SPE-14685-PA

Designing a Sucker-Rod Pumping System for Maximum Efficiency Robert H. Gault, SPE, consultant

Summary. Consideration of the energy requirements in the design of a sucker-rod pumping system is very important. Examples are given that detail how the use of the largest possible pump with the lightest, strongest rod string and special-geometry units can provide a substantial energy reduction.

Introduction A number of variables are important in the design of a sucker-rod pumping system. To get the best design for a specific application, each variable must be evaluated in terms of the particular require-ments of that specific system. A system that might be ideal for the operating conditions of one area might be a very poor selection for another area with different operating conditions.

The importance of the energy requirement is in proportion to the cost of energy. Twenty years ago, electricity sold for about $0.006/kW-hr [$0.002/MJ) and gas for about $0.25/Mcf [$0.0088/m 3 ). The energy bill was so small that it was not even considered in the design ofthe system. Because most of the exper-tise in the design of sucker-rod systems was gained in this era of low energy costs, the impact of energy costs on the system design has been largely ignored.

Today, the average cost of electricity is about $0.07 Ik W -hr [$0.019/MJ], and the average lease value of natural gas is about $3.oo/Mcf [$0.106/m 3 ). Now the energy bill is usually the larg-est operating cost item on the lease and has become a very impor-tant design consideration.

Theoretical Energy Costs A discussion of energy usage and cost should start with hydraulic horsepower. This is the theoretical work that is required to lift the pounds of well fluid from the net depth. The equation for calculat-ing hydraulic horsepower for a fluid weighing 8.34 Ibm/gal [999 kg/m3) (specific gravity of 1.0) is .

Lw hh=33,000-.

t

qx42x8.34 hh=LX X---.

1,440 33,000

hh =0.00000736qL,

where hh = hydraulic horsepower, L = net lift, ft, w = weight, Ibm t = time, minutes, and q = flow rate, BID.

In SI units, Wh = 0.0001135 qL,

where Wh = hydraulic work, L is in m, and q is in m3/d.

Copyright 1987 Society of Petroleum Engineers

284

The theoretical hydraulic horsepower to lift 500 BID [79.49 m3 /d) of fluid with a specific gravity of 1.0 from 6,000 ft [1828.8 m) would be

0.00000736 X 500 BID X 6,000 ft=22.08 hhp.

In kilowatts,

22.08 hhpxO.746 kW/hp=I6.47 kW.

In SI units,

0.0001133 x79.49 m3 Idx 1828.8 m= 16.47 kW.

The annual power bill, x, with $0.07 Ik W -hr [$0.019 IMJ) electric-ity would be

x=$0.07/kW-hrx 16.47 kW/hrx24 hrIDx365 D/yr

=$10, loo/yr. This is the theoretical cost to do the work of lifting 500 BID [79.49 m 3 /d) from 6,000 ft [1828.8 m).

Actual Energy Considerations Polished-rod horsepower starts with this theoretical work at the pump and includes the other downhole requirements of the system: (1) the horsepower required to move the sucker-rod string dynam-ically, (2) the friction

There are many parameters in a sucker-rod pumping system, and a change in anyone of the parameters alters the values of all the others, For convenience, API Bull. 11LJ2 will be used in this study. This manual is a computer printout of about 60,000 individual RP11L well calculations referenced by rod size, producing rate, and pumping depth. With this manual, it is possible to see the ef-fects that a change in one of the variables will have on the other design criteria. For example, on Pages 338 and 339 of API Bull. 11LJ, about 100 systems are listed that would produce at the rate of 500 B/D [79.49 m3 /d] from 6,000 ft [1828.8 m]. Of all the sys-tems listed, only the systems for Rod Nos. 75, 76, 85, and 86 will be used. (These are the only systems that would be considered by an experienced designer.) Polished-Rod Horsepower as a Function of Configuration An examination of the polished-rod horsepower requirements of these systems shows that changes in rod size, pump size, stroke length, and strokes per minute affect the polished-rod horsepower required to do the same hydraulic work of lifting 500 BID [79.49 m3/d] from 6,000 ft [1828.8 m]. Of the systems listed above, the one that requires the greatest polished-rod horsepower is Rod No. 86, with a pump diameter of 1.25 in. [31.75 mm], a stroke length of 192 in. [4.88 m], 13.7 strokes/min, and 54.6-hp [40.73-kW] polished-rod horsepower. The system that requires the least polished-rod horsepower is Rod No. 86, with a pump diameter of 2.75 in. [69.85 mm], a stroke length of 120 in. [3.05 m], 7.9 strokes/min, and 22.8-hp [17.0-kW] polished-rod horsepower.

These are startling differences. To do exactly the same hydraul-ic work, one system requires almost 2 V2 times as much horsepow-er at the polished rod as the other.' It is plain that any design must include consideration of the energy consequence. Total energy usage is directly related to the work done at the polished rod plus horse-power losses in the pumping unit and motor.

In the first example, where maximum polished-rod horsepower was required, a small-diameter pump was used with a heavy rod string. To get the required amount of fluid (500 BID [79.49 m3 /d]), it was necessary to use a long stroke at a fast speed (lIA-in. [31.75-mm] pump with 192-in. [4.88-m] stroke lengths at 13.7 strokes/min). This system has very large dynamic horsepow-er requirements. In the second example, where the minimum polished-rod horsepower was required, a large pump was used with a slow pumping speed (2..-in. [69.85-mm] pump with l20-in. [3.05-m] stroke lengths at 7.9 strokes/min). This system has very small dynamic horsepower requirements. Note that the polished-rod horsepower (22.8 hp [17.0 kW]) of this system is only slightly greater than the theoretical hydraulic horsepower (22.08 hp [16.47 kW]).

Total Energy Requirements of the System The polished-rod horsepower requirements listed in Bull. 11 LJ in-clude only the work that must be performed at the polished rod. The total energy requirements of the system must also include the horsepower requirements of the surface system. 3 These addition-al horsepower requirements are mechanical friction losses in the pumping unit and sheave system. This will be called motor-shaft horsepower because it is the horsepower needed at the motor shaft.

The following equations summarize the discussion so far:

hh =0.OOOOO736qL, hpr=hh +hd+hif,

and

where hpr = polished-rod horsepower, hd = dynamic horsepower, hif = rod-friction horsepower,

hms = motor-shaft horsepower, hUl = unit-loss horsepower, and Eu = unit efficiency.

SPE Production Engineering, November 1987

TABLE 1-ANNUAL POWER COSTS FOR 1 POLISHED-ROD hp

Rate ($/kW-hr)

0.05 0.06 0.07 0.08

Annual Power Cost for 1 polished-rod hp

(dollars) 548 657 767 876

In SI units,

Wh = 0.OOOI133qL,

and

where Wh = hydraulic work, kW,

Wpr = polished-rod work, kW, Wd = dynamic work, kW, W if = rod-friction work, kW,

Wms = motor-shaft work, kW, and Wul = unit-loss work.

It has been shown that the efficiency of a pumping unit and sheave system is dependent on its age, geometry, and percentage of load. 4 The average values for conventional unit efficiency, with reducer loads greater than 70%, are about 0.75 to 0.85. With an efficiency of 0.80, the motor-shaft horsepower would be

In SI units,

Note that motor-shaft horsepower should not be confused with motor-nameplate horsepower. To determine motor (nameplate) size, it is common practice to use 2Xhpr and then to use the next-larger motor size. The motor selected by this method will be large enough to start and service the unit, but the actual motor load will be only about 1.25 xhpr '

To find the energy cost of the system, it is necessary to include the motor efficiency and to convert horsepower to kilowatts. NEMA D motors used in sucker-rod pumping will have average efficien-cies from about 50% under light loads to about 85% under opti-mum load conditions. An average value of 74.6% will be used for ease of calculations. The equation for determining kilowatts from polished-rod horsepower is

(1.25hpr)(0. 746kW /hp) kW= =1.25hpro

0.746Em

where Em = motor efficiency.

In SI units,

kW = 1.676hpro

where hpr is in kW.

285

PRODUCING RATE = 500 BPD FROM 6000 FEET 34

33

~ 32 :.: ~ 0 31 ci ~ 1-...... 30

PRODUCING RATE = 500 BPD FROM 6000 FEET 26

25

~ :>-:1 0 o::.c wI-(1."'- 21

PRODUCING RATE = 500 BPO FROM 6000 rEET 34

"-33 32

-----

,. 31

" \ ~ 30 \ 0 ~ 29 \ 28 !;(~ ""---- \.. ere 27

'\ -----

~g ---

26 '\ >-5 ~~ 25

'" " 24

'" --.....

'" er 23

'\ ~ j 22 "

g 21 '\, 20

19 18

70 90 110 130 150 170 t 190 210 230 STROKE LENGTH, INCHES

1.5" PUMP + 1.75" PUMP 2" PUMP

Fig. 6-Energy use for No. 85 rod with various pump sizes.

energy cost is quite substantial. Note again that there are minimum stroke lengths that must be used to gain the lowest annual energy cost.

These figures illustrate that larger-bore pumps, when used with the optimum minimum stroke length, will give the lowest energy use. This advantage is the result of the slower pumping speeds need-ed with the greater displacement of the larger-bore pumps. These slower pumping speeds generate less dynamic and frictional horse-power losses and therefore are more energy-efficient. Another benefit of the slower pumping speeds possible with the larger pumps is the reduced number of wear strokes per year.

In spite of these obvious benefits, there are a number of reasons larger pumps would not or could not be used in a system. First, the casing size often limits the largest pump that can be run. For instance, the largest tubing that is usually run in 4'/2-in. [11.43-cm] casing has a 2%-in. [6.03-cm] 00. This limits the maximum pump size to a I %-in. [44.45-mm] tubing pump. Second, tubing pumps require that the tubing be pulled to service the pump barrel. This adds substantially to the cost of servicing. Third, the larger fluid loads and greater range ofload present with the larger pump bores may require larger or stronger rods. The use of larger rods may be limited by the maximum tubing size that can be installed in the well.

Cost Reduction With Energy-Efficient Design Table 2 displays some of the differences in energy costs for the systems used in the charts and listed in the tables of API Bull. 11 L3 . Because the basis of selection for this table was only energy cost, these would not necessarily be the best or worst systems when con-sideration is given to all the design factors. The general conclu-sion reached from the figures and Table 2 is that the proper choice of pump size, stroke length, and rod size can make an important difference in the annual energy cost.

Energy Impact of the Improved-Geometry Pumping Unit The energy benefits associated with proper downhole design have been examined. Improved-geometry units also offer the potential for substantial energy savings.

PRODUCING RATE :z:I 500 BPO FROM 6000 FEET 34 33 32 -

34 PRODUCING ~TE - 500 BPD FROM 6000'

33 32

:r 31 ~ 30 ~ 29 0

28 d ....,.

27 .-.. I-fIl

TABLE 3-TORQUE AND ENERGY REQUIREMENT~ FOR NO. 86 ROD STRING

Conventional Special- Conventional Special-Unit Geometry Unit API Geometry API

Pump Size Stroke Length Energy Cost Energy Cost Peak Gear Peak Gear (in.) (in.) Strokes/min Polished-Rod hp 1.5 74 22.2 41.3 1.5 86 20.4 42.2 1.5 100 18.6 42.5 1.5 120 16.5 42.0 1.5 144 13.2 36.7 1.5 168 11.3 35.8 1.5 192 10.1 36.5 1.75 74 19.5 35.4 1.75 86 17.6 34.7 1.75 100 15.9 34.3 1.75 120 13.1 31.5 1.75 144 10.5 28.9 1.75 168 9.0 28.7 1.75 192 7.9 28.3 2 74 17.7 32.1 2 86 15.8 31.9 2 100 14.0 30.5 2 120 10.7 26.2 2 144 8.8 25.7 2 168 7.4 25.8 2 192 6.4 25.4

This reduction in wear and fatigue strokes would add substantially to the life of the pump and rods and would reduce pulling costs.

Conclusions This study was made for a system to handle 500 BID [79.49 m3/d] from 6,OOO-ft [1828.8-m] pumping depth. Pumping requirements with less polished-rod horsepower would not show such large differ-ences in energy costs. However, it is clear that an energy study must be made of every pumping system design and included as part of the total system design. With the more sophisticated predictive methods now available, it is possible to make very precise predic-tions of the energy impact of each system component.

References 1. RP II L, API Recommended Practice for Design Calculations for Suck-

er Rod Pumping Systems (Conventional Units), third edition, API, Washington, DC (1977).

,2. Bull. lJL3, Sucker Rod Pumping System Design Book, first edition, API, New York City (1970).

290

($/yr) ($/yr) Torque Size Torque Size -- --

31,677 26,925 360 456 284 320 32,367 27,512 430 456 423 456 32,597 27,707 523 640 480 640 32,214 27,382 657 912 578 640 28,148 23,926 746 912 624 640 27,458 23,339 824 912 659 640 27,995 23,796 905 912 720 912 27,151 23,078 343 456 314 26,614 22,622 401 456 368 456 26,308 22,362 492 640 436 456 24,160 20,536 612 640 492 640 22,166 18,814 717 912 541 640 22,012 18,710 798 912 597 640 21,706 18,450 861 912 633 640 24,620 20,927 344 456 307 320 24,467 20,797 405 456 365 456 23,393 19,884 478 640 430 456 20,095 17,081 577 640 465 456 19,711 16,754 712 912 534 640 19,788 16,820 827 912 586 640 19,481 16,559 890 912 620 640

3. Gibbs, S.G.: "Computing Gear Box Torque and Motor Loading for Beam Pumping Units with Consideration of Inertia Effects," JPT (Sept. 1975) 1153-59; Trans., AIME, 259.

4. Gipson, P.W. and Swaim, H.W.: "The Beam Pumping Design Chain, Second Edition," paper presented at the Southwest Petroleum Short Course, Texas Tech U., Lubbock (April 1985).

SI Metric Conversion Factors bbl x 1.589873 E-Ol m

ft x 3.048* in. x 2.54*

kW-hr x 3.6*

Conversion factor is exact.

E-Ol E+oo E+oo

3

m

cm MJ

SPEPE

Original SPE manuscript received for review Nov. 11. 1985. Paper accepted for publica-tion Nov. 3. 1986. Revised manuscript received May 6. 1987. Paper (SPE 14685) first presented at the 1985 SPE Production Technology Symposium held in Lubbock. Nov. 11-12.

SPE Production Engineering, November 1987