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Tiêu đề Recommended Practice for Drill Stem Design and Operating Limits
Trường học American Petroleum Institute
Chuyên ngành Petroleum Engineering
Thể loại Recommended practice
Năm xuất bản 1998
Thành phố Washington, D.C.
Định dạng
Số trang 204
Dung lượng 2,12 MB

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Cấu trúc

  • 1.1 Coverage (11)
  • 1.2 Section Coverage (11)
  • 7.1 Design Parameters (56)
  • 7.2 Special Design Parameters (56)
  • 7.3 Supplemental Drill Stem Members (56)
  • 7.4 Tension Loading (56)
  • 7.5 Collapse Due to External Fluid Pressure (60)
  • 7.6 Internal Pressure (61)
  • 7.7 Torsional Strength (61)
  • 7.8 Example Calculation of a Typical Drill String Design—Based on (61)
  • 7.9 Drill Pipe Bending Resulting From Tonging Operations (62)
  • 8.1 Fatigue Damage (63)
  • 8.2 Remedial Action to Reduce Fatigue (64)
  • 8.3 Estimation of Cumulative Fatigue Damage (68)
  • 8.4 Identification of Fatigued Joints (68)
  • 8.5 Wear of Tool Joints and Drill Pipe (68)
  • 8.6 Heat Checking of Tool Joints (69)
  • 10.1 Corrosion (72)
  • 10.2 Sulfide Stress Cracking (74)
  • 10.3 Drilling Fluids Containing Oil (75)
  • 11.1 Compressive Service Applications (77)
  • 11.2 Drill Pipe Buckling in Straight, Inclined Well Bores (77)
  • 11.3 Critical Buckling Force for Curved Boreholes (88)
  • 11.4 Bending Stresses on Compressively Loaded Drill Pipe in Curved Boreholes .79 (89)
  • 11.5 Fatigue Limits for API Drill Pipe (106)
  • 11.6 Estimating Cumulative Fatigue Damage (108)
  • 11.7 Bending Stresses on Buckled Drill Pipe (111)
  • 12.1 Severe Downhole Vibration (111)
  • 12.2 Transition from Drill Pipe to Drill Collars (118)
  • 12.3 Pulling on Stuck Pipe (118)
  • 12.4 Jarring (119)
  • 12.5 Torque in Washover Operations (119)
  • 12.6 Allowable Hookload and Torque Combinations (119)
  • 12.7 Biaxial Loading of Drill Pipe (120)
  • 12.8 Formulas and Physical Constants (120)
  • 12.9 Transition from Elastic to Plastic Collapse (120)
  • 12.10 Effect of Tensile Load on Collapse Resistance (120)
  • 12.11 Example Calculation of Biaxial Loading (120)
  • 13.1 Drill String Marking and Identification (179)
  • 13.2 Inspection Standards—Drill Pipe and Tubing Work Strings (0)
  • 13.3 Tool Joints (0)
  • 13.4 Drill Collar Inspection Procedure (0)
  • 13.5 Drill Collar Handling Systems (0)
  • 13.6 Kellys (0)
  • 13.7 Recut Connections (0)
  • 13.8 Pin Stress Relief Grooves for Rental Tools and Other Short Term (0)
  • 14.1 Drill Stem Special Processes (137)
  • 14.2 Connection Break-In (137)
  • Class 2 Used) Drill Pipe (0)
  • Class 2 Used) Tubing Work Strings (0)

Nội dung

13 10 Recommended Minimum OD and Make-up Torque of Weld-on Type Tool Joints Based on Torsional Strength of Box and Drill Pipe.. R ECOMMENDED P RACTICE FOR D RILL S TEM D ESIGN AND O PERA

Coverage

This practice emphasizes the importance of selecting drill string components while also addressing factors such as hole angle control, drilling fluids, weight, rotary speed, and various operational procedures.

Section Coverage

Sections 4 to 7 outline the procedures for selecting drill string members, while Sections 8 to 12 and 15 discuss operating limitations that may affect the drill string's normal capabilities Section 13 presents a classification system for used drill pipe and tubing work strings, along with identification and inspection procedures for other drill string components Additionally, Section 14 addresses welding on downhole tools, and Section 16 introduces a classification system for rock bits.

RP 5C1 Care and Use of Casing and Tubing

Bull 5C3 Bulletin on Formulas and Calculations for

Casing, Tubing, Drill Pipe, and Line Pipe Properties

Spec 7 Specification for Rotary Drill Stem Ele- ments

RP 7A1 Recommended Practice for Testing of

Thread Compounds for Rotary Shouldered Connections

RP 13B-1 Recommended Practice Standard Proce- dure for Field Testing Water-Based Drill- ing Fluids

RP 13B-2 Recommended Practice Standard Proce- dure for Field Testing Oil-Based Drilling Fluids

D3370 Standard Practices for Sampling Water

MR-01-75 Sulfide Stress Cracking Resistant Metallic

Material for Oil Field Equipment

The bending strength ratio is defined as the comparison of the section modulus of a rotary shouldered box at the pin end connection to the section modulus of the rotary shouldered pin at the last engaged thread.

3.2 bevel diameter: The outer diameter of the contact face of the rotary shouldered connection.

3.3 bit sub: A sub, usually with 2 box connections, that is used to connect the bit to the drill string.

3.4 box connection: A threaded connection on Oil Country Tubular Goods (OCTG) that has internal (female) threads.

3.5 calibration system: A documented system of gauge calibration and control.

3.6 Class 2: An API service classiịcation for used drill pipe and tubing work strings.

3.7 cold working: Plastic deformation of metal at a tem- perature low enough to insure or cause permanent strain.

3.8 corrosion: The alteration and degradation of material by its environment.

3.9 critical rotary speed: A rotary speed at which har- monic vibrations occur These vibrations may cause fatigue failures, excessive wear, or bending.

3.10 decarburization: The loss of carbon from the sur- face of a ferrous alloy as a result of heating in a medium that reacts with the carbon at the surface.

3.11 dedendum: The distance between the pitch line and root of thread.

3.12 dogleg: A term applied to a sharp change of direc- tion in a wellbore or ditch Applied also to the permanent bending of wire rope or pipe.

3.13 dogleg severity: A measure of the amount of change in the inclination and/or direction of a borehole, usu- ally expressed in degrees per 100 feet of course length.

3.14 drift: A drift is a gauge used to check minimum ID of loops, òowlines, nipples, tubing, casing, drill pipe, and drill collars.

3.15 drill collar: Thick-walled pipe or tube designed to provide stiffness and concentration of weight at the bit.

3.16 drill pipe: A length of tube, usually steel, to which

1 American Society for Testing Materials, 100 Barr Harbor Drive, West Con- shocken, Pennsylvania 19428.

3.17 drill string element: Drill pipe with tool joints attached.

3.18 failure: Improper performance of a device or equip- ment that prevents completion of its design function.

Fatigue refers to the gradual and localized permanent structural changes in a material that occurs when it is exposed to fluctuating stresses and strains This process can lead to the development of cracks or even complete fracture after a certain number of stress cycles.

3.20 fatigue failure: A failure which originates as a result of repeated or òuctuating stresses having maximum values less than the tensile strength of the material.

3.21 fatigue crack: A crack resulting from fatigue See fatigue.

3.22 forging: (1) Plastically deforming metal, usually hot, into desired shapes with compressive force, with or without dies (2) A shaped metal part formed by the forging method.

The kelly is a steel pipe, either square or hexagonal in shape, that connects the swivel to the drill string It plays a crucial role by moving through the rotary table and transmitting torque to the drill string.

The 3.24 Kelly saver sub is a protective component designed to be attached to the bottom of the kelly Its primary function is to safeguard the pin end of the kelly from wear and tear during make-up and break-out operations.

3.25 last engaged thread: The last thread on the pin engaged with the box or the box engaged with the pin.

The 3.26 lower kelly valve is a full-opening valve positioned directly beneath the kelly, featuring an outside diameter that matches the tool joint's outside diameter This valve can be closed to facilitate the removal of the kelly under pressure and is designed for stripping operations within the hole.

3.27 make-up shoulder: The sealing shoulder on a rotary shouldered connection.

The minimum make-up torque, set at 3.28, is the essential torque required to achieve a specific tensile stress in the pin or compressive stress in the box This stress level is generally adequate in various drilling conditions to avoid downhole make-up and prevent shoulder separation due to bending loads.

The minimum outer diameter (OD) for tool joints on drill pipes with rotary shouldered connections is set at 3.29 inches This minimum OD ensures that the connection maintains a specified percentage of the drill pipe tube's strength in torsion.

Oil-base drilling fluids, also known as oil muds, are specialized drilling fluids where oil serves as the continuous phase and water acts as the dispersed phase These fluids typically include caustic soda or quick lime along with an organic acid, and may also contain silicate, salt, and phosphate Oil-base drilling fluids differ from invert-emulsion drilling fluids, which are both water-in-oil emulsions, based on the water content, viscosity control methods, thixotropic properties, wall-building materials, and fluid loss characteristics.

3.31 pin end: A threaded connection on Oil Country Tubular Goods (OCTG) that has external (male) threads.

3.32 plain end: Drill pipe, tubing, or casing without threads The pipe ends may or may not be upset.

3.33 premium class: An API service classiịcation for used drill pipe and tubing work strings.

3.34 quenched and tempered: Quench hardeningẹ Hardening a ferrous alloy by austenitizing and then cooling rapidly enough so that some or all of the austenite transforms to martensite.

TemperingẹReheating a quenched-hardened or normalized ferrous alloy to a temperature below the transformation range and then cooling at any rate desired.

3.35 range: A length classiịcation for API Oil Country

3.36 rotary shouldered connection: A connection used on drill string elements which has coarse, tapered threads and sealing shoulders.

Shear strength of 3.37 refers to the stress needed to cause fracture along a cross-sectional plane, where the loading conditions involve forces that are parallel and opposite, despite being offset by a specified minimum distance It is calculated by dividing the maximum load by the original cross-sectional area of the section experiencing shear.

3.38 slip area: The slip area is contained within a distance of 48 inches along the pipe body from the juncture of the tool joint OD and the elevator shoulder.

The stress-relief feature, a modification applied to rotary shouldered connections, eliminates the unengaged threads of the pin or box This enhancement increases the flexibility of the joint and minimizes the risk of fatigue cracking in areas subjected to high stress.

3.40 swivel: Device at the top of the drill stem which per- mits simultaneous circulation and rotation.

Tensile strength, measured at 3.41, refers to the highest tensile stress a material can endure It is determined by the maximum load applied during a tension test until rupture, divided by the original cross-sectional area of the specimen.

3.42 test pressure: A pressure above working pressure

R ECOMMENDED P RACTICE FOR D RILL S TEM D ESIGN AND O PERATING L IMITS 3

3.43 thread form: The form of thread is the thread proịle in an axial plane for a length of one pitch.

3.44 tolerance: The amount of variation permitted.

The 3.45 tool joint is a robust coupling component for drill pipes, featuring coarse, tapered threads and sealing shoulders It is engineered to support the weight of the drill stem, endure the stresses of repeated assembly and disassembly, resist fatigue, accommodate additional make-up during drilling, and ensure a leak-proof seal.

The male section, known as the pin, is connected to one end of a drill pipe, while the female section, referred to as the box, is attached to the opposite end Tool joints can be either welded to the drill pipe, screwed onto it, or a combination of both methods.

3.46 upper kelly cock: A valve immediately above the kelly that can be closed to conịne pressures inside the drill string.

A 3.47 upset refers to a pipe end characterized by an increased wall thickness, which can involve either an increase in the outside diameter, a reduction in the inside diameter, or both Typically, these upsets are created through the process of hot forging the pipe end.

3.48 working gauges: Gauges used for gauging product threads.

3.49 working pressure: The pressure to which a partic- ular piece of equipment is subjected during normal opera- tions.

3.50 working temperature: The temperature to which a particular piece of equipment is subjected during normal operations.

4 Properties of Drill Pipe and Tool Joints

Design Parameters

It is intended to outline a step-by-step procedure to ensure complete consideration of factors, and to simplify calcula- tions Derivation of formulas may be reviewed in Appendix

To establish effective design criteria for drilling operations, it is essential to determine the anticipated total depth, hole size, and expected mud weight Additionally, the desired factors of safety in tension and collapse, along with the margin of overpull, must be defined Furthermore, specifications for drill collars, including length, outer diameter (OD), inner diameter (ID), and weight per foot, should be outlined, as well as the preferred sizes and inspection classes for drill pipes.

Special Design Parameters

If inspection reveals that the actual wall thickness surpasses the values listed in API tables, it is permissible to utilize elevated tensile, collapse, and internal pressure values for the design of the drill stem.

Supplemental Drill Stem Members

All supplemental drill stem components, including subs, stabilizers, and tools, must be machined to meet API specifications and undergo appropriate heat treatment.

Tension Loading

The drill string design must ensure that the topmost joint of each size, weight, grade, and classification of drill pipe possesses adequate strength to withstand static tension loads.

R ECOMMENDED P RACTICE FOR D RILL S TEM D ESIGN AND O PERATING L IMITS 47

Recom- mended Casing OD in.

Internal Pressure at Minimum Yield

Kelly Size and Type in.

Lower Pin Connection ft-lb

Through Drive Section ft-lb

All values are calculated with a safety factor of 1.0, utilizing a minimum tensile yield of 110,000 psi for quenched and tempered connections and 90,000 psi for normalized and tempered drive sections It is important to note that fully quenched and tempered drive sections exhibit higher strength values than those indicated Additionally, the shear strength is determined to be 57.7 percent of the minimum tensile yield strength.

2 Clearance between protector rubber on kelly saver sub and casing inside diameter should also be checked.

3 Tensile area calculated at root of thread 3 / 4 inch from pin shoulder.

Table 16—Contact Angle Between Kelly and Bushing for Development of Maximum Width Wear Pattern

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Maximum Wear Pattern Width (inches)

Small contact angle Wide pattern

The maximum Wear Pattern Width is determined by averaging the Wear Pattern Widths calculated from the minimum and maximum clearances and contact angles listed in Table 16, with an accuracy of within 5 percent.

Note: Drive Edge will have a wide òat pattern with small contact angle.

Figure 33—New Kelly-New Drive Assembly Figure 34—New Kelly-New Drive Assembly

When designing drill stem operations, it is essential to consider the weight of the collars, stabilizer, and bit This load can be calculated using a specific formula, as outlined in Equation 1 Depending on the circumstances, the weights of the bit and stabilizer may either be included with the drill collar weight or disregarded.

P = submerged load hanging below this section of drill pipe, lb.,

L dp = length of drill pipe, ft.,

L c = length of drill collars, ft.,

W dp = weight per foot of drill pipe assembly in air,

W c = weight per foot of drill collars in air,

Any object floating or submerged in a liquid experiences a buoyant force that equals the weight of the displaced liquid This buoyant force reduces the effective weight of the drill string, especially when using heavier muds For instance, a one-pound weight submerged in a 14 lb/gal mud would have an apparent weight of 0.786 pounds.

Tension load data is given in Tables 2, 4, 6, and 8 for the various sizes, grades and inspection classes of drill pipe.

The tension strength values, wall thickness, and yield strengths are crucial factors to consider According to API specifications, yield strength is defined not as the exact point of permanent deformation but as the stress level at which a specific total deformation occurs, encompassing both elastic and some plastic deformation When pipes are loaded to the values indicated in the tables, permanent stretching may happen, leading to challenges in maintaining the pipe's straightness To mitigate this issue, a design factor of about 90 percent of the listed tension value is often applied; however, it is advisable to consult the drill pipe supplier for a specific factor tailored to the grade of pipe being used.

P a = maximum allowable design load in tension, lb.,

P t = theoretical tension load from table, lb., 0.9 = a constant relating proportional limit to yield strength.

The difference between the calculated load P and the max- imum allowable tension load represents the Margin of Over

Table 17—Strength of Remachined Kellys 1

Kelly Size and Type in.

Remachined Kelly Size and Type in.

Lower Pin Connection Tensile Yield Torsional Yield Yield in Bending

Through Drive Section ft-lb

Lower Pin Connection ft-lb

All values are calculated with a safety factor of 1.0, relying on a minimum tensile yield of 110,000 psi for connections and 90,000 psi for the drive section Drive sections that are fully quenched and tempered will exhibit higher strength values than indicated The shear strength is determined to be 57.7 percent of the minimum tensile yield strength.

2 Tensile area calculated at root of thread 3 / 4 inch from pin shoulder.

Note: Kelly bushings are normally available for kellys in above table.

The same values expressed as a ratio may be called the

Selecting the appropriate safety factor and margin of over pull is crucial and requires careful consideration An inadequate safety factor can lead to damage or loss of the drill pipe, while an overly conservative choice may result in a heavier and more costly drill string Designers must evaluate the overall drilling conditions, including hole drag and the risk of getting stuck, as well as the acceptable level of risk for the specific well Additionally, the safety factor should account for slip crushing and dynamic loading caused by hoisting accelerations and decelerations.

Slip crushing is not a problem if slips and master bushings are maintained Inspection class also grades the pipe with regard to slip crushing.

Designers aim to establish the maximum length of a specific size, grade, and inspection class of drill pipe suitable for drilling a particular well This can be achieved by integrating Equation 1 with either Equation 2 or Equation 3, leading to the derivation of relevant equations.

For a tapered string composed of various sizes, grades, or inspection classes of drill pipe, the pipe with the lowest load capacity should be positioned just above the drill collars The maximum length of this pipe is determined as previously described The next stronger pipe is then placed in the string, with the W L term in Equations 5 or 6 replaced by the weight in air of the drill collars plus the lower string's drill pipe assembly Subsequently, the maximum length for the next stronger pipe can be calculated, with an example provided in section 7.8.

Collapse Due to External Fluid Pressure

During drill stem testing, drill pipes can experience external conditions that may lead to collapse The differential pressure necessary for collapse has been calculated for different sizes, grades, and inspection classes of drill pipe, as shown in Tables 3, 5, 7, and 9 To determine the allowable collapse pressure, these tabulated values should be divided by an appropriate safety factor.

P p = theoretical collapse pressure from tables, psi,

P ac = allowable collapse pressure, psi.

When the fluid levels inside and outside the drill pipe are equal and the density of the drilling fluid remains constant, the collapse pressure is zero at any depth, indicating no differential pressure However, if there is no fluid inside the pipe, the actual collapse pressure can be determined using a specific equation.

L = the depth at which P c acts, ft.,

W g = weight of drilling òuid, lb/gal,

W f = weight of drilling òuid, lb/cu ft.

If the fluid level inside the drill pipe is lower than outside or if the fluid densities differ, the following equation can be applied.

Y = depth to òuid inside drill pipe, ft.,

W g ' = weight of drilling òuid inside pipe, lb/gal,

R ECOMMENDED P RACTICE FOR D RILL S TEM D ESIGN AND O PERATING L IMITS 51

Internal Pressure

The drill pipe can experience a net internal pressure, which is critical to its integrity Calculated values of the differential internal pressure necessary to yield the drill pipe are provided in Tables 3, 5, 7, and 9 By applying an appropriate safety factor, one can determine the allowable net internal pressure for safe operation.

Torsional Strength

The torsional strength of drill pipe is essential for drilling operations involving deviated or deep holes, reaming, and situations where the pipe becomes stuck Detailed discussions on this topic can be found in Sections 8 and 12 Additionally, Tables 2, 4, 6, and 8 present calculated values of torsional strength for different sizes, grades, and inspection classes of drill pipe, with the foundational calculations outlined in the Appendix.

A The actual torque applied to the pipe during drilling is dif- ịcult to measure, but may be approximated by the following equation:

T = torque delivered to drill pipe, ft-lbs,

HP = horse power used to produce rotation of pipe,

Note: The torque applied to the drill string should not exceed the actual tool joint make-up torque The recommended tool joint make-up torque is shown in Table 10.

Example Calculation of a Typical Drill String Design—Based on

DRILL STRING DESIGN—BASED ON MARGIN

The design parameters for the drilling project include a depth of 12,700 feet, a hole size of 7 7/8 inches, and a mud weight of 10 lb/gal The margin of overpull (MOP) is assumed to be 50,000 lb for this calculation, while the desired safety factor in collapse is set at 1 1/8 Additionally, drill collar data is considered in the overall design.

If the length of drill collars is not known, the following for- mula may be used: where

L c = length of drill collars, feet,

Bit wm = maximum weight on bit, lb, a = hole angle from vertical, 3 degrees,

The neutral point design factor (NP) is crucial in determining the position of the neutral point in a drill collar string For instance, an NP value of 0.85 indicates that the neutral point is located 85 percent of the total length of the drill collar string, measured from the bottom This value is assumed for the purpose of calculations.

W c = weight per foot of drill collars in air, lb,

= 618 feet, closest length based on 30 foot collars,

= 630 feet or 21 drill collars. g Drill string size: weight and gradeẹ4 1 / 2 in x 16.60 lb/ft x

Grade E75, with 4 1 / 2 in., NC46 tool joints, 6 1 / 4 in OD x 3 1 / 4 in ID, Inspection Class 2.

To successfully reach a depth of 12,700 feet, a drill pipe with higher strength is essential It is recommended to use 4 1/2 in x 16.60 lb/ft Grade X-95 drill pipe, equipped with 4 1/2 in X.H tool joints and 6 1/4 in OD x 3 in ID (18.88 lb/ft) Inspection Class Premium components.

Air weight of Number 1 drill pipe and drill collars:

This is more drill pipe than required to reach 12,700 feet, so ịnal drill string will consist of the following:

Torsional Yield of 4 1 / 2 " x 16.60 lb x Grade E75 x Inspection

Collapse Pressure of 4 1 /2" x 16.60 lb x Grade E75 x Inspec- tion Class 2 = 5951 psi.

Collapse pressure of 4 1 /2" x 16.60 lb x Grade X-95 x Pre- mium Inspection Class = 8868 psi.

Pressure at bottom of drill pipe: P c = ,

This drill pipe experiences a lower collapse pressure at depths of 12,700 feet, necessitating precautions to avoid damage when running the string dry below 10,183 feet The maximum length of the drill pipe is calculated by solving Equation 8 and dividing by a safety factor of 1.125 for collapse.

Drill Pipe Bending Resulting From Tonging Operations

It is generally known that the tool joint on a length of drill ing make-up and break-out operations to prevent bending of the pipe.

The tool joint must be positioned at a maximum height above the rotary slips and pipe to effectively resist bending, while adhering to the recommended maximum make-up or break-out torque for the tool joint.

Height limitations are influenced by various factors, with key considerations including the angle of separation between the make-up and break-out tongs As illustrated in Figure 35, Case I shows the tongs positioned at 90 degrees, while Case II presents a different angle.

180 degrees. b The minimum yield strength of the pipe. c The length of the tong handle. d The maximum recommended make-up torque

H max = height of tool joint shoulder above slips, ft.,

Y m = minimum tensile yield stress of pipe, psi,

T = make-up torque applied to tool joint (P x L T ), ft-lb,

I/C = section modulus of pipeẹin 3 (see Table 18).

Constants 0.053 and 0.038 include a factor of 0.9 to reduce

Assume: 4 1 /2-in., 16.60 lb/ft, Grade E drill pipe, with

4 1 /2-in X.H 6 1 /4-in OD, 3 1 /4-in ID tool joints.

10 lb/gal Mud (pounds) Drill Collars

R ECOMMENDED P RACTICE FOR D RILL S TEM D ESIGN AND O PERATING L IMITS 53

8 Limitations Related to Hole Deviation

Fatigue Damage

Most drill pipe failures occur due to fatigue, particularly when the pipe is rotated in sections of the hole where there is a change in angle or direction, known as a dogleg The extent of fatigue damage is influenced by several factors.

8.1.1 Tensile Load in the Pipe at the Dogleg

Following is an example calculation: a Data:

1 4 1 / 2 -inch, 16.60 lb/ft, Grade E, Range 2 drill pipe (actual weight in air including tool joints, 17.8 lb/ft) 7 3 / 4 -inch OD,

2 1 / 4 -inch ID drill collars (actual weight in air 147 lb/ft).

2 15 lb/gal (112.21 lb/cu ft) mud.

7 Drill pipe length at total depth: 11,000 ft.

8 Length of drill collar string, whose buoyant weight is in excess of the weight on bit: 100 ft. b Solution:

Tensile load in the pipe at the dogleg:

Pipe Weight Nominal lbs/ft

Figure 35—Maximum Height of Tool Joint Above Slips to Prevent Bending During Tonging

8.1.2 The Severity of the Dogleg

The number of cycles experienced in the dogleg, as well as the mechanical dimensions and properties of the pipe itself.

Tension in the pipe is crucial, and a shallow dogleg in a deep hole can lead to significant challenges Rotating off bottom is not advisable, as it increases the tensile load due to the suspended drill collars.

Nicholson 2 has outlined methods for calculating forces on tool joints and the conditions that lead to fatigue damage To minimize fatigue damage, it is crucial to stay to the left of the fatigue curves, as illustrated in Figures 36 and 37 Schenck 3 and Wilson 4 have reported programs designed to plan and drill wells that effectively reduce fatigue damage, highlighting the importance of such strategies in mitigating fatigue-related issues.

The curves depicted in Figures 36, 37, and 38, along with Figures 41, 42, and 43, represent Range 2 drill pipe with joint lengths of 30 feet, which influences the shape of the curves Additionally, data regarding the fatigue of Range 3 drill pipe, measuring 45 feet, is accessible Notably, the curves in Figures 36, 37, and 38 are unaffected by the tool joint.

OD; however, the portion of the curve for which there is pipe- to-hole contact between tool joints (dashed lines on Figures

36 and 38) becomes longer when tool joint OD becomes smaller, and conversely

The advent of electronic pocket calculators makes it easy to use the following equations instead of the curves in Figures

(16) where c = maximum permissible dogleg severity (hole cur- vature), degrees per 100 feet,

L = half the distance between tool joints, inches,

Note: Equation 15 does not hold true for Range 3 14

T = buoyant weight (including tool joints) suspended below the dogleg, pounds, d b = maximum permissible bending stress, psi,

I = drill pipe moment of inertia with respect to its diameter, in 4 , calculated by Equation 17.

D = drill pipe OD, inches, d = drill pipe ID, inches.

The maximum permissible bending stress, d b , is calculated from the buoyant tensile stress, d t (psi), in the dogleg with Equations 19 and 20 below d t is calculated with Equation 18:

A = cross sectional area of drill pipe body, square inches. For Grade E: 14

Equation 19 holds true for values of d t up to 67,000 psi.

Equation 20 holds true for values of up to 133,400 psi.

The following equation may be used instead of Figure 38:

(21) in which F is the lateral force on tool joint (1000, 2000, or

3000 pounds in Figure 38), and the meaning of the other sym- bols is the same as previously.

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