2

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.