MAIN FUNCTIONAL REQUIREMENT: Draw subterranean fluid to surface.
DESIGN PARAMETER: Sucker Rod Pump
Pump consisting of four bar linkage, plunger, and valve assemblies.
EXPLANATION OF HOW IT WORKS/ IS USED:
For name and location of parts, see Figure A.
DOMINANT PHYSICS & DESIGN:
Table 1: Variable Descriptions, Values and Units
§ Reference 1, pp. 9.279
§§ Reference 1, pp. 9.277
§§§ Reference 1, pp. 9.277
§§§§ Reference 1, pp. 9.282
§§§§§ Reference 1, pp. 9.282
To design a sucker rod pump, the depth of the well must first be determined. This value is then used to calculate the amount of fluid that can be pumped per stroke. This amount is the volume of fluid that fits in a cylinder of height L and cross sectional area Ap.
Vf = Ap L
This volume is then multiplied by the density of the fluid and by the g to find the weight of the column of fluid the pump must lift.
Ff = Mf r g
The pump must also provide enough power to lift the sucker rods (see Figure A). Manufacturers specify typical values of weight per unit length, w, for the rods they make. This number is multiplied by the length of one rod, Lr, and by the number of rods, Nr.
Fr = w Lr Nr
Since the rods are submerged in fluid, a buoyant force is present. This force is found using Archimedes Principle. It states that the buoyant force a submerged object feels is equal to the weight of the fluid it displaces. Therefore, the volume of displaced fluid is equal to the submerged volume of the rods. The weight of this fluid is equal to this volume multiplied by the fluids density and g. To obtain the volume of the rods, we multiply their cross sectional area by their total length.
Fb = Ar Nr Lr r g
Now the total load the pump must lift can be calculated.
Fl = Ff + (Fr Fb)
Two things must be noted. First, the above analysis is very rough and does not include additional factors such as impulse forces. For more detail, see Reference 1, page 9.283. Also, the forces described above vary with time and this must be taken into account.
The stroke length of the pump is the vertical distance the plunger travels in one stroke. This length depends on the amount of fluid being pumped. Once the stroke length is known, the geometry of the four bar linkage can be determined. To avoid excessive wear of the machinery, it is good engineering practice to reduce the number of cycles the pump completes per unit of time. In order to do this more fluid should be pumped per cycle. In order to increase the fluid displacement, the stroke length should be maximized. Typical values for stroke length vary from 16 to 192 inches (see Reference 1, pp. 9.282). The stroke length can be used to calculate the torque required to pump the oil according to the following formula.
T = C L Fl
Here, C is a function of the geometry of the four bar linkage and the force the counterweight exerts on the crank (see Reference 1, pp. 9.283). Typical values for torque range from 6,400 to 912,000 in-lb (see Reference 1, pp. 9.282).
On the upstroke, two forces help pump the oil from the well. The first is the "force" supplied from the torque produced by the motor and gearbox. The second force comes from the weight of the counterweight as it falls (see Figure C).
Care must be taken to choose a cross sectional area large enough so that the rods do not yield. This area can be found by dividing the total tensile load by the yield stress of the material.
Ay = Fl / Sy
The area of the rods must be greater than this area. This is a minimum. Fatigue affects (function of material and loadking) will require a larger value.
The efficiency of the sucker rod pump can be defined as the volume of oil it actually pumps divided by the volume it can theoretically pump. When the well is initially drilled, the oil contains a lot of gas. This gas displaces a small volume of oil at the beginning. This volume decreases eventually. The volumetric efficiency of this type of pump is rated at about 80%. (see Reference 1, pp. 9.277)
WHERE TO FIND SUCKER ROD PUMPS:
Sucker rod pumps are used primarily to draw oil from underground reservoirs. The mechanisms it employs however are found in a wide variety of machines. The four bar linkage can be found on door dampers, on automobile engines, and on devices such as the lazy tong. The Sterling engines manufactured in 2.670 also use a linkage similar to the one used by the pump.
1) Karassik, Igor J. et al, Pump Handbook. pp. 9.278-9.285, McGraw-Hill, New York, 1986.
2) Sucker Rod Pump (From the Internet Glossary of Pumps)
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