## 9

"Design spm (strokes per minute) is based on a Mills impulse load of 0.25 with a maximum spm of 25. This cycle rate may be exceeded; however, the values given here are considered good design practice.

"Design spm (strokes per minute) is based on a Mills impulse load of 0.25 with a maximum spm of 25. This cycle rate may be exceeded; however, the values given here are considered good design practice.

Design of a single-size string for use in wells of shallow to moderate depth is a straightforward calculation and the tables and formulas included here are sufficient. In deeper wells, tapered* strings of rods are used, frequently 1,8, and 4 in (25.4, 22.2, and 19.0 mm). Various methods are used for calculating the proper taper, but so many variables are involved that computer programs are frequently used to provide the total system design.

Surface Pumping Units Rating standards of beam pumping units have been established by the American Petroleum Institute (API). There are fourteen gear reducer torque ratings established, and these can be combined with various structures and a variety of stroke lengths to supply a pumping unit matched to virtually any well condition. Table 3 shows these torque ratings, the maximum stroke length, and the maximum structure capacity of standard units.

Pumping Installation Calculations The pump bore (ID of the pump barrel) is selected based on the quantity of fluid to be produced. A trial calculation is made to select a pump bore and a pumping unit stroke length that will produce the required volume of fluid. A volume calculation at 100% efficiency is performed using the bore factor from Table 4 and the stroke length and design strokes-per-minute value shown in Table 3. This is multiplied by 0.7 to correct for anticipated pump efficiency under average well conditions.

weight OF fluid ON plunger The trial calculation continues with the weight of the fluid on the plunger. Freshwater exerts a pressure of 0.433 lb/in2 per vertical foot (9.79 kPa per vertical meter). The weight of the fluid on the plunger can be calculated with the formula in USCS units Wf = 0.433 A^sp. gr.)

*When the sucker rod string is made up of several shorter strings, each of a different diameter, the total string is called tapered because the smallest-diameter strings are at the bottom and the largest at the top. This is done to reduce the total weight and to maintain approximately the same stress levels top to bottom.

 Pump bore, in (mm) Plunger area, in2 (mm2) Bore factor, USCS" (SI)4 1l6 (26.99) 0.887 (572.1) 0.132 (0.826) 11 (31.75) 1.227 (791.7) 0.182 (1.139) 11 (38.10) 1.767 (1140.) 0.262 (1.639) 13 (44.45) 2.405 (1552.) 0.357 (2.234) 2 (50.80) 3.142 (2027.) 0.466 (2.917) 21 (57.15) 3.976 (2565.) 0.590 (3.691) 21 (63.50) 4.909 (3167.) 0.728 (4.555) 233 (69.85) 5.940 (3832.) 0.881 (5.512) 31 (82.55) 8.296 (5352.) 1.231 (7.702) 3f (95.75) 11.045 (7126.) 1.639 (10.255)

aBore factor X stroke length in inches X spm = barrels/day (42-gal oil barrels). 6Bore factor X stroke length in meters X spm = cubic meters/day.

aBore factor X stroke length in inches X spm = barrels/day (42-gal oil barrels). 6Bore factor X stroke length in meters X spm = cubic meters/day.

where Wf = weight (force) of fluid on plunger, lb (N) Ap = area of plunger (Table 4), in2 (mm2)

D = fluid lift, distance from fluid level while pump is operating to ground surface, ft (m)

sp. gr. = specific gravity of fluid pumped, ratio of density of fluid to density of water at 60°F (16°C)

wet weight OF rods The next calculation is the weight of the rods. The dry weight (force) of the rods Wr in pounds is computed by multiplying the weight (force) per foot of the rods (Table 2) by the length of the rods. This weight (force) in newtons is kilograms per meter times the acceleration of gravity (9.807 m/s2) times the length of the rod. Because the rods have buoyancy when immersed in a fluid, their wet weight (force) Ww can be calculated with the formula

dead weight OF rods and fluid This value is needed in subsequent calculations. It is the weight (force) of fluid on the plunger plus the wet weight of the rods:

Wdf = Wf + Ww impulse load The acceleration due to the reciprocating motion of the rods causes additional stresses in the sucker rod string. Twice during each stroke,0 the rods are stopped and their motion reversed as they follow a sinusoidal acceleration pattern provided by the pumping unit. The resulting impulse load can be approximated using the Mills impulse load formula:

in SI units ## Survival Treasure

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