinos, 1. G.: "Effective Application ofBeam Pumping Diagnostics."Paper SPE 17444 presented at the SPE California Regional Meeting, Long Beach,California, March 23-25, 1988

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    Figure and Table Captions

    Fig. 1 Geometrical arrangement of a conventional pumpmg unit's drivingmechanism.Fig. 2 Dynamometer card and plotter coordinate systems.Fig. 3 Flowchart of the automated process for digitizing the upstroke portion ofthe dynamometer card.Fig. 4 Input data ofprogram CARDIGIT for an example case.Fig. 5 Partial output of program TORQANAL with the dynamometer card andthe calculated permissible loads for an example case.Fig. 6 Calculated downhole cards as output from program ANAWAVE for theexample case.

    Table 1 Calculation of crank angles valid at the start of the upstroke and thedownstroke for different pumping unit geometries.

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    Cllcu.llte SCard Coordi nate

    Calcu.late rCard Coordi nateCllcu.late X, VPlotter Coord.

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    Calcu.late rCard CoordinateCalcu.late X, VPlotter Coord.

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    Program CARDIGIT Ver. 1.3 (C) 1989 Dr G.Takacs

    DYNAMOMETER CARD DIGITIZINGandSTORAGE OF DIGITIZED DATA

    W E L L I N FOR MAT IO N D A T AName of Fie ldDate Card Taken Well Iden t i f i ca t ionTime Card Taken :

    Digi t ized Data Stored in Fi le Example.CRDD o W N H OLE E Q U I P M E N T D A T APump Depth : 6265.0 f t Liquid Rate 250.0 bpdDynamic Level 6265.0 f t Wellhead Press . 100.0 psiaPlunger Size 1.50 in Tubing Anchored YESLiquid SpGr. . 1.000

    R 0 D S T R I N G D A T AMater ia l Size Length Wr Modulusin f t l b s / f t ps iSTEEL ROD 1 1697.8 2.905 0.307E+08STEEL ROD 7/8 1641.4 2.225 0.307E+08STEEL ROD 3/4 2925.8 1.635 0.307E+08

    P U M PIN G U N I T D A T ACLOCKWISE8.0 deg8.00 SPM

    C.M.I . Corp.Rotat ionCB Offse t AnglePumping Speed :

    Manufacturer :API Designat ion : TM-640D-305-168St ruc tu ra l Unbalance : -326 lbsMeas. Stroke Leng th : 168.00 in

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