Chapter 03 Dogleg Serverity Directional and Horizontal Drilling

Chapter 3 DOGLEG SEVERITY INTRODUCTION

Dogleg severity is a measure of the amount of change in the inclination, and/or azimuth of a borehole, usually expressed in degrees per 100 feet of course length. In the metric system, it is usually expressed in degrees per 30 meters or degrees per 10 meters of course length. All directional wells have changes in the wellbore course and, therefore, have some doglegs. If not, it would not be a directional well. The dogleg severity is low if the changes in inclination and/or azimuth are small or occur over a long interval of course length. The dogleg severity is high when the inclination and/or azimuth changes quickly or occur over a short interval of course length.

To show how a change in inclination can affect dogleg severity, consider the following example:

Example 3-1 Given: MD1 = 1,000 feet MD2 = 1,100 ft

I1 = 4 I2 = 6

Determine: The dogleg severity.

Solution: The change in inclination is:

12 III = == 246I

The course length over which the change in inclination occurred is:

12 MDMDMD =

ftMD 100'000,1'100,1 == Calculation of dogleg severity:

MDIDLS

=

1002=DLS

Therefore, the dogleg severity is 2/100 feet.

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H o r i z o n t a l a n d D i r e c t i o n a l D r i l l i n g C h a p t e r 3

Suppose is equal to 8, then: 2I

12 III = == 448I

12 MDMDMD =

ftMD 100'000,1'100,1 ==

MDIDLS

=

1004=DLS

' 100/4=DLSThe dogleg severity is 4/100 feet. A greater change in inclination yields a larger dogleg severity.

To show how the change in course length can affect dogleg severity, consider the following example:

Example 3-2 Given: MD1 = 1,000 feet MD2 = 1,050 feet

I1 = 4 I2 = 6

Determine: The dogleg severity.

Solution: 12 III = == 246I

12 MDMDMD =

ftMD 50'000,1'050,1 ==

502=DLS

=

22

502oDLS

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H o r i z o n t a l a n d D i r e c t i o n a l D r i l l i n g D o g l e g S e v e r i t y


'100/4=DLS The dogleg severity is 4/100 feet. Example 3-1 and Example 3-2 show that for the same change in inclination, a shorter course length will result in a greater dogleg severity.

The previous examples were simplified cases in which only the inclination was changed and the azimuth remained constant. A change in azimuth also affects dogleg severity. Unfortunately, the effect on dogleg severity due to a change in azimuth is not as easy to understand or calculate. A 2 change in azimuth in a 100 foot course length will not yield a dogleg severity of 2/100 feet unless the inclination is 90. At low inclinations a change in azimuth will have a small dogleg severity. As the inclination increases, the dogleg severity will also increase for the same change in azimuth. Three equations for calculating dogleg severity using both inclination and azimuth are shown below.

( ) ( ) ( )[ ] ( ){ }212121211100 ICosICosACosACosASinASinISinISinCosMDDLS ++=

Equation 3-1

( )( ) ( )( ) 212212211 221002

+

= IISinAASinISinISinSin

MDDLS Equation 3-2

( ) ( ) 21212212 2100

++= AA

IISinIIMD

DLS Equation 3-3

The first two equations are very long and it is easy to make a mistake in the calculations. Equation 3-3 is more simple but not very accurate below an inclination of 5. The nomenclature is the same as for the survey calculations.

In Equations 3-1 through 3-3, the 100 changes the dogleg severity to per 100 feet. In the metric system, the 100 should be changed to 30 for dogleg severity in degrees per 30 meters or 10 for dogleg severity in degrees per 10 meters.

To illustrate the effect azimuth has on dogleg severity, consider the following problem.

Example 3-3 Given: A 10 azimuth change at inclinations of 1, 10, 20, 30, 40, 50, 60,

70, 80, and 90.

Determine: The dogleg severity at each inclination.

Solution: To make the problem easier to understand, a table can be set up with the necessary information (see Table 3-1).


Table 3-1. Data for Example 3-3

I2 A2 I1 A1 MD 1 20 1 10 100

10 60 10 70 100

20 100 20 90 100

30 140 30 150 100

40 180 40 170 100

50 210 50 220 100

60 230 60 220 100

70 270 70 280 100

80 300 80 310 100

90 360 90 350 100

Calculate the dogleg severity at 1 using Equation 3-1. In this example, the inclination remains constant at 1. The azimuth will change from 10 to 20 over a course length of 100 feet.

( ) ( ) ( )[ ] ( ){ }212121211100 IxCosICosACosACosASinASinISinISinCosMDDLS ++=

( ){ ( ) ( )[ ] ( )o112010201011100100 1 CosCosCosCosSinSinSinSinCosDLS ++= }

( ) ( ) ( ) ( )[ ] ( ){ }9998.09998.09397.09848.03420.01736.00175.00175.01 1 ++= CosDLS ( ) ( )( ) ( ){ }9996.09254.00594.00003.01 1 ++= CosDLS ( ) ( )( ) ( ){ }9996.09848.00003.01 1 += CosDLS ( ) ( ){ }9996.00003.01 1 += CosDLS ( ) ( )9999.01 1= CosDLS ( )( )1743.01=DLS

'10017.0 oDLS = Calculate the dogleg severity at a constant inclination of 10 using Equation 3-1.




( ){ ( ) ( )[ ] ( )212121211100 ICosICosACosACosASinASinISinISinCosMDDLS ++= }

( ){ ( ) ( )[ ] ( )oooooooo 1010607060701010100100 1 CosCosCosCosSinSinSinSinCosDLS ++= } ( ) ( ){ ( ) ( )[ ] ( )9848.09848.05000.03420.08660.09397.01736.01736.01 1 ++= CosDLS }

( ) ( ){ ( ) ( )}9698.09848.00301.01 1 += CosDLS ( ) ( )9698.00297.01 1 += CosDLS ( ) ( )9995.01 1= CosDLS ( )( )73.11=DLS

'10073.1 o=DLS Calculate the dogleg severity at a constant inclination of 20 using Equation 3-1.

( ){ ( ) ( )[ ] ( )212121211100 ICosICosACosACosASinASinISinISinCosMDDLS ++= }

( ){ ( ) ( )[ ] ( )oooooooo 202010090100902020100100 1 CosCosCosCosSinSinSinSinCosDLS ++= }

( ) ( ){ ( ) ( )}8830.00000.09848.01170.01 1 ++= CosDLS ( ) ( )9982.01 1= CosDLS

'100/42.3 o=DLS The dogleg severity for the remaining constant inclinations was calculated and is shown in Table 3-2.

At an inclination of 1, the dogleg severity is 0.17/100 feet for a 10 change in azimuth. At an inclination of 50, the dogleg severity is 7.66/100 feet for the same change in azimuth. The results in Table 3-2 show that the dogleg severity increases as the inclination increases for the same change in azimuth. The equation used to calculate the dogleg severities in Table 3-2 can also be used to calculate the dogleg severity in Example 3-2.


Table 3-2

I1 & I2 DLS

1 0.17/100

10 1.73/100

20 3.42/100

30 5.00/100

40 6.42/100

50 7.66/100

60 8.66/100

70 9.40/100

80 9.85/100

90 10.00/100

Example 3-4 Given: The data in Example 3-2 plus A1=42 and A2=42.

Determine: The dogleg severity using Equation 3-1

Solution:

( ) ( ) ( )[ ] ( ){ }212121211100 IxCosICosACosACosASinASinISinISinCosMDDLS ++=

( )( ) ( )[ ] ( ){ } ++= 64424242426450

100 1 CosCosCosCosSinSinSinSinCosDLS

( ) ( ) ( ) ( )[ ] ( ){ }9945.09976.07431.07431.06691.06691.01045.00698.02 1 ++= CosDLS ( ) ( )( ) ( ){ }9921.05523.04477.00073.02 1 ++= CosDLS ( ) ( )9994.02 1= CosDLS

'100/4=DLS The dogleg severity is the same as calculated previously. The equation can be used to calculate dogleg severity for any combination of changes in azimuth, inclination, and measured depth. Instead of these equations, Figure 3-1 can also be used to determine dogleg severity. The graph is relatively easy to use, and the likelihood of making a mistake is smaller. An example of how to use the charts is included on the chart.




Figure 3-1. Chart for Determining Dogleg Severity

Doglegs are not necessarily a problem in directional wells. When a dogleg becomes a problem, then it is considered severe. One of the immediate problems associated with doglegs is torque and drag. More severe doglegs will cause higher torque and drag. The drill string will experience less torque from a dogleg while drilling, because the collars are in compression except in the case of a horizontal well. They accommodate themselves to the changes in hole curvature. However, while tripping or reaming, the torque will be greater because the collars are in tension. Care should be taken when tripping after a significant change in hole inclination and/or direction. The assembly may go to the bottom, but it might not come back up through


the dogleg. An assembly should never be forced to the bottom; it should be reamed to the bottom.

Torque and drag are caused by the friction between the drill string is in tension, it tries to straighten whi exerts a force on the formation as shown in Figure 3 depth below dogleg increases and the lateral force increase.

The torque and drag can be reduced by several different means. One method is to keep the dogleg severity low. Once a severe dogleg exists in the wellbore, its effect can be decreased somewhat by reaming but only by a small amount. Torque and drag can be reduced using lubricants in the mud system. Oil and other commercially available lubricants reduce the coefficient of friction between the drill string and borehole wall; thereby, reducing the torque and drag. Another method is to reduce the tension in the drill string. This can be accomplished by removing excess collars, or replacing the collar with heviwate drill pipe. The heviwate drill pipe is more flexible and reduces the overall string weight while maintaining the same available bit weight.

As drilling continues, the drill string tension in the dogleg increases which increases the lateral force. The lateral force causes the drill string to cut into the wellbore wall at the dogleg. A keyseat is formed if the lateral force is large enough to cut into the wall. Soft formations require a lower force than hard formations to form a keyseat.

Other problems associated with severe doglegs are wearing of tool joints and worn spots in the casing which can lead to collapse. Logging tools and collars can become stuck in a keyseat.

Drill pipe fatigue is also associated with doglegs. Most failures in drill pipe are fatigue failures resulting from gradual progressive growth of minor irregularities into major cracks even when the stresses are less than the yield strength of the metal. Figure 3-2 illustrates how a severe dogleg can cause fatigue failures. Point A on the drill pipe is in maximum tension while point B is in minimum tension due to bending. (If there is no weight hanging below the joint of drill pipe, point A in compression.) As the pipe is rotated, the referencPoint A goes from maximum tension to minimum

3-8 Cthe drill string and the borehole wall. Whenle going around a dogleg. The drill string-2. As tension on the drill string increases, increases; therefore, the torque and dragwould be in tension and point B would be e points go through cyclic stress reversals. tension and back to maximum tension on

Figure 3-2. Bending of Drill Pipe in a Dogleg, Rotation causes Cyclic Stress Reversals

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each cycle. These cyclic stress reversals will cause fatigue failures. The failures usually occur within 2 feet of a tool joint because this is the point of the internal upset. They also occur in the slip area.

The cycles to failure are a function of the degree of bending, strength of the pipe, wall thickness, corrosion environment, and the tensile load on the pipe. The degree of bending is determined by the dogleg severity. It should be remembered that the dogleg severity is a measure of the curvature between survey points. This may not be a true indication of the actual dogleg severity. As an example, assume a whipstock was used to change the inclination of a well. Calculations from a 100 foot survey interval indicated a dogleg severity of 3/100 feet. The fact is that most of the inclination change occurred while drilling off the whipstock which is approximately 10 feet long. The remainder of the survey interval has only a small amount of curvature. A survey taken above and below the whipstock indicates a 3 change in 10 feet.

The degree of bending is determined by the actual dogleg severity. The yield strength of a metal has less effect on fatigue failure than one might think. Even though the yield strength of S-135 drill pipe is 1.8 times greater than Grade E drill pipe, the endurance limit is only 1.12 times greater. The endurance limit is the maximum alternating stress a material can take without causing fatigue. Figure 3-3 is a plot of the alternating stress versus the cycles to failure for grade D and E pipe and S-135 pipe. The endurance limit for Grade E and S-135 pipe are 26,000 psi and 29,000 psi, respectively. However, these values are with no tension in the pipe and no corrosion. As tension increases, the maximum bending stress (dogleg severity) will decrease.

Figure 3-3. S-N Curve for Drill Pipe


Wall thickness does have an effect on the cycles necessary to produce failure in a dogleg. Pipe with a greater cross sectional area will endure more cycling because the total stress per unit area is lower with the same amount of tension.

Corrosive environments such as salt water reduce the cycles to failure for drill pipe. As corrosion rates increase, the endurance limit decreases. Drill pipe will have more fatigue failures while drilling wells in corrosive environments. Corrosion pitting will also decrease the service life of drill pipe. Pitting reduces the cross sectional area of the drill pipe which increases the alternating stress per unit area. Also, scars inside or outside the pipe reduce the cycles to failure for drill pipe.

Tensile loading has a significant effect on the cycle to failure. Increases in tensile loads increase the total stress on the pipe. Since the stress per unit is greater, the failure will occur at fewer cycles. Therefore, if a dogleg is high in the hole with high tension in the pipe, only a small dogleg severity can be tolerated. If a dogleg is close to the bottom of the hole with low tension on the pipe, larger dogleg severities can be tolerated.

Fatigue damage in drill pipe is cumulative. If a joint of drill pipe rotates in a severe dogleg while drilling, some portion of its life is used. Even though the joint did not fail when drilling the hole with the severe dogleg, a failure can occur in the next hole where the dogleg severity is much less. Conventional inspection techniques cannot measure the amount of fatigue damage that has already accumulated unless a crack is present.

Figure 3-4 and Figure 3-5 can be used to determine the maximum dogleg severity that can be tolerated in a well. Examples for determining the maximum dogleg severity are shown on each figure. Usually if the directional program is designed to prevent drill pipe fatigue, the hole will be acceptable for conventional designs of casing, tubing and sucker rods. However, rod and tubing wear will occur in directional wells.

As the corrosion rates increase, the maximum safe dogleg severity limit will decrease. In Figure 3 3, the endurance limit for grade E drill pipe is 26,000 psi, but that is for a corrosion free environment. Lubinski indicated that the endurance limit for a normal drilling mud would be around 18,000 psi for grade E drill pipe. A simple equation for calculating the bending stress in pipe is Equation 3 4 and can be used when there is no tension. Lubinskis equationi should be used when there is tension in the drill pipe.

( )( )(DLSDpb 218= ) Equation 3-4 Example 3 5 shows how the maximum dogleg severity limit can be calculated for no tension load if the endurance limit is know.

Example 3-5

Given: The endurance limit for grade E drill pipe is assumed to be 18,000 psi.

Determine: The maximum permissible dogleg severity with no tensile stress for 4 1/2 drill pipe

Solution: Rearranging Equation 3 4 to solve for dogleg severity




Figure 3-4. Maximum Safe Dogleg Limits for S-135 Drill Pipe


Figure 3-5. Maximum Safe Dogleg Limits for Grade E Drill Pipe

( )( )( )DLSDpb 218= ( ) ( )( )pb DDLS 218=




( ) ( )( ) feetDLS 100/3.185.421818000 o==

Higher dogleg severities can be tolerated if the tension in the drill pipe is very low. Medium radius horizontal wells can be drilled without causing significant fatigue damage to the drill pipe because the tension in the dogleg is very low. The dogleg severity in a normal directional well has to be lower at the kickoff point because the tension will be a maximum at that point. The deeper the dogleg, the greater the dogleg severity that can be tolerated without causing fatigue.

PROBLEMS

1 Given the following survey data, calculate the dogleg severity.

MD1 = 100 feet MD2 = 200 feet I1 = 1 I2 = 1 A1 = 0 A2 = 180

2 Given the following survey data, calculate the dogleg severity.

MD1 = 1200 feet MD2 = 1264 feet I1 = 10 I2 = 11.5 A1 = S48W A2 = S56W

NOMENCLATURE

A = Azimuth, degrees

DLS = Dogleg severity, degrees per 100 feet

pD = Outside diameter of the pipe, inches

I = Inclination, degrees

MD = Measured Depth

b = Bending stress, psi = Denotes change in parameter

1 = Subscript denotes upper survey

2 = Subscript denotes lower survey


REFERENCES

i Lubinski, A.; Maximum Permissible Dog-Legs in Rotary Boreholes, Journal of Petroleum

Technology, February, 1961.


Dogleg SeverityIntroductionExample 31Example 32Example 33Example 34

Problems

Documents

Chapter 03 Dogleg Serverity Directional and Horizontal Drilling