Machine Design Laboratory Semester Project

Diaa Hamed Shaat Mohammad Al- Bakheet

Ali Abu Al-Haj Omar Rababah Hala Al-Adwan

Supervised By Dr. Mohammad Dado

History and development of the walking beam

pumping units

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Figure 1. The first Oil Pumping unit in History .. Interesting !

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Figure 2. Figure 1. Lufkin pumping unit from the early 1920s

Figure 3. The 1926 Lufkin Crank-Balanced

Pumping Unit is still in service today with only slight modification.

Application and usage of beam pumping Units

When the pressure in an oil producing reservoir is

high, the oil flows naturally to the surface. However,

when the reservoir does not have enough pressure

to produce by natural energy, a means of Artificial

Lift is used to lift the oil from the reservoir to the

surface. Beam Pumping is the most common type

of artificial lift-some estimates claim that as many as

71 % of artificial lift wells are occupied with beam

pumps.

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Figure 4. Usage percentages of oil Artificial left methods worldwide. Source: world oil 2005.

Structure, Specifications, operation, and

classification of Beam Pumping systems

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Figure 5. A diagrammatic drawing of a sucker rod pumping unit.

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Specifications Typical Values

Gear reducer output shaft speed (depending on well

characteristics and fluid properties)

4-40 rpm

Stroke lengths of conventional pumping units 12-200 in

Polished rod loads 3000-35000 Ib

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The power from the prime mover is transmitted to the input shaft of a gear reducer by a V-belt drive.

The output shaft of the gear reducer drives the crank arm at a lower speed .The rotary motion of the crank arm is converted to an

oscillatory by means of the walking beam through a pitman arm.

The horses head and the hanger cable arrangement is used to ensure that the upward pull on the sucker rod string is vertical at all

times (thus, no bending moment is applied to the stuffing box).

The polished rod and stuffing box combine to maintain a good liquid seal at the surface and, thus, force fluid to flow into the T

connection just below the stuffing box.

Operation of the Pumping unit:

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Figure 6. Sketch of three types of pumping units:

(a) conventional unit (b) Lufkin Mark II Unit (c) air-balanced unit

Position Analysis

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The pumping unit can be modeled as a 4-bar mechanism.

Taking the loop ADE.

Mobility analysis shows that 1 input is required to control the

motion of the mechanism M = 3(L-1) 2J = 3(4-1) 2(4) = 1.

Assumptions: 1) The ground link AE equals 10 m at an angle 20 degrees

(d1= 10 m, = 20 degrees).

2) The length of the output link DE equals 7 m (d4 = 7m).

3) The pumping angle of the output link oscillates from -30 to 30

degrees (assuming a Grashofian mechanism).

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Figure 7. Sketch of the pumping unit.

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Deriving the equation which relates theta 2 (input) with theta 4 (output):

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Deriving the equation which relates theta 3 (walking beam) with theta 2 and theta 4:

Dimensions of the pumping unit

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From the geometric constrains of the upper and lower positions of

the output link, the lengths of the input crank AB (d2) , and the

pitman arm BD (d3) are determined.

Figure 8. The lower limiting position

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Note that d1 + d4 > d2 + d3 ; so it is a grashofian mechanism of the crank-rocker

type, which means the input does a full rotation and the output oscillates.

Figure 9. The upper limiting position

Velocity Analysis

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The equation which relates the velocity of the input and output links is:

Note: the output link velocity is MAX when = 180 degrees.

. = + pi = and And = Zero at the limiting positions (

Assuming 14 stroke / min * 3.14 stroke length *6 m / 60 = 4.396 rad/sec = velocity of output walking beam. And the velocity of the

input crank = 29.4 rad/s.

Masses of the beams

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For beam 4 (the output) [ I cross section ]. D = 838 mm, B= 292 mm.

From the standard tables for steel:

Mass = 194 kg/m

Length of output link = 13 m

Then the Mass = 2522 kg

For beam 3 (the walking beam) [ Rectangular cross section ]. D = 300 mm, B= 10 mm.

From the standard tables for steel:

Mass = 23.6 kg/m

Length of walking beam link = 5.51 m

Then the Mass = 129.988 kg

D

B

D

B

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For beam 2 (the input link) [ Rectangular cross section ]. D = 300 mm, B= 10 mm.

From the standard tables for steel:

Mass = 23.6 kg/m

Length of walking beam link = 2.17 m

Then the Mass = 51.3 kg

Production Analysis and Rope Design

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Value Result

14 Strokes / min

1700 Barrel / day

3.14 m Stroke length

7.4 cm Stroke diameter

13670 N Mass of oil

1324.35 N Mass of barrel

Neglected Mass of the rod

15000 N Total force acting on the wire

27.6 cm Barrel diameter

6 Factor of safety

22.1 Mpa Stress acting on the wire section

Production Analysis and Rope Design

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Production Analysis and Rope Design

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Selecting the suitable rope and the material (lang lay 6*37) Manganese steel.

Production Analysis and Rope Design

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9 cm = the rope diameter

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Determining the life of the rod.

Torque Calculations

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Taking the critical position when the walking beam is Horizontal to calculate the MOMENT required to be supplied by the motor.

At this position theta 2 = 171.77 deg, and theta 3 = 34.36 deg.

Taking a FBD of the walking beam; the force in link 3 (two force member) is found to be 4230.223 N (compression).

Torque Calculations

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2.1730 m 4230.223 N

10000 N

34.36 deg M

171.77deg

Taking a FBD of the input crank; the moment is found to be 21.5 KN.m

Stress Analysis of the walking beam

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Figure 10. Shear force diagram.

Stress Analysis of the walking beam

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Value Result

+ 27.108 KN at 7 m Maximum Sear stress

2434380214 mm^4 Second moment of area

3354188.298 mm^3 First moment of area

14 mm Web thickness

= 2.6678 Mpa (maximum)

Bearings selection

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C10 = 26.36 KN

Value Calculation

+ 27.108 KN / 2 Fd

8760 hour (yearly) Ld

14 rpm Nd

10^6 Lr

Bearings selection

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Bearings selection

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Value Result

Bore = 40 mm 2 bearings @ E

Bore = 20 mm 2 bearings @ D