# Dogleg Severity Analysis

The most common type of drillpipe failure is fatigue wear. It generally occurs in doglegs where the pipe goes through cyclic bending stresses. These stresses occur because the outer wall of the pipe in a dogleg is stretched and creates a greater tension load (see Fig. 15-20). As the pipe rotates a half cycle, the stresses change to the other side of the pipe. For example, the stress may change from 50,000 psi to -20,000 psi and again to 50,000 psi in the course of one cycle or rotation of the pipe.

Fatigue damage from rotation in doglegs is a significant problem if the angle is greater than some critical value. Lubinski has published several works that describe this value. Rotation in angles below this value does not cause appreciable fatigue.

The maximum permissible dogleg severity for fatigue damage considerations can be calculated with the following equations;

432,000 crb tan h KL

And:

Where:

c = maximum permissible dogleg severity, °/100 ft E = Young's modulus, psi = 30 x I06 psi for steel = 10.5 x I0fi psi for aluminum D = drillpipe outer diameter, in,

L = half the distance between tool joints, 180 in. for Range 2 pipe, in. T = tension load below the dogleg, lb ob = maximum permissible bending stress, psi rr

I = drillpipe moment of inertia, —: (D4 — d"1)

The maximum permissible bending stress (ob) is calculated from the buoyed tensile stress (oy) and is grade dependent. The equation for bending stress with Grades E and S pipe are given in Eqs. 15.10 and 15.11 and are valid for o, up to 67,000 psi and 133,400 psi, respectively:

ob = 19,500 - ^ o, - (ff< " 33,500)2 (15.10) Fig. 15-20 Drillpipe rotation causes cyclic wear

Where:

crh = maximum bending stress for Grade F pipe il -

### Example 15.3

A Grade E drillstring has a tension load of 190,000 lb at 4,500 ft. Determine the maximum permissible dogleg that will not cause fatigue damage. The 4.5-in. drillpipe weighs 16.60 lb/ft (3.826-in. ID)

Solution:

1. Determine the tension stress load. The pipe area is:

### Area = pipe weight (lb/ft) x 0.2945

• 16.60 lb/ft x 0.2945
• 4.88 in.2

### 2. The maximum permissible bending stress (orh) is computed from Eq. 15.10:

• quot;b = 19,500 - ^ <tv - (§~y<.^T ~ 33,500)3 (15.10)
• 19,500 - -^(38,934) - -¿^<38,934 - 33..500)2 6/ (o/0)~
• 19,500 - 5,811 - 39

4. The maximum dogleg is computed from Eq. 15.8:

432,000 13,650 psi tan h (0.02567) (180) -ir (30 x 10fi) (4.5) (0.02567) (180)

Severe pipe damage occurs when the dogleg severity is greater than the value computed in Eq. 15.8, The damage depends on type of metal (aluminum or steel), corrosion level, stress, and dogleg angle. Metallurgists have established S-N (stress vs bending cycle) diagrams that can be used to determine the approximate number of cycles, or rotations, before pipe failure occurs.

The fraction (f) of drill pipe life expended in an interval of a dogleg can be calculated as follows:

Where:

f h fraction expended

B — number of drillpipe revolutions to drill the interval N = number of revolutions to failure of the joint of drillpipe

It is simple to show that:

Where:

R — rotary speed, rpm d = length of dogleg interval, ft V = drilling rate, ft./hr

The denominator, N, of Eq. 15.12 depends on the bending stress (o-h) in the pipe and on the ratio T/A, denoted <r.:

Where:

A = cross-sectional area of the pipe, in.3 The value can be computed as follows."

Where:

D = outside diameter of the pipe, in.

cu = maximum pipe curvature, radians/in.

The relationship between the hole curvature (c) and the maximum pipe curvature (c„) is:

Where:

L = one-half the length of a drillpipe joint, in.

The effect of bending stress on fatigue cycles before failure is well documented, as can be seen in Figs. 15-21 and 15-22. In the presence of tension, however, the fatigue effect of bending becomes more severe. To make the proper allowances for this, the actual bending stress, rrh, must be multiplied by a correction factor, t, as follows:

T = tensile strength of the pipe

The vertical axis of the graphs in Figs. 15-21 and 15-22 should be entered with the product of t and crb, or to,,. Determine the number of cycles, N, to failure. Enter N into Fq. 15,12 to determine the fraction of the pipe life expended in drilling the section.

In Lubinski's works, field studies were shown to indicate that lateral loading of tool joints can create significant damage. It was suggested that an arbitrary limit of 2,000 lb be used as the maximum, nondamaging lateral load limit. Loads above this limit would damage the tool joints. The following equation can be used to determine maximum acceptable dogleg severity for various lateral loads:

Where:

108,000 F ttL T

Where:

F — lateral force on the tool joint, lb L = one-half the length of a drillpipe joint, in. Revolutions 10 failure (X1,000)

Fig. 15-21 S-N curve for steel pipe 100,000 1.000,000 10.000.000 100,000.000 500.000,000

Endurance Limit-Cycles

100,000 1.000,000 10.000.000 100,000.000 500.000,000

Endurance Limit-Cycles

Aluminum Alloy 2014-T6

40.000

Fig. 15-22 S-N curve for aluminum drillpipe (the ordinate scale accounts for the effect of tension)

### Example 15.4

A drilling contractor has experienced significant problems with tool joint failures while drilling in a certain area in Oklahoma known for its dogleg deviations. It is not uncommon for doglegs of 4-6°/500 ft to be encountered. Determine if these doglegs can be exerting excessive lateral loads on the pipe. A maximum lateral load of 2,000 lb is permitted. Assume that a tension load of 275,000 lb is exerted on the 5.0-in., range 2 pipe.

Solution:

i. Determine the maximum acceptable dogleg severity from Eq. 15.18:

108,000 2,000

2. Doglegs greater than 1,3897100 ft will cause lateral loading to exceed 2,000 lb. Sincc doglegs of 4-6 7100 ft are encountered, it is possible that the tool joint failures result from dogleg problems.

### Example 15.5

Severe doglegs are expcctcd at 3,500 ft and 8,000 ft. If a maximum angle severity of 47100 ft is allowed, will any damage occur? The drilling conditions are as follows:

Drillpipe = 5.0 in. (OD) 4.276 in. (ID) 19.50 lb/ft (nominal) 22.50 lb/ft (with couplings) Grade S-135 Drill collars = 8,0 in. (OD) 3.0 in. (ID) 900 ft

147 lb/ft (air weight) Hole depth = 13,900 ft Mud weight = 15.0 lb/gal Slip length = 16 in. Rotary speed = 120 rpm Noncorrosive environment Maximum lateral load = 2,000 lb

### Solution;

1. The tension load on the drillpipe is computed and shown in Fig. 15—23.
2. The maximum permissible dogleg severity is computed with Eq. 15.18. Doglegs greater than this critical value will cause fatigue damage. The values of maximum permissible doglegs are calculated for the entire well, as shown in Fig. 15—24.
3. The 8,000-ft dogleg will not cause fatigue damage since the maximum permissible dogleg is greater than the actual 47100 ft dogleg. The dogleg at 3,500 ft will cause damage.
4. The amount of fatigue damage at 3,500 ft is calculated with Eqs, 15.1215.17. At 3,500 ft, approximately 5% of the pipe's life is used. Fig. 1525 shows the amount of fatigue damage throughout the drillstring.
5. The lateral load conditions are calculated and plotted for the drillstring (Fig. 15-26). The dogleg at 8,000 ft exceeds the 2,000 lb lateral load Tension, [b

Fig. 15-23 Tension load in the drillstring

Tension, [b

Fig. 15-23 Tension load in the drillstring limit. Therefore, the lateral loading on the tool joints may cause pin or box damage.

A significant amount of drillstring research is being conducted currently in the industry. Areas of interest include dynamics of a rotating siring, critical rotating rates, and tool joint improvement. The ultimate goal is to improve drilling efficiency. Maximum permissible dogleg ("100 ft)

Maximum permissible dogleg ("100 ft)

Fig. 15-24 Fatigue damage condition for Example 15.5

- Fatigue damage does not occur if dogleg is below 5.000 ft

Fatigue damage, % of total pipe life

Fig. 15-25 Fatigue damage for Example 15.5

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### Responses

• guido
What amount of dogleg is severe?
9 years ago
• Menegilda Clayhanger
WHAT FACTOR AFFECT DOGLEG WHILE DRILLING?
7 years ago
• mikolaj
What is the maximum amount of dogleg severity a horizontal well can have?
6 years ago
• Henrik
How is dog leg severity calculated?
3 years ago
• Mathilda Kauniainen
How to compute dog leg severity per 100 ft?
9 months ago
• olo
What is the limitation on dog leg severity?
6 months ago
• jason
How to graph dogleg secerity?
2 months ago