Prime mover for sucker-rod pumping unit

The prime mover (PM) rotates the gear-reducer gears through a V-belt drive. The two most common PMs are electric motors and internal combustion (IC) engines. The decision concerning which to use depends on a variety of considerations, which includes the following:

• Availability of the power source (electricity or combustible fluid)
• HP required to pump the well
• Efficiency of the system
• Ability to control the PM to match the on/off potential operation of the pumping unit
• Availability of field and/or service personnel capable of maintaining and repairing the equipment
• Condition of the gas (sweet or sour) or availability now and in the future of the gas or liquids (i.e., propane or diesel) if an IC engine is used
• Current and future expected cost for the power source
• Anticipated full-cycle total cost (including initial capital, operating, maintenance, downtime, and repairs) for the duration of the well

These considerations, as well as other factors, have been discussed in numerous publications.

Engines

There are three common types of gas engines used for beam pumping units:

• Two-cycle, slow-speed engine
• Four-cycle, slow-speed engine
• Four-cycle, high-speed engine

The characteristics of these engines are summarized here, and the detailed comparisons and field experiences have been published elsewhere.

Two-cycle, slow-speed engine (less than 750 rpm):

• A minimum number of moving parts
• Rugged, heavy-duty construction
• A heavy flywheel that provides comparatively uniform crankshaft rotation on the cyclic loading of a pumping unit
• Requires a minimum amount of maintenance
• Can be overhauled on location
• Requires a heavy foundation
• Higher cost per HP than for high-speed engines
• Weight per HP is higher than for high-speed engines
• Can usually run only on natural gas or liquefied petroleum gas (LPG)
• May have either one or two cylinders
• Fuel-injection system should be used when HP is greater than 40

Four-cycle, slow-speed engine:

• Widely used
• Relatively few moving parts
• Uniform crankshaft speed because of a large flywheel
• Can operate on governor control to compensate for load changes
• Will operate on either natural gas or LPG
• Repairs can usually be made without removing the engine from the pumping unit
• Cost and weight per HP is greater than for high-speed engines
• Limited engine sizes
• Usually has a single horizontal cylinder

Four-cycle, high-speed engines (greater than 750 rpm):

• Best suited for portable test installations vs. permanent installations
• Lower initial cost
• Lower weight per HP
• Wide speed and power range
• Operates on a variety of fuels
• Large speed variations occur during pumping cycle because of a small flywheel effect
• Operates on a fixed throttle with the governor mechanism acting only as an overspeed device
• Has relatively short life because of the fast moving parts and the close tolerances required
• Requires frequent oil changes
• Requires frequent maintenance
• Major repairs require that the engine be removed from the pumping unit

API Spec. 7B-11C contains standard test and operating procedures that are used by manufacturers to determine the ratings of engines for oilfield service. These test data should be requested and furnished to the purchaser from the manufacturer. The data should include the manufacturer's curves showing the torque, maximum brake HP, and the rated-brake HP vs. engine speed. These are important to know the speed range in which the engine would be able to operate.

A general guide for installation and maintenance of gas engines is API RP 7C-11F, which covers all three types of engines and includes a troubleshooting section. This practice should be used as a starting point for engines unless the specific manufacturer's operating manual details otherwise. Additionally, there are a number of published papers on installation, care, operation, and lubrication of engines as prime movers for pumping units.

Gas-engine performance needs to be derated for altitude and temperature. The API Spec. 7B-11C for IC engines recommends the following:

• Deduct 3% of the standard brake HP for each 1,000-ft rise in altitude above sea level
• Deduct 1% of the standard brake HP for each 10° rise in temperature greater than 60°F or add 1% for each drop in degree, if temperature is less than 60°F
• Deduct 20% if the engine is continuously operated

One of the biggest drawbacks of using IC engines is being able to automatically control their operation. There have been a few publications on automatic controllers, but these typically have had limited field use with no long-term production performance recorded.

Electric motors

Once it has been determined that an electric motor is needed vs. a gas engine, there are several things to consider, including:

• Design standard
• Unit efficiency
• Cyclic-load factor
• Motor enclosure

There have been a number of papers written on the use of electric motors for sucker-rod-lifted wells. Detailed discussions with example problems for sizing motors, along with discussion of electrical-power distribution systems for multiple-well installations, are presented in previous editions of the Petroleum Production Handbook and the Petroleum Engineering Handbook.

Common motors

The electric motor most commonly used for beam-pumping installations is an alternating-current (AC), three-phase, squirrel-cage induction motor. These motors are used for the following reasons:

• Suitability for the load requirements.
• Low initial cost.
• Availability.
• Service dependability in the field.

If three-phase power is not available, single-phase motors up to 5 HP can be used. This motor is larger and more expensive than the three-phase motor of the same HP. The amount of motor voltage (V) needed depends on V on the distribution system, distance to the transformers, and motor size.

A general guide of motor size vs. V is 115 or 230 V for single-phase motors; 115, 230, 460, or 575 V for polyphase motors up to 50 HP; and 460, 575, or 796 V for polyphase motors 50 to 200 HP. Motors for pumping units come in a variety of common sizes: 1, 1.5, 2, 3, 5, 7.5, 10, 15, 20, 25, 30, 40, 50, 60, 75, 100, and 125 HP.

NEMA design standards

NEMA, the National Electrical Manufacturers Association, publishes design standards for motors. Motors can be purchased in six standard synchronous speeds, with the 1,200-rpm motor being the most commonly used in oilwell pumping. Multiple-HP-rated motors that may be either dual- or triple-rated are sometimes used for oilwell pumping; the triple-rated is more common. Changing one of these motors from one HP rating to another requires changing leads in the motor housing, which in turn changes the motor's internal wiring system. Any capacitors, fuses, or overload relays in the circuit will also require evaluation and possible revision at the same time to make sure it agrees with the new voltage/current requirements.

NEMA presents five general design standards that provide for varying combinations of starting current, starting torque, and slip. The most commonly recommended electric motor for pumping units is a 1,200-rpm NEMA Design D. It has a normal starting current, a high starting torque (272% or more of full-load torque), and a high slip (5 to 8%). Because Design D specifications are not drawn as closely as they are for other designs, manufacturers have developed several designs with variations in slip that still fall within Design D specifications.

The other NEMA designs (A, B, C, and F) are not used as often. However, there have been publications concerning when NEMA C and/or B designs could be considered, especially with variable-speed drives.

Power factors

A power factor determines the amount of line current drawn by the motor. A high power factor is desirable because it is important in reducing line losses and minimizing power costs. A lower power factor means that the unit is not operating as efficiently as it should. Oversized motors tend to have low power factors. Typically, a NEMA D has a power factor of 0.87 when fully loaded, but decreases to 0.76 at half load. Usually, units must operate at a power factor of greater than 0.80 to avoid penalties from the power companies; thus, optimization of the pumping unit's size and motor needs to be considered as the well-fluid volume changes.

Using capacitors can increase power factors. To determine if and how much capacitance is needed, determine the power factor of an installation upon initial startup and then decide if a correction is justified. If a pumping-unit motor has a low power factor, a capacitor can be placed between the motor and disconnect. Because of the possibility of electrical shock, only qualified personnel should make this connection. Remember that changing producing conditions might require that the power factor be checked and that the motor-overload relays be resized if the capacitor is on the load side of the overload relays.

Cyclic-load factor

When a motor is used for a cyclic load, such as oilwell pumping, it will be thermally loaded more than the same average load applied on a steady-state basis. HP ratings of electrical motors depend on how much the temperature increases in the motor under load. A motor functioning cyclically must be derated from its full-load nameplate rating.

A motor's true performance and rating on a cyclic-load application cannot be determined by the use of normal indicating- or recording-type instruments. Motor heating is a function of the thermal current or root-mean-square (RMS) current, which is the square root of the mean of the squares of currents of definite time intervals. This may be more easily determined with an RMS or the thermal-type ammeter, which records RMS current corresponding to the true heating or "thermal" HP load on the motor. This current will always be higher than the average input current. The ratio of the average HP output to the "thermal HP output" corresponding to the RMS line current is called the motor derating factor and is always less than one. Its inverse is the cyclic-load factor, which is always greater than one. An average motor derating factor for NEMA Design C motors is 0.65; an average motor derating factor for NEMA Design D motors is 0.75.

Motor enclosures

There are four basic types of motor enclosures:

• Drip-proof guarded
• Splashproof guarded
• Totally enclosed fan cooled (TEFC)
• Explosion proof

“Guarded” refers to screens used over air intakes to prevent the entrance of rodents or other foreign items. The TEFC enclosure provides the maximum protection for the interior of the motor. The drip-proof motor should prove adequate for most pumping-unit installations in which the motor is elevated. This type of construction is built with a closed front-end bell to eliminate the entry of horizontal rain, sleet, or snow into the motor. The splashproof motor affords somewhat more protection against splashing liquids than does the drip-proof one. The preferred enclosure sets the motor on or close to the base; the explosion-proof enclosure will seldom be required. Motor-high mounts on pumping units have also been useful in protecting the motor from sand or snow.

Motor insulation

NEMA has established the insulation classes and the maximum total temperatures applicable to these classes for insulations used in motor winding. For normal service life, the temperature of the motor windings should not exceed the maximum allowable temperature for that particular insulation type. Class A insulation has a maximum total temperature of 105°C, Class B = 130°C, Class F = 155°C, and Class H = 185°C. Generally, the more the motor enclosure restricts the flow of outside cooling air, the higher the temperature rise will be, and in all probability, the higher the winding temperature. This temperature increase has to be incorporated into the decision regarding which insulation class is required.

The service life of an AC induction motor is determined by the bearing life, the insulation life, and routine maintenance/inspection. Temperature rise is important because studies have indicated that for every 8°C rise above the temperature values stated, the insulation life is cut approximately in half.

Motor slip

Slip is the difference between motor synchronous speed and speed under load, usually expressed in percent of synchronous speed. Synchronous speed is the theoretical, no-load speed of the motor. Slip characteristics are very important because they will determine how much HP can be converted to torque to start the gearbox gears turning. A high-slip motor permits the kinetic energy of the system to assist in carrying the peak-torque demands. A low-slip motor will respond to the instantaneous demand; in other words, the high-slip motor slows down more under peak torque demands than the low-slip motor. The result is that the high-slip motor will require lower peak currents than the low-slip motor. How high the motor slip should be for pumping installations is debatable; however, Howell and Hogwood stated, "A slip greater than 7 to 8% offers no additional advantages from the overall pumping efficiency standpoint." On the basis of this information and the slip characteristics of the various designs, the Design D motor with a 5 to 8% slip is recommended for most sucker-rod installations.

Ultrahigh-slip (UHS) motors

Higher-slip motors are available from some manufacturers; one has claimed to have slip characteristics up to 35 to 40%, also claiming that using their UHS motor would result in lower loading on the sucker rods, lower electric-current peaks, and reduced power use. However, to obtain the mechanical advantage, these systems have to be set up in the high-slip mode. When this is done, the increased slip normally decreases the operating speed and may result in a decrease in production when compared to a NEMA D installation.

Motor controls

Motor controls are housed in a weatherproof, NEMA Type 3 enclosure with special explosion-proof enclosures available. All control units should contain the following:

• Fused manual disconnect
• Hand on/off/automatic selection switch
• Lightning arrester system

Circuit breakers are sometimes used instead of fuses. The fused manual disconnect acts as a line-disconnect switch at the entrance to the control box. A fused disconnect may be located on a pole upstream of the motor starter; the lightning arrester is connected to the incoming line terminals, just ahead of the fused-manual disconnect and must be properly grounded. Depending on the inherent protection built into the motor, the control box may contain an overload relay, an undervoltage relay, and/or a sequence-restart timer.

Grounding systems

The electrical equipment must be properly grounded. Good grounding procedures are essential to personnel safety and good equipment operation. It is recommended that reference be made to the Natl. Electrical Code and the Natl. Electrical Safety Code to ensure safe grounding is met. Particular attention should be given to the connection of the ground wire to the well casing. The connection should be located where it will not be disturbed during well-servicing operations and should be mechanically secure. Periodic (yearly is recommended as a minimum) continuity measurements should be made with a volt-/ohmmeter between "a new clean spot" (not where the ground wire is terminated) on the well casing and new spot on each piece of grounded equipment. The resistance measured between any piece of equipment and the casing should not exceed 1 ohm. The resistance measured between the pumping-unit ground system and another nearby moisture ground should not exceed 5 Ω. However, these measurements should to be checked with current circulating through the system to determine if the ground is good.

Beam-pump horsepower

There are seven horsepower (HP) values that should be considered in the proper design and operation of sucker-rod-pumped wells:

• Hydraulic
• Friction
• Polished-rod
• Gear-reducer
• V-belt drive
• Brake
• Indicated

Hydraulic HP (H_HP) is the theoretical amount of work or power required to lift a quantity of fluid from a specified depth. This is a theoretical power requirement because it is assumed that there is no pump slippage and no gas breakout. The H_HP, thus, is the minimum work expected to lift the fluid to the surface and can be found with the following equations:

....................(1)

or

....................(2)

Friction HP (F_HP) is the amount of work required to overcome the rubbing-contact forces developed when trying to lift the fluid to the surface. This friction can be caused by a number of sources including:

• Plunger-on-barrel friction
• Rod- and/or coupling-on-tubing wear
• Sand
• Scale and/or corrosion products hindering pump action
• Rods and couplings moving through the fluid
• Fluid moving up the tubing
• Normal and excessive stuffing-box friction
• Liquid and gas flowing through the flowline and battery facilities

F_HP, thus, is dependent on factors such as how straight and deep the well is, the fluid viscosity, the pumping speed, and the tubing/rod buckling. In most situations, unless we know all of these factors, we do not know what F_HP is. However, for design purposes, API RP11L calculations assume the friction effects, which show up in the peak and minimum polished-rod loads and in the calculation of polished-rod HP (P_HP).

P_HP is the amount of work required to artificially lift the fluid to the stock tank. It is the sum of H_HP plus F_HP. For design purposes, API RP11L assumes these values are related to F_o/SK_r and N/N_o, where K_r is the load necessary to stretch the rod string 1 in., and N_o is the natural frequency of a straight rod string. If a surface dynamometer card is available, the P_HP can be measured because the area of the card is the work done at the polished rod to lift the fluid to the surface. The formula for calculating P_HP follows:

....................(3)

Gear-reducer HP (G_HP) is a value used to find the efficiency of the unit (i.e., how much the gear reducer is loaded, compared to required peak torque). G_HP can be calculated by the following:

....................(4)

V-belt-drive HP (V_HP) is the maximum power required by the V-belts to be transmitted to the gear reducer. API Spec. 1B states that the V_HP for a beam-pumping unit is as follows:

....................(5)

Brake HP (B_HP) is the power required by the prime mover to turn the sheave that makes the reducer's gears turn and starts the cranks going around. This power must accommodate the inefficiencies of all components involved in getting the cranks to turn to transmit the power to the polished rod. B_HP can be found with Gipson and Swaim recommendations by the following equation:

....................(6)

The efficiency factor is found from a graph by taking G_HP divided by API gearbox-torque rating and then intersecting either a worn- or new-unit efficiency curve. This efficiency factor is applied to the P_HP to convert it to B_HP at the prime mover and is required to offset power losses caused by friction in the surface equipment. Fig. 1 is a recommended curve to find the HP efficiency factor.

Additionally, a minimum estimate for this HP by NEMA for Design D and C motors is as follows:

....................(7)

This derating factor is 56,000 or 45,000 for D or C motors, respectively.

Indicated HP (I_HP) is the power required by the prime mover to meet the B_HP requirements and determines the size of motor that needs to be ordered. It is found through the following equation:

....................(8)

This derating factor accommodates continuous operation and thermal effects. The derating factors for electric motors are 0.75 and 0.65 for NEMA D and C, respectively. The derating factor for a gas engine is dependent on the type of engine and service, rotational speed, elevation, and ambient temperature. The effects of these parameters are discussed in API Spec.7B-11C, paragraphs 2.11 and 2.13. A rule-of-thumb estimate for an engine's derating factor is as follows:

....................(9)

HP problem-solving example

Given the previous HP definitions, along with the information and calculations in API RP11L (page 7), find all seven HPs:

• H_HP = [175 (BFPD) × 350 (lbf/bbl) × 0.9 × 4,500 (ft)] / (33,000 × 1,440) = 5.2 HP.
• P_HP = line 26 = 8.5 HP.
• F_HP = P_HP – H_HP = 8.5–5.2 = 3.3 HP.
• G_HP = line 25/4,960 = 133,793/4,960 = 26.9 HP.
• Assuming a 160,000-lbf-in. unit is ordered to accommodate a calculated 133,793-lbf-in. peak torque, and using Fig. 1 , find the efficiency factor of 0.86: V_HP = (133,793 × 16) / 70,000 = 35.6 HP.
• B_HP = ( P_HP / efficiency factor), where the efficiency factor is found by G_HP / reducer rating = (8.5 × 4,960) / 160,000 = 0.2635. With Fig. 1 , the efficiency factor is 0.64. Thus, B_HP = (8.5 / 0.64) = 13.28 HP.
• Assuming a NEMA D motor, I_HP = ( B_HP / derating factor) = 13.28/0.75 = 17.7 HP.

Therefore, a 20-HP motor should be purchased. However, a 15-HP motor may work, but certain aspects are not known, including actual counterbalance divided by optimum counterbalance, flowline pressure, and actual friction effects. Thermal current (amps) can be measured to determine how much motor capacity is actually being used once the unit and motor are installed. The actual motor size could then be refined for other units in the area.

Sheaves and V-belt drives

Prime movers—whether with a gas engine or an electric motor—run at a speed of 300 to 1,200 rpm. This speed must be reduced to the required pumping-unit speed of 2 to 25 spm. This is accomplished with sheaves, V-belt drives, and gear reducers. A sheave is a grooved pulley, and its primary purpose is to change the speed between the prime mover and the gearbox. The belt—usually a V-belt —is a flexible band connecting and passing around each of the two sheaves. Its purpose is to transmit power from the sheave on the prime mover to the sheave on the pumping unit. It is important to understand the basics of sheaves and V-belt to know how to select a sheave for a certain pumping speed and to determine the number of V-belt needed.

Sheave basics

Sheaves come in different widths and have from 1 to 12 grooves. They are selected on the basis of the pitch diameter (PD) relative to how many spm the unit will pump. New beam-pumping units can be purchased with different-sized sheaves on the reducer. Sheaves can also be purchased to accept different V-belt cross sections. A pumping-unit sheave should be selected that will allow as much speed variation (up and down) from the design speed as is practical without violating API Spec. 1B rules. Most unit sheaves will have grooves for more belts than are actually needed because most units seldom, if ever, operate at maximum HP. The maximum V_HP is shown in Eq. 5 above.

Only the grooves closest to the prime mover and the gear reducer should be filled, and only enough belts to transmit the V_HP should be installed because of the following considerations:

• The tension in the excessive belts, which will be further from the equipment than the required belts, will place unnecessary loads on the bearings
• Wider sheaves than necessary and extra belts increase investment costs
• It takes more energy to flex the extra belts around the sheaves, which increases operating costs

Pumping-unit manufacturers usually list all unit-sheave sizes in their catalogs. Motor sheaves are available with various PDs and numbers of belt grooves. Table A.1 in API Spec. 1B contains commonly available sheaves. Because of availability, motor sheaves should be selected from those listed in the top portion of the table.

V-belt basics

A V-belt has a trapezoidal cross section that is made to run in sheaves with grooves that have a corresponding shape. It is the workhorse of the industry, available from virtually every V-belt distributor, and it is adaptable to practically any drive. It was designed to wedge in the pulley, thereby multiplying the frictional force produced by the tension; this, in turn, reduces the belt tension required for an equivalent torque. Remember, the purpose of the belt is to transmit power from the sheave on the prime mover to the sheave on the pumping unit. Therefore, the number and size of the belts needed depend on the amount of power to be transmitted.

Reinforcing cords normally made of rayon, nylon, or other polymer materials provide the load-carrying capability of a V-belt. The cords are usually embedded in a soft rubber matrix called a cushion section. The balance of the belt is made of harder rubber, and the entire section is usually enclosed (i.e., wrapped) in an abrasion-resistant jacket or cover.

As the belt bends around a sheave, the bending-neutral axis is the only portion that does not change the circumferential length. This line (which does not change length) is called the pitch line and determines the "effective" radius of the pulley, which in turn, determines the torque and speed ratios. The position of this line as it curves around the pulley forms a pitch circle with a pitch diameter.

Classical V-belts are made in five standard cross sections designated by the letters A (the smallest cross section), B, C, D, and E (the largest cross section). The HP that a belt is able to transmit falls off rapidly as the sheave size diminishes. Smaller-PD sheaves are not recommended because of:

• Decreased HP
• Reduced transfer efficiency
• Shorter belt life
• Less economical drive

Fig. 1 shows the HP capacity a single belt can transmit for a selected small-diameter sheave for the various belt cross sections.

• 

  Fig. 1—Recommended transmitted HP per single belt for selected-OD sheave size and V-belt cross-section type.

Other types of belts

There are other types of belts (i.e., flat, narrow, and synchronous belts, as well as other variations of the V-belt). For example, narrow multi-V-belts (power bands) were developed because the maximum load capacity for a given width of belt required the use of a narrow section. This provided the maximum support of the tensile cords by joining the belts together. V-ribbed belts provide complete support with only a modest compromise in terms of additional tension.

Selecting a sheave

The first step in designing the V-belt drive for a pumping unit consists of selecting a sheave for the unit and the prime mover. To do this, the desired pumping speed (N), along with the speed (in rpm) of the prime mover and gear ratio, must be known. If the other parameters are known, this equation can be rearranged to determine any required factor:

....................(10)

The largest motor sheave in this group will provide for the greatest reduction in pumping speed for future operations merely by changing motor sheaves.

Double reduction with electric motor

A double-reduction unit run by an electric motor will require a speed reduction through the V-belt drive of approximately 2:1 at fast pumping speeds. At slow speeds, the ratio will be 6:1. When two belt sections are offered for the unit sheave, the smaller belt section will allow the use of a smaller motor sheave and a lower pumping speed. In most cases, the smaller belt section, with one of the two largest-unit sheaves, will offer the greatest flexibility.

Double reduction with gas engine

A double-reduction unit run by a slow-speed gas engine will require a speed reduction of 1:1 at a fast pumping speed; at a slow pumping speed, the ratio will be 3:1. In these cases, speed reductions (which may be anticipated through the drive) should be checked with the proposed unit and prime mover. If little or no speed reduction will ever be required through the V-belt drive, one of the two smaller-unit sheaves will enable the use of a smaller (and less-expensive) prime-mover sheave. The larger belt section could also be used and may require fewer belts.

Determining the required number of belts

The first step in determining the number of belts required is to calculate the V_HP. When the peak torque is known, this is the preferred method of calculating the design HP. When the peak torque is not known, a service correction of 1.6 is recommended.

The remainder of the calculation can be performed by following the procedure in Section 4 of API Spec. 1B, starting with paragraph 4.5 (page 11). A complete design requires that the distance between the centers of the driver and driven sheaves be known. The basic steps are given in API Spec. 1B. An example calculation is presented here.

Example problem

As an example problem, select the optimum gear-reducer sheave for a C-160D-173-86 pumping unit that will be operated with the reducer fully loaded.

Given: gear-reducer sheaves available from the pumping-unit manufacturer's catalog: 20-, 24-, 30-, 36-, and 38-in. PD-3C. Assume that the prime mover's average rpm = 1,120. The smallest C-section motor sheave that should be considered = 9 in. PD (i.e., 9.4-in. OD in Table 3.1 of API Spec. 1B). The largest sheave that should be considered to keep the design PD velocity at less than 5,000 ft/min = 16-in. PD (calculations indicate a 17-in. PD, but page 32 of API Spec. 1B indicates that 17-in. PD C-section sheaves are not generally available; economics should discourage engineers and others from recommending sheaves not listed). The liquid to be pumped has a viscosity of approximately 1 cp. The pumping-unit gear ratio is 28.67. The maximum speed with an 86-in. stroke should result in an acceleration factor of 0.3, in which the maximum spm ≤ (0.3 × 70,500/86) 0.5 ≤ 15.7. The minimum speed with an 86-in. stroke should result in an acceleration factor ≤ 0.225, in which the minimum spm ≤ (0.225 × 70,500/86) 0.5 ≤ 13.6.

Find: the optimum gear-reducer sheave and the number of C-section belts required, assuming the reducer is fully loaded and is operated at the maximum and minimum speed dictated by the sheave selected.

Solution 1. Solving for pumping speeds from Eq. 2 = [prime-mover speed (rpm) × prime-mover-sheave PD]/[(gear-reducer sheave PD) × (1/pumping-unit gear ratio)]. For example, 1,120 × 9/20 × 1/28.67 = 17.1. The rest of the speeds can be calculated similarly for the different available gear-reducer sheaves, and the smallest or largest prime-mover sheaves. The summary of these calculations is shown in Table 2.

• 

  Table 2

The table shows that the 38-in. PD-4C gear-reducer sheave should be selected; however, the 36-in. gearbox sheave is acceptable.

Solution 2.

1. V_HP at 9 spm = 160,000 × 9/70,000 = 20.6.
2. HP that can be transmitted with one C-section belt and with a 9-in.-PD prime-mover sheave (as shown in Fig. 1) = 11.
3. Number of belts required = 20.6/11 = 2 belts.
4. V_HP at 16 spm = 160,000 × 16/70,000 = 36.6
5. HP that can be transmitted with one C-section belt and with a 16-in.-PD prime-mover sheave (as shown in Fig. 1 ) = 25.
6. Number of belts required = 36.6/25 = 2 belts.

Note that neither calculation justifies filling all the grooves in the gear-reducer sheave. No justification is known for using more belts than is indicated by API Spec. 1B.

Nomenclature

a	=	casing/tubing annulus area, in.2
BHP	=	brake horsepower
D	=	plunger diameter, in.
FHP	=	friction horsepower
Fo	=	differential fluid load on the full pump-plunger cross-sectional area, lbf
Fo /SKr	=	dimensionless sucker-rod stretch load (fluid load on full plunger area divided by load necessary to stretch the total-rod string to an amount equal to the polished-rod stroke length)
G	=	specific gravity of the combined fluid in the tubing
GHP	=	gear-reducer horsepower
H	=	pump seating depth, ft
HHP	=	hydraulic horsepower
IHP	=	indicated horsepower
PHP	=	polished-rod horsepower
VHP	=	V-belt drive horsepower
L	=	pump-seating nipple depth, ft
N	=	pumping-unit speed, spm
No	=	the natural frequency of a straight rod string, spm
Q	=	slippage or leakage loss, in.3/min
S	=	surface stroke length, in.
Sp	=	downhole pump-plunger stroke length, in.

Noteworthy papers in OnePetro

Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read

External links

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See also

Prime movers

Sucker-rod lift

Sucker-rod pumping units

Surface equipment for sucker rod lift

PEH:Sucker-Rod_Lift

Page champions

John G. Svinos