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Design

As the drill string moves downhole, it is subjected to a variety of stresses, including tension, compression, vibration, torsion, friction, formation pressure and circulating fluid pressure. It is also exposed to abrasive solids and corrosive fluids.

The drill string not only must be sturdy enough to withstand this hostile environment, but it must be lightweight and manageable enough to be efficiently handled within the limits of the rig's hoisting system. At the same time, it must:

• provide weight to the bit;

• allow control over wellbore deviation; • help ensure that the hole stays "in gauge".

Drilling rates tend to increase with increasing weight on bit — although this statement is an

oversimplification, it is valid within certain limits. The drill string is the source of this applied bit weight. Drill string design depends largely on the amount of bit weight that is desirable and practical for a given situation.

Drilling engineers have long observed that there is no such thing as a perfectly straight or vertical hole. Formation characteristics, along with the rotary drilling process itself, cause wells to "drill crooked," making a certain amount of wellbore deviation inevitable. A major consideration in drill string design is to control the amount and direction of this deviation, either to stay as close to vertical as possible or to direct the well along a programmed directional or horizontal course.

Proper drill string design is also important in avoiding doglegs (abrupt changes in hole angle) and key seats (slots worn into the side of the borehole by the drill string). These conditions can lead not only to stuck pipe and possible fishing jobs, but to difficulty in running casing and even to future production problems.

Bit gauge wear, sloughing formations or heaving shales may result in a hole diameter that is considerably less than the nominal diameter of the bit. This undergauge condition can lead to such problems as stuck pipe and an inability to run casing. Selection of the right drill string tools can alleviate this condition and help produce a smooth bore, full-size, problem-free hole.

Components

The length and makeup of the drill string depends on such factors as well depth, hole size, operating parameters and directional considerations. Its major components are the kelly ( or top-drive unit ), drill pipe and bottomhole assembly ( Figure 1 ).

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Figure 1

A kelly is a square or hexagonal length of pipe that fits into a bushing in the rig's rotary table. As the rotary table turns to the right, the kelly turns with it.

The main function of a kelly is to transfer energy from the rotary table to the rest of the drill string. On modern rigs, this function is more commonly performed by a top drive unit, power swivel or power sub located directly below a conventional swivel. Of course, when a downhole mud motor is used for directional or other applications, there is normally no drill string rotation.

The longest portion of the drill string consists of connected lengths of drill pipe. The primary purposes of drill pipe are to provide length to the drill string and transmit rotational energy from the kelly to the bottomhole assembly and the drill bit. Drill pipe also serves as a conduit for the drilling fluid.

The bottomhole assembly is that portion of the drill string between the drill pipe and the drill bit. Its individual components may be arranged in any number of ways to promote drilling objectives, and can include:

• drill collars, which provide weight and stability to the drill bit, maintain tension on the drill pipe and help keep the hole on a straight course;

• heavy wall drill pipe, which serves as an intermediate-weight drill string member between the drill pipe and the much heavier drill collars, thereby reducing fatigue failures, providing additional hole stability and aiding in directional control;

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• stabilizers, which centralize the drill collars, help maintain the hole at full-gauge diameter and aid in directional control;

• jars, which can provide sharp upward or downward impact to free stuck pipe; • rotary reamers, which help maintain a full-gauge hole diameter;

• crossover subs, which join components having different types of connections. Some bottomhole assemblies may also include vibration dampeners, or shock subs which, under certain conditions, can help absorb shock loads and vibrations that might otherwise contribute to drill string failure.

A well-designed bottomhole assembly helps maximize drilling rates, produce a smooth, full-size borehole, prevent drill pipe failure, maintain directional control, avoid drilling problems, and prevent future completion and production problems.

The Kelly

The kelly is a primary link between the drilling rig's surface equipment and the bit, and is therefore a critical component of the rotary system. Although top drive systems have replaced kelly/rotary table combinations on many rigs, some knowledge of their manufacture and operation is useful.

Kellys are manufactured with either square or hexagonal cross sections ( Figure 1 ).

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Their angled surfaces, or drive flats, are designed to fit into a drive roller assembly on the kelly bushing, so that as the rotary table turns to the right, the kelly turns with it. To allow for normal right-hand rotation of the drill string, kellys have right-hand threads on their bottom connections and left-hand threads on their top connections

API Standards

The American Petroleum Institute has established manufacturing and design standards for kellys, and has included them in API RP 7G, Recommended Practice for Drill Stem Design and Operating Limits.

API kellys come in two standard lengths:

1. 40 ft overall, with a 37 ft working space; 2. 54 ft overall, with a 51 ft working space.

Performance Considerations

The ability of a kelly to turn the drill string depends on how well it fits into the kelly bushing. More specifically, it depends on the clearance between the drive flat surfaces and the rollers in the kelly bushing. For the kelly to perform properly, this clearance needs to be kept to a minimum.

Kellys most commonly wear out due to a rounding-off of the drive corners, as shown in Figure 1 (new kelly with new drive assembly) and Figure 2 (worn kelly with worn drive assembly) .

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Figure 1

This rounding is a natural wear process caused by the compressive force of the rollers on the drive flats and accelerated by rotary torque.

Figure 2

As rounding progresses, it further accelerates the wear process by increasing the clearance and the contact angle between the drive flats and the rollers.

For minimal rounding, there must be a close fit between the kelly and the roller assembly, with the rollers fitting the largest spot on the kelly flats. Manufacturing techniques and rig operating practices play important roles in determining this fit.

Both square and hexagonal kellys are manufactured either from bars with an "as-forged" drive section, or from bars with fully-machined drive sections. While forged kellys are

cheaper to manufacture, machined kellys offer the following features, which tend to result in longer useful life:

• Machined kellys, unlike forged kellys, are not subject to the metallurgical process of decarburization, or decarb. Decarburization leaves a relatively soft layer of material

(approximately V16" thick) on the drive surface that can accelerate the rounding process and increase the potential for fatigue cracks;

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• Machined kellys, because they are made to closer tolerances than forged kellys, are more likely to closely fit the roller assembly throughout their length.

A square drive section normally tolerates a greater clearance between flats and rollers than does a hexagonal drive section.

To minimize rounding, rig personnel should follow these guidelines (Brinegar, 1977): • Always use new drive-bushing roller assemblies to break in a new kelly;

• If the rollers are adjustable, adjust them to provide minimum clearance; • Frequently inspect and periodically replace drive assemblies to ensure that

clearance and contact angle between the kelly and the rollers is held to a minimum; • Lubricate drive surfaces to reduce friction and binding at the rollers, and to allow the kelly to slide freely through the kelly bushing.

Because of the high-quality steels used in manufacturing kellys, fatigue failures are not often a problem. Nevertheless, kellys should be regularly inspected for cracks and other signs of wear, particularly within the threaded connections, in the areas where the flats join the upper and lower upsets and in the center of the drive section.

The areas of highest stress concentration — and therefore the most likely locations for fatigue failure — are the areas where the drive flats join the upper and lower upsets.

In general, the stress level for a given tensile load is less in the drive section of a hexagonal kelly than in the drive section of a square kelly of comparable size. Hexagonal kellys are thus likely to last longer than square kellys before failing under a given bending load. Kellys can become crooked or bent due to improper handling. Examples of mishandling include:

• dropping the kelly;

• misaligning the kelly in the rathole exerting a side pull on the kelly; • using poor tie-down practices during rig moves;

• not using the kelly scabbard;

• using improper loading/unloading techniques.

Depending on where the bend is located, it may cause fatigue damage not only to the kelly but to the rest of the drill string, and can also result in uneven wear on the kelly bushing.

Unusual side motions or swaying of the swivel are good indicators of a crooked kelly. A good field service shop has equipment for straightening bent kellys, making this an

easily-corrected problem.

Up to a certain point, a worn kelly can be repaired either by reversing the ends, ( Figure 3 ) or by remachining it to a smaller size.

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Figure 3

Auxiliary Equipment

A kelly saver sub should always be run between the kelly and the top joint of drill pipe. This protects the kelly's lower connection threads from wear, as joints of drill pipe are continually made up and broken out. A saver sub is much less expensive and much easier to replace than the kelly itself, and it can also be equipped with a rubber protector to help keep the kelly centralized and to protect the top joint of casing against wear.

A kelly cock is a valve installed above or below the kelly, which prevents fluid from escaping through the drill string if the well should begin to flow or "kick." As an extra well control precaution, an upper kelly cock (having left-hand threads) should be installed directly above the kelly, while a lower kelly cock (having right-hand threads) should be installed below the kelly. Installing two kelly cocks ensures that at least one of them is always accessible, regardless of the kelly's position.

Automatic check valves, designed to close when the mud pumps are shut off, are also available, and can be installed below the kelly to prevent mud from spilling onto the rig floor during connections.

Dimensions and Strengths

Like other oilfield tubulars, drill pipe comes in a variety of lengths, outside diameters, weights and grades of steel. Drill pipe is also specified according to its upset (i.e., the type of end section that is provided for weld-on connections or tool joints).

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Hole size, well depth, casing and cementing requirements, subsurface pressures, circulating system and drilling mud parameters, hoisting capacity, pipe availability and contract

provisions are among the factors that influence drill pipe selection.

The American Petroleum Institute has established standards for drill pipe manufacturing practices, dimensions, strengths and performance properties. These standards appear in the following publications:

• API Spec 5D, Specification for Drill Pipe;

• API Bul 5C2, Bulletin on Performance Properties of Casing, Tubing and Drill Pipe; • API RP 7G, Recommended Practice for Drill Stem Design Operating Limits.

API-standard drill pipe is available in three length ranges: Range 1(18-22 ft), Range 2 (27-30 ft) and Range 3 (38-45 ft). Range 2 is the length most commonly used, making the "average" length of a drill pipe joint about 30 feet.

Table 1., below, lists outside diameters and nominal weights for API standard drill pipe.

Note that these diameters and weights apply only to the drill pipe tube-in drilling

operations, the engineer also must account for the weight and diameter of the tool joints and upsets. This information is available in API Spec SD and API RP 7G.

Outside diameter, inches Nominal weights, lb/ft*

2 7/8 10.40 3 1/2 9.50 13.30 15.50 4 14.00 4 1/2 13.75 16.60 20.00 5 16.25 19.50 25.60 5 1/2 21.90 24.70 6 5/8 25.20 27.70

Table 1. Diameters and nominal weights of API-standard drill pipe.

There are four standards for measuring drill pipe strength:

• torsional yield strength, a measure of the pipe's resistance to torque, or "twisting" force; • tensile yield strength, a measure of the pipe's resistance to axial tension, or "pulling" force;

• collapse resistance, a measure of the pipe's ability to withstand external pressures; • internal yield, a measure of the pipe's ability to withstand internal pressure.

The strength of a drill pipe joint depends on its dimensions and configuration, and on the grade of steel used in its manufacture. Table 2., below, lists some standard grades of steel used in drill pipe, along with their minimum yield strengths.

Steel Grade Minimum Yield, psi

E 75,000

X-95 95,000

G-105 105,000

S-135 135,000

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Table 2. Standard steel grades for drill pipe.

Upsets

"Upset" refers to the end portions of a joint of drill pipe, to which are attached its threaded connections, or tool joints. These upset areas have thicker walls than the rest of the drill pipe tube to provide for stronger welds. Drill pipe upsets can be either internal, external or internal-external ( Figure 1 ,

Figure 1

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Figure 2

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Figure 3

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Figure 5

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Figure 6

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Figure 4

• In an internal upset joint, extra wall thickness is added by decreasing the pipe's inside diameter at the upset area; the outside diameter does not change.

• In an external upset joint, extra wall thickness is added by increasing the pipe's outside diameter at the upset area; the inside diameter does not change.

• In an internal-external upset joint, extra wall thickness is added by decreasing the pipe's inside diameter and increasing its outside diameter at the upset area.

Tool Joints

Tool joints are box-pin connections with rounded threads, which are fabricated separately from the drill pipe tube and then welded on at the upset ends.

Torsional yield strength is an important consideration in tool joint design, with respect to both tool joint make up and the rotational forces encountered while drilling. Tool joint performance specifications therefore include information on torsional yield strength and on recommended makeup torque. Proper make-up torque is a function of tool joint type, size, outside diameter, inside diameter and condition.

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API RP 7G lists standards for various tool joint types used for the different drill pipe upsets, including:

· Internal flush (IF): includes NC26,* NC31, NC38, NC46 and NC50 connections; · Full hole (FH): includes NC40 connections;

· Open hole (OH);

· Slim hole (SH): includes NC26, NC31 and NC38 connections; · Slim line (SL): H-90/PAC;

· Wide open (WO): includes NC38, NC46 and NC5O connections; · "Xtra" hole (XH): includes NC46 and NC5O connections.

* "NC" designate API Numbered Connection. These API connections were developed for incorporation into the old tool joint connection types, and for design of new connections. The number size is simply the size of the pitch diameter in inches at the gauge point of the threads rounded off to the first two digits with the decimal point removed. For example, the gauge point of the pin in Figure 1 , measured 5/8" from the shoulder, is 5.616 inches giving a number size of 56.

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Table 1. , below, illustrates the differences between some of these basic tool joint types for

the case of 4 ", 16.60 lb/ft, new Grade 95 drill pipe. API RP 7G Table 1:

Properties of New Tool Joints, 4-1/2", 16.60 lb/ft, Grade 95 Drill Pipe Upset Tool Joint OD, inches ID, inches Tensile yield, lb Torsional yield, ft-lb

Recommended make-up torque, ft-lb Int.-Ext. 4 " FH 6.000 3.00 976,156 34,780 21,149 Int.-Ext. NC46 6.250 3.25 1,084,426 39,659 16,997 Int.-Ext. NC50 6.375 3.75 939,095 37,676 18,838 Int.-Ext. 4 " H90 6.000 3.25 938,984 39,021 22,616

Tool joints also vary according to the number of threads per inch (ranging between 3 and 5 threads per inch, with most connections having 4 or 5 threads per inch), the amount of taper per foot and the overall length of the box and pin.

Identification

An examination of the tool joint connections listed above, indicates that some of them are identical/ For example, the NC 26 connection applies to both Internal Flush and slim hole upsets. This is indeed the case; API RP 7G lists these interchangeable and equivalent connections.

Tool joints are identified by a series of 5 markings stenciled at the base of the pin connection:

· The first marking designates the company symbol;

· The second marking is a number from 1 to 12, indicating the month that the tool joint was welded;

· The third marking denotes the last two digits of the year in which the tool joint was welded (e.g., 86 1986);

· The fourth marking is the pipe mill code, designated as follows:

Pipe Mill Symbol

Armco A British Steel B CF&I Steel Corp C Dalmine S.p.A., Italy D Falck, Italy F

Kawasaki Steel H Nippon Steel Corp. I

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J&L Steel J

Nippon Kokan Kabushiki K Lone Star L

Mannesmannrohren-Werke M U.S. Steel N

Ohio Steel Tube O Wheeling-Pittsburgh P Republic Steel R Sumitomo Metal Ind S TAMSA T

Vallourec V

Babcock & Wilcox W Algoma X

Youngstown Y TI Steel Tube Div. Z

American Seamless Tube AI Tubemeuse TU

Voest VA (Used) U

· The fifth symbol is the pipe grade code, designated as follows: Pipe Grade Symbol

N-80 N E E C-75 C X-95 X G-105 G S-135 S G-150 V

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(Heavy Wall) Double-stencil pipe grade code For example, the markings

ZZ 5 89 B E

at the base of the pin designate the company initials ZZ, and indicate that the tool joint was welded in May 1989 by British Steel on Grade E drill pipe.

Capacity and Displacement

Capacity refers to the amount of fluid that can be contained in a pipe or an annulus, and is generally expressed in units of volume per unit length (e.g., barrels per foot).

Displacement may be expressed either in terms of the length of pipe required to displace a unit volume of fluid (e.g., feet per barrel), or the volume of fluid displaced by a unit length of pipe (e.g., barrels per foot).

Knowing pipe capacities and displacements is important in many drilling operations, particularly those that have to do with drilling fluids, cementing and well control. These quantities can be calculated using formulas, or as is more often done, read from service company tables.

The following formulas are based on the dimensions of the pipe body only, and do not account for differences in diameter of upsets and tool joints. They provide good approximate values, however, and are useful for quick calculations.

Pipe Capacity = (π/4) (inside diameter)2 ( 1 )

Annular Capacity = (π/4) [(hole diameter)2 - (pipe OD)2] ( 2

)

(Note: in a cased hole, casing ID would replace hole diameter)

Example:

Drill Pipe size = 4 ", 16.60 lb/ft, internal upset, 3.826" ID Hole size = 8 "

Pipe Capacity = (π/4) (3.826)2 = 11.49 in3/in = 0.0142 BBL/ft

Annular Capacity = (π/4) [(8.75)2 - (4.50)2] = 44.21 in3/in = 0.0547 BBL/ft

Because capacity and displacement calculations are so common in field work, a number of pipe manufacturers and oilfield service companies have developed tables that list these quantities for various sizes of pipe in different hole sizes. When using these tables, it is important to note the assumptions (for example, the type of upset or tool joint) under which the calculations were made.

Handling Guidelines for Drill Pipe

Mishandling, rough treatment and improper make-up can severely weaken oilfield tubulars. This is especially true for drill pipe, which is relatively thin and flexible compared to the rest

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of the drill string. Such weakening can lead to pipe or tool joint failures. To avoid such failures (and the fishing jobs that usually result), drilling personnel need to handle pipe with care.

Although the actual handling of drill pipe is the job of the rig crew, it is important for engineers to be familiar with proper pipe handling procedures and to observe that they are being followed. Such attention to detail will, in the long run, prevent well problems. The guidelines in this section, taken from Rowe and Wilson (1981), provide a summary of good handling practices.

Thread Protection

Steel thread protectors should always be used when picking up, laying down, moving or storing oilfield tubulars.

· Before picking up drill pipe from the racks, remove the thread protectors,

thoroughly clean all connections and inspect the connections for damage. If solvent or other liquid is used for cleaning, the connections must be dried before applying thread compound. This thread compound should be of a high grade, and API-recommended for tool joint use.

· Re-install the thread protectors before moving the pipe onto the catwalk. Do not remove them again until the joint is picked up and the connection is ready to be made.

Pick-Up, Tripping and Lay-Down

Pick-up, tripping and lay-down procedures can have punishing effects on drill pipe and can increase the chances of failure. Here are some guidelines for minimizing these effects:

· Before picking up, tripping or laying down pipe, inspect all handling equipment for proper operation and signs of wear, including the elevators, the rotary table, the master bushing, the slip bowl, slips, tongs and pull lines. Worn elevator bores, shoulders or latches could result in dropping the drill string, while a damaged or worn rotary table, master bushing, bowl or slips could lead to crushing of the drill pipe tube;

· Stagger breaks on each trip so that each connection can be checked and thread compound reapplied every second or third trip;

· Exercise care when running in the hole — run in slowly enough to avoid sudden impact on ridges or shoulders, to avoid tagging bottom and to prevent high surging or swabbing pressures;

· Do not use the slips as a brake to stop the downward drill pipe movement when tripping in the hole;

· Do not allow the slips to "ride" the pipe when tripping out of the hole;

· Use backup tongs when breaking connections; do not depend on the weight of the drill string to keep the pipe from turning in the slips;

· Set the slips with the tool joint as near as practical to the rotary table — this minimizes the possibility of bending the pipe during make-up or breakout;

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· When picking up, laying down or standing back pipe, make sure that the catwalk, V-door and derrick floor are clear of foreign objects that could cause impact damage, and that the pipe is cleaned of any damaging or corrosive fluids.

Connections

Initial make-up is probably the most important factor affecting the life of tool joint connections. The following practices should be a part of make-up procedures:

· Pre-determine proper make-up torque, as specified for the particular connection, size, outside diameter and inside diameter;

· Use care when stabbing the pin connections into the box end, making sure that the pin does not strike the box shoulder or glance off the box threads;

· Make up connections slowly-high-speed kelly spinners or the spinning chain, when used on initial make-up, can cause galling of the threads. The driller should never jerk on the tong line to obtain proper make-up torque;

· Use a properly working, accurately calibrated torque gauge to measure the required line-pull as joints are made up to the required torque. This line pull is equal to the length of the tong arm (measured from the center of the tool joint, with the tongs in the set position at a 900 angle to the pull line) multiplied by the tong line pull.

Inspection

The IADC and the API have established detailed inspection guidelines for drill pipe and tool joints, which can be found in API RP 7G .

Drill string failures result primarily from fatigue. The API defines a fatigue failure as one "which originates as a result of repeated or fluctuating stresses having maximum values less than the tensile strength of the material." These stresses are products of the bending, torsion, vibration, tension and friction inherent in drilling operations, and are aggravated by corrosion, erosion, poor handling and other factors.

Fatigue failures are progressive; they generally begin as small cracks, which propagate as continued stress is applied. Unfortunately, fatigue is hard to detect in its early stages, and there are no accepted procedures for determining the amount of accumulated fatigue damage or the remaining life of pipe.

Accepted methods for inspecting the drill pipe tube involve:

· visual or magnetic particle inspection to locate cracks, pits and other surface marks;

· remaining wall thickness measurement, using either: — pipe-wall micrometers;

— sonic pulse echo (resonance measurements);

— gamma ray devices, calibrated to within 2% accuracy; — outside diameter measurement;

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— cross-sectional area measurement, either by means of a direct-indicating instrument calibrated to within 2% accuracy, or by integrating wall thickness measurements taken at 1-inch intervals. Required API procedures for inspecting tool joints involve:

· measuring outside diameter;

· checking shoulders for galls, nicks, washes, fins or other evidence of wear; · randomly checking 10% of the joints for manufacture markings and installation dates to determine if the tool joint has been reworked.

Optional tool joint inspection procedures include:

· determining minimum acceptable shoulder width, as specified in API RP7G; · measuring for box swell and/or pin stretch;

· examining thread profile for indications of overtorque, insufficient torque, lapped threads, galled threads and stretching;

· conducting a magnetic particle inspection if evidence of stretching or swelling is found.

Fatigue failure can occur rapidly under certain conditions. In areas that experience a high incidence of washouts or pipe failures, drilling personnel must be particularly selective about what they run in the hole, even if it means discarding joints for which the only signs of fatigue might be a few gouges in the slip area.

API 7G lists standards for classifying and identifying used drill pipe; Figure 1 shows where identification marks are applied.

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Figure 1

Automatic Pipe Handling

Automatic pipe racker systems provide a means of handling drill pipe by remote control. Operated from consoles on the rig floor (and, in some systems, from a derrick console) they use hydraulic, pneumatic or air power to latch and unlatch elevators, pull and set slips, make or break pipe connections, and lay down and pick up pipe. These systems are used primarily on floating drilling vessels, but are also available for use on platforms, jack-up rigs and land rigs.

Automatic pipe handling systems can provide dramatic savings on trip time and manpower, but their greatest benefit is increased safety. Safety is an especially important consideration on floating drilling vessels, where rough weather and heavy seas frequently render manual methods of pipe handling not only impractical, but dangerous.

Drill Collars

For a number of years after the introduction of rotary rigs and rolling cutter rock bits, a typical bottomhole assembly consisted merely of a short crossover sub, or collar, between the bit and the drill pipe.

As rotary drilling technology improved from these early beginnings and better equipment became available, operators observed that increasing the amount of weight applied to the bit resulted in faster penetration rates. They began inserting more and longer part sections of heavy pipe in the drill string to replace the old crossover subs (although the original term

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"collar" remained in use). Today, drill collars are routinely used to provide weight to the bit and optimize drilling rates.

Using drill collars in the bottomhole assembly, however, can also increase the potential for drill pipe failure. As the driller slacks off more weight from the brake to take advantage of the added weight provided by the drill collars, the compressive force on the drill pipe increases, causing the drill pipe (which is thin and flexible compared to the drill collars) to bend or buckle. This bending occurs in the body of the pipe between the end upsets. The abrupt change in cross-sectional area between the pipe body and the upsets sets up stress concentrations just above and below the much stiffer tool joint.

When drill pipe rotates in this compressed state, it experiences cyclic stress reversals. Each rotation of the string causes the drill pipe fibers to go from compression to tension to compression. This high cyclic stress bending causes metal fatigue, which is cumulative and eventually leads to drill pipe failure ( Figure 1 ).

Figure 1

To avoid fatigue failures, the drill pipe and uppermost drill collars need to be kept in tension at all times. Tension can be maintained by running an adequate number of collars in the bottomhole assembly to ensure that the neutral point (that is, the point below which the drill string is in compression, and above which it is in tension) will always be below the drill pipe ( Figure 2 ).

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Figure 2

Weight Requirements

The weight of drill collars required to keep drill pipe in tension may be determined as follows:

Weight of drill collars in air = (W.O.B./BF) (SF) ( 1 ) where:

W.O.B. = required weight on bit, pounds (based on manufacturer recommendations) BF = buoyancy factor of drilling fluid

SF = predetermined safety factor

The weight of the pipe in fluid is equal to its weight in air times the buoyancy factor. Table 1., below, lists buoyancy factors for various mud weights.

Fluid Weight, lb/gal Buoyancy Factor

8.33 .872 8.5 .870 9.0 .862 9.5 .855 10.0 .847 10.5 .840

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11.0 .832 11.5 .824 12.0 .817 12.5 .809 13.0 .801 13.5 .794 14.0 .786 14.5 .778 15.0 .771 15.5 .763 16.0 .756 16.5 .748 17.0 .740 17.5 .733 18.0 .725 18.5 .717 19.0 .710 19.5 .702 20.0 .694

Table 1. Buoyancy factors for steel pipe.

Safety factors may range from 1.10 to 1.25, depending on hole conditions and drilling location. In any case, the safety factor must be high enough to ensure that the neutral point will always be in drill collars or heavy-wall drill pipe, never in the drill pipe string.

The number of drill collars needed to attain the required weight on bit is simply equal to the total weight of the collars in air divided by their weight per foot and length of each collar: Example:

Bit weight required = 55,000 lb Mud weight = 12 lb/gal Buoyancy factor = 0.82 Safety factor = 1.15 Drill collars available:

• Nine 8" OD 2 " D 31' length, 150 lb/ft • 6 " OD 2 " ID 30' length, 100 lb/ft If all nine 8" OD collars are used, how many 6 " collars are needed? Solution:

Required weight of collars in air = (55,000/0.82) 1.15 = 77,134 lb Weight of 8" collars = 9 31 150 = 41,850 lb

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Number of 6 " OD collars = (35,284)/(100 30) = 11.77 Pick up twelve (12) 6 " drill collars

There are also graphical methods available for determining drill collar requirements

Dimensions and Strengths

Drill collars are available in both API and non-API sizes. Length ranges for API collars are Range 2 (30, 31 ft) and Range 3 (42, 43 ft).Drill collars are also specified according to their outside diameters, inside diameters and weights.

Tapered Strings

When using large-diameter drill collars (for example, on a deep well), it is necessary to taper the drill collar string so that changes in cross-sectional area from the larger to the smaller drill collar are not too abrupt. Otherwise, there is an increased potential for connection failures and fatigue damage.

The largest-diameter collars should be placed at the bottom of the string, and should gradually be tapered upwards toward the smallest drill collars or heavy-wall drill pipe. The following rules of thumb apply to running tapered drill collar strings:

• The stiffness of the larger-diameter collar should never exceed 3.5 times that of the smaller adjacent collar;

• Never reduce drill collar outside diameter (OD) more than two inches at any crossover (for example, if the bottom collar OD is 10", the collar above the crossover should have an OD no smaller than 8");

• Run at least three collars — one stand — of the next smaller size with each size change.

Special Features

Special features of drill collars include fishing necks, stepped bores, slip and elevator recesses, spiral grooves and hard-facing ( Figure 1 ,

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Figure 1

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Figure 2

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Figure 3

A fishing neck (so called because of its ability to receive a fishing overshot and grapple in case the collar parts in the hole) is a section of reduced outside diameter at the end of a drill collar. It is machined to allow smaller connections, which can be properly torqued using available rig tongs and catheads. Fishing necks are common in drill collars of more than 8" outside diameter, but are occasionally found on smaller sizes when the clearance between the collar and the hole is very small.

Stepped bores are reduced ID sections through pin connections of drill collars; they are used to increase the pin strength in small and medium diameter collars when large bores are needed for circulating fluid. A typical example would be a 6 " drill collar with a 2 " bore that is reduced to 2 1/4" through the pin.

Slip and elevator recesses eliminate the need for safety clamps and lift subs, enabling the rig crew to simply change elevators and handle drill collars as they would handle drill pipe. Machining and repairing these recesses, however, requires extreme caution and close adherence to manufacturer specifications — even slight deviations in recess depth, curvature on the ends, surface finish and cold rolling can cause serious high stress

problems. Slip and elevator recesses should not be used in highly corrosive environments because of the increased potential for stress corrosion.

Small-to-medium OD drill collars with spiral grooves help prevent differential sticking by reducing the contact area between the collars and the borehole wall, and by allowing the hydrostatic mud pressure to equalize around the drill collars. Note that the weight of a round drill collar will be reduced by approximately 4% by spiral conversion.

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Many drill collars are hard-faced with tungsten carbide for areas where abrasive formations cause rapid OD wear. As is the case with machining slip and elevator recesses, hard facing requires extreme care. The steel used in drill collars is very sensitive to quench effect, and can easily be cracked or left with high residual stresses that can cause cracks to form later. An additional concern is that rough hard-facing can result in costly casing wear.

Connections

Design of the best rotary-shouldered connection for a drill collar calls for the pin and box to be balanced in bending fatigue. It has been found that the pin and box are equally strong in bending if the section modulus of the box in its critical zone (ZB) is 2.5 times greater than the section modulus of the pin at its critical zone (ZP). These zones are shown in Figure 1 .

Figure 1

In the box connection, the critical zone is just short of the end of the pin at the root of the last engaged thread. It is not supported by the mating pin threads, and it is the weakest section in the box. The critical zone of the pin is about " from the shoulder, at the root of the thread.

Section modulus ratios from 2.25 to 2.75 work very well under most conditions, and in some cases, ratios from 2.0 to 3.2 give satisfactory performance. These numbers for

bending fatigue balance are only valid if the connection is properly tightened so that the pin gets sufficient shoulder support.

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Torsional strength is another important structural property of rotary-shouldered

connections. Critical areas of pin (AP) and box (AB) that are used for torsional strength are also shown in Figure 1 . This torsional strength determines the required make-up torque. API RP 7G provides complete torque information for the various sizes of connections and collars.

Drill Collars vs. Drill Pipe

The difference between the treatment and properties of drill collar connections and drill pipe tool joint connections is often misunderstood. A drill collar connection can never be made as strong as the drill collar body. It is a sacrificial element — when it becomes worn, it is cut off and replaced by machining new threads.

Drill pipe tool joint connections, on the other hand, are much stiffer and stronger than the pipe itself. They seldom experience bending fatigue damage. The most common damage to tool joint threads results from leaking joints, rough handling, thread wear and swelled boxes made thin by OD wear. Damaged tool joints can often be reworked and returned to service by chasing (that is, straightening and cleaning) the threads, thus losing only a fraction of an inch in length.

API Numbered Connections

Historically, the nominal size of a rotary-shouldered connection was the actual drill pipe OD that the tool joint was designed to fit. The same connections have been used on drill collars, although the nominal size has no meaning when applied to drill collars. Many old

connections have been incorporated into the API Numbered Connection series.

The numbered connection series provides a good selection of connections for almost any size drill collar. Any other API connection with four threads per inch works well. A thread with a 0.038" root radius will have less notch effect than a thread with a smaller radius.

Selection Criteria

Avoid using drill collar connections with five threads per inch. The 90° threads make good drill collar connections, but relative to API threads, recommended make-up torques result in reduced shoulder loads. Higher hoop stresses are developed and thin boxes must be

avoided.

Good connections are designed to fit drill collars through 11" OD. A problem, however, is that only large rigs may have tongs and line pull capacities to handle a 7 " joint that would be used on a 9" or 9 " drill collar. Only a very few rigs can handle an 8 " connection on a 10" or 11" drill collar. There are two methods for alleviating this problem:

· A fishing neck can be used, where the drill collar diameter is reduced for about one foot on the pin end and three feet on the box end ( Figure 2 ).

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Figure 2

For example, a 9" drill collar may be reduced to 8 " for a 6 " connection, while a 10" drill collar may be reduced to 9 " for a 7" connection.

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Figure 3

In some cases, a combination of fishing necks and low torque faces may be used. The important thing to remember is that sufficient torque on a modified end or, if necessary, a smaller joint is far better than inadequate torque on a full-size end and a larger joint. A feature recommended for all drill collars is cold rolling of thread roots. Cold rolling forces metal fibers into compression in the thread root area, making the connection more resistant to bending fatigue. This is standard procedure for most manufacturers. Good repair shops are also equipped to cold roll re-cut drill collars. This process improves resistance to notch fatigue and has not shown any adverse effects.

Stress relief features are highly recommended for drill collars, and are almost universally used on drill collars five inches in diameter or larger ( Figure 4 ).

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Figure 4

The only disadvantage of these features is that more of the collar must be removed to re-cut a joint. However, a damaged drill collar joint is usually in such poor condition that it is good practice in any event to remove most of the old joint before cutting.

Drill collars smaller than five inches OD are seldom damaged by fatigue. Most damage while in service results from high torque. Drill collars with a 4 " OD 2" ID are manufactured about equally with and without relief features. In this case, no set rules apply, and operating conditions dictate the preference.

Stress relief features only slightly reduce the torsional strength of a connection. On medium and large connections, this strength reduction is insignificant — it should, however, be considered on small connections. Collars with a 2 " internal flush bore, or smaller joints, should never be supplied with stress relief features.

Heavy Wall Drill Pipe

Heavy wall drill pipe is an intermediate drill string member — heavier, stronger and stiffer than regular drill pipe, but at the same time more flexible than drill collars. Because it has the same external dimensions as regular drill pipe, it is much easier to handle than drill collars. Figure 1 and Figure 2 illustrate some of its important features.

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Figure 2

The most important drill string application for heavy wall drill pipe is in the so-called zone of destruction — the area above the topmost drill collars where drill pipe fatigue failure is most likely to occur. To reduce fatigue failures in this area of the borehole, 18 to 21 joints of heavy wall drill pipe should be run above the drill collars. This provides a gradual change in stiffness between drill collars and drill pipe. Also, the ability of the heavy wall drill pipe to bend (unlike drill collars) serves to relieve high stresses at the connections.

To prevent too great a change in stiffness between the drill collars and the heavy wall drill pipe, the guidelines in Table 1., below, can be used.

Heavy Wall Drill Pipe OD ( inches ) Maximum Drill Collar OD ( inches )

3.50 6.00

4.00 6.50

4.50 7.25

5.00 8.25

Table 1. Sizing guidelines for heavy wall drill pipe and drill collars

Heavy wall drill pipe was first used in directional drilling, which generally requires flexibility in the drill string. It is now widely used in vertical and horizontal drilling as well. With less wall contact than would be experienced with drill collars, its usage reduces torque and wall-sticking tendencies. Its smaller degree of wall contact, together with its greater stiffness relative to regular drill pipe, results in increased stability and better directional control.

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Heavy wall drill pipe is also useful in reducing hook loads, making it ideal for smaller rigs drilling deeper holes.

In certain special applications (most notably horizontal drilling) heavy wall drill pipe may be run in compression. It is important to keep in mind, however, that a joint of heavy wall drill pipe is not as strong as a drill collar, and that it is still susceptible to buckling and fatigue failure. In a vertical hole, heavy wall drill pipe must be maintained in tension.

Stabilizers

Stabilizers, by centralizing the drill string at selected points in the borehole, can be used to: • ensure that the weight of the drill collars is concentrated on the bit;

• reduce torque and bending stresses in the drill string; • prevent wall-sticking or key-seating of the drill collars; • build, drop or maintain hole angle in directional drilling; • maintain constant bit direction in straight-hole drilling.

The type and placement of stabilizers in the drill string depends on local drilling conditions and well objectives.

In areas with a tendency toward crooked drilling, the stabilizer(s) immediately above the bit must have adequate wall contact to provide bit stability and guidance. The stabilizer(s) must also have wear properties which will permit them to stay in gauge for the life of the bit, and must be able to centralize the drill string without digging into the borehole wall. In an angle-holding, or packed-hole assembly, which requires maximum stiffness to "lock in" the direction of the drill string, the stabilizers should have the largest possible cross-sectional area that will permit adequate circulation passage.

For packed-hole drilling techniques, stabilizers act like drill bushings to minimize drift and hole angle change by centering the drill string. When utilizing a pendulum, or angle-dropping assembly, stabilizers are frequently used to increase the effectiveness of the pendulum. They similarly serve to increase the effectiveness of an angle-building assembly. Stabilizers are also designed to prevent wall-sticking of the drill collars and to guide them out of key seats.

There are a variety of stabilizer types available for different drilling environments, the most common of which are:

• integral blade stabilizers;

• replaceable sleeve stabilizers; • replaceable wear pad stabilizers; • non-rotating sleeve stabilizers; • welded blade stabilizers.

These stabilizer types are designed either for bottomhole configuration (to be run just above the bit), or string configuration (to be run at various points in the drill string).

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The integral blade stabilizer ( Figure 1 ) is designed for use in all degrees of formation hardness.

Figure 1

Its long ribs are designed to provide the wall contact necessary for proper stabilization, and are contoured to minimize torque while drilling. The ribs are milled directly on the stabilizer body.

For larger hole sizes, the integral blade stabilizer can be manufactured with a shop-replaceable sleeve. Its long ribs are milled directly on the sleeve to provide unitized

construction, thus preventing loss of ribs in the hole as sometimes happens with welded rib stabilizers.

These stabilizers can be provided with pressed-in tungsten-carbide compacts or welded-on hardfacing on the wear surfaces to increase gauge life. Integral blade stabilizers are available in both string and bottom hole types.

The replaceable steel sleeve stabilizer ( Figure 2 ) has the benefit of being replaceable at the wellsite.

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Figure 2

Sleeves can be changed in the rotary table, making this stabilizer type economical for remote locations. Replaceable sleeve stabilizers are available both in bottomhole and string configuration. They can be used for more than one hole size by changing sleeve size. Deep-grooved passages between the sleeve ribs assure adequate circulation past the tool. The replaceable wear pad stabilizer, with rig-replaceable wear pads ( Figure 3 (string) and Figure 4 (bottomhole)),

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Figure 3

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Figure 4

The wear pads, which can easily be changed out in the rotary table with hand tools, provide long wall contact area, and pressed-in tungsten carbide and carburized wear surfaces provide maximum downhole life. Within limits, changing wear pads permits body use in more than one hole size ( Figure 5 ).

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Figure 5

Built-in wear indicators are available to indicate the need for replacement before body damage occurs. The stabilizer body has a fluted configuration to provide for adequate circulation. This stabilizer type is available in either bottomhole or string configuration, so that two or three tools can be run in tandem hookups to provide additional wall contact as required.

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Figure 6

A true "drill bushing," it can be used in hard to medium-hard non-abrasive formations, since the sleeve does not rotate or dig into the borehole wall. The one-piece, rig-replaceable sleeve is molded over a mild steel inner bushing to prevent it from being lost downhole, and has fluted marine-type inner bearings, designed to allow continuous cleaning by the

circulating fluid. Drilling fluid acts as a lubricant and coolant to avoid friction between the mandrel and the non-rotating sleeve. The non-rotating sleeve stabilizer is always a string-type tool.

The welded blade stabilizer ( Figure 7 ) is designed to centralize drill collars and provide better borehole alignment.

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Figure 7

Its rotating blade is especially effective in soft formations, where balling-up of mud and cuttings on the drill string can cause problems.

Jars

Jars are used to provide quick, sharp, upward or downward motion to free stuck pipe. Although we most commonly associate them with fishing operations, they can also be run on drilling bottomhole assemblies as a precautionary measure. They are especially

appropriate for drilling in sticky, heaving, sloughing or crooked holes. Jars also have

applications in controlled-weight directional drilling, as well as in coring operations. Figure 1 shows a mechanical rotary drilling jar.

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Figure 1

Jars are usually identified according to type, inside and outside diameter, thread connection and stroke length. There are a number of jar types available, and the type of jarring action utilized will depend on the jar being used and the specific operating conditions. For typical mechanical or hydraulic jars, upward or downward motion is initiated by pulling up or slacking off on the drill string until a pre-set triggering load is reached, initiating a sharp blow. A few such blows may be sufficient to free a stuck drill string without the expense and risk of a fishing job.

In drilling operations, jars are generally run high in the drill collar string, with some drill collars above them. Optimum jar placement and triggering load, along with the need to enhance the jarring impact by running a companion tool known as ajar accelerator, is best determined individually for each bottomhole assembly, with input from the service company providing the tools.

Reamers

In very hard (or hard and abrasive) formations, the outside cutting structure of a bit gradually wears away if it is not protected. The bit becomes "pinched" or undergauge, resulting in a hole diameter that becomes smaller with increasing depth. Figure 1 shows an extreme example of an under-gauge bit — this 6 " bit,

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Figure 1

with no stabilization, wore down to 4 " OD after making 428 ft in 59 hours.

When a hole is severely undergauge, it is necessary to ream each new bit back to bottom before drilling can resume. This not only costs rig time and reduces bit life, but it increases the possibility of sticking the drill string.

Roller-cutter rotary reamers, with either three points or six points of wall contact ( Figure 2 and Figure 3 ), have proven to be effective for keeping holes in gauge.

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Figure 2

This not only prolongs bit life, but it also minimizes wear on other tools used in packed-hole assemblies in crooked hole drilling areas.

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Figure 3

Three-point bottomhole reamers are designed to be run between the bit and the drill collars, with the spacing from the bit to the reamer kept to a minimum. This set-up keeps the hole in gauge to ensure minimum time spent reaming back to bottom, protects the gauge of tools above the reamer and provides some stabilization to the bit.

Three-point string rotary reamers are sometimes run in the drill collar or drill pipe strings to centralize the strings in crooked hole areas. When run above the drill collars, they can be effective in reaming out dog-legs, key-seats and ledges. Both types of three-point reamers contain wall contact points spaced 120° apart.

Six-point bottomhole reamers are run between the bit and drill collars, and are used when greater reaming capacity is required than can be provided by the three-point design. They are especially effective in hard, abrasive formations where extremely hard cutters can be run in the lower points and regular hard cutters in the upper points. The six points of contact, spaced 60 °C apart, provide better stabilization than a three-point reamer in crooked hole areas.

A variety of roller reamer cutters are available for different formation types. For hard formations that require a scraping action, such as dolomite, hard lime and chert, the "Q" cutter ( Figure 3 , top) may be used. For extremely hard formations, the "K," or knobby cutter ( Figure 3 , bottom) may be used. Its tungsten carbide compacts act as teeth to fracture the formation.

The reamer bodies shown here utilize drive-fit hardened reamer pins and bearing blocks, which can be easily replaced at the wellsite without the need for special tools or welding.

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Crossover Subs

Crossover subs join drill string components of different sizes or thread connections. For example, a double-box crossover would be needed to join a bit with an API Regular pin connection to a drill collar with API Full Hole pin connection. It is important to keep track of the types of connections on each component of the drill string, and to make sure that the appropriate crossovers are available.

Vibration Dampeners

One of the more important considerations in drill string design is dealing with the vibrations and shock loads that are produced as the bit rotates on bottom. Such vibrations can cause "rough running" at the surface, and can result in damage to the bit, drill collars, drill pipe and other components.

There are a number of drilling parameters that determine whether vibration will occur, including:

• formation lithology (e.g., hard rock, broken formations, and formations with intermittent hard and soft streaks);

• depth;

• bottomhole assembly configuration; • weight on bit;

• rotary speed.

Engineers can use these and other parameters during the well planning process to develop computer models for optimizing drill string design. They can also monitor vibrations during the drilling of the well by means of surface or downhole (MWD) sensors.

We can often control or eliminate downhole vibrations by modifying the bottomhole assembly configuration, or simply by adjusting rotary speed and/or weight on bit. A vibration dampener, or shock sub ( Figure 1 ,

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Figure 2 , and Figure 3 ), may be useful in some cases for absorbing vibrations and shock loads.

Figure 2

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A vibration dampener is a type of shock absorber designed to prevent vibrations generated by the bit from traveling up the drill string to the surface. It is commonly run between the bit and the drill collars, or above the large-diameter short drill collar segment of a packed-hole drilling assembly. When properly used, vibration dampeners can result in faster drilling rates, longer bit life, less damage to the drill string and surface equipment, and reduced torsional impact.

Because of the complexity and magnitude of the forces acting on the bit and drill string, vibration dampeners cannot be considered a cure-all for vibration problems. They should not be routinely added to drill strings without first modeling their effects. Improperly applied, a shock sub may not only fail to absorb severe vibrations, but could even create additional vibrations, thereby accelerating, rather than preventing, drill string failure.

REFERENCES

American Petroleum Institute (1987). Performance Properties of Casing, Tubing and

Drill Pipe. API Bull. 5C2, Twentieth Edition. Washington D.C., USA.

American Petroleum Institute (1990). Recommended Practice for Drill Stem Design &

Operating Limits. API RP7G, Fourteenth Edition. Washington D.C., USA.

American Petroleum Institute (1988). Specification for Drill Pipe. API Spec. 5D, First

Edition. Washington D.C., USA.

Brinegar, Doyle W (1977). "What You Should Know About Kellys." Oil and Gas Journal.

(May 2).

Burgoyne, Adam T. Jr., Milheim, Keith K., Chenevert, Martin E. and Young, KS. Jr. 1986. Applied Drilling Engineering. Richardson, TX: Society of Petroleum Engineers. Craddock, Anthony J. (1973). "Present, Future Trends in Downhole Drilling Tools."

Petroleum Engineer (August): 61-64. Houston: Hart Publications, Inc.

Garret, W.R. and Wilson, Gerald E. (1974). "Proper Field Practices for Drill Collar

Strings." SPE Technical Paper 5124, prepared for the 49th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, Houston, October 6-9. Richardson, TX: Society of Petroleum Engineers.

Garret, W.R. (1962). "The Effect of a Down Hole Shock Absorber on Drill Bit and Drill

Stem Performance." Presented at the Petroleum Mechanical Engineering Conference of the American Society of Mechanical Engineers, Dallas, September 23-26.

Gatlin, Carl. (1960). Petroleum Engineering. Drilling and Well Completions. Englewood

Cliffs, NJ, USA: Prentice Hall, Inc.

Halliburton Services. (1981 ). Halliburton Cementing Tables. Duncan, OK, USA:

Halliburton Services.

Brandon, B.D. et. al (1992). "First Revision to the IADC Fixed Cutter Dull Grading

System." SPE/IADC Technical Paper 23939, presented at the SPE/IADC Drilling Conference, New Orleans (18-21 February). Richardson, TX: Society of Petroleum Engineers.

Lubinski, Arthur. (1961). "Maximum Permissible Dog-Legs in Rotary Boreholes." Journal

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Rollins, H.M. (1966). "Drill Pipe Fatigue Failure." Oil& Gas Journal (April 18). Rowe, Morris E. (1976). Heavy Wall Drill Pipe. A Key Member of the Drill Stem.

Publication No. 45. Houston: Drilco Division of Smith International, Inc.

Rowe, Morris E. and Wilson, Gerald E. (1981). "How to Get the Most Out of Your

Drillstring." Petroleum Engineer International (September).

Smith International, (1988-89). Datadril/Drilco/Dyna-Drill/Servco Tools and Services,

General Catalog. Houston

Smith International, Inc. (1988). DRILCO Drilling Assembly Handbook.. Fourth Edition.

Houston.

Wilson, Gerald E. (1976). "How to Drill a Usable Hole." Four Parts. World Oil (August,

September, October, November).

Wilson, Gerald E. (1979). "How to Select Bottomhole Drilling Assemblies." Two Parts.

Petroleum Engineer International (March, April).

Wilson, Gerald E. (1977). "Operators Slash Deep Drilling Costs with RWP® Stabilizers."

Oil and Gas Journal (August 8).

Woolley, Steve (1978). "MudChek® Kelly Valve Cuts Waste of Time, Mud." Oil and Gas

Journal (February 20).

ADDITIONAL READING

Hill, T., Ellis, S., Lee, K., Reynolds, N., and Zheng, N. (2004). "An Innovative Design

Approach to Reduce Drill String Fatigue". SPE 87188, presented at the IADC/SPE Drilling Conference held in Dallas, Texas, USA.(2-4 March) . Richardson, TX, USA : Society of Petroleum Engineers.

Lou, A., and Souder, W. (1998). "Composite Drill Pipe for Oil and Gas E&P Operations".

SPE 48888, presented at the SPE International Oil & Gas Conference and Exhibition in China held in Beijing, China (2-6 November). Richardson, TX, USA : Society of Petroleum

Engineers.

Murch, C. (1996). "Application of Top Drive Drilling to Horizontal Wells". SPE 37100,

presented at the SPE Horizontal Well Technology Conference held in Calgary, Alberta, Canada (18-20 November) . Richardson , TX, USA : Society of Petroleum Engineers.

Shepard, S., Reiley, R., and Warren, T. (2001). "Casing Drilling: An Emerging

Technology". SPE 67731, presented at the SPE/IADC Drilling Conference held in Amsterdam, The Netherlands (27 February-1 March). Richardson, TX, USA: Society of Petroleum Engineers.

Summers, M., and Crabtree, S. (1998). "Drill String Management to Reduce Drilling

Risks". SPE 39325, presented at the IADC/SPE Drilling Conference held in Dallas, Texas (3-6 March). Richardson, TX, USA: Society of Petroleum Engineers.

References

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