Model predicts drill pipe fatigue in horizontal wells

Jiang Wu
Maurer Engineering Inc.
Houston

• Equations [42490 bytes]

Drill pipe fatigue, and subsequent failure, can be a major problem when drill pipe is rotated in short radius build sections of horizontal wells.

Rotating the drill pipe during downhole motor drilling can often increase penetration rates 50-200% in short and medium radius wells because of the reduction in frictional drag. Rotating drill pipe in short radius (30-50 ft) horizontal wells, however, can result in drill pipe fatigue failures after four to eight wells.

Monitoring drill pipe fatigue damage for each joint of drill pipe used in rotary drilling horizontal wells is therefore crucial to prevent drill pipe failures.

According to fatigue theory, drill pipe fatigue damage accumulates until the pipe fails. The accumulative drill pipe fatigue damage is determined by drill pipe bending stresses, rotating revolutions, and drill pipe S-N curves. Fatigue damage is also related to drill pipe material, bit weight, penetration rate, and other drilling variables.

Drill pipe S-N curves are important in predicting drill pipe fatigue. Drilling conditions, such as drilling fluid corrosion and axial load, are considered in modifying the typical S-N curves to give more reliable drill pipe fatigue predictions.

Drillstring failures are costly because of the loss of rig time, tubular goods, and even the well in some cases. Metal fatigue causes the majority of drillstring failures. Rotary drilling of horizontal wells increases drill pipe fatigue problems, especially in intermediate and short radius horizontal wells because the build rates in these wells are greater than the permissible dogleg limit recommended by the American Petroleum Institute (API).1 It is therefore important to predict and monitor fatigue damage to help prevent drillstring failures when the pipe is rotated in horizontal wells.

Lubinski and Hansford studied drill pipe bending stresses and fatigue damage as a function of axial tensile load.^2-4 Paslay and Cernochy studied drill pipe bending stresses and fatigue damage for both axial tensile and compressive load conditions, but drill pipe weight was ignored.⁶

This article presents a basic drill pipe fatigue analysis and a computer program developed to predict drill pipe fatigue damage by considering well bore curvature, axial compressive load, drill pipe weight, and drill pipe body contact with the well bore. It is applicable to the current operations of rotary drilling of intermediate and short radius horizontal wells where the drill pipe is rotated in the build section under axial compressive loading.

Bending stress

For jointed drill pipe in the build section of horizontal wells, the axial tensile load tends to straighten the middle portion of the drill pipe (Fig. 1 [19703 bytes]), causing the maximum bending stress to be located next to the tool joint for large axial tensile loads (Equations 1-3).³

However, if the axial tensile load is small, the maximum bending stress may be located at the middle of the drill pipe joint because of the drill pipe weight (Equation 4).

The axial compressive load tends to deflect further the middle portion of jointed drill pipe in the build section of horizontal wells (Fig. 2 [19202 bytes]). The maximum bending stress in this case occurs at the middle of the drill pipe joint (Equation 5).³

These maximum bending stresses were derived based on the assumption that the drill pipe body does not contact the well bore wall. However, when jointed drill pipe is under large tensile or compressive axial load, the drill pipe body will contact the well bore wall, and the bending stress distribution will change.

For axial tensile loads, the maximum bending stress will still be located next to the tool joint after the drill pipe body contacts the well bore, but for axial compressive loads, it may be located within the noncontacting portion of the drill pipe instead of the middle of the drill pipe joint.

The maximum bending stress for this case is much more complicated to calculate and will not be discussed here. An important point to note is that the maximum bending stress will be smaller than predicted using these equations after the drill pipe body contacts the well bore wall because the drill pipe bending deflection is confined within the well bore.

Lubinski defined the permissible dogleg severity below which no fatigue damage of drill pipe will occur, no matter how long it rotates in the well bore.³ A permissible build rate is defined in the same way in this article for the build rate of horizontal wells.

The permissible build rate is therefore resolved by making the maximum bending stress equal to the fatigue (endurance) limit of the drill pipe. For large axial tensile load condition, the permissible build rate (Equation 6) is derived from Equation 1.

Note this permissible build rate can be simplified to the API equation if the drill pipe weight is ignored (q = 0).¹ Similarly, the permissible build rate for the small axial tensile load condition (Equation 7) is derived from Equation 4.

The permissible build rate for the axial compressive load condition (Equation 8) is derived from Equation 5.

Fig. 3 [11187 bytes] shows a drill pipe S-N curve (Grade E steel) from where the fatigue (endurance) limit is about 20,000 psi (defined at 108 revolutions).⁴

Fig. 4 [13622 bytes] shows the permissible build rate predicted by the computer program, Dplife1, for both axial tensile and compressive load conditions. The API equation (1990) ignoring drill pipe weight is also plotted for comparison. The permissible build rate is lowest for axial compressive loading.

The permissible build rate equations derived above are again based on the assumption that the drill pipe body does not contact the well bore wall. When the jointed drill pipe body contacts the well bore under large tensile or compressive axial load, the above permissible build rate equations give a conservative estimate of permissive build rate.

Higher build rates could be achieved without causing drill pipe fatigue damage, because the maximum bending stress will be smaller than predicted by Equations 1, 4, and 5, because of the confinement of drill pipe bending deflection in the well bore.

Fatigue damage

Drill pipe fatigue damage occurs when the maximum bending stress becomes larger than the fatigue (endurance) limit. This usually happens when the permissible build rate is exceeded in drilling intermediate or short radius horizontal wells. The drill pipe life, in terms of revolutions, becomes limited when drill pipe fatigue damage occurs. For example, Grade E drill pipe can only rotate about 100,000 revolutions at a maximum bending stress of 32,000 psi (Fig. 3).

The whole S-N curve is used to specify the drill pipe life in revolutions and drill pipe fatigue damage if the maximum bending stress exceeds the fatigue (endurance) limit. Drill pipe fatigue damage is defined as the ratio of actual drill pipe revolutions and limiting drill pipe life in revolutions from the S-N curve (Equation 9).

In Equation 9, n is the actual drill pipe revolutions at a certain bending stress level, and N is the drill pipe fatigue life in revolutions at that bending stress level from the S-N curve.

For example, if the maximum bending stress is 32,000 psi, and the actual revolutions are 10,000, the fatigue damage will be 0.1, or 10%, for Grade E drill pipe because N = 100,000 revolutions (Fig. 3).

For a series of rotating events at different bending stress levels, the cumulative drill pipe fatigue damage is the sum of the fatigue damage at each event. According to the current fatigue theory, the final failure of drill pipe occurs when the cumulative fatigue damage reaches 1 (Equation 10).

During rotary drilling of a horizontal well, the drill pipe fatigue damage also depends on pipe sequence. Only those joints of drill pipe that rotate through the build section experience severe fatigue problems. Drill pipe in the vertical and horizontal sections may not have a fatigue problem because of very small or no bending stress.

Fatigue computer program

A user-friendly computer program, "Dplife1" (Drill Pipe Fatigue Life), was developed for use with Microsoft Windows to predict permissible build rate/dogleg severity, cumulative fatigue damage, and total revolutions before fatigue failure. Well bore curvature, axial load, drill pipe weight, and drill pipe body contact with the well bore wall are used to calculate the maximum bending stress.

Different S-N curves (bending stress versus revolutions to failure) are incorporated into the computer program for different types of drill pipe (steel, titanium, and aluminum). These S-N curves are based on published full size drill pipe test data and modified small sample test data. S-N curves for other materials can be easily input by the user. Drilling conditions such as drilling fluid corrosivity and axial loads are also considered in modifying the typical S-N curves to give more reliable prediction of drill pipe fatigue.

In one example, Dplife1 predicted the drillstring fatigue damage for rotary drilling of a horizontal well with a build rate of 45°/100 ft. The total well depth was 4,000 ft measured depth (MD) with an 800-ft horizontal section and a kick-off point at 3,000 ft MD. The drillstring consisted of 31/2-in. Grade G drill pipe (Range 2, 4-in. tool joint) and 43/4-in. drill collars.

The previous fatigue damage was assumed to be 0.2% for new pipe. Dplife1 predicted that 7% of the total drill pipe fatigue life would be used up rotating through the build section. In other words, this drill pipe could only be used to drill 14 such wells before total failure, if the same joints would always be used in the build section. The top 1,500 ft of drill pipe and the 1,500 ft of drill collars were in the vertical section of the well and experienced no fatigue damage.

Besides predicting fatigue damage for a whole drillstring in rotary drilling of horizontal wells, Dplife1 also analyzes a single joint of drill pipe for permissible build rate and total revolutions to final fatigue failure. The total revolutions or rotating hours to final fatigue failure depend on many factors, including build rate, axial load, length of one-joint of drill pipe, and drill pipe materials.

For 31/2-in. Grade G drill pipe (Range 2, 5-in. tool joint) in a 45°/100 ft build well bore, the drill pipe body does not contact the well bore wall when the axial compressive load is 1,500 lbf, and the total revolutions to failure is predicted as 147,895 revolutions.

As the axial compressive load increases, the drill pipe body starts to contact the well bore wall, first as a point contact and then as a wrap contact. The total revolutions to failure does not change much, because the drill pipe body contact confines the bending deflection development and limits the maximum bending stress.

Fig. 5 [11471 bytes] shows Dplife1 predictions of total revolutions to failure for different joint lengths of drill pipe in a 30°/100 ft build well bore. Generally, the shorter the joint length, the higher the fatigue life. However, the Range 3 drill pipe (45-ft joint length) surprisingly has a higher fatigue life than the Range-2 drill pipe under 5,000 lbf axial compressive load condition because the maximum bending stress for Range 3 drill pipe becomes smaller due to drill pipe body contact with the well bore. For 20,000 lbf axial compressive load, all three joint lengths have nearly the same fatigue life.

If drill pipe protectors or compressive service drill pipe/heavy wall drill pipe is used, the distance from tool joint to protector/intermediate upsets should be used as the effective joint length, since the intermediate upsets/protector act like tool joints contacting the well bore wall.

Dplife1 has also predicted very agreeable results with Marathon Oil Co.'s field experience on rotary drilling of short-radius horizontal wells where drill pipe failure was encountered after drilling four short-radius wells.

S-N curve

S-N curves are important factors in predicting drill pipe fatigue damage and fatigue life and must be accurate to make accurate fatigue life predictions. S-N curves for steel, titanium, and aluminum drill pipe are built into Dplife1, using published full-size drill pipe test data and modified small sample test data.4-6 The drill pipe yield strength is used to define the fatigue bending stress at 103 revolutions.

The typical S-N curves are modified to account for the effects of axial load (mean stress) and drilling fluid corrosion. Drill pipe axial tensile load reduces fatigue bending stress (drill pipe S-N curve value), while axial compressive load increases fatigue bending stress (Fig. 6 [9915 bytes]).

The Goodman line is used to account for this axial load effect (Fig. 7 [7361 bytes]). The fatigue (endurance) limit is reduced as the axial tensile load increases in the manner used by Lubinski and API RP 7G.^{1 2} The same amount of reduction in fatigue (endurance) limit is applied to the whole S-N curve to reduce the fatigue stress, since the fatigue bending stress has a more or less uniform reduction over the whole S-N curve under axial tensile load. The benefit from the axial compressive load is not considered in modeling drill pipe fatigue, resulting in a conservative estimate of fatigue life.^7-9

Drilling fluid corrosion also reduces the drill pipe S-N fatigue curve. The more corrosive the drilling fluid is, the more reduction in the fatigue bending stress. Unlike the effect of axial tensile load, the fatigue bending stress reduction due to drilling fluid corrosion is higher in the high fatigue life (revolutions) region and lower in the low fatigue life (revolutions) region. For very corrosive drilling fluids, a 40% reduction of the fatigue (endurance) limit was suggested by Lubinski.² In our modeling of drill pipe fatigue, the drilling fluid is accordingly classified into four categories: freshwater, 0% reduction of endurance limit; mild mud, 10%; corrosive mud, 25%; and very corrosive mud, 40%.

The reduction of fatigue bending stress over the entire drill pipe S-N curve is considered to vary linearly, with the largest reduction to the fatigue limit (108 revolutions) by the above values and zero reduction to the yield strength (1,000 revolutions).

Results

Drill pipe fatigue can be a major problem when drill pipe is rotated in short-radius (30-50 ft) build sections. Drill pipe fatigue is affected by many factors, including build rate/dogleg severity, drill pipe properties (size, material, and joint length), axial load, and drilling fluid corrosion. Drill pipe body contact with the well bore wall reduces drill pipe maximum bending stress and drill pipe fatigue damage.

The Dplife1 computer program accurately predicts permissible build rate, cumulative fatigue damage, and total revolutions to failure for rotary drilled horizontal wells. It also has a user-friendly input/output system and a good graphic ability. Dplife1 accurately predicted a drillstring failure that occurred after drilling four 35-ft short radius horizontal wells.

Additional work is required to verify the model's use for other field applications and to improve the model.

Acknowledgment

The author wishes to thank Maurer Engineering Inc. for permission to publish this article and the participants of the joint-industry project DEA-44 for sponsoring this work.

References

1. Recommended Practice for Drill Stem Design and Operating Limits, American Petroleum Institute RP 7G, 14th edition, August 1990.

2. Lubinski, A., "Fatigue of Range 3 Drill Pipe," Revue de l'Institut Franais du Ptrole, March 1977.

3. Lubinski, A., "Maximum Permissible Dogleg in Rotary Boreholes," Journal of Petroleum Technology, February 1961.

4. Hansford, J.E., and Lubinski, A., "Effects of Drilling Vessel Pitch or Roll in Kelly and Drill Pipe Fatigue," Journal of Petroleum Technology, January 1964.

5. Hansford, J.E., and Lubinski, A., "Cumulative Fatigue Damage of Drilling Pipe in Dog-Legs," Journal of Petroleum Technology, March 1966.

6. Paslay, P.R., and Cernocky, E.P., "Bending Stress Magnification in Constant Curvature Dogleg with Impact on Drillstring and Casing," paper No. 22547, presented at the Society of Petroleum Engineers 66th Annual Technical Conference and Exhibition, Dallas, October 1991.

7. Ballantine, J.A., Comer, J.J., and Handrock, J.L., Fundamentals of Metal Fatigue Analysis, Prentice Hall, Englewood Cliffs, New Jersey, 1990.

8. Fuchs, H.O., and Stephens, R.I., Metal Fatigue in Engineering, John Wiley & Sons, New York, 1980.

9. Schuh, F.J., "The Critical Buckling Force and Stresses for Pipe in Inclined Curved Boreholes," paper No. 21942, presented at the Society of Petroleum Engineers/International Association of Drilling Contractors Drilling Conference, Amsterdam, Mar. 11-14, 1991.

The Author