Drillstring Design Manual

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Author: M. Andrea Reviewed by: Approved by:

Engineering Recommendations

Ref.: Page: 1 of 23 Issued: Revision: 00

Drill String Design Recommendations

Summary

This document provides the principals utilized for drill string design in the oil well drilling industry. These specifications can be used whenever designing a drill string, with agreement from the Regional Technical/Operations Managers

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

00 First Issue 20/04/98

Revision Number

Description of amendments / page changes/comments Date dd/mm/yy

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1. Purpose

These procedures shall be used whenever designing a drillstring, unless otherwise decided with the Region Technical/Operations Managers.

2. Scope

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

Tension 1.1

Margin of over pull 50,000 to 100,000 lbs Excess BHA weight 1.15

Torsion 1.0 (based on lesser of pipe body or connection strength)

Collapse 1.1. to 1.15

Burst 1.2

The design process shall address the following items: 1. Selection of drill collar diameter

2. Selection of BHA connections

3. Determination of drill collar and or HWDP length 4. Tool joint torsional capacity check

5. Tension design limitations 6. Burst pressure determination 7. Collapse pressure determination 8. Slip crushing load

9. Fatigue limits

10. Combined tension and torsional load limits

3. Responsibility

The Region Technical/Operations Managers are responsible of the enforcement of this standard throughout the SF organization

4. References

Engineering Standard RE-ST-516-01 issued November 1992

API specification 5D (SPEC 5D), 3 rd edition, August 1, 1992 or latest edition API specification 7 (SPEC 7), 38 th edition, April 1994, or latest edition

API Recommended Practice 7G (RP 7G), 15 th edition, January 1, 1995, or latest edition

5. Distribution, filing and storage of this document

In accordance with Procedure RE-PR-M&M-02, this document shall be inserted in: - MPP manual volume 4, PSS Family Number: 516

6. Abbreviations and Definitions used

6.1. Abbreviations

SF: Sedco Forex

HQS : the Headquarters of SF located in Montrouge France

Eng: the Engineering Department of SF located in Montrouge.

M & M: Materials & Maintenance department within R & E

PSS: Property Symbolization System used within Sedco Forex.

MPP: Maintenance Policies and Procedures

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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 yield strength of the pipe. This value is important because it is used in burst, collapse, and tension calculations. Common grades are as follows:

Grade Letter Designation

Assumed Average Yield Strength (psi) (used for collapse)

Minimum Yield Strength (psi) D-55 65,000 55,000 E-75 85,000 75,000 X-95 110,000 95,000 G-105 120,000 105,000 S-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 worn condition. Casing and tubing are usually new when installed in a well. As a result, “classes” are given to drill pipe to account for wear. Therefore, drill pipe must be defined according to its nominal weight, grade, and class. The API has established guidelines for pipe classes in API Recommended Practice 7G. Although the class definitions can be extensive, they are summarized as follows:

New - 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, based on 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, regardless of the drill pipe tube grade on which they are installed, are made of 120,000 psi yield strength material. Several types are widely used:

IEU (internal-external upset) Tool joint is larger than the pipe such that the tool joint ID is less than the drill pipe. The tool joint OD is larger than the drill pipe. Generally IEU connections are the strongest available couplings.

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

IU (internal upset) Tool joint ID is less than the pipe. Tool joint OD is approximately the same as the pipe. This type is often termed “slim-hole” pipe because of the reduced outer clearance.

An important note about tool joints is that they are designed to be run in tension.

Hardfacing, of hardbanding, tool joints has become a common practice in the drilling industry. To minimize tool joint wear while rotating on abrasive rock, a band of abrasion-resistant material is applied to the outside of the box tool joint. This material is usually sintered tungsten carbide particles in a welded metal matrix. The problem that often arises from the use of hardfaced tool joints is excessive wear on the internal diameter on the casing.

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7.4 Thread Form

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

Besides thread form and number of threads per inch, a connection can also be distinguished by dimensional data relating to the small and large diameters of pin, box bore, length of pin and box, etc. API suggests the use of the term “number connection” (NC) to distinguish the various sizes and styles of rotary connections. The NC refers to the pitch diameter of the pin thread at gauge point when rounded to units and tenths of inches, Thus if the pitch diameter is 1.063 in, the first two figures are used, i.e. 10, to provide a description of the connection as NC10.

8. Drill Collars

8.1 Drill Collar Selection

Drill collars are the predominant components of the bottom-hole assembly. Some of the functions of the drill collars are as follows:

• Provide weight for the bit

• Provide strength needed to run in compression

• Minimize bit stability problems from vibrations, wobbling, and jumping

• Minimize directional control problems by providing stiffness to the BHA

Proper selection of drill collars (and BHA ) can prevent many drilling problems. Drill collars are available in many sizes and shapes, such as round, square, triangular, and spiral grooved. The most common types are round (slick) and spiral grooved. Spiral-grooved collars reduce the surface contact area between the pipe and well bore. The lower contact area reduces the probability of differential pressure sticking. Table 8.1 (below) shows the API dimensions for collars of various outer diameters.

Drill Collar Number OD, in. Bore +1/16 -0, in.

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

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8.2 Size Criteria

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

For Example:

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

10 625

12 25

9

2 .

"

hole

=

. "

Bit dia

.

+

"

Drill collar dia

.

More commonly drill collar size is selected based on stresses. Components subject to bending have both tensile and compressive forces induced in them. When rotated under bending, individual metal fibers are subject to rapidly alternating tension and compression, which may induce fatigue failure. BHA’s are subject to both bending and rotation. Fatigue failures commonly occur where stresses are concentrated. Stresses are concentrated at connections and changes in pipe size. Stress concentration is restricted by ensuring that changes in bending resistance are within tolerable ranges. The bending resistance of a BHA component is dependent upon its section modulus, which is defined as follows:

(

)

Z x I OD OD ID OD =2 ÷ = − 32 4 4 π

Where Z = Section modulus, in I = Second moment of area, in OD = Outside diameter, inches ID = Inside diameter, inches

3 4

Minimum effective hole dia.=Bit size+Drill collar dia. 2

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Generally, the change in bending resistance is expressed in terms of a bending resistance ratio (BRR), which may be calculated as follows:

(

)

(

)

BRR

Z

OD

ID

OD

ID

OD

=

−

1 2 1 4 1 4 2 2 4 2 4 1

The terms are illustrated at right The bending resistance ratio should be checked at changes in pipe size. BRRs are calculated using the pipe body dimensions and should generally be below 5.5

8.3 Drill Collar Connections

The bending resistance ratio of drill collar connections is defined as the section modulus of the box (measured 4” from the end) divided by the section modulus of the pin (measured 3” from the end). The inside diameter of the box and outside diameter of the pin are determined by the type of connection; therefore, only the outside diameter of the box and inside diameter of the pin need to be measured. This is illustrated at right

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

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

Conditions Acceptable BRR Range

DCs < 6” OD 2.75 - 2.25

High RPM with DCs << hole size 2.85 - 2.25 Low RPM with DCs close to hole size 3.20 - 2.25

OD2

OD1

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.

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9. Allowable Weight on Bit

9.1. Discussion Vertical Holes

An important function of the bottom hole assembly (BHA) is to protect the drill pipe from buckling. In straight holes, buckling of the pipe is prevented by using a BHA of sufficient weight to ensure that the neutral point of bending is kept within the BHA. A common misconception is that the neutral point of tension and compression is relevant in BHA design.

When a drillstring is run into a straight hole, the forces acting on the string are self-weight and hydrostatic pressure of the drilling fluid. This hydrostatic effect, commonly called buoyancy, results from the pressure exerted vertically on the cross-sectional area of the drillstring. For a drillstring of constant cross section, the resulting hook load can be calculated as follows:

(

)

(

)

HL

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 compression and reduces the hook load.

Buckling occurs only below the neutral point of bending, which is defined as the point where the average of the radial and tangential stress in the string equal the axial stress.

The neutral point of bending occurs where the effective hydrostatic force equals the compressive force in the drillstring. With no WOB, this point is at the bottom of the string; therefore, the drillstring is not buckled. Stress conditions within the drillstring in a vertical hole are shown at right.

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

The height of the neutral point of bending above the bottom of the drillstring can be calculated as follows. Neutral point of bending Neutral point of tension/compression Pipe stress Equivalent mud hydrostatic force Compression Tension

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(

)

(

) (

)

(

)

(

)

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

(

)

= WTstringx1−0 015. x MW

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

To prevent the neutral point of bending from being in the drill pipe, the buoyed weight of the BHA must exceed the applied WOB. In practice, field applications commonly allow for a safety factor. It is recommended that the applied WOB should be limited to 85% of the buoyed weight of the BHA (provided the HWDP is not buckled)

Heavy-weight drill pipe is generally run as transition pipe between the drill collars and the drill pipe. Sedco Forex field experience indicates that it is not acceptable to run heavy-weight drill pipe for WOB in

vertical holes.

9.2. Discussion Inclined Holes

In inclined holes, two additional factors must be

considered when calculating the maximum weight on bit that can be run without buckling the drill pipe. • Weight on bit is applied at the inclination of the well, but the weight of the BHA

continues to act vertically.

• To allow for the reduction in available BHA weight, the buoyed weight must be reduced by a factor equal to the cosine of the well inclination.

The drillstring generally lies on the low side of the hole and obtains some lateral support from the bore hole wall. In these circumstances, pipe above the neutral point of bending buckles only when the compressive forces in the drillstring exceeds a critical load, calculated as follows:

(

)

(

)

F

_crit ODpipe IDpipe x BF x OD_D _ODpipe IDpipe x Sin

hole tj

=

1617

− ₋ −

4 4 2 2 _θ

Neutral point

of bending Neutral point of tension/compression Pipe stress Equivalent mud hydrostatic force Compression Tension WOB

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Where

F = 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 θ

The curve in Appendix 1 represents a graphical solution to the equation for critical buckling. 9.3 Vertical Hole Calculation Procedure

Available weight on bit can be calculated as follows:

(

)

WOB

_max

=

0 85

.

x L

_dc

x WT

_dc

1 −

0 015

.

x MW

Where WOBMAX = Available weight on bit, lb

Ldc = Length of drill collars, ft

WTdc = Air weight of drill collars, lb/ft

MW = 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. This recorded value can then be used as the maximum allowable weight on bit, provided that the mud weight is unchanged.

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

New WOB

Old WOB

MW

new old

=



−

₋











max

.

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 is the available weight on bit.

372’ of 8” x 3” drill collars with an air weight of 147 lb/ft

465’ of 5” x 3” heavy weight drill pipe with an air weight of 50 lb/ft

Because the hole size does not exceed the nominal tool joint size by more than 6”, the HWDP is used for drilling weight. The weight on bit available from the BHA is

(

)

WOB

_max

=

0 85

.

x L

_dc

x WT

_dc

1 −

0 015

.

x MW

= .85 x 372 x 147 x (1-0.015 x 13) = 37,418 lbf

What would be the available weight on bit if, while drilling, the mud weight is increased to 16.5 ppg?

New WOB

Old WOB

MW

new old

=



−

₋











max

.

1 0 015

=



−

₋











37 418

1 0 015 16 5

1 0 015 13

,

.

x

= 34,987 lbf

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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

_dc

=

L

_dc

x WT

_dc

1 −

0 015

.

x MW x Cos

θ

Where WOBDC = Available weight provided by collars, lb

Ldc = Length of drill collars, ft

WTdc = Air weight of drill collars, lb/ft

MW = Mud weight, ppg

θ = Bottom hole inclination, degrees 2. Calculate the maximum available WOB provided by the HWDP.

(

)

WOB

HWDP

=

L

HWDP

x WT

HWDP

1 −

0 015

.

x MW x Cos

θ

Where WOBHWDP = Available weight provided by HWDP, lb

LHWDP = Length of HWDP, ft

WTHWDP = Air weight of HWDP, lb/ft

MW = Mud weight, ppg

θ = Bottom hole inclination, degrees 3. Calculate the critical force to buckle the HWDP.

(

)

(

)

F

_crit ODHWDP IDHWDP x BF x OD_D _ODHWDP IDHWDP x Sin hole tj

=

1617

− − − 4 4 2 2 _θ Where

F = Critical buckling force for HWDP,

OD = Outside diameter of pipe of HWDP, inches

OD = Max OD of pipe, inches ID = Inside diameter of pipe, inches BF = Buoyancy factor, = (1 -.015 x MW) D = Diameter hole, inches

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

(

)

(

)

F

crit

OD ID x BF x OD ID x Sin

D OD

pipe pipe pipe pipe

hole tj

=

1617

− − −

4 4 2 2 _θ

Where

F = 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

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

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

WOBMAX = WOBDC + WOBHWP + Fdp

The maximum allowable weight on bit calculated above should be reduced by a safety factor. Generally, a safety factor of 85% is adequate.

9.5 Weight of BHA Required

Weight of DC’s required is estimated from the bit specifications and formation classification. Weight on bit and rotary speed

Formation Classification lb / in of diameter RPM

Soft 2270 - 6750 100 - 250

Medium 4500 - 9000 40 - 100

Hard Milled Tooth Insert 5600 - 11250 35 - 70

Hard Insert Bit 2250 - 9000 35 - 70

Hard 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 of each size, weight, grade and classification of drill pipe to support the submerged weight of all the drill pipe plus the submerged weight of the collars, stabilizers, and bit. This load may be calculated as shown in the following equation. The bit and stabilizer weights are either neglected or are included with the drill collar weight.

(

)

(

)

[

]

F

_TEN

=

L

_dp

x WT

_dp

+

L

_dc

x WT

_dc

BF

where F 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 permanent deformation of the material begins, but the stress at which a certain total deformation has occurred. This deformation includes all of the elastic deformation as well as some plastic (permanent) deformation. The tensile strength can be calculated from the equation.

F

_yield

=

Y A

_m where

F_yield Y_m

A

= 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 permanent stretch will occur and difficulty may be experienced in keeping the pipe straight

10.2 Margin of Over Pull

To prevent this condition a design factor of approximately 90% of the tabulated tension value is recommended.

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F

_design

=

F

_{yield x}

0 9

.

where

F

_design

F

_yield

= minimum tensile strength, lb

0.9 = a constant relating proportional limit yield to strength

The difference between the calculated load F_TEN and the maximum allowable tension load represents the Margin of Over Pull (M.O.P.).

M O P

. . .

=

F

_design −

F

_TEN

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

S F

F

design TEN

. .

=

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

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

L

F

x

M O P

WT

x BF

L

WT

dp yield 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 2

Depth 12,700 feet

Hole Size 7 7/8 inches

Mud Weight 10 lb/gal

Margin of Overpull (MOP) 50,000 lb. Length of Drill collars 630 feet Weight per foot 90 lb.

L

F

x

M O P

WT

x BF

L

WT

dp yield dp dc dc dp 1 1 1

0 9

=

.

−

. . .

−

L

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”, 16.60 lb/ft Grade X-95, with 4 ½” X.H. Tool Joints, 6 ¼” O.D. x 3” I.D. (18.88 lb/ft) Inspection class premium. Air weight of number 1 class drill pipe and drill collars:

(

)

(

)

[

]

(14)

11.Burst

11.1 Pipe Burst Calculation

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

P

Y Wt

D

i m

=

2

where

P

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 and squeeze cementing. Drill stem testing (DST) causes the most severe collapse loading on the drill pipe. API specifications for collapse resistance of drill pipe is calculated assuming either plastic, transition, or plastic failure based on the pipes D/t (diameter / wall thickness ratio). The applicable equations can be found in the API RP 7G publication.

12.2 Effect of tensile load on collapse

The effect of tensile load applies only to greater than transition load on normally elastic item, and to any load on plastic collapse items. The collapse resistance of drill pipe corrected for the effect of tension loading may be calculated with the following equation:

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

(

) (

)

[

]

Total Weight

x

lb

=

+

=

+

=

6759

18 37

630

90 124 163

56 700

180 863

.

,

.

Determine the length of the second string of drill pipe.

L

F

x

M O P

WT

x BF

L

WT

L

WT

L

x

L

feet

dp yield dp dc dc dp dp dp dp dp 2 2 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 the following:

Weight in Air Weight in Mud

Item Feet lb. Lb. .

Drill Collars 630 56,700 48,025

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

(15)

Where

R

Z

x Z

R

=

− +

4 −

3

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)

Collapse (% of yield stress)

Compression Burst

Compression & Collape

Tension & burst

Tension and Collapse

Axial Stress % of Yield

(16)

12.3 Slip crushing

The maximum allowable tension load must be determined to prevent slip crushing. In an analysis of the slip crushing problem, Reinhold, Spini, and Vreeland, proposed an equation to calculate the relation between the hoop stress (SH) caused by the action of the slips and the tensile stress in the pipe (ST),

resulting from the load on the pipe hanging in the slips. If the dimensions for the cross-sectional area of the pipe (A) and the cylindrical surface are of the pipe under the slips (AS) are used, the equation can be

presented as follows: where

S

DK

L

DK

L

H T S S

= +

+

























≈

1

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

µ

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

where

T

x

S

S L H 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. Determine the actual collapse resistance of the bottom joint of drill pipe.

Rated collapse for New, 5”, 19,5 ppf, grade G pipe is = 12,999 psi Cross section area = 5.275 sq. in.

Average Tensile yield = 120,000 psi

Z = 80,000 lbs / (5.275 sq. in. x 120,000) = .126 or 12.6%

From figure 11.1 for biaxial loading, a tensile ratio 12.6% reduces the collapse resistance to 95%. Thus, the collapse resistance of the bottom joint of drill pipe = .95 x 12,999 psi = 12,350 psi

(17)

13. Pipe Torsion

13.1 Torsion Only

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

where

(

)

Q x J x Y D Q 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, the minimum torsional yield strength under tension is given as follows

where

(

)

Q J D Y P A Q D d t m t m = − − 0 096167 ₂ 2 2 4 4 .

= minimul torsional yield strength under tension, ft - lb

J = polar moment of inertia, 32

D = Pipe OD, inches d = Pipe ID, inches 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 slip crushing force on the drill string.

(

)

S S DK L DK L K S S x x x x H T S S H T = + +              = + = + +              1 2 2 1 9 27 45 0 08 1 4 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 T S S T S L H 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.)

(18)

14. Fatigue

14.1 Limits

The most common type of drill pipe failure is fatigue wear. It generally occurs in dog legs where the pipe goes through cyclic bending stresses. These stresses occur because the outer wall of the pipe in a dog leg is stretched and creates a greater tension load. As the pipe rotates a half cycle, the stresses change to the other side of the pipe, For example, the stress may change from 50,000 psi to -20,000 psi and again to 50,000 psi in the course of one cycle or rotation of the pipe.

Fatigue damage from rotation in dog legs is a significant problem if the angle is greater than some critical value. Lubinski has published several works that describe this value. Rotation in angles below

this value does not cause appreciable fatigue. The maximum permissible dogleg severity for fatigue damage consideration can be calculate with the following equations:

(

)

C

K L

E D K L

K

T

E I

C

ft

E

D

L

T

I

D

d

b

=

−

432 000

64

4 4

,

tanh

/100

σ

π

σ

π

= 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

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 the maximum torque which can be applied to the pipe (neglecting connection strength in this example) if 100,000 lbs of over pull is applied

(

)

J = polar moment of inertia,

32 = 28.53 inches

D = Pipe OD, inches d = Pipe ID, inches A = cross - sectional area, in = 5.27 in

= 0.096167 x 28.5383 5 = 44,640 ft - lbs 4 2 2 π 5 4 276 105 000 350 000 527 4 2 2 2 − − . , , . Q

(19)

σ

t

T

A

=

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

For Grade E:

( )

(

)

σ

b

=

19500

−

σ

t

−

σ

t

−

10

67 0 6

670

2

33500

2

.

This equation holds true for values of

σ

_tup to 67,000 psi. For Grade S-135:

σ

b

σ

t

=

20000 1



_

−



_

145000

This equation holds true for values of

σ

_tup to 133,400 psi. 14.2 Fraction of Drill Pipe Life Expended in Dogleg

Severe pipe damage occurs when dogleg severity is greater than the value computed for

C

above. The damage depends on the type of material (aluminum or steel), corrosion level, stress, and dogleg angle. Metallurgists have established S-N (stress vs bending cycles) diagrams that can be used to determine the approximate number of cycles, or rotations, before pipe failure occurs. The fraction (f) of drill pipe life expended in an interval of a dogleg can be calculated as follows:

f

=

B

N

where

f = fraction of life expended

B = number of drill pipe revolution to drill interval

N = number of revolutions to failure of joint of drill pipe

It is simple to show that:

B =

60 R d

V

where

R = rotary speed , rpm

d = length of dogleg interval, ft

V = drilling rate ft / hr.

In order to determine (N) the number of revolution to failure of the joint of drill pipe we need to know the actual bending stress (

σ

_b). This value can be computed as follows:

σ

b o

E D c

=

2

where

D = 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

o

=

c K L

where

c = hole curvature, radians / in.

(20)

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) Bending stress ( x 1,000)

In the presence for tension, however, the fatigue effect of bending becomes more severe. To make the proper allowances for this , the actual bending stress, (

σ

_b), must be multiplied by a correction factor, τ, as follows:

τ

=

T

_σ

T -

_t

where

T = tensile strength of the pipe

The vertical axis of the S-N curve should be entered with the product of τ and

σ

_b, or τ

σ

_b. Determine the number of cycles, N, to failure. Enter N into the first equation to determine the fraction of the pipe life expended in drilling the section.

15. Tool Joint Performance

15.1 Make-up and Yield Torque

The make up torque of a rotary shouldered connection is calculated by using the Farr’s formula API 7G:

T SA P R f Cos R f t s =  + +      12 2π ϑ where T 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 thread

ϑ

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

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(

)

[

]

T = SA 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 π 4 4 2 2

For the standard connections in use within the company the values of X, M, B, and Q are given in the following table. Type of Connection X M B Q NC 31 ( 2 7/8 IF) 0.1753 9.133 11.496 3.4531 NC 38 (3 ½ IF) 0.2022 13.30 16.124 4.0780 NC 46 (4 IF) 0.2381 19.94 23.460 4.9060 NC 50 ( 4 ½ IF) 0.2573 23.82 27.560 5.3125 6 5/8 Regular 0.2885 31.04 36.000 6.0625 7 5/8 Regular 0.3228 42.48 49.000 7.0940 8 5/8 Regular 0.3660 55.80 63.250 8.0470

Values of stress (S) to be taken for:

Make up Torque Calculation

Maximum allowable Torque 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 shouldered connection. The loads considered in this simplified approach are torsion and tension. Bending and internal pressure are not included, nor is the contribution of shear stress due to torsion. A design factor

EXAMPLE: Tool joint Performance

A new string of 5”, 19.5 ppf, grade G, drill pipe with NC 50 connections, tool joint OD = 6 ½” , tool joint ID = 3 ¼”

(

)

(

)

(

)

[

]

A = 4 = 10.41 inches A = 4 = 11.54 inches So, A = 10.41 in T = S x 10.41 12 Make - up Torque = 72,000 x .43 = 30,960 ft - lb

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

pin 2 box 2 2 π π 2382 325 65 27 56 0 2573 0 02 65 53125 0 43 2 2 2 2 . . . . . . . . . − − + + =S x

(22)

of 1.1 should be used to provided some safety margin. This safety margin may not be sufficient for cases involving severe bending or elevated temperature.

The failure criteria is either torsional yield or shoulder separation. The end points for the limits are defined by five equations:

P Ym Ap T Ym x Ab x P Rt f Cos Rs f T Ym x Ap x P Rt f Cos Rs f T Ym x Ap x P Rt f Cos T Ym x Ap Ab Ap Ab P Rt f Cos Rs f 1 11 1 11 12 2 2 11 12 2 3 11 12 2 4 11 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 T1 and T2.

Applied Tension

Applied Torsion

Shoulder Separation

P1

T1

T2

T3

T4

Box Yield Pin Yield Recommended Zone of Operation

0

The line (0,0) to (T4, P1) represents shoulder separation for low make-up torque. The line (T2, 0) to (T3, P1) represents pin yield under the combination of torque and tension. The line (T1, 0) to (T1, P1) represents box yield due to torsion. The horizontal line from P1 represents maximum tension load on the pin.

Figure 15.2.1

16. Combination Tube and Connection Performance

Unless we have inadvertently reduced the tool joint tensile capacity by excessive make-up, the tensile capacity or combined tension-torsion capacity of the string will probably be limited by the tensile capacity of the drill pipe tubes. Curves of combined load capacity for tool joints and tubes can be used to estimate the tensile and combined tension / torsion load capacity for the string as a whole. This is easily done by superimposing the combined load curve for the appropriate tube onto the combined load chart for the tool joint. An example is shown in Figure 16.1 for 5 inch 19 ppf, grade S-135 tube with a 3 ¼” ID NC-50 tool joint.

(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 applied torsion on the tube. Point E is the tube’s load capacity in torsion with no tension.

Line DE is the combined load capacity of the tube under simultaneous tension and torsion. Tube weakness in pure tension and tool joint weakness in pure torsion are typical for common tube / tool joint combinations.

Point G is the absolute limit of make-up torque without reducing the pin neck’s ability to carry external tension to less than the tensile capacity of the tube.

17. Critical Rotary Speeds

17.1 Transverse Vibration

The approximate critical rotary speeds which induce nodal (transverse) vibration can be calculated using the following shown below.

Where

Critical RPM

L D d

= 476000₂ 2 + 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 be calculated using the following shown below.

Where Critical 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 the above equation. Vibrations of spring pendulum type are probably less significant than nodal type. Each higher harmonic of the spring pendulum type vibration is also less significant. Care should be taken to avoid operating under these conditions which would be the critical speed for both types of vibration because the combination would be particularly bad.

Drillstring Design Manual

Engineering Recommendations

Drill String Design Recommendations

Table of Contents

1.

Purpose

2.

Scope

3.

Responsibility

4.

References

5.

Distribution, filing and storage of this document

6.

Abbreviations and Definitions used

7.

Drill Pipe Properties

8.

Drill Collars

10 625

12 25

9

2

.

"

hole

=

. "

Bit dia

.

+

"

Drill collar dia

.

(

)

(

)

(

)

BRR

Z

Z

OD

ID

OD

OD

ID

OD

=

=

−

−

9.

Allowable Weight on Bit

(

)

(

)

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

=

−

=

₋