Drillstring Design Manual

Schlumberger Sedco Forex

Engineering Department

Author:M. AndreaReviewed by:

Approved by:

Engineering Recommendations

Ref.:

Page: 1 of 23

Issued:

Revision: 00

Drill String Design Recommendations

SummaryThis 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 theRegional Technical/Operations Managers

This uncontrolled document has been issued using Microsoft WORD 7.0 for Windows 95. Copies areavailable from Drilling Engineering in Montrouge.

00 First Issue 20/04/98

RevisionNumber

Description of amendments / page changes/comments Datedd/mm/yy

ENG-

Revision: 00DRILL STRING DESIGN Issued:

Page: 2 of 23

Table of Contents1. 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..................................................................................................36.1. Abbreviations.............................................................................................................................36.2. Definitions .................................................................................................................................4

7. Drill Pipe Properties.........................................................................................................................47.1 Drill Pipe Grade..........................................................................................................................47.2 Drill Pipe Class ...........................................................................................................................47.3 Tool Joints ..................................................................................................................................47.4 Thread Form...............................................................................................................................5

8. Drill Collars ......................................................................................................................................58.1 Drill Collar Selection ..................................................................................................................58.2 Size Criteria................................................................................................................................68.3 Drill Collar Connections .............................................................................................................7

9. Allowable Weight on Bit ..................................................................................................................89.1. Discussion Vertical Holes...........................................................................................................89.2. Discussion Inclined Holes ..........................................................................................................99.3 Vertical Hole Calculation Procedure.......................................................................................... 109.4 Inclined Hole Calculation Procedure ........................................................................................ 119.5 Weight of BHA Required ......................................................................................................... 12

10. Tension.......................................................................................................................................... 1210.1 Static Load.............................................................................................................................. 1210.2 Margin of Over Pull ................................................................................................................ 12

11.Burst............................................................................................................................................... 1311.1 Pipe Burst Calculation............................................................................................................. 14

12. Collapse......................................................................................................................................... 1412.1 Drill pipe collapse ................................................................................................................... 1412.2 Effect of tensile load on collapse.............................................................................................. 1412.3 Slip crushing........................................................................................................................... 16

13. Pipe Torsion.................................................................................................................................. 1713.1 Torsion Only........................................................................................................................... 1713.2 Torsion and Tension ............................................................................................................... 17

14. Fatigue .......................................................................................................................................... 1814.1 Limits ..................................................................................................................................... 1814.2 Fraction of Drill Pipe Life Expended in Dogleg....................................................................... 19

15. Tool Joint Performance ................................................................................................................ 2015.1 Make-up and Yield Torque...................................................................................................... 2015.2 Combined Torsion and Tension to Yield a Rotary Shouldered connection ............................... 21

16. Combination Tube and Connection Performance........................................................................ 22

17. Critical Rotary Speeds ................................................................................................................. 2317.1 Transverse Vibration............................................................................................................... 2317.2 Axial Vibration ....................................................................................................................... 2317.3 Harmonic Vibrations............................................................................................................... 23

ENG-


Page: 3 of 23

1. PurposeThese procedures shall be used whenever designing a drillstring, unless otherwise decided with theRegion Technical/Operations Managers.

2. ScopeThe manual gives the theory, guidelines and design factors for proper drillstring design. The followingdesign factors shall apply when designing a drillstring:

Tension 1.1Margin of over pull 50,000 to 100,000 lbsExcess BHA weight 1.15Torsion 1.0 (based on lesser of pipe body or connection strength)Collapse 1.1. to 1.15Burst 1.2

The design process shall address the following items:

1. Selection of drill collar diameter2. Selection of BHA connections3. Determination of drill collar and or HWDP length4. Tool joint torsional capacity check5. Tension design limitations6. Burst pressure determination7. Collapse pressure determination8. Slip crushing load9. Fatigue limits10. Combined tension and torsional load limits

3. ResponsibilityThe Region Technical/Operations Managers are responsible of the enforcement of this standardthroughout the SF organization

4. ReferencesEngineering Standard RE-ST-516-01 issued November 1992API specification 5D (SPEC 5D), 3 rd edition, August 1, 1992 or latest editionAPI specification 7 (SPEC 7), 38 th edition, April 1994, or latest editionAPI Recommended Practice 7G (RP 7G), 15 th edition, January 1, 1995, or latest edition

5. Distribution, filing and storage of this documentIn 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: Sedco ForexHQS : the Headquarters of SF located in Montrouge FranceEng: the Engineering Department of SF located in Montrouge.M & M: Materials & Maintenance department within R & EPSS: Property Symbolization System used within Sedco Forex.MPP: Maintenance Policies and ProceduresAPI: American Petroleum Institute

ENG-


Page: 4 of 23

6.2. 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 yieldstrength of the pipe. This value is important because it is used in burst, collapse, and tensioncalculations. Common grades are as follows:

GradeLetter Designation

Assumed Average YieldStrength (psi)

(used for collapse)

Minimum Yield Strength(psi)

D-55 65,000 55,000E-75 85,000 75,000X-95 110,000 95,000

G-105 120,000 105,000S-135 145,000 135,000

7.2 Drill Pipe Class

Drill pipe is unlike most other oil-field tubulars, such as casing and tubing, because it is used in a worncondition. Casing and tubing are usually new when installed in a well. As a result, “classes” are givento 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 Practice7G. Although the class definitions can be extensive, they are summarized as follows:

New - No wear and has never been used.Premium - Uniform wear and minimum wall thickness of 80%.Class 2 - 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, basedon not more than 20% uniform wall reduction.

Class 3 - Allows drill pipe with a minimum wall thickness of 55% with all wear on one side.

7.3 Tool Joints

Tool joints are screw-type connectors that join individual joints of drill pipe. Most tool joints, regardlessof 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) Tool joint is larger than the pipe such that the tool joint ID is less thanthe drill pipe. The tool joint OD is larger than the drill pipe. GenerallyIEU connections are the strongest available couplings.

IF (internal flush) Tool joints ID is approximately the same as the pipe. The OD isupset.

IU (internal upset) Tool joint ID is less than the pipe. Tool joint OD is approximately thesame as the pipe. This type is often termed “slim-hole” pipe becauseof 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. Tominimize tool joint wear while rotating on abrasive rock, a band of abrasion-resistant material is appliedto the outside of the box tool joint. This material is usually sintered tungsten carbide particles in awelded metal matrix. The problem that often arises from the use of hardfaced tool joints is excessivewear on the internal diameter on the casing.

ENG-


Page: 5 of 23

7.4 Thread Form

The term “rotary shouldered connection” refers to the threads of the pin or box of drill pipe or drillcollars. The threads of the pin of one joint engage with the threads of the box of another joint duringmake-up . The actual seal is provided by the metal contact of the shoulders of the tool joints. Theengaged threads are not made to provide a seal and open channels between the threads exist, evenwhen the joint is torqued.

Besides thread form and number of threads per inch, a connection can also be distinguished bydimensional 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 stylesof rotary connections. The NC refers to the pitch diameter of the pin thread at gauge point whenrounded to units and tenths of inches, Thus if the pitch diameter is 1.063 in, the first two figures areused, 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 ofthe 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 availablein many sizes and shapes, such as round, square, triangular, and spiral grooved. The most commontypes are round (slick) and spiral grooved. Spiral-grooved collars reduce the surface contact areabetween the pipe and well bore. The lower contact area reduces the probability of differential pressuresticking. Table 8.1 (below) shows the API dimensions for collars of various outer diameters.

Drill Collar Number OD, in. Bore +1/16 -0, in.NC23-31 (tentative) 3 1/8 1 ¼NC26-35 (2 3/8 IF) 3 ½ 1 ½NC31-41 (2 7/8 IF) 4 1/8 2NC35-47 4 ¾ 2NC38-50 (3 1/2 IF) 5 2 ¼NC44-60 6 2 ¼NC44-60 6 2 13/26NC44-62 6 ¼ 2 ¼NC46-62 (4IF) 6 ¼ 2 13/26NC46-65 (4IF) 6 ½ 2 ¼NC46-65 (4IF) 6 ½ 2 13/16NC46-67 (4IF) 6 ¾ 2 ¼NC50-70 (4 ½ IF) 7 2 ¼NC50-70 (4 ½ IF) 7 2 13/16NC50-72 (4 ½ IF) 7 ¼ 2 13/16NC56-77 7 ¾ 2 13/16NC56-80 8 2 13/166 5/8 REG 8 ¼ 2 13/16NC61-90 9 2 13/167 5/8 REG 9 ½ 3NC70-97 9 ¾ 3NC70-100 10 3NC77-110 (tentative) 11 3

ENG-


Page: 6 of 23

8.2 Size Criteria

Selection of drill collar diameter for a slick or pendulum assembly is based on the required effectiveminimum hole diameter. That is, the size of the bottom drill collar would be the limiting factor for lateralmovement of the bit.

For Example:Drilling a 12 ¼” hole would require 9” drill collars to result in a hole large enough to run 9 5/8” casingwith 10.625” OD couplings.

1062512 25 9

2. "

. " . " .hole

Bit dia Drill collar dia=

+

More commonly drill collar size is selected based on stresses. Components subject to bending haveboth tensile and compressive forces induced in them. When rotated under bending, individual metalfibers 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 areconcentrated. Stresses are concentrated at connections and changes in pipe size. Stressconcentration 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 definedas follows:

( )Z x I OD

OD ID

OD= ÷ =

−2

32

4 4π

Where Z = Section modulus, in

I = Second moment of area, in

OD = Outside diameter, inches

ID = Inside diameter, inches

3

4

Minimum effective hole diaBit size Drill collar dia

..

=+

2

ENG-


Page: 7 of 23

Generally, the change in bending resistanceis expressed in terms of a bending resistanceratio (BRR), which may be calculated asfollows:

( )( )BRR

Z

Z

OD ID OD

OD ID OD= =

−

−1

2

14

14

2

24

24

1

The terms are illustrated at right

The bending resistance ratio should bechecked at changes in pipe size. BRRs arecalculated using the pipe body dimensionsand should generally be below 5.5

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 ofconnection; therefore, only the outside diameter of the box and inside diameter of the pin need to bemeasured. This is illustrated at right

For any combination of connection, box OD, and pin ID, the tables given in API RP7G can be used todetermine the bending resistance ratio.

Experience had shown that a bending resistance ratio of 2.5 results in a balanced connection. Therange of acceptable BRRs depends on the severity of the service to which the drill collars will besubjected. The following recommendations are given for guidance, but local operating experience mayshow closer tolerances are required.

Conditions Acceptable BRR RangeDCs < 6” OD 2.75 - 2.25High RPM with DCs << hole size 2.85 - 2.25Low RPM with DCs close to hole size 3.20 - 2.25

OD2

OD1

ID2

ID2

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.

ENG-


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. Instraight holes, buckling of the pipe is prevented by using a BHA of sufficient weight to ensure that theneutral point of bending is kept within the BHA. A common misconception is that the neutral point oftension 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 andhydrostatic pressure of the drilling fluid. This hydrostatic effect, commonly called buoyancy, resultsfrom the pressure exerted vertically on the cross-sectional area of the drillstring. For a drillstring ofconstant cross section, the resulting hook load can be calculated as follows:

( ) ( )HL WT x D CSA x x MW x D

HL Hookload lbf

WT Weight of drillstring lb ft

D Depth of well ft

CSA Cross tional area of drillstring wall in

MW Mud weight ppg

string string

string

string

= −

==

=

= −

=

0 052

2

.

,

, /

,

sec ,

,

Buoyancy acting at the bottom of the drillstring places the lower portion of the drillstring in compressionand reduces the hook load.

Buckling occurs only below the neutral pointof bending, which is defined as the pointwhere the average of the radial andtangential stress in the string equal the axialstress.

The neutral point of bending occurs wherethe effective hydrostatic force equals thecompressive force in the drillstring. With noWOB, this point is at the bottom of the string;therefore, the drillstring is not buckled.

Stress conditions within the drillstring in avertical hole are shown at right.

If weight is placed on the bit, there is additional compression in the bottom of the drillstring, and theneutral point of tension and compression moves up the drillstring. The neutral point of bending alsomoves up the drillstring to the point where the equivalent mud hydrostatic force is again equal to thecompressive force in the drillstring.

The height of the neutral point of bending above the bottom of the drillstring can be calculated asfollows.

Neutralpoint

of bending

Neutral pointof

tension/compression

Pipestress

Equivalent mudhydrostatic

force

Compression Tension

ENG-


Page: 9 of 23

( )( ) ( )

( )( )

F D H x x MW x CSA

F WOB D x x MW x CSA H WT

H x x MW x CSA WOB H x WT

H WOB WT x MW CSA

H WOB BUOYED WT

ft

lbf

lbf

BUOYED WT lbf

hyd String

comp String string

string string

string string

string

string

= −

= + − −

=

= +

= −

=

=

==

0 052

0 052

0 052

0 052

.

.

,

,

/

,

,

At the neutral point of bending F F , and the calculation is as follows:

Where H = Height of neutral point of bending,

F Compressive force in drillstring

WOB Weight on bit,

Buoyed weight of drillstring

hyd comp

comp

( )= WT x x MWstring 1 0 015− .

The height of the neutral point of bending above the bottom of the string is thus the weight on bit dividedby the buoyed weight per foot of the drillstring. The forces in the drillstring in this situation are shownbelow.

To prevent the neutral point of bending frombeing in the drill pipe, the buoyed weight of theBHA must exceed the applied WOB. Inpractice, field applications commonly allow for asafety factor. It is recommended that theapplied WOB should be limited to 85% ofthe buoyed weight of the BHA (provided theHWDP is not buckled)

Heavy-weight drill pipe is generally run astransition pipe between the drill collars and thedrill pipe. Sedco Forex field experienceindicates that it is not acceptable to run heavy-weight drill pipe for WOB in vertical holes.

9.2. Discussion Inclined Holes

In inclined holes, two additional factors must beconsidered 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 BHAcontinues to act vertically.

• To allow for the reduction in available BHA weight, the buoyed weight must bereduced 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 borehole wall. In these circumstances, pipe above the neutral point of bending buckles only when thecompressive forces in the drillstring exceeds a critical load, calculated as follows:

( ) ( )Fcrit

OD ID x BF x OD ID x Sin

D ODpipe pipe pipe pipe

hole tj=

− −−1617

4 4 2 2 θ

Neutralpoint

of bending Neutral pointof

tension/compression

Pipestress

Equivalent mudhydrostatic

force

Compression Tension

WOB

ENG-


Page: 10 of 23

WhereF = Critical buckling force,

OD = Outside diameter of pipe, inches

OD = Max OD of pipe, inches

ID = Inside diameter of pipe, inches

BF = Buoyancy factor, = (1 -.015 x MW)

D = Diameter hole, inches

= Hole inclination, degrees

crit

pipe

tj

pipe

hole

lbf

θThe 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:

( )WOB x L x WT x MWdc dcmax . .= −085 1 0 015

Where WOBMAX = Available weight on bit, lbLdc = Length of drill collars, ftWTdc = Air weight of drill collars, lb/ftMW = Mud weight, ppg.85 = 85% safety factor

The actual weight of drill collars in mud should be measured and recorded when going in the hole. Thisrecorded value can then be used as the maximum allowable weight on bit, provided that the mud weightis unchanged.

If the mud weight is altered, the maximum allowable weight on bit must also be altered as follows:

NewWOB Old WOBMW

MWnew

old

=−−

max

.

.

1 0 015

1 0 015

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 isthe 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 usedfor drilling weight. The weight on bit available from the BHA is

( )WOB x L x WT x MWdc dcmax . .= −085 1 0 015

= .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?

NewWOB Old WOBMW

MWnew

old

=−−

max

.

.

1 0 015

1 0 015

=−−

37 418

1 0 015 16 5

1 0 015 13,

. .

.

x

x

= 34,987 lbf

ENG-


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.

( )WOB L x WT x MW x Cosdc dc dc= −1 0 015. θWhere WOBDC = Available weight provided by collars, lb

Ldc = Length of drill collars, ftWTdc = Air weight of drill collars, lb/ftMW = Mud weight, ppgθ = Bottom hole inclination, degrees

2. Calculate the maximum available WOB provided by the HWDP.

( )WOB L x WT x MW x CosHWDP HWDP HWDP= −1 0 015. θWhere WOBHWDP = Available weight provided by HWDP, lb

LHWDP = Length of HWDP, ftWTHWDP = Air weight of HWDP, lb/ftMW = Mud weight, ppgθ = Bottom hole inclination, degrees

3. Calculate the critical force to buckle the HWDP.

( ) ( )Fcrit

OD ID x BF x OD ID x SinD OD

HWDP HWDP HWDP HWDP

hole tj=

− −−1617

4 4 2 2 θ

WhereF = Critical buckling force for HWDP,

OD = Outside diameter of pipe of HWDP, inches






crit

pipe

tj

pipe

hole

lbf

θ

4. Calculate the critical force to buckle the drill pipe.

( ) ( )Fcrit

OD ID x BF x OD ID x Sin

D ODpipe pipe pipe pipe

hole tj=

− −−1617

4 4 2 2 θ

WhereF = Critical buckling force,

OD = Outside diameter of pipe, inches






crit

pipe

tj

pipe

hole

lbf

θ

5. If WOBHWP + Fdp > FHWDP, Then the maximum allowable weight on bit is given by the following:

WOBMAX = WOBDC + FHWDP

ENG-


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 speedFormation Classification lb / in of diameter RPM

Soft 2270 - 6750 100 - 250Medium 4500 - 9000 40 - 100Hard Milled Tooth Insert 5600 - 11250 35 - 70Hard Insert Bit 2250 - 9000 35 - 70Hard Friction Bearing 4500 - 6750 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 ofeach size, weight, grade and classification of drill pipe to support the submerged weight of all the drillpipe plus the submerged weight of the collars, stabilizers, and bit. This load may be calculated asshown in the following equation. The bit and stabilizer weights are either neglected or are included withthe drill collar weight.

( ) ( )[ ]F L x WT L x WT BFTEN dp dp dc dc= +

whereF

L

L

WT

WT

BF

TEN

dp

dc

dp

dc

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

= length of drill pipe, ft

= length of drill collars, ft

= air weight of drill pipe, lb / ft

= air weight of drill collars, lb / ft

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 permanentdeformation 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.

F Y Ayield m=where

Fyield

YmA

= minimum tensile strength, lb

= 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 permanentstretch 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 isrecommended.

ENG-


Page: 13 of 23

F F .design yield x= 0 9

whereFdesign

Fyield



0.9 = a constant relating proportional limit yield to strength

The difference between the calculated load FTEN and the maximum allowable tension load represents

the Margin of Over Pull (M.O.P.).

M O P F Fdesign TEN. . . = −

The same values expressed as a ratio may be called the Safety Factor (S. F.)

S FF

Fdesign

TEN

. . =

The selection of the proper safety factor and/or margin of over pull is of critical importance and shouldbe approached with caution. Failure to provide and adequate safety factor can result in loss or damageto the drill pipe while an overly conservative choice will result in an unnecessarily heavy and moreexpensive drill string.

Normally the designer will desire to determine the maximum length of a specific size, grade, andinspection class of drill pipe which can be used to drill a certain well. By combining the above equationsthe following equation results:

LF x M O P

WT x BF

L WT

WTdpyield

dp

dc dc

dp

=−

−0 9. . . .

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 2Depth 12,700 feetHole Size 7 7/8 inchesMud Weight 10 lb/galMargin of Overpull (MOP)50,000 lb.Length of Drill collars 630 feetWeight per foot 90 lb.

LF x M O P

WT x BF

L WT

WTdpyield

dp

dc dc

dp1

1 1

0 9=

−−

. . . .

Lx

x

x

L Feet

dp

dp

1

1

225 771 0 9 50 000

18 37 847

630 90

8 37

9846 3087 6759

=−

−

= − =

, . ,

. . .

It is apparent that drill pipe of a higher strength will be required to reach 12,700 feet. Add 4 ½”, 16.60lb/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 L x WT L x WTdp dp dc dc= +1 1

ENG-


Page: 14 of 23

11.Burst

11.1 Pipe Burst Calculation

The drill pipe internal yield pressure can be calculated as follows:

PY Wt

Dim=

2

whereP

Y

Wt

D

i

m

= burst pressure, psi

= specified minimum yield strength, psi

= pipe wall thickness, in.

= 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 andsqueeze 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, orplastic failure based on the pipes D/t (diameter / wall thickness ratio). The applicable equations can befound 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 anyload on plastic collapse items. The collapse resistance of drill pipe corrected for the effect of tensionloading may be calculated with the following equation:

EXAMPLE: (continue) Typical drill string design based on margin of overpull

( ) ( )[ ]Total Weight x x

lb

= +

= + =

6759 1837 630 90

124 163 56 700 180 863

.

, , , .

Determine the length of the second string of drill pipe.

LF x M O P

WT x BF

L WT L WT

WT

Lx

x

L feet

dp

yield

dp

dc dc dp dp

dp

dp

dp

22

2

1 1

2

2

2

0 9

329 542 0 9 50 000

18 88 847

180 863

18 88

15 420 9 580 5840

=−

−+

=−

−

= − =

. . . .

, . ,

. .

,

,

, ,

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

Weight in Air Weight in MudItem Feet lb. Lb. .

Drill Collars 630 56,700 48,025No. 1 Drill Pipe 4 ½” 16.6 lb, Grade E 6,759 124,163 105,166No. 1 Drill Pipe 4 ½” 16.6 lb, Grade E 5,311 100,272 84,930

12,700 281,135 238,121

ENG-


Page: 15 of 23

Where

RZ x Z

R

=− + −4 3

2

2( )

Z = Total tensile load (lbs)

Cross section area x Average yield strength

= Effective collapse resistance under tension (psi)

Nominal plastic collapse resistance (psi)

This equation is shown graphically below.

Figure 12.1

Ellipse of Biaxial Yield Strength

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

Tension (% of yield stress)

Co

llap

se (

% o

f yi

eld

str

ess)

Compression Burst

Compression &Collape

Tension & burst

Tension and Collapse

Axial Stress % of Yield

Hoo

p St

ress

% o

f Y

ield

ENG-


Page: 16 of 23

12.3 Slip crushing

The maximum allowable tension load must be determined to prevent slip crushing. In an analysis of theslip crushing problem, Reinhold, Spini, and Vreeland, proposed an equation to calculate the relationbetween 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 ofthe pipe (A) and the cylindrical surface are of the pipe under the slips (AS) are used, the equation can bepresented as follows:

where

S

S

DK

L

DK

LH

T S S

= + +

≈

12 2

2 1 2/

S = hoop stress, psi

S = tensile stress, psi

D = oustside diameter of the pipe, in.

K = lateral load factor on slips, 1 / tan (y + z)

y = slip taper, usually 9 27' 45"

z = arctan

= coefficient of friction ( 0.08)

L = length of slips, in.

H

T

0

S

µµ

Slips are typically 12 or 16 in. long. The friction coefficient ranges from 0.06-0.14. Inasmuch as tooljoint lubricants are usually applied to the back of rotary slips, a coefficient of friction of 0.08 should beused for most calculations. The equivalent tension load from slip crushing can be calculated as follows:

where

T T xS

S

S

S

S LH

T

H

T

=

T = tension from slip crushing

T = tensile load in string

= hoop stress, tension stress ratio from previous equation

S

L

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. Determinethe actual collapse resistance of the bottom joint of drill pipe.

Rated collapse for New, 5”, 19,5 ppf, grade G pipe is = 12,999 psiCross 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

ENG-


Page: 17 of 23

13. Pipe Torsion

13.1 Torsion Only

Drill pipe torsional yield strength when subject to pure torsion is given by the following:

where ( )

Qx J x Y

DQ

D d

m

m

=

−

0 096167

4 4

.

= minimul torsional yield strength, ft - lb

J = polar moment of inertia, 32

D = Pipe OD, inches d = Pipe ID, inches

Y = minimum unit yield strength, psi

π

13.2 Torsion and Tension

When drill pipe is subject to both torsion and tension, as is the case during drilling operations, theminimum torsional yield strength under tension is given as follows

where

( )

QJ

DY

P

AQ

D d

t m

t

m

= −

−

0 0961672

2

2

4 4

.

= minimul torsional yield strength under tension, ft - lb

J = polar moment of inertia, 32


Y = minimum unit yield strength, psi

P = total load in tension, lbs

A = cross - sectional area, in2

π

EXAMPLE: Slip crushing calculation

A 4 ½” OD drill string has a hanging weight of 192,00 lbs. Determine the equivalent tension due to slipcrushing force on the drill string.

( )

S

S

DK

L

DK

L

K

S

S

x

x

x

x

H

T S S

H

T

= + +

=+

= + +

12 2

1

9 27 45 0 08

14 5 4 0

2 16

4 5 4 0

2 16

2 1 2

0

2 1 2

/

/

tan ' " arctan .

. . . .

= 4.00

= (2.17159)

= 1.4736

1/2

T TS

S

T

S LH

T

S

=

= 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.)

ENG-


Page: 18 of 23

14. Fatigue

14.1 Limits

The most common type of drill pipe failure is fatigue wear. It generally occurs in dog legs where the pipegoes through cyclic bending stresses. These stresses occur because the outer wall of the pipe in a dogleg is stretched and creates a greater tension load. As the pipe rotates a half cycle, the stresseschange to the other side of the pipe, For example, the stress may change from 50,000 psi to -20,000psi 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 somecritical 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 fatiguedamage consideration can be calculate with the following equations:

( )

CK L

E D K L

KT

E I

C ft

E

D

L

T

I D d

b=

=

−

432 000

644 4

, tanh

/100

σ

π

σπ

= maximum permisible dogleg severity,

= Young' s modulus, psi

= 30 X 10 psi for steel

= 10.5 X 10 psi for aluminium

= drill pipe outer diameter, in.

= half the distance between toll joints, 180 in. for Range 2 pipe, in.

= tension below the dog leg, lb

= maximum permissible bending stress, psi

= drill pipe moment of inertia,

O

6

6

b

The maximum permissible bending stress, σ b , is calculated from the buoyant tensile stress, σ t (psi), in

the dogleg with the following equations:

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 themaximum torque which can be applied to the pipe (neglecting connection strength in this example) if100,000 lbs of over pull is applied

( )J = polar moment of inertia, 32

= 28.53 inches


A = cross - sectional area, in = 5.27 in

= 0.096167 x 28.5383

5 = 44,640 ft - lbs

4

2 2

π5 4 276

105 000350 000

527

4

22

2

−

−

.

,,

.Q

ENG-


Page: 19 of 23

σ t

T

A=

where A = cross-sectional area of drill pipe body, in2

For Grade E:

( )( )σ σ σb t t= − − −19500

10

67

0 6

670335002

2.

This equation holds true for values of σ t up to 67,000 psi.

For Grade S-135:

σσ

bt= −

20000 1145000

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 doglegangle. Metallurgists have established S-N (stress vs bending cycles) diagrams that can be used todetermine the approximate number of cycles, or rotations, before pipe failure occurs. The fraction (f) ofdrill pipe life expended in an interval of a dogleg can be calculated as follows:

f =B

Nwhere

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

Vwhere

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 theactual bending stress (σ b ). This value can be computed as follows:

σboE D c

=2

whereD = outside diameter of the pipe, in.

E = Young' s modulus, lb / in

c = maximum pipe curvature, radians / in.

2

o

The relationship between the hole curvature ( c ) and the Maximum pipe curvature ( co ) is:

( )c c K Lo =

wherec = hole curvature, radians / in.

L = one half the length of a drill pipe joint, in.

ENG-


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

0

10

20

30

40

50

60

10 100 1000 10000

Revolutions to failure ( x 1,000)

Ben

din

g s

tres

s (

x 1,

000)

In the presence for tension, however, the fatigue effect of bending becomes more severe. To make theproper allowances for this , the actual bending stress, (σ b ), must be multiplied by a correction factor, τ,

as follows:

τσ

=T

T - t

whereT = 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 τσ b . Determine

the number of cycles, N, to failure. Enter N into the first equation to determine the fraction of the pipelife 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:

TSA P R f

CosR ft

s= + +

12 2π ϑ

whereT

S

A

P

R

R R L

L

f

s

t t t

t

= 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) is determined / 2 .

For API connections is calculated as the total pin length minus

the box counterbore depth, specified as in API Spec. 7.

= Coefficent of friction on mating surfaces (thread or shoulder)

= 1 / 2 included angle of threadϑ

As the use of the formula is complicated, it has been rewritten under a simplified form with pre-calculated parameters.

ENG-


Page: 21 of 23

( )[ ]TSA

X OD Q= + +12

0 02.

where

( )

( )

A

A M ID

A OD B

ID

OD

pin

box

= The smaller of A or A

= Inside diameter (inches)

= Oustside diameter (inches

pin box

= −

= −

π

π4

4

2

2

For the standard connections in use within the company the values of X, M, B, and Q are given in thefollowing table.

Type of Connection X M B QNC 31 ( 2 7/8 IF) 0.1753 9.133 11.496 3.4531NC 38 (3 ½ IF) 0.2022 13.30 16.124 4.0780NC 46 (4 IF) 0.2381 19.94 23.460 4.9060NC 50 ( 4 ½ IF) 0.2573 23.82 27.560 5.31256 5/8 Regular 0.2885 31.04 36.000 6.06257 5/8 Regular 0.3228 42.48 49.000 7.09408 5/8 Regular 0.3660 55.80 63.250 8.0470

Values of stress (S) to be taken for:

Make up TorqueCalculation

Maximum allowableTorque Calculation

Tool joint of drill pipes S= 72,000 psi S = 120,000 psi (2)Drill collar (OD < 7”) 62,500 (1) 110,000 (2)Drill collar (OD> 7”) 62,500 (1) 100,000 (2)

(1) API recommendation (RP7G)(2) Minimum yield strength of material, specified by API (Spec. 7)

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 shoulderedconnection. The loads considered in this simplified approach are torsion and tension. Bending andinternal pressure are not included, nor is the contribution of shear stress due to torsion. A design factor

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 jointID = 3 ¼”

( )

( )

( )[ ]

A = 4

= 10.41 inches

A = 4

= 11.54 inches

So, A = 10.41 in

T = S x 10.41

12Make - up Torque = 72,000 x .43 = 30,960 ft - lb

Maximum Allowable Torque = 120,000 x .43 = 52,000 ft - lb

pin2

box2

2

π

π

2382 325

65 2756

0 2573 0 02 65 53125 0 43

2 2

2 2

. .

. .

. . . . .

−

−

+ + = S x

ENG-


Page: 22 of 23

of 1.1 should be used to provided some safety margin. This safety margin may not be sufficient forcases 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:

PYm

Ap

TYm

xAb x

P Rt f

CosRs f

TYm

xAp x

P Rt f

CosRs f

TYm

xAp x

P Rt f

Cos

TYm

x

Ap Ab

Ap Ab

P Rt f

CosRs f

111

111 12 2

211 12 2

311 12 2

411 12 2

=

=

+ +

=

+ +

=

+

=

+

+ +

.

.

.

.

.

π θ

π θ

π θ

π θ

Depending on the connection geometry, T3 may be greater or smaller than T4. The same is true for T1and T2.

App

lied

Ten

sion

Applied Torsion

Shou

lder

Sep

arat

ion

P1

T1 T2

T3T4

Box

Yie

ld

Pin Yield

RecommendedZone of Operation

00

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 onthe pin.

Figure 15.2.1

16. Combination Tube and Connection PerformanceUnless we have inadvertently reduced the tool joint tensile capacity by excessive make-up, the tensilecapacity or combined tension-torsion capacity of the string will probably be limited by the tensilecapacity of the drill pipe tubes. Curves of combined load capacity for tool joints and tubes can be usedto estimate the tensile and combined tension / torsion load capacity for the string as a whole. This iseasily done by superimposing the combined load curve for the appropriate tube onto the combined loadchart for the tool joint. An example is shown in Figure 16.1 for 5 inch 19 ppf, grade S-135 tube with a 3¼” ID NC-50 tool joint.

ENG-


Page: 23 of 23

Drillstring combined tension-torsion load capcacity superimposed over the

load capacity of tool joint

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

0 10,000 20,000 30,000 40,000 50,000 60,000

Torsion (ft-lb)

A B

C

E

D

G

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 appliedtorsion 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. Tubeweakness in pure tension and tool joint weakness in pure torsion are typical for common tube / tool jointcombinations.

Point G is the absolute limit of make-up torque without reducing the pin neck’s ability to carry externaltension 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 calculatedusing the following shown below.

Where

Critical RPML

D d= +476000

22 2

L = length of one pipe, inches

D = Outside diameter of pipe , inches

d = inside diameter of pipe, inches

17.2 Axial Vibration

The approximate critical rotary speeds which induce pendulum or spring (axial) vibration can becalculated using the following shown below.

WhereCritical RPM

L ft=

258000

( )

L(ft) = Total length of string, feet

17.3 Harmonic Vibrations

Secondary and higher harmonic vibrations will occur at 4, 9, 16, 25, 36, … etc. time the speed in theabove equation. Vibrations of spring pendulum type are probably less significant than nodal type. Eachhigher harmonic of the spring pendulum type vibration is also less significant. Care should be taken toavoid operating under these conditions which would be the critical speed for both types of vibrationbecause the combination would be particularly bad.

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Drillstring Design Manual