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Drill-string problem
The oil exploitation has begun around 1850 in the United States
of America with oil wells of approximately twenty meters of depth. The
depth achieved in a perforation has been growing over the years due to
the increasing demand and the technological innovations of the sector. For
example, the maximum depth achieved by a drill-string in 1977 was of 277
meters in Brazil, nowadays it is common to see drill-strings 2000 meters
long. The exploitation of oil and gas is a complex activity. This thesis
analyzes one step of the oil exploitation, which is the drilling process, with
special attention to the dynamic behavior of the structure. Figure 2.1 shows
the main components of a drilling equipment. A quick explanation of each
component can be found in the glossary http://www.glossary.oilfield.
slb.com/.
The exploitation of oil and gas involves the following steps (http:
//www.lrc.usace.army.mil):
1) Identi�cation of the local where the exploitation will be done,
2) Economic viability analysis,
3) Identi�cation of the best places for the drilling process,
4) Drilling process,
5) Analysis of the geological formation found,
6) Construction of an unit of exploitation and beginning of the
exploitation.
There are many units of exploitation that use rotating columns
(drill-strings) for the drilling process. This process consists on cutting the
rock using a bit, in rotation, conducted by a column that transmits the
torque generated by the rotary table located at the surface. The column
gives the necessary weight (weigh on bit, WOB) to drill the rock. A
drill-string is composed by drill pipes, drill collars and a bit. The lower
part of the column is called Bottom Hole Assembly (BHA) and it has a
length of approximately two hundred meters, even though the total length
Stochastic drill-string dynamics 28
1. Crown block
2. Traveling block and hook
3. Drawwork
4. Swivel
5. Hose
6. Tube
7. Mud pump
8. Kelly
9. Rotary drive
10. Rotary table
11. Drill pipe
12. Tool joint
13. Stabilizers
14. Drill collar
15. Bit
16. Casing
17. Blowout preventer
18. Derrick
Figure 2.1: Typical drilling equipment.
of the column might have some kilometers. This part is under compression
and is composed by the drill-collars, tubes with larger diameters and thicker
walls. The drill-string is a slender structure that might be twisted several
times because of the torque on bit (TOB).
Another important element on the drilling process is the drilling �uid
(or mud) (see Fig. 2.2, http://www.lrc.usace.army.mil). The mud is
used for: refrigeration, displacement of the drilled solids and stability of the
well wall. It plays also a role in the drill-string dynamics.
The dynamics of a drill-string is complicated, consisting on coupled
axial, lateral and torsional vibrations. Figure 2.3 illustrates these vibrations.
The relation between excessive vibration and instability in the drilling
process was observed in [104], where in two case studies the instability was
due to vibration problems, such as stick-slip, bit-bounce and whirl. They
are described as following:
• Stick-slip happens when the friction between the bit and the rock
is big. The bit might eventually get stuck and then, after accumulating
energy in terms of torsion, be suddenly released. This phenomenon generates
torsional vibrations and can be identi�ed by periodic oscillations on the
Stochastic drill-string dynamics 29
Figure 2.2: Drilling �uid (mud).
Torsional vibrations
Lateral vibrations
Axial vibrations
Figure 2.3: Axial, lateral and torsional vibrations are coupled.
torque.
• Bit-bounce happens when the bit looses contact with the rock,
hitting it in the sequence with great strength. This phenomenon generates
axial vibrations and can be identi�ed by periodic vibrations on the weight
of the column.
• Whirl is a lateral instability that is intensi�ed by impacts between
the column and the borehole. This phenomenon generates lateral vibrations
and can be identi�ed by the increasing of these vibrations and harmonics
in the frequency spectrum.
Stochastic drill-string dynamics 30
The drill-string vibrations are induced by the characteristics of the
bit-rock interaction and by the impacts that might occur between the
column and the borehole [31]. If not controlled, vibrations are harmful to
the drilling process causing:
1. Premature wear and consequent damage of the drilling equipment,
resulting many times in failures, especially due to fatigue.
2. Decrease of the rate of penetration (ROP), increasing the well cost
[28].
3. Interferences on the measurements performed during the drilling
process and damage of the measurement equipment [64].
4. Signi�cant waste of energy.
5. BHA instability, reducing the directional control [31].
Some typical drill-string failures are discussed in the following article
[70]. The cost of repairing a failure is approximately two times the cost
of the prevention. The most common types of failures are: ductile failure,
fragile failure, and crack due to fatigue and corrosion under tension (see
Fig. 2.4, taken from [70]). Although the mechanisms of failure are well
understood, the harmful environment and the type of excitation make
the failure di�cult to be avoided. The equipment performance is getting
better with the improvement of the control and inspection techniques. At
this point, the understanding of the structure dynamics is essential. A
computational model of the drill-string can and should be used to develop a
strategy of vibration control, allowing the optimization of its performance.
Nevertheless, the controlling strategy is not considered in this work.
It should be noted that it is very limiting to analyze each vibration
(axial, lateral and torsional) separately, since usually they are all coupled.
Some computational models have been developed to analyze the coupling
between two or three vibration directions (see, for instance, Yigit and
Christoforou works [134, 135, 24], or Khulief et al. [55], and also Sampaio
et al. [128, 101]). The mentioned works and the present work consider only
a vertical well, however, there are other possibilities for the drilling process,
as illustrated in Fig. 2.5 (http://www.lrc.usace.army.mil).
Stochastic drill-string dynamics 31
Figure 2.4: Typical failures: A) ductile, B) fragile, C) and D) fatigue.
Figure 2.5: Di�erent directions of drilling.