API RP 11L - Design calculation for sucker rod pumping system

RP LLL-BB

3 0732290

0003654 L

ERRATA October 1,1988 to

API RP 11L RECOMMENDED PRACTICE for

DESIGN CALCULATIONS for

SUCKER ROD PUMPING SYSTEMS (Conventional Units) FOURTH EDITION JUNE 1,1988

Issued by AMERICAN PETROLEUM INSTITUTE Production Department 2535 One Main Place Dallas TX 75202 COPYRIGHT American Petroleum Institute Licensed by Information Handling Services

r

Alo. In determining thenatural frequency, the velocity of force propagation “a” plays a key role. Thetheoretical value for this velocity is about 17,000 feet per second. In practice, however, it has been found that lower frequencies normally occur. The speed of sound in longnarrowrods is usually somewhat lower than in normal size vessels.Also, the effect of the rod coupling can cause an apparent increase in density resulting in a decrease in propagation velocity. In practice, it has been found that “a” equals about 16,300 feet per second.With this value, the nondimensional pumping speed c a n be calculated by:

N NL No’ - 246,000Fo

“

A l l . Another dimensionless parameter of importance in describing the behavior of the sucker rod stringis the dimensionless rod stretch, Fo/Skr. In this parameter, the spiing constant, kr, is involved. For untapered rod strings,it is evaluated by the relation: EA kr =L For tapered rod strings, the spring constant is computed from the familiar reciprocal formula: 1 1 L1 L2 -I J E A1 The complete term, Fo/Skr gives the rod stretch caused by staticapplication of the fluidload as a percentage of the polishedrod stroke. For example,

--[-+z+.. .

”

Fo -= skr

0.1

means that the rod stretch is 10% of the polished rod stroke when the fluidload is statically applied. Atvery low speedswhere static conditions are approached, the dimensionless rod stretch and pump atroke are related as follows: At higher speeds, this relation breaks down as dynamic effects become more important.

A12. The chartsare used to determine the dependent parameters as defined in the report. Three forces of particular importance are determined from thecharts. F1 is the fluidload plusthe maximum dynamic effect on the up stroke. Fz is the dynamic effects during the down stroke taken away from the load on the polished rod. FSis a force which will give horsepower when applied tothefullstroke length at the speed of the pumping unit. A13. Thesurface dynamometer card which is generated in the analog computer is independent of the weight of the rod string involved. The shape of the card will be the same and a different rod load will simply shift the card up or down in relation to the zero line. In calculating allparameters except torque, this can be handled very easily by calculating fluid and dynamic loads independent of the rod load and then adding in the rod load. In the case of COPYRIGHT American Petroleum Institute Licensed by Information Handling Services

torque, the amount of rod load is important in determining the tor ue involved in the unit. All torque values were calcuyated using a rod load of:

Skr--

0.3

If a rod load different from this is used, a correction must be made a s shown in Fig. 4.6. A14. Inthe analog model, it has been assumed thatthetubingis anchored and no tubing motion occurs during the pumping stroke. If the tubing is unanchored, then a correction must be made for the shortening of pump stroke whichwilloccur. This happens because the tubing shortens when the rod string and then load is transferredtothe lengthens during down stroke when the fluid load istransferred back to the tubing. A correction in pump strokeis made by simply calculatingthe amount of tubing stretch whichwilloccur with the in the designand subtracting this fluidloadused amount of strokefromthenetplungerstroke at the bottom of the hole. This should give a reasonable correction. It will not be absolutely correctdue to thefactthat dynamic effects occur in the tubing string as well as in the rod string and these dynamic effects are not taken into account. A15. An average conventional atlon. S 1s geometry has beenused in the sim$-pinkur$ a conventional unit with the counterweights in phase with the crank and the tail bearing being over the slow speed shaft at midpoint of the stroke. For units with drastically different geometrg fromthatassumed, the simulation will not be accurate and the values calculated will be more approximate. It is believed, however, that the values for maximum and minimum loads and for pump stroke will be reasonably good. The calculated value for torque w i l l not be even approximately right and a torque c a l d a tion must be made by some other method. A16. Pumping unit motion was assumed based on a medium slip motor. Generally speaking, a higher slip prime mover results in slight decreases in the maximum load and a slight increase in the minimum load but also tends to reduce the subsurface pump stroke; therefore! some error may be introduced in the calculations rf a prime mover with a considerably different slip characteristic than a medium slip electric motor is used. Also, the assumption is made that no friction occurs in the stuffing box or in the pump itself. This, of course, is an unreal assumption although the values for friction in this case should be minor and of negligible importance in the design.

AIT. One note of caution in using the new design technique should be pointed out. This method of design will generally give values for load and torque values calculated by many that are higherthan previously used pumping design formulas. This tendency of previously used formulas to underestimate the loads has frequently beenoffset to some degree by a tendency to overestimate the well requirements. The new design methodshould predict actual well loads to a reasonable degree of accuracy if true well conditions are assumed.

Recommended Practice for Design Calculations for Sucker Rod Pumping Systems (Conventional Units)

API RECOMMENDED PRACTICE 11L (RP 11L) FOURTH EDITION, JUNE 1,1988

American Petroleum Institute 1220 L Street. Northwest Washington, DC 20005

11’

COPYRIGHT American Petroleum Institute Licensed by Information Handling Services

RP ILL-BB

0732290 0003657

Issued by AMERICAN PETROLEUMINSTITUTE Production Department

FOR INFORMATION CONCERNING TECHNICAL CONTENTSOF THIS PUBLICATION CONTACT THEAPI PRODUCTION DEPARTMENT, 21 1N. ERVAY, SUITE 1700, DALLAS, TX 75201 - (214) 220-91 11. SEE BACK SIDE FOR INFORMATION CONCERNING HOW TO OBTAIN ADDITIONAL COPIES OF THIS PUBLICATION.

Users of this publication should become completely familiar with its scope and content. This publication is intended to supplement rather than replace individual engineering judgment.

OFFICIAL PUBLICATION

REG. U.S. PATENT OFFICE

Copyright COPYRIGHT American Petroleum Institute Licensed by Information Handling Services

@

1988 American Petroleum Institute

7

2

Institute

Petroleum

American

TABLE OF CONTENTS *

Page 2 3

Nomenclature ....................................................... Policy ............................................................... Sect. 1: Introduction .......................................... :. ..... 4 Sect. 2: Validity of Calculations.. ..................................... 4 Sect. 3: Discussion .............................. '. .................... 5 Sect. 4: DesignProcedure ............................................ 6 Appendix A: Discussion of Nondimensional Parameters .............. 18 NOMENCLATURE

SP PD

-Bottom Hole Pump Stroke, inches " P u m p Displacement, barrels per day PPRL -Peak Polished Rod Load, pounds (See Figure 3.1) MPRI, "Minimum Polished Rod Load,pounds(See Figure 3.1) PT -Peak Crank Torque, pound inches PRHP -PolishedRod Horsepower CBE -Counterweight Required, pounds H -Net Lift, feet L " P u m p Depth,feet N -Pumping Speed, Strokes Per Minute S "Polished RodStroke,inches(SeeFigure 3.1) D "Plunger Diameter, inches G "Specific Gravity of Produced Fluid Wr "Average Unit Weight of Rods in air, pounds per foot (Table 4.1, Column 3) Er "Elastic ConstantcRods, inches per pound foot (Table 4.1, Column 4) Note: Er represents the inches of elongation caused by the application of a load Of One pound to a rod One foot in length. F, -Frequency Factor (Table 4.1, Column 5) Et "Elastic Constant--Tubing, inchesperpound foot (Table 4.2, Column 5) Note: Et represents the inches of elongation caused by application of a load of one pound t o a section of tubing one foot in length. F0 -Differential Fluid Load on full plunger area, pounds(SeeFigure 3.1)

l/k,

Skr N O

Nu' l/k[

W Wrf

h F2

T F3

T,

"Elastic Constant-Total Rod String,inches per pound Note: kr = SpringConstant of thetotal rod strlngandrepresentsthe load inpoundsrequiredtostretchthe lotal rod string one inch. -Pounds of load necessary to stretch the total rod string an amount equal to the polishedrodstroke, S. NaturalFrequency of Straight Rod String, strokes per minute. -NaturalFrequency of Tapered Rod String, strokes per minute. "Elastic Constant-Unanchored Portion of Tubing String, inches per pound Note: kt = Spring Constant of the unanchoredtubingandrepresentsthe to stretch load inpoundsrequired the unanchored portion of the tubing, betweentheanchorandthe pump, one inch. -TotalWeight of Rods in air, pounds -TotalWeight of Rods in fluid, pounds(See Figure 3.1)

-

-PPRLFactor(SeeFigure

-MPRLFactor(SeeFigure

3.1) 3.1)

-CrankTorque,poundinches PRHP Factor -TorqueAdjustmentConstantforvalues Wrf/Skr other than 0.3

-

of

Attention Users of this Publication: Portions of this publication have been changed from the previous edition. The location of changes has been marked with a bar in the margin. In some cases the changes are significant,whileinothercasesthechangesreflectminor editorial adjustments. The bar notations in the margins are provided as an aid to users to identify those parts of this publication that have been changed from the previous edition, but API makes no warrantyas to the accuracy of such bar notations. This edition covers editorial changes in API RP 11L (Third Edition, February 1977): Recommended Practice for Design Calculatio?ts for Sucker Rod Pumping Sgstems (Conventional Units), approved a t the 1978 StandAmerican Petroleum Institute ardization Conference as reported in Circ PS-1589.

COPYRIGHT Licensed by Information Handling Services

to -reproduceor translate all or any Requests for permission part of the material pllblished he,rein should be addressed to the Director, Prodmtion Departnzent, 21 1 N. Emay, Suite 1700, Dallas TX 75201.

RP 1 1 L - B B R P 11L:Design Calculations

for Sucker Rod Pumping Systems (Conventional Units)

fi 0732290 0003659 O h 3

POLICY APIPUBLICATIONSNECESSARILYADDRESS PROBLEMSOF A GENERALNATURE.WITH RESPECT TOPARTICULARCIRCUMSTANCES, LOCAL, STATE AND FEDERAL LAWS AND REGULATIONS SHOULD BE REVIEWED. API IS NOT UNDERTAKING TO MEET DUTIES OF EMPLOYERS, MANUFACTURERS OR SUPPLIERS TO WARN AND PROPERLY TRAIN AND EQUIPTHEIREMPLOYEES,ANDOTHERSEXPOSED;CONCERNINGHEALTHANDSAFETY RISKS AND PRECAUTIONS, NOR UNDERTAKING THEIR OBLIGATIONS UNDER LOCAL, STATE, OR FEDERAL LAWS. NOTHING CONTAINED IN ANY API PUBLICATION IS TO BE CONSTRUED AS GRANTING ANY RIGHT,BYIMPLICATION OR OTHERWISE,FOR THE MANUFACTURE,SALE, OR USE OF ANY METHOD, APPARATUS, OR PRODUCT COVERED BY LETTERS PATENT. NEITHER SHOULD ANY-


THINGCONTAINED INTHE PUBLICATION BE CONSTRUEDASINSURINGANYONEAGAINST LIABILITYFORINFRINGEMENT OF LETTERS PATENT. GENERALLY, API STANDARDS ARE REVIEWED AND REVISED, REAFFIRMED, OR WITHDRAWN AT LEAST EVERY FIVE YEARS. SOMETIMES A ONE-TIME EXTENSION OF UP TO TWO YEARS WILL BE ADDED TO THIS REVIEWCYCLE. THIS PUBLICATION WILL NO LONGER BE IN EFFECT FIVEYEARSAFTERITS PUBLICATIONDATE AS AN OPERATIVE API STANDARD OR, WHERE ANEXTENSIONHASBEENGRANTED,UPON REPUBLICATION. STATUS OF THEPUBLICATION CAN BE ASCERTAINED FROM THE APIAUTHORING DEPARTMENT (TEL.214-220-9111). A CATALOG OF API PUBLICATIONS AND MATERIALS IS PUBLISHED ANNUALLY AND UPDATED QUARTERLY BY API, 1220 L ST., N.W., WASHINGTON, D.C. 20005.

4

Institute

Petroleum

American

SECTION 1 INTRODUCTION 1.1 In 1964 a group of usersandnlanufacturers of sucker rod pumping equipment undertook a study in depth of the many complexproblemsassociated with this means of lifting fluid from a well. To controlanddirecttheeffort,Sucker Rod Pumping a non-profit organization Research, Incorporated, of Midwest Research was created. The services Institute at KansasCitywereretainedtoperform the work necessary to achieve the objectives of the organization.

500 f t and for production rates of 100 barrels pep day to over 1500 barrels per day in varying increments. Rod and pump size combinations as listed in Table 1 of R P 11L were used, except for the elimination of rods 88 and 99. All API stroke lengths aile covered. Thismaterialisprinted as Bulletin l l L 3 and is availablefrom API ProdnctionDepartment, Dallas, Texas, 75201. Theotherprogram developed a series of curves for selectingbeampumpingunits fordepths of 1600 f t to 9900 f t andvariousrates of production and and combinations of rod sizes, pump sizes, speeds.Generally, thelimitingfactor on thecurve is the peak torque rating of the unit. This material as Bulletin l l L 4 and is alsoavailable isprinted fromAPIProductionDepartment,Dallas,Texas.

1.2 Thedesigncalculationsarebasedoncorrelations of thetestdatathatwereobtainedduring of the project. Sucker Rod the research phase its dissoluPumpingResearch,Incorporated,before to Amertion, released these correlated test results ican Petroleum Institute for publication, This R e c m m d e d Practice for the Design Calculations of Sucker Rod PumpingSystems usingconventional pumpingunits is basedonthesecorrelations.

1.6 American Petroleum Institute (API) Recommended Practices are published to facilitate the broad availability of proven,sound engineering and operating practices. These Recommended Practices are not intended \o obviatethe need forapplyingsoundjudgmentas to when and where these Recommended Practices should be utilized.

1.3 Three discussions included in the final reports of testresultsbyMidwestResearchInstitutehave in API been published forpermanentreference Drilling and Prodzcction Practice (1968), p. 232 under the title “Electric Analog Study of Sucker-rod Pumping Systems.”Thesediscussionsinclude the following topics: a. Vibration Characteristics of Sucker-rod Strings b. PhysicalCharacteristics of SuckerRods c. DimensionalAnalysis of Sucker-rodPumping Systems

1.7 The formulation and publication of API Recommended Practices is not intended to, in any way, inhibit anyone from using any otherpractices. 1.8 Any Recommended Practice may beusedby anyone desiring to do so, and a diligent effort has been made by API to assure the accuracy and reliability of the data contained herein. However, the Institute makes no representation, warranty, or guarantee in connection with the publication of any Recommended Practice and hereby expressly disclaims any liability or responsibility for loss or damage resulting fromits use, for any violation of any federal, state or municipal regulation with which an API recommendation may conflict, or for the infringement of any patent resulting from the use of this publication,

1.4 A catalog of over 1100 dynamometer cards derived from the electronic analog computer for many combinations of the independent non-dimensional N/No mas included in the parametersFo/Skrand Rod Pumping materialreleased t o APIbySucker been printed .as Research, Inc. Thiscataloghas Bulletin l l L 2 and is available from APT Production Department, Dallas, Texas. 1.5 Twocomputerprograms have been developed fromthedatainRP 11L and purchasedbyAPL One program developed tabular materialcalculated for depths of2000 f t to 12,000 f t in increments of

SECTION 2 VALIDITY OF CALCULATIONS 2.1 In a large majority of cases, it has been found that the values calculated by the followingmethod have been in reasonably close agreement with measured values. Several groups, conducting independent this designmethodtogive surveys,havefound betterresultsthanothermethodsformerlyused. However,sincethismethod is basedonthebest coninterpretations of averagevalues,theactual ditionsfoundinindividualcasesmaynotalways yield valid predictions of pumping system performance. 2.2 Thedesignermustrealizethatthereare a number of unusual conditions which may be present COPYRIGHT American Petroleum Institute Licensed by Information Handling Services

in a well that could causemisleadingconclusions from these design calculations. Some of these unusual

conditions are:

a. Slanted or crookedholes, b. Very viscous fluid,

c. Excessivesandproduction, Excessive gas productionthroughthe and

cl.

pump,

e. Well flawing-off,

I

2.3 “he researchwork was limitedtosimulated problems in which the tubing was assumed as being

B 07322700003663

RP I L L - A B RP 1 1 L Design Calculations


anchored atthe pump.Therefore,thetestresults reflected onlythiscondition.However,because of the many known cases in which tubing is unanchored, a formulaisincludedwhich,experienceindicates, will giveavery close approximation of relative plunger travel with respect to the pump. This value is identified with the symbol Sp. Examination of the formula will revealthatthecontraction of the tubing caused by the transfer of the fluid load from the standing valve to the traveling valve is subtracted from the calculated plunger stroke, It is realized that this formula is highly simplified and not mathe-

7 5

matically correct, but it is close enough for practical application. 2.4 Thesedesigncalculationsmaybeusedwith confidence whenappliedtothebroadcategory of average, normal pumping wells fitting the assumed conditionsoutlinedinAppendix A. Unusualconwill cause deviaditions not fitting the assumptions tionsfromcalculatedperformance.Thedesigner must recognize this fact even though he cannot calculate quantitative values f o r this deviation,

SECTION 8 DISCUSSION b. 3.1 An understanding of the formulas utilized for the solution of sucker rod pumping problems will 3.1. Thevariables be gained by referring to Figure Fo, FI, Fz, W,!, and S are illustrated with this figure. 2T/Szkr PT: Torque,

Thedependentnondimensionalvariablesare:

Peak Polished Rod Load, PPRL: FdSkr Minimum Polished Rod Load,MPRL:Fz/Skr Peak F3/ Skr Polished Rod Horsepower, PRHP: Stroke,Plunger Sp: sp/s 3.3 In the research project the sucker rod pumpingsystemwassimulatedbyanelectronicanalog computer. Computer runs were made for many combinations of N/NOand Fo/Skr with the dependent nondimensionalvariablesbeingmeasured on each test. Test results were correlated by R. D. Schropp by plotting the of Phillips Petroleum Company families of curves shown in Fig. 4.1 through 4.5. From these curves, values for the various non-dimensional variables may be determined for substitution in the following design calculation formulas:

FIGURE 3.1 BASICDYNAGRAPH a. At Pumping Speed,

N c;?:

CARD

O

PeakPolished Rod Load, PPRL = Wri 4- FO Minimum Polished Rod Load, MPRL = Wri

b. For Pumping Speed, N

>O

PeakPolished RodLoad, PPRL Minimum Polished Rod Load, MPRL

= Wrf -I-FI = Wrt "F2

.3.2 The problem is generalized by using parameters of variables that are nondimensional. a. The independent nondimensional variables are:

N/No (Dimensionally = SPM/SPM Fo/Skr (Dimensionally

= l ) , and

=

Pounds =I) Inches x Pounds/Inch

Where:

N = SPM No = SPM at natural frequency of rod string S = Surface stroke COPYRIGHT Institute kr American = SpringPetroleum constant of rod atring Licensed by Information Handling Services

Plunger Stroke, SP= [(Sp/S) X SI - [Fo X l / k t ] NOTE: When tubing i s anchored, the value o f l / k t equals zero, therefore the formulu for Sp with anchored tubing become8 (Sp/S)x S . Pump Displacement, PD = 0.1166 X S p X N X D' Peak Polished Rod Load, PPRL = Wrt [(FdSkr) X Skr] Minimum Polished Rod Load, MPRL = Wrt - [(Fz/Skr) X Skr] Peak Torque, PT = (2T/Szkr) X Skr X S/2 X Ta Polished Rod Horsepower, PRHP = (FdSkr) X Skr X S X N X 2.53 X 10-6 Counterweight required, CBE = 1.06 (Wrt -I- % F o )

+

r

American Petroleum Institute

6

SECTION 4 DESIGN PROCEDURE 4.1 The final solution h this designproblem is reached through trial and error methods. Generdly, three steps are required in designing an installation. a. A preliminary selection of components for the installation must be made. b. The operating characteristics of the preliminary selection are calculated by use of the formulas, tables, and figures presented herein. c. The calculated pump displacement and loads are compared with the volumes, load ratings, stresof thepreliminary ses,andotherlimitations selection. It will usually be found necessary to make more than one calculation to bring the limitations of the variouscomponents of theinstallationintoagreement. 4.2 Theminimumamount of informationwhich must be known (or assumed) for a particular sucker rod pumping unit installation design calculation must include : Fluid Level H, the net lift in feet L, feet Pump Depth N, strokes per minute Pumping Speed S, inches Length of Surface Stroke D, inches Pump Plunger Diameter Specific Gravity of the fluid G "he nominal tubing diameter and whether it is anchored or hanging free. Suckerrodsizeanddesign

--

-

4.3

-

Withthesefactors,thedesigner

o l calculate the following:

-

w i l l beable

Plunger Stroke SPIinches PD, barrels per day Pump Displacement PPRL, pounds Peak Polished Rod Load Minimum Polished Rod Load " M P R L , pounds PT, poundinches Peak Crank TorquePolished Rod Horsepower PRHP CBE, pounds Counterweight required

-

-

--

4.4 Accumulatetheknown(orassumed)factors on API Form 11L-1 or similar sheet. An example of a completed design calculations form is included on page 6. Form 11L-1 maybeobtainedin100-sheet pads by ordering from the API Production Department office in Dallas a t a cost of $2.00 per pad. 4.5 RefertoTable 4.1, usethesuckerrodstring designationin LColumn 1 and the plunger diameter in Column2 a s guides, read and record the values for W;, E , and F, found in Columns 3, 4, and 6 respectively. Table 4.2, Column 5 will give the value of Et. This factor becomessignificantonlywhen If the workingwith an unanchoredtubingstring. tubing is anchored, Et need not be recorded.


NOTE: The valrrm of .rod percentages, rod weights, elastic constanis, and frequency factors shown in Table '4.1 d i f f e r f r o mthose in previous editions of R P l l L andthoseshown in Tables1and 2, API B d l e t i n llL3, First Edition, May 1970. Values in cwrent Table 4.1 were adopted at theJune1976 Sta.ndardiza.tionConference,basedonthearticle Sucker Rod String Design by A. B. Neely,published i n PETROLEUM ENGINEER, March 1976. d have negligibleeffect u p o n Changed ~ o percentages vallies calculated in B d l l L 3except f o r the weight of rods in fluid (WT!). A sxpplementtothefirst edition of Bu1 íIL3 has been published which conan tains an explanationofthedifferencesand example for correcting values in Bu1 l l L 3 based on the new rod percentages in Table 4.1. 4.6 Performtheindicatedmathematicalopera11. If thetubingis tionsindicatedthroughstep anchored, l / k t (step11)isequaltozeroandneed notbe calculated. "hevaluesare nowavailable Sp, and withwhichthebottomholepumpstroke, the pump displacement, PD, may be calculated.

4.7 Withthecalculatedvalues of Fo/Skrand N/NO' record the value of Sp/S from Figure 4.1 and 14. Pump dissolve for Sp and PD in steps 13 and placement is the first test being made to see if the

preliminary selection of components for the installation is satisfactory. If the pump displacement calknown or anticiculated in step 14 fails to satisfy patedrequirements,appropriateadjustmentsmust be made in the assumed data and steps 1 through 14 repeated. When the calculated pump displacement is acceptable,proceedwiththedesigncalculationsby performing steps 15, 16, and 17. 4.8 By using the calculated values of Fo/Skrand of F1/Skr(Figure 4.2), Fz/Skr (Figure- 4.3), 2T/S2kr (Figure 4.4), and F3/Skr (Figure 4.5) are read from the curves and recorded. When referring to Figures 4.1 and 4.6 to determine S P I S and Ta, the value of N/NO'must be used. Record . the value of' T

N/NO, thevalues

4.9 Substitution of theappropriatevaluesinthe variousformulasandperformance of theindicated 23 through 27 willyield the mathematicsinsteps variousloadstobeexpectedfromthepreliminary selection of equipment. It is now necessary to compare these calculated loads with limitations imposed by thepreliminary selection. Calculatethestress if it iswithin inthesuckerrodstodetermine acceptablelimits,

4.10 Generally,morethanone selection of equipment and calculation of operating conditions is necessav before the optimum selection can be made.

R P 11L:Design Calculations


7

EXAMPLE DESIGN CALCULATIONS CONVENTIONAL SUCKER ROD PUMPING SYSTEM

Object: To solve for-Sp, PD, PPRL, MPRL, PT, PRHP, and CBE Known or Assumed Data:

Fluid Level, H

= .*tf

= “SPM

Pumping Speed, N

Plunger Diameter, D

Pump Depth, L = a o a . f t .

Length of Stroke, S = f i n .

Tubing S i z e L i n . Is it anchored? Yes,@

Sucker Rods

.33#8‘,r n

=

Spec. Grav. of Fluid, G

&52 ”/d

-&it v

.-,J.

I

m i n . =

II

I

Record Factors from Tables4.1 S: 4.2:

/*e3*3

1. Wr =

(Table 4.1. Column 3)

3.

= L ! & ? ! / & j n ” ( T a b l e 4.1. Column 4)

2. E r

Fc

OBIz

=

4. Et = * 3 0 7 X / O

(Table 4.1, Column 5)

-G (Table 4.2. Column 5)

CalculateNon-DimensionalVariables:

= .340xGxD2xH = .

5. F.

6. l / k r = E r X L =

’i.

~

*g‘d.X/D

Skr = S + l / k r = &S

8. F d S k r

- 098 -4

~

O

X

~

X

~

X

~

.

=

-6

/<

+íJ423

-

I23/

,

%

!

N/NO = NL+245,000 =

~ ~ ~ 6 D u = L i r D ~ O -3in/lb. X / 9. f i

4 d z d A l.@-!= 4-?3Abs.

~lbs.O

10. N/NO’= N/No+Fc 11.

?

k ~ $ ~ . + 2 4 5 , 0 0 0= &

x¿.

+

082

-6 l / k t = E t x L =*319.78’/& x
= -.3&/

=&34%/¿&1b.

Solve for S,, and PD:

12. S ~ / S= d h L ( F i g u r e 4.1) 13.

Sp

= [(SplS) xS] - [ F o ~ l / k t ]=]-X&[

14. PD

= 0.1166 X S p X N X D* = 0.1166 X

-

u

x / 6

[m&, u=

X

/Ø3”35A

/i = 4< / ,7

=barrels

in.

per day

If the calculated pump displacement fails to satisfy known or anticipated requirements, appropriate adjustments must be made in the assumed data and steps 1 through 14 repeated. When the calculated pump displacement is acceptable, proceed with the Design Calculation. DetermineNon-DimensionalParameters:

15. W

= Wr X L = /‘S J.-?

16. Wrt

= W [ l - (.128G)]

X L L $ =Z -lbs. L

= g K [ 1 - ( . 1 2 8 ~ L ) ]= 9

17. Wrc/Skr = L l b s .

Record Non-Dimensional Factors from Figures4.2 through 4.6: 18. F1/Skr = =(Figure

4.2)

20. 2T/S2kr = &(Figure

= e&(Figure

4.3)

21. F3/Skr

19. Fa/Skr

Solve for OperatingCharacteristics: 23. 24. 25.

’6. 27. COPYRIGHT American Petroleum Institute Licensed by Information Handling Services

= &(Figure

4.4) 4.5)

g++-w,

=

b@4

a

Institute

Petroleum

American

TABLE 4.1

Roi) AND

PUXP DATA

See Par. 4.5.

3

2 Plunger Rod Diam., Weight, Rod* inches lb p e r f t No. D W,

7

1

8

9

10

11 ~~

Elastic Constant, in.per lb f t E,

Frequency Factor, Fc

Rod String, "/o of each size I

1%

1

76

%

%

?fi2

44

All

0.726

1.990 x 10-0

1.000

.......

........

........

........

........

100.0

54 54 54 54 54 54 54

1.06 1.25 1.50 1.75 2.00 2.25 2.50

0.908 0.929 0.957 0.990 1.027 1.067 1.108

1.668 x 1.633 x lom6 1.584 x 1.525 x 10-G 1.460 x 1.391 x 10-G 1.318 x 10-G

1.138 1.140 1.137 1.122 1.095 1.061 1.023

......

...... .....

.....

.....

.....

.....

.....

44.6 49.5 56.4 64.6 73.7 83.4 93.5

55.4 50.5 43.6 35.4 26.3 16.6 6.5

55

All

1.135

1.270 S

1.000

.......

......

......

G4

1.OG

........ .......

..... ........ . . . ...... ........

.......

.......

........

....

G4 G4 G4

1.25 1.50 1.75

1.164 1.211 1.275 1.341

1.382~ 1.319 x 1.232 x 1.141 x

1.229 1.215 1.184 1.145

........ ........ ....... ........

..... ...... ........ .....

65 65 65 65 65 65 65 65 65

1.O6 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.25

1.307 1.321 1.343 1.369 1.394 1.426 1.460 1.497 1.574

1.138 x 10-6 1.127 x 10-6 1.110 x 10-6 1.090 x 10-6 1.070 x 1.045 x 1.018 x 0.990 x 10-6 0.930 x

1.098 1.104 1.110 1.114 1.114 1.110 1.099 1.082 1.037

.....

......

6G

All

1.634

0.883 x 10-G

1.000

75 75 75 75 75

1.06 1.25 1.50 1.75 2.00 2.25

1.566 1.604 1.664 1.732 1.803 1.875

0.997 x 10-6 0.973 x lo6 0.935 x 10-0 0.892 x 0.847 x 10-G 0.801 x 10-6

1.191 1.193 1.189 1.174 1.151 1.121

76 76 76 76 76 76 76 76 76 76

1.06 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.25 3.75

1.802 1.814 1.833 1.855 1.880 1.908 1.934 1.967 2.039 2.119

0.816 x 0.812 x 0.804 x loeG 0.795 x 0.785 x 0.774 x 0.764 x 10-O 0.751 x lom6 0.722 x 0.690 x

1.072 1.077 1.082 1.088 1.093 1.096 1.097 1.094 1.078 1.O47

........

77

All

2.224

0.649 x

1.000

85 85 85 85

1.06 1.25 1.50 1.75

1.883 1.943 2.039 2.138

0.873 x 10-6 0.841 x 10-6 0.791 x 0.738 x 10-6

1.261 1.253 1.232 1.201

Pr Id


...... ....... ...... ......

........ .....

.......

...... ........

.......

100.0 33.3 37.2 42.3 47.4

33.1 35.9 40.4 46.2 65.6 62.7 58.2 53.1 48.0 41.6 34.8 27.5 11.9

33.5 26.9 17.3 7.4

.....

.....

34.4 37.3 41.8 46.9 52.0 58.4 65.2 72.5 88.1

.

..

100.0

.....

........

27.0 29.4 33.3 37,8 42.4 46.9

27.4 29.8 33.3 37.O 41.3 45.8

45.6 40.8 33.3 25.1 16.3 7.2

.....

....... ........

71.6 69.4 66.2 62.5 58.3 53.5 49.2 43.5 31.3 17.7

. . .

......

. . .

28.5 30,6 33.8 37.5 41.7 46.5 50.8 56.5 68.7 82.3

........

....

100.0

........

22.2 23.9 26.7 29.6

22.4 24.2 27.4 30.4

........ .....

...... ........

.....

....

........

..... ...... ..

....

.......

.....

...... .....

. . .

........

....

.

... ... . . .

........

....

.....

....

. . . .

....

....

-

...... .....

. .

... ... . .

....

.

.

...

......

.... ......

........ ........

....

........

........

........ .......

........

......

........ .......

.....

..... .....

. . .

...... . .

........ .......

.......

........

.......

........

......

........

....... ........

........

........

........

........

22.4 24.3 26.8 29.6

33.0 27.6 19.2 10.6

........ ........

........

I 0 7 3 2 2 7 0 0003665 6 r

I

RP ILL-B8 RP 1 1 L Design Calculations Sucker for

Rod Pumping Systems (Conventional Units)

9

TABLE 4.1 (Continued) See Par. 4.5. 53 4 2 Rod Elastic Plunger Constant, Frequency Diam., Weight, in. per lb f t Rod* inches lb p e r f t No. D W, E7

7

.___ 16

-

136

1

33

........

22.6 24.3 26.8 29.4 32.8 36.9 40.6 44.5

23.0 24.5 27.0 30.0 33.2 36.0 39.7 43.3

24.3 25.7 27.7 30.3 33.2 36.4 39.9 43.9 51.6 61.2 83.6

75.7 74.3 72.3 69.7 66.8 63.6 60.1 56.1 48.4 38.8 16.4

100.0

....

...

19.2

19.5 20.7 22.8 25.1 27.4 29.8

42.3 38.3 32.3 25.1 17.6 9.8

0.742 x 0.732 x 0.717 x 0.699 x 0.679 x 0.656 x 0.633 x 0.610 x

1.151 1,156 1.162 1.164 1.161 1.153 1.138 1.119

87

1.06 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.25 3.75 4.75

2.390 2.399 2.413 2.430 3.450 2.472 2.496 2.523 2.575 2.64 1 2.793

0.61 2x 0.610 x 0.607 x loe6 0.603 x 0.598 x 0.594 x 0.588 x 0.582 x 0.570 x 0.556 x 0.522 x

1.055 1.058 1.062 1.066 1.071 1.075 1.079 1.082 1.084 1.078 1.038

A 11

2.904

0.497 x los6

1.000

....

1.OG

2.382 2.435 2.511 2.607 2.703 2.80G

0.670 x 0.655 x 0.633 x 0.606 x 0.578 x 0.549 I

1.222 1.224 1.223 1.213 1.196 1.172

19.1 20.5 22.4 24.8 27.1 29.6

96 9G 96 96 9G

1.25 1.50 1.75

8.00 2.25

..

."

.. . . .

.......

.

.

20.6

22.5 25.1 27,!) 30.7

97 97 97 97 97 97 97 97

1.06 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.25

2.645 2.670 2.707 2.751 2.801. 2.856 2.921 2.989 3.132

0.568 x 0.563 x 0.556 x 0.548 x 10-8 0.538 x 0.528 x 10-6 0.515 S 0.503 x 0.475 x

1.120 1.124 1.131 1S37 1.141 1.143 1.141 1S35 1.111

22.5 24.5 26.8 29.4 32.5 36.1 42.9

20.0 21.2 23.0 25.0 27.4 30.2 33.1 35.3 41.9

98 98 98 98 98 98 98 98 98 98 98

1.06 1.25 1.50 1.75 3.00 2.25 2.50 2.75 3.25 3.75 4.75

3.068 3.076 3.089 3.103 3.118 3.137 3.157 3.180 3.231 3.289 3.412

0.475 x 0.474 x 0.472 S 0.470 x 0.468 x 0.465 x 0.463 x 0.460 x 0.453 x 0.445 x 0.428 x

1.048 1.045 1.048 1.051 1.055 1.058 1.062 1.066 1.071 1.074 1.064

21.2 22.2 23.8 25.7 27.7 30.1 32.7 35.6 42.2 49.7 65.7

78.8 77.8 76.2 74.3 72.3 69.9 67.3 64.4 57.8 50.3 34.3

99

All

3.676

0.393 x 10-G

1.000

100.0

........

97


%i 94

Fc

2.058 2.087 2.133 2.185 2.247 2.315 2.385 2.455

9ti

10

11

A

r

1.06 1.25 1.50 1.76 2.00 2.25 2.50 2.76

88

9

Rod String, $6 of each size Factor,

86 86 86 86 813 86 86 8(i 87 87 87 87 87 87 87 87 87 87

8

19.t;

20.8

54.3 51.2 46.3 40.6 33.9 27.1 19.7 12.2 .. -

........

.... .... . .

. . . . . . ...

60.3 58.0

54.5 50.4 45.7 40.4 34.4 28.6 15.2

.

.

.....

.... .....

...... .......

..... .... ....

.....

.....

......

........

....... ...... ""

._

.......

.......

........

........

........

YZ

10

Institute

Petroleum

American

TABLE 4.1 (Continued) See Par. 4,5.

3 4 2 Rod Elastic Plunger Constant, Frequency Diam., Weight, Rod* inches lb p e r f t . in. per lb ft No. D W, E, 1

107 1.06 0.5242.977 107 1.25 0.517 3.019 1.50 107 3.085 107 1.75 3.158 0.480 107 3.238 2.00 107 3.336 2.25 0.447 3.435 107 2.50 107 3.5372.75 108 108 108 108 108 108 108 108 108 108

0.363

1.06 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.25 3.75

3.325 3.345 3.376 3.411 3.452 3.498 3.548 3.603 3.731 3.873

109 1.06 0.378 3.839 1.25 109 0.378 3.845 1090.377 3.855 1.60 109 1.76 3.867 0.375 109 3.8802.00 l m0.374 3.896 2.25 0.372 109 3.911 2.50 109 2.75 3.930 109 0.367 3.9713.25 4.020 109 3.75 0.354 1094.120 4.75

I

1010

5

6

7

8

9

1% 1

1%

%

x 1.184 x 10-G 17.9 1.189

16.9

16.8 17.1 17.8 46.318.0

49.1

1.195 1.197 21.0 21.221.0 1.195 23.1 22.8 22.7 1.187 25.025.025.025.0 26.927.1 27.7 1.174 1.15629.330.229.1

S/a

18.2 11.3

........

41.9 36.9 31.4

~

17.8 18.6 19.9 21.4 23.0 25.0 27.2 29.6 33.9 39,5

64.9 63.2 60.7 57.7 54.3 50.5 46.3 41.6 31.6 19.9

........

........

.......

x 1.035 18.9 x 1.036 19.6 x 10-6 1.038 79.320.7 0 . 3 7 6 ~10-O 77.9 22.11.040 x 1.043 23.7 x 10-o 1.046 74.625.4

81.1 80.4

........

........ ........

........

........

........ ........ ........

x 10-G 0.371 x 10-G x 10-G

All 0.318 4.538

x x x

1.097 1.101 1.106 1.111 1.117 1.121 1.124 1.126 1.123 1.108

1.048 72.8 27.2 1.061 29.4 1.057 34.2 39.9 1.063 51.5 1.066

....... ....... ......

76.3 70.6 65.8 60.1 48.5

"_ 1.000 100.00 "_ "_

......

....... ...... ... ...

_.._.

.......

%

........ ........ ........ ........ ,._.._. ........ ........ ........ ........ ....... ........ ........ ........ ........ ........ ........

17.3 18.1 19.4 20.9 22.6 24.5 26.5 28.7 34.6 40.6

0.447 x 10-0 0.445 x 10-6 0.441 x 10-6 0.437 x 0 . 4 3 2 ~10-6 0.427 x 10-G 0.421 x 10-6 0.416 x 10-G 0.400 x 10-G 0.383 x

11

Rod String, 95 of each size Factor, Fe

19.50.50619.2 x 10-G 19.4 0.494 x 10-G x 10-G 0.464 x 10-G x 10-o 0.430 x 10-G

10

........ ........

........

........ ........ ........

........

........ ........ ........ ........

....... ....... ........ ......

........

........ ........

........

.......

....... ........

........

........

........

........

........ ........ .......

........ ........ ........ ........ ........ ........ ........ ........ ....... ........ ........ ........ ......

........

....... ........ ........ ........

........

........

........

""-

""-

........

........

*Rod No. shownin first columnreferstothelargestandsmallestrodsizeineighths of a n inch. Forexample, Rod NO. 76 is a t w o - w a yt a p e r of 7/8 a n d 6/8 rods.Rod No. 85 i s a four-waytaper of 8/8, 7/8, 6/8, a n d 5 / 8 rods. Rod No. 109 is a two-way taper of 1% a n d 1% rods.Rod No. 77 is a s t r a i g h t s t r i n g of 7/8 rods, etc.


RP 1 1 L Design Calculations for Sucker Rod Pumping Systems (Conventional Units)

TABLE 4.2 TUBING DATA

_-

1 Tubing Size

-

2

3

4

Outside Diqeter,

Inside Diameter,

Metal Are.% sq. m.

in.

m.

2%

1,900 2,376 2,876

3%

3,600

4

4,000 4.600

1,900 2%

4%

1

Rod Size

3-5 56

% 74 1 1%

1,610 1,995 2;441 2,992 5,476 3.968

6 Elastic Constant, in. per lb f t Et 0.600 x loTa 0,307x loF6 0,221x 10-8 0,164x 0.130 x 0.111 x 10-6

0,800 1,304

L;812 5.690 3.077

3.601

TABLE 4.3 SUCKER ROD DATA 2 3 4 Rod Weight Elastic Metal inair, Constant, in.per lb ft Area, lb per f t sq in. Wr Er

0.196 0.307 0.442 0.601 0.786 0.994

r

1.990 x 10-6 1.270 x 10-6 0.883 x 10" 0.649 x 10" 0.497 x los 0.393 x

0.72 1.13 1.63 2.22 2.90 3.67

r

1 Plunger Diameter,

in. D

I* 1% 1% 1%

6.0626 6.2600

2 2% 2% 2%

3% 4%

TABLE 4.4 PUMP CONSTANTS 2 3 Plgr.Diam. Fluid Load Squared Factor* Sa. in. lb Der f t D 2

1.1289 1.6626 2.2600 3.0626 4.0000

7.6626 14.0626 22.6625

COPYRIGHT American Petroleum Institute *For fluids with specific Licensed by Information Handling Services

(SrÕ x

11

4

-P Factor

D e ) (.1166 z D p )

0.384 0.631 0.766 1.041 1.360 1.721 2.126 2.671 4.781 7.671 gravity of 1.00.

0.132 0.182 0.262 0.367 0.466 0.690 0.728 0.881 1.840 2.630

RP 1LL-88 0732270 12



0003668 L

r

0.1

G.2

Fr , PEAE Skr


O. 3

0.4

FIGURE 4.2 POLISHED ROD LOAD

05

06

RP ILL-B8 American Petroleum Institute

14

4

.3

.I

t

O0

FIGURE 4.3

*a ' r , MINIMUM POLIISHED ROD LOAD COPYRIGHT American Petroleum Institute Licensed by Information Handling Services

B 0732270

0003670 0

r

RP 11L-BB RP 11L Design Calculations


FIGURE 4.4

m , PEAK TORQUE 8%


0732290 0003673

3 15

r

R P L L I " ~ ~ Ö ~ 7 3 2 Z0 070 306 7 2 3 16

Institute

Petroleum

American

N NO

FIGURE 4.5

'' , POLISHED ROD HORSE POWER m? COPYRIGHT American Petroleum Institute Licensed by Information Handling Services

1-

R P 11L: Design Calculations


TOTAL ADJUSTMENT= 3 X 3 o/' Ta 1.00+ 0.09 = 1.09

NûTEilF

Wr f sir, IS

=

9%

LESS T H A N 0-3 AGJlJSThlENT BECGMES NEGATIVS.

FIGURE 4;6

T,, ADJUSTMENT FOR PEAK TORQUE

FORInstitute VALUES OF COPYRIGHT American Petroleum Licensed by Information Handling Services

WH ;5kr OTHER "HAN

03

17

0732270 0003671.1 7

RP 11L-88 18

Institute

Petroleum

American

APPENDIX A

DISCUSSION OF NONDIMENSIONAL PARAMETERS Al. A mathematical evaluation of sucker-rod pumping, forpracticalpurposes,revolvesaround the development of equations to express the motion and the state of stress of sucker rods. The developis mathematically ment of representativeformulas complicatedbecause of thedifficulty of expressing boundary conditions which suitably reflect the openingandclosing of thevalves of thepumpwhen these are themselves a function of the motion of the system and the fluid-flow conditions in the pump. A2. Thecriteriagenerallyusedforthedesign of sucker rod installationsarebasedongreatly oveximplifled concepts of pumpingsystemmechanics. Consequently,theformulasderivedfromthese viewpoints a t best represent average conditions yield occurring in pumpingsystemsandmaynot validpredictions of systemperformance,especially in deep wells and a t high pumping speeds. A3. Thetendency to oversimplify the methods forpredictingsystemperformanceisnotduetoa limited knowledge concerning the operation of sucker rodequipment, Quite thecontrary,thebasicoperatingcharacteristics of suckerrodsystemshave beenreasonablywellunderstood formanyyears. Rather,oversimplificationsinthemethodsforpredicting rod system behavior have arisen a s a result of computers of mathematicaldifficultiesandlack to handle the mass calculations required to describe pumping performance accurately.

A4. The simplifications in the mathematical model of suckerrodpumpingcan be groupedinto two broadcategories: a. Inadequaterepresentation of therodstring. b. Inadequate treatment of the downholepump action.

A5. Many of thecurrentmethodshavebeen developed on the basis that the mass of the sucker rod is concentrated at a point. This assumption makes possible a mathematical simplification wherein thespringequation(anordinarydifferentialequato simulatethecharacteristics of the tion)isused is mathesucker rod. Althoughthisassumption matically convenient, it destroys the analogy between the mathematicalmodel theactualsuckerrodand used to represent the sucker rod. In reality, the mass of the sucker rod is distributed along its length, and this factmust be incorporatedinto any realistic mathematicalmodel of the rod. Without this provision, theanalysisdoesnotincludethe effect of force waves traveling within the sucker rod, which is an important characteristic of real systems. A6. Some of thelater techni uesforpredicting rod performance have used an alequate representation of thesucker rod. Such a representationrequires that the wave e uation (a partid differential equation)beusedto%escribethebehavior of the sucker rod. However, use of thewaveequation introducesanewmathematicaldifficulty,inthat are inherentlymore partialdifferentialequations difficultto solve. Much of thedifficultyarisesin formulatingtheboundaryconditionsthatdescribe COPYRIGHT American Petroleum Institute Licensed by Information Handling Services

at theextremities of the the loading andmotion rod. The boundary condition which describes the behavior of the downholepumppresentsparticular difficulties, and investigators in the past have made its regard. manyspecializedassumptionsin A7, Theapparentnecessityformaking specialized assumptions about pump action has been brought aboutbypeculiarities in thesuckerrodproblem. a particular difThesuckerrodproblempresents ficulty, in that the pump boundary condition depends upon thebehavior of thesuckerrodstringitself, which is the very thing to be established by solution of the problem. This apparent impasse has led to the special assumptions mentioned heretofore, which, in effect, amounttoidealizedguessesaboutpump operation.Consequently,themethodsbasedonthe special assumptions yield usable results only to the extent to which the idealizations approximate pump action, A8. Inthework a t MidwestResearchInstitute, suckerrodpumpingsystemsmeresimulatedby an electronicanalogcomputer.Numerousrunswere made representing a wide range of conditions. These runs werecorrelated on thebasis of two nondiare N/NO', mensional parameters. These parameters the dimensionlesspumpingspeed,andFo/Sk,the dimensionlessrodstretch.Theuse of thesenondia complete suite of mensionalparametersallows sucker rod pumping conditions to be correlated without having to run an infinite number of cases. A9. Thedimensionlesspumpingspeed, N/NO',is a highly important indexof the rod strings' behavior. This parameter is the ratio of the forcing frequency, N (thepumpingspeed),totheundampednatural frequency of the rod string, No'. Theundamped to naturalfrequency is showninvibrationtheory be inverselyproportional to thetimerequiredfor a force wave to make four traversals along the sucker rod. Thus,theundampednaturalfrequencyis given by:

No' =-Fea 4L

where Fc is a constant of proportionalitywhich depends on the rod design and r'alJ is the speed of Fe equale sound in steel. For untapered rod strings, 1. Fromtheoreticalconsiderations, it canbeshown that the natural frequency of a tapered rod string is greaterthanthat of a uniform string of equal Fc has a value length. Thus, fortaperedstrings, Fc intaperedrod greaterthanunity.Valuesfor 4.1. The formula for strings can be found in Table dimensionless pumping speed N/NO' immediately follows as: N 4NL -=-

No'

Fca

Figures A S through A.6 contain charts from which most of the frequency factors, Fc, in Table 4.1 were to determine FC obtained. These charts may be used for any arrangement of rodsizes for some of the A.6 plots most commonly used tapered strings. Fig. a number of rod combinations on a single curve as a function of pump diameter.

1

RP 1 1 L Design Calculations Sucker for

Rod Pumping Systems (Conventional Units)

I

I O0

CHANGE OF FUNDAMENTAL FREQUENCY I F O R li 8 i 8 8 TAPERED ROD STRING

z

8C

60

%

27 ROD 40

20

C

FIG. Al PERCENTAGE INCREASE IN FUNDAMENTAL FREQUENCY l=¶/& 1; AND 7IS-INCH THREE-WAY TAPER STRING COPYRIGHT American Petroleum Institute Licensed by Information Handling Services

19

RP I L L - 8 8

B 0732270

0003676 O


20

100

CHANGE OF FUNOAMENTAL FREOUENCY

FOR I, 80

ia $ TAPERED R O D

STRING

\

60

3

f

x ROD

L

O

2

40

60 @/a

80

1 ROD

FIG. A.2 PEBCENTAGE INCREASE IN FUNDA6IENTAL FREQU&NCP 7/4 AND 8/4-INCa THREE-WAY TAPER STBING COPYRIGHT American Petroleum Institute Licensed by Information Handling Services

IO 0

RP 11L: Design Calculations Sucker for

Rod Pumping Systems (Conventional

Units)

21

CHANGE OF FUNDAMENTALFREQUENCY

FOR

8C

f

I

3

8

2 0

TAPERED ROD STRING

6(

\

%

8 ROD

20.9Y

4c

2(

C

60

FIG. A 3 PERCENTAGE INCREASE IN FUNDAMENTAL FREQUENCY

7/8, 3/4, AND 6/8-INCH THREE-WAY TAPER STRING COPYRIGHT American Petroleum Institute Licensed by Information Handling Services

eo [IIL-A.3J

100

RP J

l

L

-

b

I 0732290 0003678 4

22

100

CHANGE OF FUNDAMENTAL FREOUENCY FOR Q a + TAPERED ROD STRING

S,

FIG. A 4 PMtCENTAGE INCREASE IN FUNDAMENTAL FREQUENCY COPYRIGHT American Petroleum Institute 3/4, 5/8, AND 1/2-INCH THREE-WAY TAPER STRING Licensed by Information Handling Services

I

R P 1 1 L Design Calculations for Sucker Rod Pumping Systems (Conventional Units)

S! b r

1

\ d

o

\ \ \ \ \

\

O

d


\

23

RP I L L - 8 I 087 3 2 2 9 8003680 American Petroleum Institute

24

O

1

3

2

a

PLUNGER DIAMETER, INCHES

FIGURE A.6 PERCENTAGE INCREASE IN FUNDAMENTAL FREQUENCY SPECIFIC ROD COMBINATIONS ~


2

r

API RP 11L - Design calculation for sucker rod pumping system

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