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Research Papers

The Effects of Drilling Mud and Weight Bit on Stability and Vibration of a Drill String

[+] Author and Article Information
Ali Asghar Jafari

 Department of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Tehran, Iranajafari@kntu.ac.ir

Reza Kazemi

 Department of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Tehran, Irankazemi@kntu.ac.ir

Mohammad Faraji Mahyari1

 Department of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Tehran, Iranfarajimahyari@yahoo.com

1

Corresponding author.

J. Vib. Acoust 134(1), 011014 (Dec 28, 2011) (9 pages) doi:10.1115/1.4005033 History: Received January 05, 2011; Revised July 08, 2011; Accepted September 06, 2011; Published December 28, 2011; Online December 28, 2011

The main goal of this research is to analyze the effects of drilling mud flow rate, drill string weight, weight on bit and angular velocity on stability and vibration of a drill string. To this end, kinetic and potential energies of a rotating drill string are written while axial and lateral vibrations are considered. The effects of the drill string’s weight, weight on bit and geometrical shortening are considered in the model. Drilling mud’s effects are modeled by the Paidoussis formulations. The finite element method is employed to discrete the formulations. The stabilizers are modeled by dropping the coincided nodes. Linear (Flutter method) and non-linear methods are employed to analyze a drill string’s stability for different weight on a bit, angular velocity, drilling mud flow rate and numbers and arrangements of stabilizers. These results represent the significant effects of non-linear terms. Also, the effects of drilling mud flow rate and weight on bit on the natural frequencies and time responses are illustrated. Increasing drilling mud flow rate causes decreasing of natural frequencies and vibrational amplitude. Furthermore, increasing weight on bit leads to decreasing natural frequencies and increasing vibrational amplitude. These formulations can be used to choose the safest working conditions in the drilling process.

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References

Figures

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Figure 1

The scheme of drill string

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Figure 2

Linear instability threshold of drill string while there are not stabilizers on the drill collar. Parameters are according to Table 2.

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Figure 3

Non-linear instability threshold of drill string while there are not stabilizers on the drill collar. Parameters are according to Table 2.

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Figure 4

Linear instability threshold of drill string while there is one stabilizer on a drill collar at xs(m) shown in the legend. Parameters are according to Table 2.

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Figure 5

Non-linear instability threshold of drill string while there is one stabilizer on a drill collar at xs(m) shown in the legend. Parameters are according to Table 2.

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Figure 6

The effect of DMFR and WOB on the first forward and backward natural frequencies of a drill string while Ω = 200. Parameters are according to Table 2.

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Figure 7

The effect of DMFR and WOB on the second forward and backward natural frequencies of drill string while Ω = 200 (rpm). Parameters are according to Table 2.

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Figure 8

The effect of neutral point position on the first mode shape of drill string while Ω = 200 (rpm) and Q = 0 (lit/s). Parameters are according to Table 2.

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Figure 9

The effect of nonlinear term on the lateral vibration of drill string. In this case, H(t) = 10+10sin(10πt/3)(m), Ω = 100 (rpm) and Q = 0 (lit/s). Other parameters are the same as Table 2 except the lengths which are according to Ref. [8].

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Figure 10

The effect of DMFR on the lateral vibration of drill string. Q(lit/s) are shown in the legend. In this case, H(t) = 20+10sin(10πt/3)(m) and Ω = 100 (rpm). Other parameters are the same as Fig. 9.

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Figure 11

The effect of WOB (neutral point position) on the time response of drill string. H(m) are shown in the legend. In this case Q=0(lit/s) and Ω=100(rpm), the dynamic height of neutral point and other parameters are the same as Fig. 9.

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