Schlumberger Sedco Forex Engineering Department Author: M. Andrea Reviewed by: Ref.: Page: 1 of 23 Engineering Recommendations Issued: Approved by: Revision: 00 Drill String Design Recommendations Summary This document provides the principals utilized for drill string design in the oil well drilling industry. These specifications can be used whenever designing a drill string, with agreement from the Regional Technical/Operations Managers This uncontrolled document has been issued using Microsoft WORD 7.0 for Windows 95. Copies are available from Drilling Engineering in Montrouge. 00 Revision Number First Issue Description of amendments / page changes/comments 20/04/98 Date dd/mm/yy ENG- DRILL STRING DESIGN Revision: 00 Issued: Page: 2 of 23 Table of Contents 1. Purpose ............................................................................................................................................. 3 2. Scope ................................................................................................................................................. 3 3. Responsibility.................................................................................................................................... 3 4. References......................................................................................................................................... 3 5. Distribution, filing and storage of this document............................................................................. 3 6. Abbreviations and Definitions used.................................................................................................. 3 6.1. Abbreviations............................................................................................................................. 3 6.2. Definitions ................................................................................................................................. 4 7. Drill Pipe Properties......................................................................................................................... 4 7.1 Drill Pipe Grade.......................................................................................................................... 4 7.2 Drill Pipe Class........................................................................................................................... 4 7.3 Tool Joints .................................................................................................................................. 4 7.4 Thread Form ............................................................................................................................... 5 8. Drill Collars ...................................................................................................................................... 5 8.1 Drill Collar Selection .................................................................................................................. 5 8.2 Size Criteria................................................................................................................................ 6 8.3 Drill Collar Connections ............................................................................................................. 7 9. Allowable Weight on Bit .................................................................................................................. 8 9.1. Discussion Vertical Holes........................................................................................................... 8 9.2. Discussion Inclined Holes .......................................................................................................... 9 9.3 Vertical Hole Calculation Procedure.......................................................................................... 10 9.4 Inclined Hole Calculation Procedure ........................................................................................ 11 9.5 Weight of BHA Required ......................................................................................................... 12 10. Tension.......................................................................................................................................... 12 10.1 Static Load.............................................................................................................................. 12 10.2 Margin of Over Pull ................................................................................................................ 12 11.Burst............................................................................................................................................... 13 11.1 Pipe Burst Calculation............................................................................................................. 14 12. Collapse......................................................................................................................................... 14 12.1 Drill pipe collapse ................................................................................................................... 14 12.2 Effect of tensile load on collapse.............................................................................................. 14 12.3 Slip crushing........................................................................................................................... 16 13. Pipe Torsion.................................................................................................................................. 17 13.1 Torsion Only........................................................................................................................... 17 13.2 Torsion and Tension ............................................................................................................... 17 14. Fatigue .......................................................................................................................................... 18 14.1 Limits ..................................................................................................................................... 18 14.2 Fraction of Drill Pipe Life Expended in Dogleg....................................................................... 19 15. Tool Joint Performance ................................................................................................................ 20 15.1 Make-up and Yield Torque...................................................................................................... 20 15.2 Combined Torsion and Tension to Yield a Rotary Shouldered connection ............................... 21 16. Combination Tube and Connection Performance........................................................................ 22 17. Critical Rotary Speeds ................................................................................................................. 23 17.1 Transverse Vibration............................................................................................................... 23 17.2 Axial Vibration ....................................................................................................................... 23 17.3 Harmonic Vibrations............................................................................................................... 23 ENG- DRILL STRING DESIGN Revision: 00 1. Issued: Page: 3 of 23 Purpose These procedures shall be used whenever designing a drillstring, unless otherwise decided with the Region Technical/Operations Managers. 2. Scope The manual gives the theory, guidelines and design factors for proper drillstring design. The following design factors shall apply when designing a drillstring: Tension Margin of over pull Excess BHA weight Torsion Collapse Burst 1.1 50,000 to 100,000 lbs 1.15 1.0 (based on lesser of pipe body or connection strength) 1.1. to 1.15 1.2 The design process shall address the following items: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 3. Selection of drill collar diameter Selection of BHA connections Determination of drill collar and or HWDP length Tool joint torsional capacity check Tension design limitations Burst pressure determination Collapse pressure determination Slip crushing load Fatigue limits Combined tension and torsional load limits Responsibility The Region Technical/Operations Managers are responsible of the enforcement of this standard throughout the SF organization 4. References Engineering Standard RE-ST-516-01 issued November 1992 API specification 5D (SPEC 5D), 3 rd edition, August 1, 1992 or latest edition API specification 7 (SPEC 7), 38 th edition, April 1994, or latest edition API Recommended Practice 7G (RP 7G), 15 th edition, January 1, 1995, or latest edition 5. Distribution, filing and storage of this document In accordance with Procedure RE-PR-M&M-02, this document shall be inserted in: - MPP manual volume 4, PSS Family Number: 516 6. Abbreviations and Definitions used 6.1. Abbreviations SF: HQS : Eng: M & M: PSS: MPP: API: Sedco Forex the Headquarters of SF located in Montrouge France the Engineering Department of SF located in Montrouge. Materials & Maintenance department within R & E Property Symbolization System used within Sedco Forex. Maintenance Policies and Procedures American Petroleum Institute ENG- Issued: DRILL STRING DESIGN Revision: 00 6.2. Page: 4 of 23 Definitions Bench mark: reference mark machined on the pin and box areas adjacent to the shoulder. 7. Drill Pipe Properties 7.1 Drill Pipe Grade Each joint of drill pipe includes the tube body and the tool joint, which connects the sections of drill pipe. Drill pipe is available in several sizes and weights. The grade of drill pipe describes the minimum yield strength of the pipe. This value is important because it is used in burst, collapse, and tension calculations. Common grades are as follows: Grade Letter Designation D-55 E-75 X-95 G-105 S-135 7.2 Assumed Average Yield Strength (psi) (used for collapse) 65,000 85,000 110,000 120,000 145,000 Minimum Yield Strength (psi) 55,000 75,000 95,000 105,000 135,000 Drill Pipe Class Drill pipe is unlike most other oil-field tubulars, such as casing and tubing, because it is used in a worn condition. Casing and tubing are usually new when installed in a well. As a result, “classes” are given to drill pipe to account for wear. Therefore, drill pipe must be defined according to its nominal weight, grade, and class. The API has established guidelines for pipe classes in API Recommended Practice 7G. Although the class definitions can be extensive, they are summarized as follows: New Premium Class 2 - Class 3 7.3 - No wear and has never been used. Uniform wear and minimum wall thickness of 80%. Allows drill pipe with a minimum wall thickness of 65% with all wear on one side so long as the cross-sectional area is the same as premium class; that is to say, based on not more than 20% uniform wall reduction. Allows drill pipe with a minimum wall thickness of 55% with all wear on one side. Tool Joints Tool joints are screw-type connectors that join individual joints of drill pipe. Most tool joints, regardless of the drill pipe tube grade on which they are installed, are made of 120,000 psi yield strength material. Several types are widely used: IEU (internal-external upset) IF (internal flush) IU (internal upset) Tool joint is larger than the pipe such that the tool joint ID is less than the drill pipe. The tool joint OD is larger than the drill pipe. Generally IEU connections are the strongest available couplings. Tool joints ID is approximately the same as the pipe. The OD is upset. Tool joint ID is less than the pipe. Tool joint OD is approximately the same as the pipe. This type is often termed “slim-hole” pipe because of the reduced outer clearance. An important note about tool joints is that they are designed to be run in tension. Hardfacing, of hardbanding, tool joints has become a common practice in the drilling industry. To minimize tool joint wear while rotating on abrasive rock, a band of abrasion-resistant material is applied to the outside of the box tool joint. This material is usually sintered tungsten carbide particles in a welded metal matrix. The problem that often arises from the use of hardfaced tool joints is excessive wear on the internal diameter on the casing. ENG- Issued: DRILL STRING DESIGN Revision: 00 7.4 Page: 5 of 23 Thread Form The term “rotary shouldered connection” refers to the threads of the pin or box of drill pipe or drill collars. The threads of the pin of one joint engage with the threads of the box of another joint during make-up . The actual seal is provided by the metal contact of the shoulders of the tool joints. The engaged threads are not made to provide a seal and open channels between the threads exist, even when the joint is torqued. Besides thread form and number of threads per inch, a connection can also be distinguished by dimensional data relating to the small and large diameters of pin, box bore, length of pin and box, etc. API suggests the use of the term “number connection” (NC) to distinguish the various sizes and styles of rotary connections. The NC refers to the pitch diameter of the pin thread at gauge point when rounded to units and tenths of inches, Thus if the pitch diameter is 1.063 in, the first two figures are used, i.e. 10, to provide a description of the connection as NC10. 8. Drill Collars 8.1 Drill Collar Selection Drill collars are the predominant components of the bottom-hole assembly. Some of the functions of the drill collars are as follows: • Provide weight for the bit • Provide strength needed to run in compression • Minimize bit stability problems from vibrations, wobbling, and jumping • Minimize directional control problems by providing stiffness to the BHA Proper selection of drill collars (and BHA ) can prevent many drilling problems. Drill collars are available in many sizes and shapes, such as round, square, triangular, and spiral grooved. The most common types are round (slick) and spiral grooved. Spiral-grooved collars reduce the surface contact area between the pipe and well bore. The lower contact area reduces the probability of differential pressure sticking. Table 8.1 (below) shows the API dimensions for collars of various outer diameters. Drill Collar Number NC23-31 (tentative) NC26-35 (2 3/8 IF) NC31-41 (2 7/8 IF) NC35-47 NC38-50 (3 1/2 IF) NC44-60 NC44-60 NC44-62 NC46-62 (4IF) NC46-65 (4IF) NC46-65 (4IF) NC46-67 (4IF) NC50-70 (4 ½ IF) NC50-70 (4 ½ IF) NC50-72 (4 ½ IF) NC56-77 NC56-80 6 5/8 REG NC61-90 7 5/8 REG NC70-97 NC70-100 NC77-110 (tentative) OD, in. 3 1/8 3½ 4 1/8 4¾ 5 6 6 6¼ 6¼ 6½ 6½ 6¾ 7 7 7¼ 7¾ 8 8¼ 9 9½ 9¾ 10 11 Bore +1/16 -0, in. 1¼ 1½ 2 2 2¼ 2¼ 2 13/26 2¼ 2 13/26 2¼ 2 13/16 2¼ 2¼ 2 13/16 2 13/16 2 13/16 2 13/16 2 13/16 2 13/16 3 3 3 3 ENG- DRILL STRING DESIGN Revision: 00 8.2 Issued: Page: 6 of 23 Size Criteria Selection of drill collar diameter for a slick or pendulum assembly is based on the required effective minimum hole diameter. That is, the size of the bottom drill collar would be the limiting factor for lateral movement of the bit. Minimum effective hole dia. = Bit size + Drill collar dia. 2 For Example: Drilling a 12 ¼” hole would require 9” drill collars to result in a hole large enough to run 9 5/8” casing with 10.625” OD couplings. 10.625" hole = 12.25" Bit dia. + 9" Drill collar dia. 2 More commonly drill collar size is selected based on stresses. Components subject to bending have both tensile and compressive forces induced in them. When rotated under bending, individual metal fibers are subject to rapidly alternating tension and compression, which may induce fatigue failure. BHA’s are subject to both bending and rotation. Fatigue failures commonly occur where stresses are concentrated. Stresses are concentrated at connections and changes in pipe size. Stress concentration is restricted by ensuring that changes in bending resistance are within tolerable ranges. The bending resistance of a BHA component is dependent upon its section modulus, which is defined as follows: Z = 2 x I ÷ OD = Where π (OD 4 − ID 4 ) 32 OD Z = Section modulus, in 3 I = Second moment of area, in 4 OD = Outside diameter, inches ID = Inside diameter, inches ENG- Issued: DRILL STRING DESIGN Revision: 00 Page: 7 of 23 Generally, the change in bending resistance is expressed in terms of a bending resistance ratio (BRR), which may be calculated as follows: OD2 ID2 (OD1 4 − ID1 4 ) OD2 Z1 = BRR = Z2 (OD2 4 − ID2 4 ) OD1 The terms are illustrated at right ID2 The bending resistance ratio should be checked at changes in pipe size. BRRs are calculated using the pipe body dimensions and should generally be below 5.5 OD1 EXAMPLE: bending resistance ratios A proposed BHA consists of 9” X 3” drill collars. Is it acceptable to make this up directly to 5” X 3” HWDP? BRR = ([ 9.04 - 3.04 ] * 5.0) / ([ 5.04 - 3.04 ] * 9.0) = 6.62 which is unacceptable (greater than 5.5) Is it acceptable to make this up directly to 8” X 3” drill collars? BRR = ([ 9.04 - 3.04 ] * 8.0) / ([ 8.04 - 3.04 ] * 9.0) = 1.44 which is acceptable (less than 5.5) Is it acceptable to make the 8” collars to the 5” X 3” HWDP? BRR = ([ 8.04 - 3.04 ] * 5.0) / ([ 5.04 - 3.04 ] * 8.0) = 4.61 which is acceptable (less than 5.5) Therefore, if 9” X 3” drill collars are required on bottom, one acceptable BHA would include both 8” X 3” drill collars and 5” X 3” HWDP above them. 8.3 Drill Collar Connections The bending resistance ratio of drill collar connections is defined as the section modulus of the box (measured 4” from the end) divided by the section modulus of the pin (measured 3” from the end). The inside diameter of the box and outside diameter of the pin are determined by the type of connection; therefore, only the outside diameter of the box and inside diameter of the pin need to be measured. This is illustrated at right For any combination of connection, box OD, and pin ID, the tables given in API RP7G can be used to determine the bending resistance ratio. Experience had shown that a bending resistance ratio of 2.5 results in a balanced connection. The range of acceptable BRRs depends on the severity of the service to which the drill collars will be subjected. The following recommendations are given for guidance, but local operating experience may show closer tolerances are required. Conditions DCs < 6” OD High RPM with DCs << hole size Low RPM with DCs close to hole size Acceptable BRR Range 2.75 - 2.25 2.85 - 2.25 3.20 - 2.25 ENG- Issued: DRILL STRING DESIGN Revision: 00 Page: 8 of 23 9. Allowable Weight on Bit 9.1. Discussion Vertical Holes An important function of the bottom hole assembly (BHA) is to protect the drill pipe from buckling. In straight holes, buckling of the pipe is prevented by using a BHA of sufficient weight to ensure that the neutral point of bending is kept within the BHA. A common misconception is that the neutral point of tension and compression is relevant in BHA design. When a drillstring is run into a straight hole, the forces acting on the string are self-weight and hydrostatic pressure of the drilling fluid. This hydrostatic effect, commonly called buoyancy, results from the pressure exerted vertically on the cross-sectional area of the drillstring. For a drillstring of constant cross section, the resulting hook load can be calculated as follows: ( ) ( HL = WTstring x D − CSAstring x 0.052 x MW x D ) HL = Hookload , lbf WTstring = Weight of drillstring , lb/ ft D = Depth of well , ft CSAstring = Cross − sec tional area of drillstring wall , in 2 MW = Mud weight , ppg Buoyancy acting at the bottom of the drillstring places the lower portion of the drillstring in compression and reduces the hook load. Compression Buckling occurs only below the neutral point of bending, which is defined as the point where the average of the radial and tangential stress in the string equal the axial stress. The neutral point of bending occurs where the effective hydrostatic force equals the compressive force in the drillstring. With no WOB, this point is at the bottom of the string; therefore, the drillstring is not buckled. Equivalent mud hydrostatic force Neutral point of bending Tension Pipe stress Neutral point of tension/compression Stress conditions within the drillstring in a vertical hole are shown at right. If weight is placed on the bit, there is additional compression in the bottom of the drillstring, and the neutral point of tension and compression moves up the drillstring. The neutral point of bending also moves up the drillstring to the point where the equivalent mud hydrostatic force is again equal to the compressive force in the drillstring. The height of the neutral point of bending above the bottom of the drillstring can be calculated as follows. ENG- Issued: DRILL STRING DESIGN Revision: 00 Page: 9 of 23 ( ) Fhyd = D − H x 0.052 x MW x CSAString ( ) ( Fcomp = WOB + D x 0.052 x MW x CSAString − H − WTstring ) At the neutral point of bending Fhyd = Fcomp , and the calculation is as follows: ( H x 0,052 x MW x CSAstring = WOB + H x WTstring ( H = WOB WTstring − 0,052 x MW CSAstring ) ) H = WOB / BUOYED WTstring Where H = Height of neutral point of bending, ft Fcomp = Compressive force in drillstring, lbf WOB = Weight on bit, lbf BUOYED WTstring = Buoyed weight of drillstring , lbf ( = WTstring x 1 − 0.015 x MW ) The height of the neutral point of bending above the bottom of the string is thus the weight on bit divided by the buoyed weight per foot of the drillstring. The forces in the drillstring in this situation are shown below. To prevent the neutral point of bending from being in the drill pipe, the buoyed weight of the BHA must exceed the applied WOB. In practice, field applications commonly allow for a safety factor. It is recommended that the applied WOB should be limited to 85% of the buoyed weight of the BHA (provided the HWDP is not buckled) Compression Equivalent mud hydrostatic force Neutral point of bending Heavy-weight drill pipe is generally run as transition pipe between the drill collars and the drill pipe. Sedco Forex field experience indicates that it is not acceptable to run heavyweight drill pipe for WOB in vertical holes. 9.2. Tension Pipe stress Neutral point of tension/compression Discussion Inclined Holes WOB In inclined holes, two additional factors must be considered when calculating the maximum weight on bit that can be run without buckling the drill pipe. • Weight on bit is applied at the inclination of the well, but the weight of the BHA continues to act vertically. • To allow for the reduction in available BHA weight, the buoyed weight must be reduced by a factor equal to the cosine of the well inclination. The drillstring generally lies on the low side of the hole and obtains some lateral support from the bore hole wall. In these circumstances, pipe above the neutral point of bending buckles only when the compressive forces in the drillstring exceeds a critical load, calculated as follows: Fcrit = 1617 (OD 4 pipe ) ( ) − IDpipe4 x BF x ODpipe2 − IDpipe2 x Sin θ Dhole − ODtj ENG- DRILL STRING DESIGN Revision: 00 Issued: Page: 10 of 23 Where Fcrit = Critical buckling force, lbf OD pipe = Outside diameter of pipe, inches OD tj = Max OD of pipe, inches ID pipe = Inside diameter of pipe, inches BF = Buoyancy factor, = (1 -.015 x MW) D hole θ = Diameter hole, inches = Hole inclination, degrees The curve in Appendix 1 represents a graphical solution to the equation for critical buckling. 9.3 Vertical Hole Calculation Procedure Available weight on bit can be calculated as follows: WOBmax = 0.85 x Ldc x WTdc (1 − 0.015 x MW ) Where WOBMAX Ldc WTdc MW .85 = Available weight on bit, lb = Length of drill collars, ft = Air weight of drill collars, lb/ft = Mud weight, ppg = 85% safety factor The actual weight of drill collars in mud should be measured and recorded when going in the hole. This recorded value can then be used as the maximum allowable weight on bit, provided that the mud weight is unchanged. If the mud weight is altered, the maximum allowable weight on bit must also be altered as follows: 1 − 0.015 MWnew New WOB = Old WOB max 1 − 0.015 MWold EXAMPLE: available WOB calculations for vertical hole The following bottom hole assembly is run into a 12 ¼” vertical hole containing 13.0 ppg mud. What is the available weight on bit. 372’ of 8” x 3” drill collars with an air weight of 147 lb/ft 465’ of 5” x 3” heavy weight drill pipe with an air weight of 50 lb/ft Because the hole size does not exceed the nominal tool joint size by more than 6”, the HWDP is used for drilling weight. The weight on bit available from the BHA is WOBmax = 0.85 x Ldc x WTdc (1 − 0.015 x MW ) = .85 x 372 x 147 x (1-0.015 x 13) = 37,418 lbf What would be the available weight on bit if, while drilling, the mud weight is increased to 16.5 ppg? 1 − 0.015 MWnew New WOB = Old WOB max 1 − 0.015 MWold 1 − 0.015 x 16.5 = 37,418 1 − 0.015 x 13 = 34,987 lbf ENG- Issued: DRILL STRING DESIGN Revision: 00 Page: 11 of 23 9.4 Inclined Hole Calculation Procedure The available weight on bit is calculated as follows. 1. Calculate the available WOB provided by the drill collars. WOBdc = Ldc x WTdc (1 − 0.015 x MW ) x Cos θ Where WOBDC = Available weight provided by collars, lb Ldc = Length of drill collars, ft WTdc = Air weight of drill collars, lb/ft MW = Mud weight, ppg θ = Bottom hole inclination, degrees 2. Calculate the maximum available WOB provided by the HWDP. WOB HWDP = L HWDP x WTHWDP (1 − 0.015 x MW ) x Cos θ Where WOBHWDP = Available weight provided by HWDP, lb LHWDP = Length of HWDP, ft WTHWDP = Air weight of HWDP, lb/ft MW = Mud weight, ppg θ = Bottom hole inclination, degrees 3. Calculate the critical force to buckle the HWDP. Fcrit = 1617 (ODHWDP 4 − IDHWDP 4 ) x BF x (ODHWDP 2 − IDHWDP 2 ) x Sin θ Dhole − ODtj Where Fcrit = Critical buckling force for HWDP, lbf OD pipe = Outside diameter of pipe of HWDP, inches OD tj = Max OD of pipe, inches ID pipe = Inside diameter of pipe, inches BF D hole θ = Buoyancy factor, = (1 -.015 x MW) = Diameter hole, inches = Hole inclination, degrees 4. Calculate the critical force to buckle the drill pipe. Fcrit = 1617 (OD pipe 4 ) ( ) − ID pipe 4 x BF x OD pipe 2 − ID pipe 2 x Sin θ Dhole − ODtj Where Fcrit = Critical buckling force, lbf OD pipe = Outside diameter of pipe, inches OD tj = Max OD of pipe, inches ID pipe = Inside diameter of pipe, inches BF D hole = Buoyancy factor, = (1 -.015 x MW) = Diameter hole, inches θ = Hole inclination, degrees 5. If WOBHWP + Fdp > FHWDP, Then the maximum allowable weight on bit is given by the following: WOBMAX = WOBDC + FHWDP ENG- DRILL STRING DESIGN Revision: 00 Issued: Page: 12 of 23 If WOBHWP + Fdp < FHWDP, Then the maximum allowable weight on bit is given by the following: WOBMAX = WOBDC + WOBHWP + Fdp The maximum allowable weight on bit calculated above should be reduced by a safety factor. Generally, a safety factor of 85% is adequate. 9.5 Weight of BHA Required Weight of DC’s required is estimated from the bit specifications and formation classification. Weight on bit and rotary speed Formation Classification lb / in of diameter Soft 2270 - 6750 Medium 4500 - 9000 Hard Milled Tooth Insert 5600 - 11250 Hard Insert Bit 2250 - 9000 Hard Friction Bearing 4500 - 6750 RPM 100 - 250 40 - 100 35 - 70 35 - 70 35 - 60 10. Tension 10.1 Static Load The design of the drill string for static tension loads requires sufficient strength in the topmost joint of each size, weight, grade and classification of drill pipe to support the submerged weight of all the drill pipe plus the submerged weight of the collars, stabilizers, and bit. This load may be calculated as shown in the following equation. The bit and stabilizer weights are either neglected or are included with the drill collar weight. FTEN = [( L dp ) ] x WTdp + ( Ldc x WTdc ) BF where FTEN Ldp = submerged load hanging below this section of drill pipe, lb = length of drill pipe, ft Ldc = length of drill collars, ft WTdp = air weight of drill pipe, lb / ft WTdc = air weight of drill collars, lb / ft BF = buoyancy factor The tension strength values are based on minimum area, wall thickness and yield strength of the pipe. The yield strength as defined in API specifications is not the specific point at which permanent deformation of the material begins, but the stress at which a certain total deformation has occurred. This deformation includes all of the elastic deformation as well as some plastic (permanent) deformation. The tensile strength can be calculated from the equation. Fyield = Ym A where Fyield = minimum tensile strength, lb Ym A = specified minimum yield strength, psi = cross section area, sq. in. If the pipe is loaded to the extent shown in the API formula above it is likely that some permanent stretch will occur and difficulty may be experienced in keeping the pipe straight 10.2 Margin of Over Pull To prevent this condition a design factor of approximately 90% of the tabulated tension value is recommended. ENG- DRILL STRING DESIGN Revision: 00 Issued: Page: 13 of 23 Fdesign = Fyield x 0.9 where Fdesign = minimum tensile strength, lb F yield = minimum tensile strength, lb 0.9 = a constant relating proportional limit yield to strength The difference between the calculated load FTEN the Margin of Over Pull (M.O.P.). M . O . P . = Fdesign − and the maximum allowable tension load represents FTEN The same values expressed as a ratio may be called the Safety Factor (S. F.) S. F. = Fdesign FTEN The selection of the proper safety factor and/or margin of over pull is of critical importance and should be approached with caution. Failure to provide and adequate safety factor can result in loss or damage to the drill pipe while an overly conservative choice will result in an unnecessarily heavy and more expensive drill string. Normally the designer will desire to determine the maximum length of a specific size, grade, and inspection class of drill pipe which can be used to drill a certain well. By combining the above equations the following equation results: Ldp = Fyield x 0.9 − M . O. P. WTdp x BF − Ldc WTdc WTdp EXAMPLE: Typical drill string design based on margin of overpull Design parameters: Pipe Size 4 ½”, 16.6 lb/ft, Grade E w/ 4 ½” tool joints 6 ¼” O.D. x 3 ¼” I.D., Class 2 Depth 12,700 feet Hole Size 7 7/8 inches Mud Weight 10 lb/gal Margin of Overpull (MOP) 50,000 lb. Length of Drill collars 630 feet Weight per foot 90 lb. Ldp1 = F yield x 0.9 − M . O. P. WTdp1 x BF − Ldc WTdc WTdp1 225,771 x 0.9 − 50,000 630 x 90 − 18.37 x .847 8.37 = 9846 − 3087 = 6759 Feet Ldp1 = Ldp1 It is apparent that drill pipe of a higher strength will be required to reach 12,700 feet. Add 4 ½”, 16.60 lb/ft Grade X-95, with 4 ½” X.H. Tool Joints, 6 ¼” O.D. x 3” I.D. (18.88 lb/ft) Inspection class premium. Air weight of number 1 class drill pipe and drill collars: [( ) Total Weight = Ldp1 x WTdp1 + ( Ldc x WTdc ) ] ENG- DRILL STRING DESIGN Revision: 00 Issued: Page: 14 of 23 EXAMPLE: (continue) Typical drill string design based on margin of overpull [( ) ( )] Total Weight = 6759 x 18.37 + 630 x 90 = 124,163 + 56,700 = 180,863 lb. Determine the length of the second string of drill pipe. Ldp2 = F yield 2 x 0.9 − M . O. P. WTdp2 x BF − Ldc WTdc + Ldp1 WTdp1 WTdp2 329,542 x 0.9 − 50,000 180,863 − 18.88 x .847 18,88 = 15,420 − 9,580 = 5840 feet Ldp 2 = Ldp 2 This is more drill pipe than required to reach 12,700 feet, so the final drill string will consist of the following: Weight in Air Weight in Mud Item Feet lb. Lb. . Drill Collars 630 56,700 48,025 No. 1 Drill Pipe 4 ½” 16.6 lb, Grade E 6,759 124,163 105,166 No. 1 Drill Pipe 4 ½” 16.6 lb, Grade E 5,311 100,272 84,930 12,700 281,135 238,121 11.Burst 11.1 Pipe Burst Calculation The drill pipe internal yield pressure can be calculated as follows: Pi = 2 Ym Wt D where Pi = burst pressure, psi Ym = specified minimum yield strength, psi Wt = pipe wall thickness, in. D = outside pipe diameter, in. 12. Collapse 12.1 Drill pipe collapse Drill pipe is used for several purposes, including providing a fluid conduit for pumping drilling mud, imparting rotary motion to the drill bit, and conducting special operations such as drill stem testing and squeeze cementing. Drill stem testing (DST) causes the most severe collapse loading on the drill pipe. API specifications for collapse resistance of drill pipe is calculated assuming either plastic, transition, or plastic failure based on the pipes D/t (diameter / wall thickness ratio). The applicable equations can be found in the API RP 7G publication. 12.2 Effect of tensile load on collapse The effect of tensile load applies only to greater than transition load on normally elastic item, and to any load on plastic collapse items. The collapse resistance of drill pipe corrected for the effect of tension loading may be calculated with the following equation: ENG- Issued: DRILL STRING DESIGN Revision: 00 Page: 15 of 23 2 − Z + 4 − (3 x Z ) R= 2 Total tensile load (lbs) Z = Cross section area x Average yield strength Where R = Effective collapse resistance under tension (psi) Nominal plastic collapse resistance (psi) This equation is shown graphically below. Ellipse of Biaxial Yield Strength Tension (% of yield stress) 0 10 20 30 40 50 60 70 80 90 100 0 10 30 40 50 60 Axial Stress % of Yield 70 Tension & burst Compression Burst 80 Hoop Stress % of Yield Collapse (% of yield stress) 20 90 Tension and Collapse Compression & Collape 100 Figure 12.1 ENG- DRILL STRING DESIGN Revision: 00 Issued: Page: 16 of 23 EXAMPLE: actual collapse resistance A drill string consists of 10,000 ft of drill pipe and a length of drill collars weighing 80,000 lbs. Determine the actual collapse resistance of the bottom joint of drill pipe. Rated collapse for New, 5”, 19,5 ppf, grade G pipe is = 12,999 psi Cross section area = 5.275 sq. in. Average Tensile yield = 120,000 psi Z = 80,000 lbs / (5.275 sq. in. x 120,000) = .126 or 12.6% From figure 11.1 for biaxial loading, a tensile ratio 12.6% reduces the collapse resistance to 95%. Thus, the collapse resistance of the bottom joint of drill pipe = .95 x 12,999 psi = 12,350 psi 12.3 Slip crushing The maximum allowable tension load must be determined to prevent slip crushing. In an analysis of the slip crushing problem, Reinhold, Spini, and Vreeland, proposed an equation to calculate the relation between the hoop stress (SH) caused by the action of the slips and the tensile stress in the pipe (ST), resulting from the load on the pipe hanging in the slips. If the dimensions for the cross-sectional area of the pipe (A) and the cylindrical surface are of the pipe under the slips (AS) are used, the equation can be presented as follows: 2 SH DK DK = 1 + + S T 2 LS 2 LS 1/ 2 S H = hoop stress, psi where S T = tensile stress, psi D = oustside diameter of the pipe, in. K = lateral load factor on slips, 1 / tan (y + z) y z µ LS = = = = slip taper, usually 9 0 27' 45" arctan µ coefficient of friction (≈ 0.08) length of slips, in. Slips are typically 12 or 16 in. long. The friction coefficient ranges from 0.06-0.14. Inasmuch as tool joint lubricants are usually applied to the back of rotary slips, a coefficient of friction of 0.08 should be used for most calculations. The equivalent tension load from slip crushing can be calculated as follows: SH ST TS = tension from slip crushing TL = tensile load in string SH = hoop stress, tension stress ratio from previous equation ST TS = TL x where ENG- DRILL STRING DESIGN Revision: 00 Issued: Page: 17 of 23 EXAMPLE: Slip crushing calculation A 4 ½” OD drill string has a hanging weight of 192,00 lbs. Determine the equivalent tension due to slip crushing force on the drill string. 1/ 2 SH ST K 2 DK DK = 1 + + 2 LS 2 LS 1 = 0 tan (9 27' 45" + arctan 0.08) = 4.00 2 SH 4.5 x 4.0 4.5 x 4.0 = 1 + + ST 2 x 16 2 x 16 = (2.17159)1/ 2 1/ 2 = 1.4736 S TS = TL H ST TS = 192,000 lbs x 1.4736 = 282,931 lbs (Since new 4 1/ 2", grade G, 16.6 ppf, Drill pipe has a tensile load rating of 462,781 lbs the pipe will not yield.) 13. Pipe Torsion 13.1 Torsion Only Drill pipe torsional yield strength when subject to pure torsion is given by the following: 0.096167 x J x Ym D Q = minimul torsional yield strength, ft - lb π J = polar moment of inertia, D4 − d 4 32 D = Pipe OD, inches d = Pipe ID, inches Ym = minimum unit yield strength, psi Q= where ( ) 13.2 Torsion and Tension When drill pipe is subject to both torsion and tension, as is the case during drilling operations, the minimum torsional yield strength under tension is given as follows 0.096167 J P2 Ym2 − 2 D A Qt = minimul torsional yield strength under tension, ft - lb π J = polar moment of inertia, D4 − d 4 32 D = Pipe OD, inches d = Pipe ID, inches Ym = minimum unit yield strength, psi P = total load in tension, lbs Qt = ( where A = cross - sectional area, in2 ) ENG- DRILL STRING DESIGN Revision: 00 Issued: Page: 18 of 23 EXAMPLE: Torsion and tension A new string of 5”, 19.5 ppf, grade G, drill pipe with a hook load of 250,000 lb is stuck. What is the maximum torque which can be applied to the pipe (neglecting connection strength in this example) if 100,000 lbs of over pull is applied ( ) π 4 5 − 4.276 = 28.53 inches4 32 D = Pipe OD, inches d = Pipe ID, inches J = polar moment of inertia, A = cross - sectional area, in2 = 5.27 in2 0.096167 x 28.5383 350,0002 105,0002 − 5 . 2 527 = 44,640 ft - lbs Q= 14. Fatigue 14.1 Limits The most common type of drill pipe failure is fatigue wear. It generally occurs in dog legs where the pipe goes through cyclic bending stresses. These stresses occur because the outer wall of the pipe in a dog leg is stretched and creates a greater tension load. 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 dog legs 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 consideration can be calculate with the following equations: C= 432,000 σ b tanh K L K= π E DKL T EI C = maximum permisible dogleg severity, O /100 ft E = Young' s modulus, psi = 30 X 10 6 psi for steel 10.5 X 10 6 psi for aluminium D drill pipe outer diameter, in. L half the distance between toll joints, 180 in. for Range 2 pipe, in. T tension below the dog leg, lb σ b maximum permissible bending stress, psi π I = drill pipe moment of inertia, ( D4 − d 4 ) 64 The maximum permissible bending stress, σ b , is calculated from the buoyant tensile stress, σ t (psi), in = = = = = the dogleg with the following equations: ENG- DRILL STRING DESIGN Revision: 00 Issued: Page: 19 of 23 T A σt = where A = cross-sectional area of drill pipe body, in2 For Grade E: 10 0.6 2 σt − σ − 33500) 2 ( t 67 ( 670) This equation holds true for values of σ t up to 67,000 psi. σ b = 19500 − For Grade S-135: σt σ b = 20000 1 − 145000 This equation holds true for values of σ t up to 133,400 psi. 14.2 Fraction of Drill Pipe Life Expended in Dogleg Severe pipe damage occurs when dogleg severity is greater than the value computed for C above. The damage depends on the type of material (aluminum or steel), corrosion level, stress, and dogleg angle. Metallurgists have established S-N (stress vs bending cycles) 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: f = B N where f = fraction of life expended B = number of drill pipe revolution to drill interval N = number of revolutions to failure of joint of drill pipe It is simple to show that: B = 60 R d V where R = rotary speed , rpm d = length of dogleg interval, ft V = drilling rate ft / hr. In order to determine (N) the number of revolution to failure of the joint of drill pipe we need to know the actual bending stress ( σ b ). This value can be computed as follows: σb = E D co 2 where D = outside diameter of the pipe, in. E = Young' s modulus, lb / in 2 c o = maximum pipe curvature, radians / in. The relationship between the hole curvature ( c ) and the Maximum pipe curvature ( co ) is: c o = c ( K L) where c = hole curvature, radians / in. L = one half the length of a drill pipe joint, in. ENG- DRILL STRING DESIGN Revision: 00 Issued: Page: 20 of 23 The effect of bending stress on fatigue cycles before failure is well documented, as be seen below. S-N Curve for Steel Pipe Bending stress ( x 1,000) 60 50 40 30 20 10 0 10 100 1000 10000 Revolutions to failure ( x 1,000) In the presence for tension, however, the fatigue effect of bending becomes more severe. To make the proper allowances for this , the actual bending stress, ( σ b ), must be multiplied by a correction factor, τ, as follows: τ= T T - σt where T = tensile strength of the pipe The vertical axis of the S-N curve should be entered with the product of τ and σ b , or τ σ b . Determine the number of cycles, N, to failure. Enter N into the first equation to determine the fraction of the pipe life expended in drilling the section. 15. Tool Joint Performance 15.1 Make-up and Yield Torque The make up torque of a rotary shouldered connection is calculated by using the Farr’s formula API 7G: T= SA P R f + t + Rs f 12 2π Cos ϑ where T S A P Rs Rt = = = = = = Make up torque (ft / lbs) Stress in the considered area A (psi) The weakest critical area (square inches) Laed of thread (inches) Average mean radius of thread (inches) Mean radius of shoulder (inches) Rt is determined Lt / 2 . For API connections Lt is calculated as the total pin length minus the box counterbore depth, specified as in API Spec. 7. f = Coefficent of friction on mating surfaces (thread or shoulder) ϑ = 1 / 2 included angle of thread As the use of the formula is complicated, it has been rewritten under a simplified form with precalculated parameters. ENG- Issued: DRILL STRING DESIGN Revision: 00 Page: 21 of 23 T= [ SA X + 0.02 ( OD + Q) 12 ] where A = The smaller of A pin or A box π M − ID2 4 π Abox = OD2 − B 4 ID = Inside diameter (inches) OD = Oustside diameter (inches Apin = ( ) ( ) For the standard connections in use within the company the values of X, M, B, and Q are given in the following table. X 0.1753 0.2022 0.2381 0.2573 0.2885 0.3228 0.3660 Type of Connection NC 31 ( 2 7/8 IF) NC 38 (3 ½ IF) NC 46 (4 IF) NC 50 ( 4 ½ IF) 6 5/8 Regular 7 5/8 Regular 8 5/8 Regular M 9.133 13.30 19.94 23.82 31.04 42.48 55.80 B 11.496 16.124 23.460 27.560 36.000 49.000 63.250 Q 3.4531 4.0780 4.9060 5.3125 6.0625 7.0940 8.0470 Values of stress (S) to be taken for: Make up Torque Calculation S= 72,000 psi 62,500 (1) 62,500 (1) Tool joint of drill pipes Drill collar (OD < 7”) Drill collar (OD> 7”) Maximum allowable Torque Calculation S = 120,000 psi (2) 110,000 (2) 100,000 (2) (1) API recommendation (RP7G) (2) Minimum yield strength of material, specified by API (Spec. 7) EXAMPLE: Tool joint Performance A new string of 5”, 19.5 ppf, grade G, drill pipe with NC 50 connections, tool joint OD = 6 ½” , tool joint ID = 3 ¼” π 2382 . 2 − 325 . 2 = 10.41 inches2 4 π 65 . 2 − 27.562 = 11.54 inches2 = 4 A pin = ( ) A box ( ) So, A = 10.41 in2 S x 10.41 T = 0.2573 + 0.02 65 . + 53125 . = S x 0.43 12 Make - up Torque = 72,000 x .43 = 30,960 ft - lb Maximum Allowable Torque = 120,000 x .43 = 52,000 ft - lb [ ( )] 15.2 Combined Torsion and Tension to Yield a Rotary Shouldered connection The following figure 14.2.1 shows the limits for combined torsion and tension for a rotary shouldered connection. The loads considered in this simplified approach are torsion and tension. Bending and internal pressure are not included, nor is the contribution of shear stress due to torsion. A design factor ENG- Issued: DRILL STRING DESIGN Revision: 00 Page: 22 of 23 of 1.1 should be used to provided some safety margin. This safety margin may not be sufficient for cases involving severe bending or elevated temperature. The failure criteria is either torsional yield or shoulder separation. The end points for the limits are defined by five equations: Ym P1 = Ap 11 . Ym P Rt f T1 = + + Rs f Ab x . x 12 11 2π Cos θ Ym P Rt f T2 = + + Rs f Ap x . x 12 11 2π Cos θ Ym P Rt f T3 = + Ap x . x 12 11 2π Cos θ Ym Ap Ab T4 = . x 12 Ap + Ab 11 P Rt f + + Rs f 2 Cos π θ Depending on the connection geometry, T3 may be greater or smaller than T4. The same is true for T1 and T2. T4 T3 Box Yield rS lde Recommended Zone of Operation Sh ou eld epa Yi rat Pin ion Applied Tension P1 T1 T2 0 0 Applied Torsion The line (0,0) to (T4, P1) represents shoulder separation for low make-up torque. The line (T2, 0) to (T3, P1) represents pin yield under the combination of torque and tension. The line (T1, 0) to (T1, P1) represents box yield due to torsion. The horizontal line from P1 represents maximum tension load on the pin. Figure 15.2.1 16. Combination Tube and Connection Performance Unless we have inadvertently reduced the tool joint tensile capacity by excessive make-up, the tensile capacity or combined tension-torsion capacity of the string will probably be limited by the tensile capacity of the drill pipe tubes. Curves of combined load capacity for tool joints and tubes can be used to estimate the tensile and combined tension / torsion load capacity for the string as a whole. This is easily done by superimposing the combined load curve for the appropriate tube onto the combined load chart for the tool joint. An example is shown in Figure 16.1 for 5 inch 19 ppf, grade S-135 tube with a 3 ¼” ID NC-50 tool joint. ENG- Issued: DRILL STRING DESIGN Revision: 00 Page: 23 of 23 Drillstring combined tension-torsion load capcacity superimposed over the load capacity of tool joint 1,200,000 A B 1,000,000 800,000 600,000 D 400,000 200,000 E 0 0 10,000 20,000 G 30,000 Torsion (ft-lb) 40,000 C 50,000 60,000 Figure 16. 1 The area above and to the right of line ABC represents all the conditions of combined external (string) tension that would yield the tool joint pin. Point D is the tensile capacity of 5”, 19.50 ppf, grade S premium class tube in the absence of applied torsion on the tube. Point E is the tube’s load capacity in torsion with no tension. Line DE is the combined load capacity of the tube under simultaneous tension and torsion. Tube weakness in pure tension and tool joint weakness in pure torsion are typical for common tube / tool joint combinations. Point G is the absolute limit of make-up torque without reducing the pin neck’s ability to carry external tension to less than the tensile capacity of the tube. 17. Critical Rotary Speeds 17.1 Transverse Vibration The approximate critical rotary speeds which induce nodal (transverse) vibration can be calculated using the following shown below. 476000 D2 + d 2 2 L Where L = length of one pipe, inches D = Outside diameter of pipe , inches d = inside diameter of pipe, inches Critical RPM = 17.2 Axial Vibration The approximate critical rotary speeds which induce pendulum or spring (axial) vibration can be calculated using the following shown below. 258000 L ( ft ) Where L(ft) = Total length of string, feet Critical RPM = 17.3 Harmonic Vibrations Secondary and higher harmonic vibrations will occur at 4, 9, 16, 25, 36, … etc. time the speed in the above equation. Vibrations of spring pendulum type are probably less significant than nodal type. Each higher harmonic of the spring pendulum type vibration is also less significant. Care should be taken to avoid operating under these conditions which would be the critical speed for both types of vibration because the combination would be particularly bad.