SPE PP. Copyright 2011, Society of Petroleum Engineers

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1 SPE PP Comparing the Results of a Full-Scale Buckling Test Program to Actual Well Data: New Semi-Empirical Buckling Model and Methods of Reducing Buckling Effects Sarah Mitchell, SPE and Norman Bruce Moore, SPE, WWT International Inc. James Franks, Pioneer Natural Resources Gefei Liu, SPE, and Yanghua (Lily) Yang, Pegasus Vertex Inc. Copyright 2011, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Western North American Regional Meeting held in Anchorage, Alaska, USA, 7 11 May This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. Abstract Buckling and its effects are topics of economic and technical interest as ERD and horizontal wells become critical to maximizing recoverable reserves, particularly in the Continental United States and Alaska. Previous work has resulted in important discoveries about drill string buckling, but to date, little testing has been done on actual drill pipe in a controlled manner, particularly in measuring drill string whirl. As a result, there can be disparities between theoretical predictions of buckling effects versus actual field results. These disparities can result in unrealistically high friction factors required to bring calculated values close to actual data, or in many cases, operational difficulties such as high torque, low ROP, drill string failures, inability to maintain directional control, or reach the planned depth can result. To learn more about drill string behavior in buckling conditions, a full-scale buckling test fixture was developed to evaluate the effects of buckling on 2 ⅞-, 3 ½-, and 4-inch drill pipe while sliding and rotating inside 7 inch casing. The test fixture incorporated a variety of sensors and cameras to characterize torque, drag, vibration, and drill string deformation under buckling loads. As part of the test program, low friction non-rotating protectors were also tested to measure performance under buckling conditions. The test results show that drill string buckling occurs at far lower loads than predicted by current models, possibly caused by minor deformations inherent in real drill pipe. The results also show that for a given amount of torque or drag, protectors increased the available compressive load by 20 to 30% and substantially reduced vibration caused by drill string whirl. The test results were used to develop a new Semi-Empirical Buckling Model that predicts contact forces resulting from drill string buckling and also the torque and drag effects of drill string whirl. This model was then incorporated into torque and drag modeling software where it was compared against actual data from a large number and variety of wells. The results show an ability to more accurately predict torque, drag, and vibration caused by buckling and whirl. Definitions Buckling: For the purposes of this paper, buckled pipe is defined as compressively loaded pipe that is laterally deviated from its unloaded position resulting in a localized increase in drag. Whirl: For the purposes of this paper, whirl is defined as compressively loaded rotating pipe that is precessing within the casing or wellbore resulting in a localized increase in vibration, torque, and drag. It is important to note that the terms sinusoidal and helical buckling are relative terms. Buckling is not digital, meaning that there is not always a clear boundary between buckling states. Instead it is a relatively steady analog progression, with thresholds that serve to mark changes in mathematical relationships and starting points where there are changes in the shape and behavior of the buckled pipe.

2 2 SPE Background The purpose of this paper is to detail the development of a new Semi-Empirical Buckling Model. Over the course of running torque and drag analyses on hundreds of wells each year, it has become clear that in many situations, the existing buckling models that are available are not accurate in predicting the onset and effects of buckling. Problems with inaccurately predicting buckling have been explained by C.Mason and D.Chen (2007). This inaccuracy has manifests in several ways, including: Existing models require a higher than normal open hole friction factor near the end of a lateral or horizontal hole section to match the actual and calculated torque and drag results. Reduced weight on bit is required to maintain ROP at the end of horizontal wells. Severe stick-slip and vibration at high WOB or high RPM in high angle or horizontal wells. Drill string wear or failures in areas where buckling was not previously predicted. Inability to run liner to desired depth because of far higher than predicted friction factors. To address these inaccuracies, a Joint Industry Program was started to run full-scale buckling and whirl tests to attempt to learn more about buckling, with the goal of developing an improved buckling model. Process 1. Test Set-Up: Develop, build, and calibrate a full scale test fixture capable of running full-scale buckling tests to measure the effect of compressive loading on several sizes of actual drill pipe over a range of conditions representing running into the hole, slide drilling, and rotary drilling, using bare pipe and using low-friction nonrotating protectors. 2. Evaluate Test Results: Plot and evaluate the results of these tests to determine actual buckling loads and the effect of rotation, drill pipe size, etc. 3. Develop Semi-Empirical Model: Develop a Semi-Empirical Buckling Model based on the results from the full-scale tests using existing buckling theory to the extent possible. 4. Correlate Model to Test Data: Compare the values predicted by the new model against measured test data. 5. Update Torque and Drag Software: Incorporate the model into a proven torque and drag software program, with the ability to run torque and drag well models using existing or currently available models and the new Semi-Empirical Buckling Model. 6. Correlate the Semi-Empirical Model to Actual Well Data: Perform back-models on a wide range of wells, including horizontal and high angle wells, rotary drilling, slide drilling, running liner, casing floatation, etc. Compare the results between the existing buckling model and the new Semi-Empirical Model. Adjust the model as necessary so that the model predicts both the test data and actual well data. Test Set-Up The Buckling Test Fixture is outfitted to apply compressive load while simultaneously rotating and sliding in water or drilling mud. Tests were run with 2 ⅞-, 3 ½- and 4-inch drill pipe inside 7 inch casing/tubing with an inside diameter of 6.06 inches. The test fixture was fully instrumented to record all test parameters. Instrumentation included load cells for recording compressive load, drag, and torque. Three cameras were also installed to record events inside the casing at approximately mid-span at each joint of drill pipe to record the movement of the drill pipe while the test is running. When running tests with rotation, a vibration sensor was attached to the casing to record vibration transmitted through the drill pipe to the casing. The test fixture was constructed using a steel load frame designed to accommodate up to 100,000 lb compressive load. The frame holds the casing in place, and allows for 12 inches of lateral and 4 inches vertical adjustment of the casing trajectory. The frame also houses sleds on both the uphole and downhole end of 120 feet of casing. The test length was chosen to allow testing a full stand of pipe with partial joints at the ends to help minimize end effects. Sleds on each end of the drill pipe hold it in place with minimal outside friction while sliding and rotating. These same sleds also measure the forces acting on the drill pipe. The sleds were fitted with 50,000 lb load cells, each with an accuracy of +/- 50 lbs and a 1000 ft-lb torque load cell with an accuracy of +/- 1 ft-lb. Also, a vibration recording device was attached to the outside of the test fixture when running rotating tests to record increasing vibration with any buckling or whirl that occurred. Diagrams and pictures of the test fixture are shown below in Figures 1 through 4. The specifications for the drill pipe are shown below in Table 1. TABLE 1. DRILL PIPE SPECIFICATIONS Nominal Tube OD (inches): 2 ⅞ 3 ½ 4 Tube Weight (lbs/ft): 10.4 lbs/ft 13.3 lbs/ft 14.0 lbs/ft Connection OD (inches): Length: Range 2, Average Length Approx. 31ft Condition: Used, Premium or Class II

3 SPE The tests were run to simulate conditions experienced in normal drilling environments as shown by test matrix outlined in Table 2. The first condition simulated tripping into the hole. In this case, the drill pipe is allowed to slide down the hole while an increasing axial load is applied to the pipe. The second condition replicates drilling, where the drill pipe is rotated while sliding down the hole. The third condition represents setting weight on the pipe on bottom without rotating. In this condition, the downhole end was fixed, and an axial load was applied to the uphole end. And finally, the fourth condition replicated setting weight on bottom while rotating. In this condition, the drill pipe was rotated and then axial load was applied to the drill pipe while the downhole end was fixed. Calibration tests were run with the uphole and downhole sleds directly attached to one another without any drill pipe or casing between them. These calibration tests were run to determine the torque and drag present in the test fixture under load. This torque and drag was then subtracted from the test values so that there could be an accurate determination of torque and drag caused solely by the contact between the buckled drill pipe and casing. TABLE 2 BUCKLING TEST MATRIX Drill Pipe Fluid Protectors Dog Leg Test 2 ⅞ Mud None 0 R/S 3 ½ Mud None 0 R/S 3 ½ Mud Low 2/joint 0 R/S 4 Mud None 0 R/S/F 4 Mud Low 2/Joint 0 R/S Calibration run, without casing R/S S= Sliding (Tripping In), R=Rotating (Rotate on Bottom), F=Fixed End The test matrix was created to demonstrate a wide range of test conditions, including various sizes of drill pipe creating a wide range of clearance within the casing. Also, tests were run to evaluate the effectiveness of protectors in reducing the effects of buckling. Figure 1. Schematic of buckling test fixture, including instrumentation.

4 4 SPE Figures 2, 3, and 4. Photo of the buckling test fixture, with renderings of the sleds used to convey load and torque to the drill pipe. Buckling Test Results Sliding Tests The buckling tests followed a consistent series of events, as shown in Figures 5 and 6. In general, the pipe buckled at loads far below what would be predicted by existing buckling models. The cause for the early onset buckling is unknown, but it may be related to small amounts of deformation that are inherent in all drill pipe. In non-vertical wells, the tube is supported between the tool joints and sags under its own weight. Also, pipe used in a compressive manner in high angle wells, has often experienced buckling in previous wells, so the pipe may have taken some permanent set. Also, many wells are not perfectly straight, even with the use of modern directional drilling techniques. All of these can have the effect of introducing instability into the compressively loaded pipe, and greatly reduce the buckling initiation load. Results from all the sliding buckling tests are shown with the Semi-Empirical Model in Figure 13 in this report. 1. Static to Dynamic Friction: There was an immediate decrease in drag due to the change from static to dynamic friction as the drill pipe started to slide along the bottom of the casing. 2. Buckling Initiation: As the compressive load increased, the drill pipe would deviate in a sinusoidal manner along the bottom of the casing. This sinusoidal deviation occurred at loads significantly below the buckling threshold predicted by most models. Initially, this snaking wave form results in low levels of drag as shown in Figure Increase in Sinusoidal Buckling (lateral snaking): As compressive load increases further, the amplitude of the sinusoidal deviations in the drill pipe increases, with a corresponding, nearly linear increase in side load and resulting drag as the drill pipe presses with more force against the casing. 4. Onset of Helical Buckling: At some point the drill pipe has climbed halfway up the casing. At this point, increasing the axial load causes the drill pipe to snap to the point where part of the pipe is pressed against the high side of the casing as shown in the bottom left image in Figure Helical Buckling: At this point any increase in load causes compression of the pipe in the buckled state, and an additional increase in drag at a linear rate that is substantially greater than in the climbing phase.

5 SPE Figure 5. Graph showing compressive load vs. drag, combined with a visual depiction of the buckling progression and lateral deflection of the pipe during a sliding buckling test. Figure 6. Above is a series of images showing a typical sliding buckling test using 3 ½ inch bare drill pipe. The dotted lines represent the initial location of the drill pipe within the casing. Notice the lower left quadrant showing the deviation in the pipe at the location of maximum amplitude, and the snap of the pipe to the top of the casing in the photo at 37,000lbs.

6 6 SPE Rotating Tests The buckling behavior of the rotating pipe is different than sliding pipe. When rotating, the friction between the drill pipe and casing influences buckling behavior, resulting in drill string whirl. The buckling behavior when rotating is described below and shown in Figure 7. Results from all the rotating buckling tests are shown with the Semi-Empirical Model in Figures 15, 16, and 17 later in this report. 1. Buckling Initiation: As the compressive load increases, the drill pipe starts to deviate in a sinusoidal manner along the bottom of the casing. This sinusoidal deviation occurs at loads significantly below the buckling threshold predicted by most models. Initially, this snaking causes little or no increase in drag. 2. Increase in Snaking (Horizontal Amplitude and Vibration): As compressive load increases further, the amplitude of the sinusoidal deviations in the drill pipe increases, with a corresponding increase in side load and corresponding increase in drag as the drill pipe presses with more force against the casing. As the compressive load increases, there is not an equal distribution in the increase to torque and drag, resulting in a change in the friction force vector direction with increased load. As load is applied, the drill pipe begins to climb up the wall and fall down again, decreasing the effective RPM, and directing additional buckling related contact force more into drag and less into torque as shown below in Figure Fully Developed Whirl: At some point the drill pipe has climbed halfway up the casing. At this point, increasing the axial load causes the drill pipe to gain enough load and friction to whirl completely around the inside of the casing. This comes with a dramatic increase in torque and an erratic drag behavior as shown below in Figure 7. Notice that the drag fluctuates wildly up and down as the drill pipe vibrates and whirls around within the casing, grabbing the casing wall, and then releasing. It does appear that rotating at higher RPM may increase the the severity of the whirl or reduce the loads at which whirl occurs as shown by the higher torque and greater drag fluctuations as shown in Figure 8, although due to the scatter in the test data, quantifying this effect was difficult. Further testing may look to isolate and quantify this effect. 4. Beyond Whirl Buckling: At this point any increase in load causes a dramatic increase in torque and drag, with very large amounts of lateral and torsional vibration as the pipe grabs onto the wall while climbing and then releasing as it falls down the other side. After testing, there would often be bands of polished pipe in the center of the drill pipe tube showing the location of contact with the casing, indicating an approximate buckling wavelength of 60ft. Figure 7. Measured torque and drag as a function of axial load during a 120rpm rotating buckling test.

7 SPE Figure 8. Chart showing the effect of rotational speed on buckling behavior. Note that at 180rpm, there is a possible decrease in load at which there are spikes in drag, incdicating the onset of whirl. Differences Between Static, Sliding, and Rotating Buckling Behavior A static test was conducted, with the drill pipe fixed at the down hole end and a compressive load applied to the uphole end, resulting in an increase in the buckling load by 20-25% compared a test with sliding drill pipe. The difference in static and sliding buckling behavior may be related to to the difference in static and dynamic friction. In actual well conditions, because of stretch in the drill pipe, setting down weight invariably causes most of the drill string to slide, likely eliminating these effects. When the same test was run on rotating pipe with a fixed downhole end, the buckling loads were the same as with the drilling (rotating plus sliding) tests. Buckling Behavior with Non-Rotating Drill Pipe Protectors Installed Sliding Tests Low-friction Non-Rotating Protectors have been proven to reduce rotating friction and sliding drag as shown in papers by N.B. Moore (1996) and A.Fuller (2002). The addition of low-drag NRPs reduced sliding friction resulting in lower incremental drag caused by buckling. Also, the protectors tended to reduce the amount of overall deformation. The overall onset and shape of the buckling drag graph is similar. But, the protectors tended to reduce the initial drag, and at the transition between sinusoidal and helical buckling, the low-friction NRPs reduced the drag caused by buckling by approximately 20% as shown in Figure 9, or approximately 20% additional compressive load could be applied for the same level of drag. Figure 9. Buckling behavior while sliding with and without protectors. Notice that the compressive load to reach any given amount of drag is approximately 20% greater with protectors installed.

8 8 SPE Rotating Tests Non-Rotating Protectors (NRP s) lift the pipe off the casing, eliminating any initial rotational contact between the drill pipe and casing. The NRP, with a fluid bearing geometry, results in substantially reduced torque, although because rotating pipe has dramatically less drag, the overall drag is not substantially reduced. Increasing load beyond the loads required to initiate buckling results in dramatically more vibration and erratic spikes in drag as the pipe climbs the casing and then falls down again. Because protectors prevent contact between the drill pipe and casing or wellbore, these erratic spikes in drag are reduced until higher compressive loads are applied as shown in Figure 10. These effects also result in much lower vibration as shown in Figures 11 and 12, comparing vibration between rotational buckling tests on 3 ½ inch drill pipe with and without NRP s installed. Figure 10. Buckling drag comparison with and without low-friction Non-Rotating Protectors installed. Note that the drag without protectors is higher and more erratic at higher compressive loads due to the increased whirl and vibration with bare drill pipe. Figures 11 and 12. Vibration as recorded on the outside of the casing during a rotating buckling test at 60 to 180 rpm using bare drill pipe and then pipe with low-friction Non-Rotating Protectors installed.

9 SPE Comparison with Existing Buckling Models A comparison of industry methods of computing buckling loads was performed using several commercially available torque and drag well modeling software packages. In overview, existing torque and drag software divides the drill string into small sections, and then calculates the forces acting on each section. Based on the axial loads within each section, additional buckling related contact force or side force may be added. The amount of side force is based on each software company s buckling algorithm, but generally there is no side force added for any axial load less than the calculated sinusoidal buckling threshold. A small but increasing amount of buckling side force is added for axial loads between the sinusoidal and helical buckling load, and a large amount of load is added for any axial loads above the helical buckling threshold. Existing buckling models used in the oil and gas industry offer a wide range of predictions regarding buckling onset as shown in Table 3. Many of these software models are based on other models noted in the literature and elsewhere in this paper, while many models are based on the Dawson-Paslay buckling criteria to predict the onset of sinusoidal buckling. TABLE 3. COMPARISON OF EXISTING BUCKLING MODEL RESULTS: STRAIGHT, HORIZONTAL WELL Drill Pipe 2 7/8 Inch 3 1/2 Inch 4 Inch Casing 7 Inch 7 Inch 7 Inch Dawson-Paslay Buckling Threshold Based on Drill Pipe Diameter 12 kip 23 kip 32 kip Based on Tool Joint Diameter 15 kip 32 kip 47 kip Drill Pipe Standard Sliding Sinusoidal 14 kip 27 kip 39 kip Rotating Sinusoidal 14 kip 27 kip 39 kip Software Package 1 Sliding Sinusoidal 17 kip N/A N/A Helical 24 kip N/A N/A Rotating Sinusoidal 17 kip N/A N/A Helical 24 kip N/A N/A Software Package 2 Sliding Sinusoidal 14 kip 30 kip 42 kip Helical 40 kip 85 kip 119 kip Rotating Sinusoidal 14 kip 30 kip 42 kip Helical 20 kip 43 kip 59 kip Software Package 3 Sliding Sinusoidal 11 kip 21 kip 29 kip Helical 21 kip 38 kip 53 kip Rotating Sinusoidal 11 kip 21 kip 29 kip Helical 21 kip 38 kip 53 kip Buckling Test Results Sliding Sinusoidal 3 kip 5 kip 6 kip Helical 15 kip 28 kip 38 kip Rotating Sinusoidal 3 kip 5 kip 6 kip Helical 15 kip 28 kip 38 kip

10 10 SPE Semi-Empirical Buckling Model Based on the modeling conducted in this investigation, the Dawson-Paslay buckling model (Dawson and Paslay, 1984) and other buckling models, including previous work by numerous authors, including those referenced in works by Timoshenko (1955), R. Mitchell (1988,1999, 2006, 2008), G. Gao and S. Miska, (1996, 2008), S. Miska (1995,1996), J.C. Cunha (2003), Kuru (1999),and S. Menand (2008), to name a few, have helped in furthering the development of models that predict drill string buckling behavior, particularly in helically buckled pipe. Work by Mitchell (2000) considers the effects of drill pipe sag on sinusoidal buckling. But, based on modeled well data and full-scale buckling tests, these models are often unable to accurately predict the initial onset of buckling, and its effects. Static buckling tests in actual well conditions by Weltzin (2008) verifies that buckling occurs at loads below previously predicted values, and that sinusoidal buckling behavior appears to play a dominant role, with very little helical buckling present even in buckling lock-up conditions. These models may not factor in all the conditions present in a real well. Often, information such as a measurement of drill pipe straightness, down hole measurements of cased and open hole dimensions and conditions, and precise wellbore trajectories, just aren t available for running torque, drag, and buckling models. Also, predicting the extent of the variation in these factors in the planning stages prior to drilling a well is often difficult. Therefore, an empirical method of predicting the additional buckling related contact force, based on actual full-scale tests and then substantiated by numerous back-models of actual wells should provide more accurate buckling predictions than other theoretically based models. Thus, a Semi-Empircal Buckling Model was created. This model is largely based on existing buckling equations found in the literature, including relations developed by Dawson and Paslay and others listed above. This Semi-Empirical Model makes several important changes to the equations based on results from the full scale buckling test program and iterative back modeling of numerous wells. The Dawson-Paslay equation relies on the radial clearance between the pipe and casing or wellbore, but makes no distinction between clearance based on the drill pipe tube radius or tool joint radius. The new model relies on a weighted average between the two radii. Also, there is a constant C SB applied to the sinusoidal buckling threshold. Based on testing and numerous back-models of actual wells, this value is normally 0.2, meaning that sinusoidal buckling appears to normally occur at approximately 20% of the value predicted by the Dawson-Paslay equation, but this value may vary from approximately 0.10 to 0.50 depending on many factors including quality of available data, analysis settings, well conditions, etc. Further testing may attempt to isolate the variables affecting this value. This new model, when calculating additional buckling-related torque and drag on rotating pipe, provides an experimentally derived distribution between how additional contact force is divided between torque and drag, represented by a constant C R. Experimentally, the value of this constant was found to be 0.37, but additional testing may find that the constant varies with friction, inclination, etc. Increasing RPM or friction may have the effect of decreasing F HB, or may increase the value of C R, although due to the scatter in the test data, quantifying this effect was difficult. Further testing is recommended to isolate and quantify this effect, if present. Although the semi-empirical buckling model presented in this report should represent a step forward in accuracy when modeling torque, drag, and whirl in horizontal and ERD wells, there are assumptions that were made in the empirical model that require additional testing to be thoroughly explored and verified. There is an assumed effect of friction on whirl that appears to generally agree with back-modeled well data, but the effect of friction factor in calculating the change of direction of the friction force vector has not been verified. Further testing in a low friction environment with either lubricated water based mud or oil based mud would be required to verify the model. Also, all of the tests were performed using a horizontal wellbore. There is an assumed effect of inclination on buckling loads based on existing buckling models that appears to correlate well with back-modeled well data, but the effect has not been evaluated in full-scale testing. Further testing would be required to verify the effect of inclination on buckling loads. The semi-empirical buckling model is presented in equations 1 to 15 below. Graphs showing comparisons between the torque and drag measured in the buckling tests and the values predicted by the Semi-Empirical Buckling Model are shown in Figures Modified Dawson-Paslay Critical Buckling Load: (1)

11 SPE Euler Based Critical Buckling Load: (2) Sinusoidal Deflection Coefficient: Equivalent Weight: sin sin (3) (4) Effective Diameter: Effective Radial Clearance: 2 2 Sinusoidal Buckling Load: (Whichever is greater) or Helical Buckling Load: Additional Side Load Caused by Sinusoidal Buckling: Additional Side Load Caused by Helical Buckling: (5) (6) (7) (8) (9) NOTE: The initial torque or drag is calculated based upon the relative velocity of the drill pipe to obtain a vector direction for the initial friction vector (α) to determine the division of friction into torque and drag. Note that when applying load, V A can be very small, but cannot be zero. In practicality, this is always the case, as applying load to the pipe results in movement of the pipe. (10) tan (11) Additional Drag Due to Buckling: 1 (12) Additional Torque Due to Buckling: (divide by 12 for ft-lbs) (13)

12 12 SPE The ratio R B is used to determine the radius for calculating torque, because when buckled, approximately half the torque is generated through contact with the drill pipe tube and not the tool joint. The rotating friction factor is also broken up into separate friction factors for the tool joint (or protector) and the drill pipe. Division of Additional Buckling Side Load Between Torque and Drag: (14) R TD represents the fraction of additional side load that goes into torque, so R TD is zero for sliding without rotation, and one if rotating without sliding. Buckling Transition Ratio: (15) A value of zero represents completely unbuckled pipe and a value of one represents fully buckled pipe. Abbreviations: W SB Added contact force due to buckling prior to F CR (lbs / joint) W HB Added contact force due to buckling above F CR (lbs / joint) W B Added contact force due to buckling (lbs / joint) W E Equivalent weight of the drill pipe (lbs/in) W F Buoyed weight of the drill pipe (lbs/in) L Length of joint of drill pipe (in/joint) L TJ Total length of tool joint or stabilizers on each joint of drill pipe (in/joint) D C Inside diameter of casing or wellbore (in) D DP Outside diameter of drill pipe tube (in) D TJ Outside diameter of drill pipe tool joint or stabilizer (in) D E Equivalent outside diameter of drill pipe+tool joint (in) r DP radial clearance between casing and drill pipe body OD (in) r TJ radial clearance between casing and drill pipe tool joint or stabilizer maximum OD (in) r e effective radial clearance (in) θ Wellbore inclination (rad) θ Wellbore inclination change (rad/length) β Wellbore azimuth (rad) β Wellbore azimuth change (rad/length) F Axial compressive load in the drill pipe (lb) F CR Dawson-Paslay Buckling Threshold (lb) (based on OD of drill pipe) F SB Sinusoidal Buckling Threshold (lb) F HB Helical Buckling Threshold (lb) μ S Sliding Friction Factor μ R Rotating Friction Factor, can be broken up into: μ RTJ Rotating friction factor of the tool joint or torque reduction device. μ RDP Rotating friction factor of the drill pipe tube. V R Rotational Speed of the Drill Pipe (in/min) V A Axial Speed of Drill Pipe (in/min) E Young s Modulus of Drill Pipe (lbs/in 2 ) I Moment of Inertia (in 4 ) α Direction of velocity vector of drill pipe (rad) φ Sinusoidal deflection coefficient (dimensionless) D Additional drag due to buckling (lbs/jt) T Additional torque due to buckling (ft-lbs) C SB Empirical Correlation Coefficient for sinusoidal buckling. Default = 0.20, range from 0.1 to 0.5 C HB Empirical Correlation Coefficient for helical buckling Default = 2, Can range from 2 to 4, Mitchell (2006). C R Torque-Drag ratio constant Default = 0.37 R TD Torque-Drag ratio (dimensionless) Buckling Transition Ratio (dimensionless) R B

13 SPE Comparison Between Full Scale Buckling Test Results and Semi-Empirical Buckling Model Figures 13 through 16 below show the measured buckling data along with the values predicted by the Semi-Empirical buckling model. Figure 13. Comparison of calculated and measured drag while buckling during sliding. Figure 14. Comparison of measured torque and drag and predicted values using the Semi-Empirical Buckling model during rotating buckling tests on 2 7/8 inch drill pipe.

14 14 SPE Figure 15. Comparison of measured torque and drag and predicted values using the Semi-Empirical Buckling model during rotating buckling tests on 3 1/2 inch drill pipe. Figure 16. Comparison of measured torque and drag and predicted values using the Semi-Empirical Buckling model during rotating buckling tests on 4 inch drill pipe.

15 SPE Implications for a Typical Horizontal Well In a typical horizontal well, Figures 17 and 18 illustrate the differences in contact force and compressive load and drag caused by buckling between current buckling models and the new Semi-Empirical Model. In the example well below in Figure 17, there is no additional contact force due to buckling until drag causes compressive loads in the drill pipe to increase beyond the buckling threshold. In the new Semi-Empirical Model, contact force due to buckling begins at a much lower load than previous models. This earlier increase in contact force, even though low at first, results in a progressively larger increase in compressive loading and therefore buckling problems likely occur earlier and more severely than previously thought. This also means that, when drilling ahead at high WOB, buckling can occur lower in the well, where whirl and vibration can cause problems with stick-slip and reduced bit performance, ROP, and BHA life. Further, the result is that hole enlargement can have a more detrimental effect than previously thought. To match actual torque and drag results with previous buckling models often required artificially higher than normal friction factors, and the comparative illustrations below show why this would be necessary. The artificially higher friction factors would compensate for the previous models calculating lower contact force than was actually present within the horizontal wellbore. For a model to be accurate, given consistent parameters, the friction factors should remain essentially constant regardless of the direction of the pipe. Figrure 17. Typical horizontal well, showing contact loads and compression in the drill pipe through the horizontal section. Notice that the buckled zone would be limited to higher in the well. Figrure 18. Typical horizontal well with new semi-empirically based model, showing contact loads and compression in the drill pipe through the horizontal section. Notice that the buckled zone would cover more of the horizontal section, but much of this area would be have relatively low buckling contact force loads.

16 16 SPE Case Histories: Correlation of the Semi-Empirical Buckling Model to Actual Well Data The case histories presented here were chosen to represent similar wells from the same field, using the same rig, but each with different outcomes that demonstrate the spectrum of buckling problems and their prediction. The first case represents a well in which there was severe buckling present when drilling, and when running into the hole. The second case represents a well in which there was a definitive loss of weight, down to the block weight of approximately 50,000 lbs while running into the hole, but no problems drilling. The third case represents a well in which there were no significant problems associated with buckling, with no complete loss of weight while running into the hole, and no problems associated with buckling while drilling. This represents only a small fraction of the wells evaluated in correlating the Semi-Empirical Buckling Model, but these cases were chosen as similar wells, with high quality data available, with varying levels of buckling related effects. Case History 1: Buckling and Whirl While Drilling RIH: 13,200ft MD Drilling: 16,000ft MD Figure 19. Graphic showing the well trajectory and buckling within the string of Case History 2 while RIH and while drilling. Yellow zones represent sinusoidal buckling, and red zones represent helical buckling. Notice that there is a small but definite area of helical buckling, in the larger open hole zone where the drill string failure occurred. Summary This well is a 6,000 ft TVD, 8,000 ft VS well that was drilled in Alaska, with a 7 inch casing string was set at approximately 8,500 ft MD. While drilling the 6 1/8 inch section using 4 inch drill pipe, at approximately 16,000 ft MD, there was a drill string failure at 9,000ft MD, likely caused by drill string bending fatigue. The well had to be sidetracked around the fish. There were indications of an enlarged hole, to approximately 11 inches in diameter, just outside of the 7 inch casing shoe at the time of the drill string failure. The side track did not have the same hole enlargement, and there were no additional drill string failures. More than 100 joints of pipe had to be laid down due to excessive wear, with the most severe pipe wear located from 10,000 to 14,500 ft with the bit at 16,000 ft MD. There was an also high torque and high levels of stick-slip measured, with torque rising up to 17,000 ft-lbs. While running into the hole, loss of weight occurred at approximately 12,800 ft MD Analysis The as-drilled data was entered into the Semi-Empirical Buckling Model, as well as several other soft string and stiff string based existing standard buckling models. The friction factors were adjusted to match pick-up weight so that friction could be determined at a time when buckling was not a factor. Then, the analysis was run while drilling ahead and when running into the hole. The results show that when drilling ahead at 16,000 ft, the string was well into a buckled state, with severe whirl present, with very high side forces due to buckling centered at approximately 9,000 ft as shown in Figures 20 and 21. Comparative analyses with existing buckling models with the enlarged hole area included did not accurately predict the buckling problems that occurred while drilling ahead at 16,000ft MD as shown in the side force graph in figure 20. These other other buckling models, including both soft string and stiff string models from various commercially available torque and drag software, predicted a maximum side force of approximately 1,500 lbs/joint, whereas the Semi-Empirical Model predicted side forces approaching 8,000 lbs/joint. This level of force is high enough to cause high stress in the pipe and cyclic fatigue problems after rotating for a relatively short period of time. When RIH, the current buckling model predicted loss of weight at approximately 14,100ft MD, while the Semi-Empirical Buckling Model predicted loss of weight at approximately 13,200 ft MD as shown in the hookload graph in Figure 22.

17 SPE Figures 20 and 21. Chart showing calculated side force using existing buckling models using multiple settings and software packages compared to results from the Semi-Empirical Buckling Model. Also shown is a 2-D Chart showing calculated side force using the Semi-Empirical Buckling Model. Notice the spike in side force in the heel of the well, marking the location of the parted drill string in an area of enlarged open hole. Figure 22. Chart showing actual and calculated hookload using both the existing and new Semi-Empirical Buckling Model, with the same input data for both analyses. Note that the block weight was approximately 50,000 lbs.

18 18 SPE Case History 2: Buckling Only When Running Into the Hole RIH: 18,800ft MD Drilling: 20,000ft MD Figure 23. Graphic showing the well trajectory and buckling within the string of Case History 2 while RIH and while drilling. Yellow zones represent sinusoidal buckling, and red zones represent helical buckling. Notice that although the drill string is locked up, only a very small amount of the string is in the helical buckling mode. Summary This well is a 6,000 ft TVD, 13,000 ft VS well that was drilled in Alaska, with a 7 inch casing string was set at approximately 12,500 ft MD, and a 6 1/8 inch hole that was drilled to approximately 20,000 ft MD using 4 inch drill pipe. While running into the hole, weight was lost from 17,500 to 18,500 ft MD, depending on the run. The section was drilled with an average of 150 RPM and ROP of more than 100 ft/hr. Analysis The as-drilled data was entered into the Semi-Empirical Buckling Model, with the friction factors adjusted to match pick-up weight to find the actual friction at a point where there is no buckling in the string. Then the analysis was run while drilling ahead and when running into the hole. The results show that when drilling ahead, there was not a significant issue with buckling predicted by either buckling model at WOB less than 20,000 lbs. The current buckling model did not predict buckling when RIH as shown in Figure 24. The Semi-Empirical Buckling model predicted losing all weight when running into the hole at about 18,800 ft MD. Figure 24. Chart showing actual and calculated hookload using both the existing and new Semi-Empirical Buckling Model, with the same input data for both analyses. Note that the block weight was approximately 50,000 lbs.

19 SPE Case History 3: No Buckling Issues When Drilling or Running Into the Hole RIH: 20,000ft MD Drilling: 20,000ft MD Figure 25. Graphic showing the well trajectory and buckling within the string of Case History 3 while RIH and while drilling. Yellow zones represent sinusoidal buckling. Summary This well is a 6,000 ft TVD, 9,000 ft VS well that was drilled in Alaska, with a 7 inch casing string was set at approximately 14,000 ft MD, and a 6 1/8 inch hole that was drilled to approximately 20,000 ft MD using 4 inch drill pipe. Weight was available to run into the hole to 20,000 ft without rotation. The section was drilled with an average of 150 RPM and ROP of more than 100 ft/hr without significant problems. Analysis The as-drilled data was entered into the Semi-Empirical Buckling Model, with the friction factors adjusted to match pick-up weight to find the actual friction factor with the string in tension. Then the analysis was then run when drilling ahead and when running into the hole. The results show that when drilling ahead, there was not a significant issue with buckling predicted by either buckling model at WOB less than 20,000 lbs as shown in the hookload graph in Figure 26. The models also indicate that although close to running out of weight, neither model predicted running out of weight when running into the hole to 20,000 ft MD. Notice, that sinusoidal buckling can be present without significant symptoms of buckling appearing at the surface. The extent to which sinusoidal buckling presents problems when running into the hole or while drilling depends on the extent and severity of the buckling. Figure 26. Chart showing actual and calculated hookload using both the existing and new Semi-Empirical Buckling Model, with the same input data for both analyses. Note that the block weight was approximately 50,000 lbs.

20 20 SPE Summary A new Semi-Empirical Model for buckling of pipe is presented. The model is experimentally verified with full-scale drill pipe buckling tests, and later demonstrated in a multiplicity of actual well drilling conditions. The full-scale tests examined buckling under conditions representing a variety of sliding and drilling operations. A comparison of several current industry models for buckling is made to actual buckling test results illustrating variation and limits of existing buckling models. Empirical testing of full-sized drill pipe in various sizes of pipe in casing was performed showed that buckling occurs at lower loads than predicted by current models. The testing also demonstrated that low friction non-rotating protectors on the pipe can increase the available compressive load by 20% and substantially reduce vibration and drill string whirl. The Semi- Empirical Buckling Model was incorporated into proven torque and drag software and then exercised to back model three Alaskan wells with a range of drilling conditions that presented severe buckling and whirl, buckling when running in hole, and no buckling issues; all of which were predicted accurately by the Semi-Empirical model. The new model highlights the need to monitor hole size, weight on bit, and focus on friction reduction and other buckling mitigation methods to reduce the effects of buckling when drilling in high-angle wells. Additional development work for the full scale testing and model development is described. Recommendations It is recommended that additional testing be performed to further verify the model in other operational conditions. These additional tests include the following: 1. Further testing to quantify the effect of varying friction on buckling and whirl effects such as torque, drag, and vibration. 2. Effect of various water and oil based fluids on buckling. 3. Varying the inclination, including buckling tests in a vertical wellbore. 4. Buckling tests on floated casing. 5. Buckling tests on aluminum or composite drill pipe. References Chen, Y.C., and Cheatham, J.B. 1990, Wall Contact Forces on Helically Buckled Tubulars in Inclined Wells, Trans., ASME Cunha, J.C., March 2003 Buckling of Tubulars Inside Wellbores: A review on Recent Theoretical and Experimental Works, SPE Dawson, R. and Paslay, P.R., October 1984, Drillpipe Buckling in Inclined Holes, SPE11167 Duman, O.B. et al, September 2003, Effect of Tool Joints on Contact Force and Axial Force Transfer in Horizontal Wellbores, SPE85775 Dunayevksy, V.A. and Judis, A., September 1984, Onset of Drillstring Precession in a Directional Borehole, SPE13027 Fuller, A. et al, May 2002 Improved Means of Reducing Drag in ERD Applications, SPE Gao, G. and Miska, S., March 2008, Effects of Boundary Conditions and Friction on Static Bucklign of Pipe in a Horizontal Well, SPE Gao, G. and Miska, S., September 2008, Dynamic Buckling and Snaking Motion of a Rotating Drilling Pipe in a Horizontal Well, SPE Kuru, E., March 1999, The Buckling Behavior of Pipes and Its Influence on the Axial Force Transfer in Directional Wells, SPE Lubinski, A., 1950, A Study on the Buckling of Rotary Strings, API Drilling Production Practice Mason, C. and Chen, D., February 2007, Step Changes Needed To Modernize T&D Software, SPE Menand, S. et al, September 2006, Buckling of Tubulars in Actual Field Conditions, SPE Menand, S. et al, March 2008, How Drillstring Rotation Affects Critical Buckling Load, SPE Miska, S., and Cunha, J.C., April 1995 An Analysis of Helical Buckling of Tubulars Subjected to Axial and Torsional Loading in Inclined Wellbores, SPE Mitchell, R.F., September1988, New Concepts for Helical Buckling, SPE Mitchell, R.F., March 1997, Effects of Well Deviation on Helical Buckling, SPE Mitchell, R.F., December 1999, Buckling Criterion for Constant Curvature Wellbores, SPE Mitchell, R.F., February 2000, Lateral Buckling of Pipe with Connectors in Horizontal Wells, SPE Mitchell, R.F., September 2006, Tubing Buckling State of the Art, SPE Mitchell, R.F., and Miska, S., March 2004, Helical Buckling of Pipe With Connectors and Torque, SPE Mitchell, R.F., October 2005, Tubing Buckling-The Rest of the Story, SPE Moore, N.B. et al, May 1996, Reduction of Drill String Torque and Casing Wear in Extended Reach Well Using Non-Rotating Drill Pipe Protectors, SPE Quigley, M.S. et al, March 1990, A Full Scale Wellbore Friction Simulator, SPE Samuel, R. February 2010, Friction Factors: What are They for Torque, Drag, Vibration, Bottom Hole Assembly and Transient, SPE Timoshenko, S. 1955, Strength of Materials, Krieger Pub Co; 3 rd Edition, 1983 Timoshenko, S. 1961, Theory of Elastic Stability, Dover Publications; 2 nd Edition, 2009 Weltzin, T., August 2008, Measuring Drill Pipe Buckling Using Gyro Challenges Existing Theories, SPE