spe 21942critical buckling inclined ms

8/19/2019 SPE 21942critical Buckling Inclined MS

1/16

SPE I DC

SPE IADC 2 942

The Critical Buckling Force and Stresses

or Pipe n Inclined Curved Boreholes

F.J. Schuh, Drilling Technology Inc.

SPE Member

Copyright 1991, SPEJIADC Drilling Conference.

This paper was prepared for presentation at the

99

SPEJIADC Drilling Conference held in Amsterdam,

4

March 1991.

This paper was selected for presentation by an SPEJIADC Program Committee following review of information contained in an abstract submitted by the author s . Contents of the

paper, as presented, have not been reviewed by the International Association

of

Drilling Contractors or the Society of Petroleum Engineers and are subject to correction by the author s .

The material, as presented, does not necessarily reflect any position of the SPE or IADC, its officers, or members. Papers presented at SPEJIADC meetings are subject to publication

review by Editorial Committees of the SPE and IADC. Permission to copy is restricted to an abstract

of

not more than 300 words. Illustrations may not be copied. The abstract should

contain conspicuous acknowledgment of where and by whom the paper is presented. WritePublicationsManager,

SPE

P.O. Box833836, Richardson,

1

75083-3836. Telex, 730989SPEDAL.

STR CT

A

number

of papers

have been

presented

that

define

the critical

buckl

ing force in incl ined straight

holes This paper presents a

method

for calculat-

ing

the

critical

buckling force in

vertically and

laterally

curved and inclined boreholes

The paper includes

methods

for computing the

bend-

ing

stress of buckled pipe with tool

joints It

also includes a method for

computing if

the deflec-

tion of the pipe

at

midspan

will cause the pipe

body

to touch the wall

of

the hole This approach

resolves the question of

how

tool

joints affect

the critical

buckl

ing force the curvature of the

pipe

and maximum

bending

stresses

The

paper includes plots of the

critical

buckling

force versus hole curvature for common sizes of

drillpipe

and Heviwate

We

also include plots of

the

maximum bending

stress versus axial force

and

hole curvature for several sizes of

drillpipe and

Heviwate

I

NTRODUCTI

The

optimum drillstring

design for horizontal

wells

must meet

the following objectives:

Provide the required axial

bit

loads

and

torsional

steering control for oriented

drill

ing

2

Provide the required bi t loads torsional

strength

and

fatigue resistance for rotary

drilling

3 Provide adequate overpull

4 Minimize the weight of the drill string compo-

nents without exceeding operating limits

References

and

figures

at end

of paper

403

Pasl

ey and Dawson

l

publ ished the

first

paper

concerned with hori zonta1 drill

stri

ng des i

gn

re-

quirements

In this

paper they presented a

method

for

calculat ing the

critical bucking

force

and

selecting drillstring tubulars for

drilling

in

straight

inclined or horizontal boreholes

The horizontal well designer is also interested in

selecting tubulars for the curved portions of the

borehole especially for the

high

curvature build

curve areas To

select

tubulars for these areas

we

need:

1. A method for determi

ni ng

the

crit

ical

buck-

ling force in curved boreholes

2 A method for determining the maximum bending

stress

of both

buckl ed and nonbuckl ed

pipe

in straight and

curved boreholes

3 A method for determi ni ng

when

the

pi pe

body

of the

drillstring component

will

be

in

con-

tact

with the wall of the hole

This paper presents another useful building block

for designing

drillstrings

for

high

curvature

and

horizontal holes

UCKLING IN

CURVED OREHOLES

The

industry

needs an

experimentally verified ana-

lytical

expression fo r

the critical

buckling

force

lateral

contact force

and

the

maximum bend-

ing

stresses of tool jointed pipe in three dimen-

sionally

curved boreholes Unfortunately

al l

that we

have

available are two conflicting deriva-

tions for the

critical buckl

ing force of smooth

pipe in

straight

incl ined boreholes Neither of

the authors have defi ned the

pi

tch the curvature

of the buckled pipe the lateral contact force or

analyzed

how

tool jointed pipe should

behave when

buckled

Although this

paper

falls

short of

this

requirement

we have utilized

a collection of


2/16

2

CRITICAL BUCKLING

FORCE

ND STRESSES

FOR

PIPE IN INCLINED

CURVED

BOREHOLES

SPE IADC

2

angle, we can combine th e

r el at io ns hi ps f or

pit

developed by Lu b i n s k P with th e Pasley/Daws

c ri t i c a l buckling f orc e equatio n

to

develope

relationship

between

th e vertical

build

rate

a

th e c ri t i c a l bucking force. In Appendix A th

relationship

is

shown

to be :

There is a s in gl e v e rt ic a l

build

rate and compre

sive

axial

force

fo r

which th e pipe is on th

verge

of being buckled

o r p os it io ne d

on

either th

to p or th e bottom

of th e

hole. This point

repr

sents

th e

minimum possible

axial force

that

c

buckle the pipe and th e maximum n eg a ti v e c u rv a tu

at th at

load

t h a t th e

pi pe

wi

11

no t

r i se

to

th

to p of t he h ol e. The s ol ut io n o f this point repr

sents the

minimum

axial

force

fo r

which Eq. 2 a

3 apply. This

point is

defined

as:

In a

vertically

c ur vi ng b or eh ol e

t h a t is

curvi

downward, the dri 11 str i

ng

can produce

three

mo

of

operations. For loads

less

than

th e c ri t i c

buckl i ng

force, the pi

pe

wi

11 1ay across

th e

bo

tom

side o f th e

hole. See

Fig.

5. For h ol es w

1arge

negat

i ve curvatures and loads greater

th

th e minimum c ri t i c a l buckling force th e pipe w

remain on

th e to p

side

o f

th e hole. See

Fig.

For

loads

above

th e

c ri t i c a l

buckling

force

a

negative

curvatures

less

than th e

cr i t ical

t

pipe will

be buckled as is

depicted

in

Fig.

Note

that th e

vertical

dimensions o f th e he lix f

negative

hole

c ur va tu re s a re greater

than

t he a ct

al

dimensions

o f th e curved

borehole.

Negati

curvatures i nc re as e t he

effective

radial

clearan

of th e pipe which in turn reduces th e c ri t i c

buckling

force.

This

is shown

in

Fig. 8.

By

adopti

ng

a cons i st e n t sign convent i on fo r

ho

curvature,

we can ut i l ize the same

equation

f

defi ni ng th e cr i t i ca1 bucki ng force of droppi

curvatures as was used

to represent

th e

c ri t i c

buckling

force

f or p os it iv e

hole

curvatures.

Fig. 9 depicts t he n eg at iv e hole curvature

that

required to

place

th e full dri l l st ri ng on th e t

of

th e hole and preclude

helical

buckling.

Th

relationship is derived in

Appendix A and

is i

cluded as follows.

. . . 2)

. • . . 3

12

W

m

•

si n

9 . 5730

5730 . W

m

. sin 9

FL

16

-4 . 5730 . 12

4 Fe .

5730

V R

c

=

1 2 · I

r .

F

L

V R

L

z

1 2 • E

Fe

z [

4 •

E . I . W

m

.

si n 9 ] 1/2

. . . .

l)

r .

12

Al th ou gh c ur ve d

boreholes

have both vert i

ca 1

and

1

atera

1

components o f curvature, vert i ca

1

curva-

ture

is

th e more

important

design consideration.

In a

v e r t i c a l l y curving

borehole, a compressively

loaded dri l l st ri ng can exhibit two modes o f behav

ior. See Fig. 1 and 2. For loads

less

than th e

c ri t i c a l l y buckl in g force, the path o f

th e

pipe

will be across th e bottom o f th e hole. I f th e

axial load exceeds

th e c ri t i c a l

bucking

force, the

pipe

will

be buckled

as

is

depicted

in Fig. 2. In

an

a ng le b Ui ld in g

interval,

th e shape o f th e

hole

reduces

th e

height

o f th e helix.

This

is

depicted

in Fig.

3. where th e dimensions of a st r a i g h t in -

clined

hole

are superimposed

on th e

helix

produced

in

a positively c ur vi ng b o re h ol e . The pipe would

actually f i t into a

hole

of an el l ipt ic shaped

cross section where th e width o f th e

hole

would be

unchanged but only th e height would be

altered.

However, in l ight

o f th e apparent relationship

between later al contact force and th e c ri t i c a l l y

buckl i

ng

force, i t is no t

unreasonable

to assume

that th e vertical dimensions dominate th e

buckling

mechanics.

p ub li sh ed b uc kl in g relationships and some simple

e n gi n ee r in g c o nc e pt s

to estimate

most

o f th e re -

quired information.

The f i rs t dilemma facing a designer interested in

buckling phenomena

is selecting

th e

appropriate

equation

to define the c ri t i c a l

buckling

force.

We have selected the Pasley/Dawson

relationship

over the

Cheatham s2

derivation

by

evaluating

th e

pi

pe

to

wall

contact

force

that

ex i

s ts

at

th e

to p of

th e

hel

ix

at th e

c ri t i c a l

force

condition.

As is

shown

in Appendix C the application of

Pasley/Dawson c ri t i c a l buckling force in a hori-

zontal hole

produces a positive ne t later al con

tact force a t a ll points along th e

helix

except

at

th e to p of

th e

he1ix where

the conta ct

force

is

found to be e xa ct ly z er o. With th e Cheatham s

cr itical buckling

force, the contact force is much

higher and

pushes

th e

pipe

a ga in st t he to p o f

th e

hole

with a

load equal to

twice

th e

weight

of

th e

pipe

fo r

a ne t contact force equal to the buoyant

weight

per fo ot o f th e

pipe. I t

seems i n t u i t i v e l y

obvious

t h a t

the Pasley/Dawson

equation

provides a

more

rational definition

of th e c ri t i c a l force

because minor r ed uc ti on in the axial force would

decrease

th e

contact

force

to

a

load

that

would be

unabl e

to

hold up

th e

weigh t

o f th e pi

pe across

th e

to p

o f th e

arch.

The Pasley/Dawson equation

is:

The Pasl ey/Dawson

equation

can be

modified to

predict th e c ri t i c a l buckl in g force

fo r

curving

boreholes by

replacing

t he r adi al

clearance in

th e

Pasley/Dawson equation with

an effective radial

clearance which accounts

fo r th e

curvature

o f th e

borehole.

Fig. 4 is a sketch t h a t shows th e rela-

t i onsh ip between

borehol

e

c urvature , the

di

f f e r -

ence

in radi

al

cl

earance,

Ar, and

the pitch

length of the buckled pipe. Assuming that th e

pitch o f

buckl

ed pipe is independent o f

hole

404


3/16

SPE IADC 21942

FR NK

J. SCHUH

3

and th e

corresponding hole curvature is:

4 5730 1 2 · r . Fcb

VBRcb

•

2 E· I

16 5730 • W

m

. si n 9

• • 4

solution

from Roark

4

to

the

compressively load

ed

dri ll pipe s it ua ti on .

We have also chosen to

neglect the gravity forces

as

th e

gravity

load

deflections ar e small compared with

the

tool joint

clearance. Fig.

17

is a

sketch of

a compressively

loaded joint of pipe in a curved borehole. The

maximum bending stress

occurs

at the

center

of the

span between tool joints.

The

maximum bending

stress

fo r

tool

jointed

pipe

under compression

is

given by:

TBR . L . E • OD

Sm ..

4 5730·

12

. j .

sin 57.3

.

L/j

• 6

5

Fig.

10

is a

plot of

th e

critical

buckling force

equations

fo r 5 in . 19.50 lb f t nominal

grade

E

drillpipe in an 8

1/2

in . hole. The minimum possi

ble buckling force is

shown

to be about 22,000 lb

with

the

vertical

hole

curvature

of

-6

deg/l00ft.

The bucking

force

rapidly increases

with

increas

ing hole curvature

to

49,000 lb fo r a straight

hole to

nearly

100,000 lb at 5 deg/l00 f t

The

plot

shows the

combinations of vertical

hole

curvature and axial

load

fo r which the

pipe

will

be buckled. For

hole

curvatures to the left of

this area

the

pipe

will

be posit ioned across

the

top of the hole. For combinations of

axial

comp-

ressive

load and vertical curvature less than and

to the right of the buckling curve, the pipe will

be

positioned along th e bottom

of the

hole. Fig.

11

compares

the critical

buckling force curva tu re

and curvatures fo r 5

in .

19.50 1b grade E dri l l -

pipe in

45

and

90

deg boreholes. Note that the

lower hole angle reduces

the critical

buckling

forces

although

th e

effect

is

not

highly

sensitive

to hole angle.

Fig.

12

and 13 show the critical

buckling force

relationships

fo r 4 1/2

in .

dri l l -

pipe in

an

8 1/2

in .

hole and 3 1/2

in . drillpipe

in

a 6 1/8 in .

hole. Fig.

14-16 show the critical

buckling forces for 5 in . and 4

1/2

in . Heviwate

in 8 1/2

in . holes

and 3 1/2

in .

Heviwate in

6 1/8 in .

holes.

M XIMUM

BENDING STRESSES

FOR COMPRESSIVELY LO DED

NON UCKLED PIPE

The

use

of

tool

jointed

pipe

in

curved boreholes

produces two

effects.

One good and the other

bad. The good

effect is that

t he sur face area of

contact

subject to

wall

sticking

forces is mini

mized.

The

bad

effect is that

the tool joints

increase th e maximum bending stresses produced by

the tensile or compressive

loads on

pipe

in

curved

boreholes. Lubinski f i rs t

derived the

relation

ship

fo r determining

the maximum

bending stress

of

tensilely loaded drillpipe in curved boreholes.

Hi s solution represents

the

dri l lpipe as a

tensilely loaded beamed column that

neg le cts th e

effect of gravity forces.

Appendix B includes a

similar

so lu tion for

the

compressively loaded tool

jointed

pipe used

in

horizontal drilling

applications.

We were quite

fortunate

in that

we

could adapt a beam column

405

This equat ion only appl

ies to

loading condi tions

where

the

pipe body at

th e center of the

span is

not laterally

supported

by th e wall of the hole.

The

maximum

hole curvature

fo r

which Eq 6

applies

is

defined

by

the loading conditions

where

the

center of the

pipe

body just

touches

the wall of

the hole but is not supported by i t This

condi

tion

is

dep ic ted in

Fig.

18 and

occurs

when:

2 . 5730 .

12

.

rc

T R =

m j L .

[tan 57.3

. L/4 j - L/4 . j]

• • • • .

7

For combinations of hole curvature and axial load

where a portion of the pipe body must be touching

the wall of

the

hole,

the


must

be

calculated

by an

iterative procedure. For

such conditions, Eq 7 must be

solved

by t r ia l and

error to

determine a pipe joint length that would

just

touch the wall of the

hole

at the ce nter of

the

span

for the defined conditions of

total

build

rate, axial load, and other dimensions. If this

value of

pipe joint length is then

substituted

in

Eq

6,

th e maximum bending stress calculated repre

se nts the maximum stress

on th e pip e.

The differ

ence between th e above determined 1ength and

the

actual

pipe length

r ep re sent s t he

amount

of

pipe

touching the wall of the hole.

M XIMUM

BENDING STRESSES OF

UCKLED PIPE IN

CURVED

OREHOLES

The maximum

bending

stress for

buckled pipe

in

curved boreholes can be ca l cul ated us i ng the

fo

1

lowing procedure.

1. Determine i f the pipe is buckled.

2. Determine

th e

maximum curvature of the

hel ix.

3. Using

t he curva tu re of the

hel

ix

determine

the

pipe

body of the tool jointed

pipe

will

touch th e wall of

the

hole.

4A If the

pipe

body does

not

touch, use the

curvature

of the helix

and

the

actual pipe

joint length to determine th e maximum bend

ing

stress

of th e buckled pipe.


4/16

4

CRITICAL

BUCKLING FORCE

ND

STRESSES FOR

PIPE IN INCLINED CURVED

OREHOLES

SPE/IADC 2

The

curvature

fo r which

the center

of th e pipe

body will

ju st

touch

th e

wall

of th e hole is

given

by:

4B If th e

pipe body

touches for the buckling

curvature

and

actual j oi nt length, deter

mine an

equivalent jo in t

length

that

would

ju st

touch

th e

wall of

th e hole

and using

i t

and

th e

helical curvature, calculate

th e

maximum bending s t r e s s fo r th e buckled

pipe.

The

maximum curvature of

th e

helically buckled

pipe i n a curved

borehole

is

as

deri

ved

in

th e

Appendix B to

equal:

5730 . 12

r·

F 2

TBR

Bbuc

,.

2 • E 8

. • 8)

In

th e plot

of 5

in. dril1pipe in an

8

1/ 2

hole, buckling only occurs in a straight hole

o

hole wit h negative

curvature.

The

conditions

when

th e pipe

body touches vary from 50,000 1b

a 4 deg/100

build to 26,000 1b in a 12 d

100

f t

b ui ld c ur va tu re . The plot fo r 4 1/ 2

dri11pipe

in an 8

1/ 2 in . hole

shows

sligh

lower

loads fo r

both

buck1

i

ng

and

th e

condit io

fo r which th e pipe body touches th e wall of

hole.

The

plot of

3

1/2

in .

dri11pipe in

6

1/ 8 in . ho1

e shows a very

lim ited area

acceptable axial loads and stress fo r high

h

curvatures.

Fig. 22-25

ar e similar plots fo r

4 1/2 and 3

1/ 2 in.

Heviwate

dril1pipe in

cur

boreholes. The

cen ter

span support pad

Heviwate reduces

th e

span

length

L

to 1/ 2

jo i nt

1

ength.

Thi s improves

th e

performance

high

curvature

holes. For

th e conditions

cover

none

of

th e

Heviwate

pipe will be

b uc kl ed n or

w

th e pipe body touch th e wall of th e

holes.

CONCLUSIONS

10)

1

th e

Pasley/Dawson

critical

buckling

equat

is the bes t rep resen ta tion

o f

th

phenomenon.

2. That

th e

Pasley/Dawson

equation

can

be

tended

to

curved

boreholes by adjusting

geometry

to

account

for

th e

shape

of

buckled pipe in

th e

curved borehole.

3. The maximum bending stress

fo r

compressiv

loaded

pipe

with tool

joints

can be compu

from

beam

column

theory.

4.

The beam

column

re1ati9nships also

allow

to predict ano th er u sefu l

design

limit

wh

is

th e

conditions fo r

which th e pipe b

will

touch

th e

wall

of

th e

hole.

We

would like

to

acknowledge

th e

significant c

t rib utio ns o f

those that have worked

to

prov

th e

industry

with

a

b e t t e r

understanding

buck1

i

ng

phenomena and

drill

s t r i

ng

stresses.

most significant of those are: John B Cheatha

CKNOWLEDGMENTS

We recommend that

th e

industry s buck1 i

ng expe

direct th eir attention to th e

needs

f or a na ly ti

solutions

to

th e cr i t ica l bucking force,

pitch, t he c ur va tu re

and

lateral c on ta ct f or ce

buckled

pipe in

three

dimensionally

curved bo

holes, the effect of tool joints on th e maxim

curvature

and

stresses o f

buckled

pipe,

and

experimental

measurements need

to

confirm

solutions.

RECOMMEND TIONS

5.

The

maximum bending stress of buckled p

in curved

boreholes

can be computed from

curvature of th e helix

and

th e

maximum be

in g s t r e s s for

compressively-loaded

to

jointed pipe in curved boreholes.

We conclude

that:

c

j

-

L/4 •

j ]

. . • . • •

9)

2 . 5730 . 12

B

c

L .

[tan 57.3

. L/4

If

th e

curvature

due to buckling Eq. 8)

is

1

es s

than

t he c urv atu re r eq uir ed fo r th e pipe

body

to

touch Eq.

9) ,

then th e pipe

body

is not touching

and

th e


fo r th e

buckled

pipe

is

given by Eq. 10.

Bbuc

L

E · OD

5mb

45730

.

12

j

sin 5 7 . 3 .

L/j)

I f B

c

is le ss than

Bbuc then Eq 9 must be

so1

ve


5/16

SPEjlADC 21942

FRANK

J.

SCHUH

5

Rapier

M

Dawson, David L. Garrett, Hans C.

Junkam

Wa1d, Edward

Lindsley, Arthur Lubinski,

Robert F.

Mitchell, Carey

Murphey,

and

Paul R

Pasley.

We hope

that these individuals will continue to

work

in this area and will eventually derive and

experimentally verify exact solutions to the cases

covered by this paper.

NOMENCLATURE

z Curvature at which the pipe body

would

just

touch

the

wall

of the hole, degjl00

ft).

Bbuc z Maximum helical curvature of buckled

pipe in a curved borehole, degjl00 ft).

E •

Young s modulus

29.6 x 10

6

psi for

steel, psi).

F

=

Axial compressive force, lbf).

VBRL • Maximum negative hole curvature with

which the pipe will be buckled with F

L

,

(deg/lOO ft).

•

Buoyant

weight of pipe,

lbjft).

=

Hole

angle

from

vertical, deg).

REFERENCES

Dawson,

Rapier; Pasley P.R.: Drillpipe

Buckling in Inclined Holes, JPT, Oct. 1987)

1734.

2.

Chen, Yu-Che;

Lin, Yu-Hsu;

and Cheatham,

John

B.:

Tubing

and Casing Buck1 ing in Horizontal

Wells, SPE,

Rice U.,

JPT, (Feb.

1990)

140.

3. Lubinski, Arthur; Althouse, W S.;

Logan, J.

L He1 ica1 Buck1 ing of Tubing Sealed in

Packers,

JPT,

(June

1962) 655

.

VBR

c

=

Vertical hole curvature for which F is

the

critical

buckling force, degjI60ft).

VBRcb =

Crit ical vert ical build rate hole

curvature for buckling, degjl00 ft).

TBRm

=

Critical hole curvature

at which

the pipe

body just

touches the

wall

of the hole

at

the center of the span, degjl00 ft).

U = Ljj

sin 9 ]

1/2.

. . . A-I)

12

4 E ·

r

l

F

c

=

APPENDIX

A

F

c

= [

4 . E . I • W

m

. sin 9 ]

1/2.

. . . (A-2)

12 r

- Ar)

Critical

Buckling

Force in

Curved

Boreholes

Pasley

and Dawson

define the

critical

buckling

force for straight inclined borehole as:

This equation

has

been modified to estimate the

critical buckling force for vertically

curved

bore

holes by adjusting the radial clearance to account

for the effec t of hole curvature on the

upper

half

of the helical buckle. Fig. 4 shows the effect of

curvature on the radia1

c1

earance for pi pe

in a

build interval increasing curvature). Fig. 8

shows the effect of curvature

on

the radial clear

ance for pipe in a dropp ing interva1 decreasi ng

curvature).

The critical

buckling force for

verti-

cally curving borehole becomes:

Where

Ar

is

positive for positive or building

curvatures and negative for negative or dropping

curvatures.

4. Roark,

R J.,

Formulas for Stress

and

Strain,

4th Edition, McGraw Hill, (1965)

150.

5.

API

RP7G

IIRecommended

Practice for Drill

Stem

Design

and

Operating Limits, 14th edition,

API,

1220

L Stree t, NW Washington, 2005

(Aug. 1, 1990).

6. Mitchell, R. F. , IINew Concepts of He1 ica1

Buck1 ing, SPEDE, Sept. 1988) 303.

• Cri tical bucking force (minimum) for

curved

borehole,

lbf).

=

Minimum

buckling force in a curved

borehole,

lbf).

=

Critical buckling force limit associated

with the limiting minimum vertical

curvature,

lbf).

=

Moment of inertia of pipe body, in.

4

=

(E

. IjF)1/2,

in.).

•

Maximum

bending stress, psi).

= Maximum

bending

stress

of

buckled

tool

jointed pipe, psi).

=

Total hole curvature, degjl00 ft).

j

L

r

= Average

length between centers of tool

joints on dri11pipe or from the center of

a tool

joint to the center of the support

pad

on

Heviwate, in.).

=

Outside diameter of pipe

body,

in.)

=

Radial clearance between the tool joints

and wall of the hole, in.).

rc = Radial clearance between the tool

joint

00

and

the pipe

body 00, in.).

TBR

00

407


6/16

6

CRITICAL

BUCKLING FORCE AND STRESSES

FOR

PIPE IN INCLINED CURVED BOREHOLES

SPE/IADC

2

The value of

Ar

can be calculated

from

the

pitch length of the buckled pipe

and

the curvature

of the hole.

Lubinski Eq. 2)

defines the pitch

length for

helically

buckled pipe as:

P

=

..

[

8 • E

F

• I ] 1/2.

R

A-3)

Since his derivation

was

for weightless pipe. the

solution should apply to buckling at any hole

angle.

From the geometry of the curved borehole Ar

can be

defined

as

follows:

Fig. 5.

For

holes with

low

curvature

and h

axi

a1 forces. the

pi pe can be buckl

ed

as is sho

in Fig.

7;

and for high loads

and

high curvatur

the

pi pe

will

be

forced against the top of

hole

as is shown

in

Fig

6. Fig. 9

is

a ske

that shows the curvature that will prevent

p

from

buckl

ing

in a hole with

high

negative cur

ture. As

is

indicated in the sketch. the

critic

condition occurs when

Ar

• r

which

will p

vent the pipe

from

buckl

ing. This

critical

lo

ing occurs when the

lifting

force due to the c

pressive load

on

the upward curving pipe j

equals the

buoyant downward

gravity force. T

occurs

when:

F

L

. B

L

-------- =

W

m

• sin 9 A-8

5730

b . p

2

[

VBR ] p

2

Ar =

=

12

5730 32

. . . . A-4)

From the

geometry:

Combining

Eq. A-3

and

A-4.

Ar

becomes:

1 2 • B

L

• E • I

ArL

= • • • • • • •

A-9

4 .

5730

. 12 . F

L

[

1 2 • E . I . VBR ]

Ar =

4 . 5730 . 12 . F

. . . . . . A-5)

In terms

of

rand Ar

using the previously

fined sign convention:

Substituting equation

A-4

for

Ar in A-2

gives:

4 . E . I

W

m

. sin 9 / 12

Fc

=

ArL =

r -Ar

and from the geometry:

A-I0

1 2 • E . I . VBR

r -------------------

4 . 5730 .

12

. F

c

. . . . A-6)

J 2 • VBR . E I

Ar = • • • •

A-II

4 .

5730

•

12

Fc

A

more

convenient form of

Eq. A-6 is

achieved by

solving for the critical hole curvature in terms

of the buckling force:

Combining

Eq.

A-9 . A-I0 and A-II we get:

r . F

c

.

5730

• 12

J 2 E· I

4

VBR

c

=

16

W

m

. sin 9 . 5730

• • A-7

4 . 5730 . - 12 . F

L

Solving for B

L

gives:

J 2 • VBR . E I

r

4 5730·

12

F

. . . . A-12

Solving for VBR:

A-14

Substituting

A-12

for B

L

in

Eq. A-8

gives:

-4

. 12 . r .

FL

2

VBR·

F

L

------------------- - =

W sin 9

J 2

•

E . I 5730 m

In

a borehole with positive hole curvature

and

compressive loads on the drillstring there are

two

modes

of behavior.

The

drillstring can

lie

across

the

bottom

of the hole

as is

depicted in Fig. 1 or

the

dri 11 st ri ng wi 11 be

buckl

ed as shown

in

Fig.

2.

Fig. 4

shows

the relationship between

vertical build

rate

and axial force

that

separate

the

two

areas.

In

a borehole with negative curvature. a

drill-

stri ng under a

compress

i

ve

load can function in

three modes.

For

low loads the pi pe will 1ay on

the bottom

side

of the hole as depicted in

408

-4 5730· 12 · F

=

L

VBR

J 2

• E •

A-13


7/16

SPE/IADC

21942

FR NK J.

SCHUH

7

-4

5730

. 12 • r •

FL

V R

L

•

2 • E • I

Ar • r

from Eq.

A-I:

A-19)

A-IS)

Ar • . . • • . • . . A-21)

5730

• W

m

• sin 9

F

L

Eq. A-IS defines the maximum negative curvature

for which the pipe can

be

buckled. The previously

derived

Eq. A-6

defines the minimum axial force

required to buckle pipe in a decreasing hole curva

ture. The point at which both equations are equal

defines the minimum axial force for which the pipe

can

be

buckled. This point is defined by equating

Eq.

A-6 and A-IS:

4 • E I

12

and

from the geometry:

2 •

E •

I . L R

4 .

5730

• 12 . F

. •

A-20)

Substituting Eq.

A-I9

and

A-20

in A-IS yields:

16 5730 W

m

· sin

9

L Rcb

= -------=:....-_

• F

. . . A-22)

Equating

Fe. and

F

L

gives the desired minimum

axial force

tor which

pipe can

be

buckled:

Eq. A-21 defines the

maximum

lateral curvature

L Rcb

at

which hel

ical

buckl ing can

occur

under

an

axial load of

F.

The equation applies

whenever

F exceeds

the F

c

defined for

straight

inclined

holes

by Eq.

A-I.

NOMENCL TURE

F

P

b

V R

c

• Vertical hole curvature for

which

F

c

is

the

critical

buckling force,

deg/100

ft .

=

Pitch length of a helical buckle,

in. .

= Radial

clearance

between

the tool

joints

and wall

of the hole, in. .

V R • Hole curvature upward- downward,

deg/100 ft .

r

= Hole curvature, radius/in. .

= Curvature eqUivalent to

Arc,

deg/100

ft .

= Young s

modulus 29.6 x

10

6

psi for

s teel, psi .

•

Axial

compressive load,

lbf .

=

Critical

bucking

force

minimum)

for

curved

borehole,

lbf .

• Minimum buckling force, lbf .

= Critical buckling force limit associated

with the limiting minimum vertical

curvature,

lbf .

• Moment of inertia of pipe body, in.

4

L Rcb

= Critical lateral curvature that prevents

helical buckling, deg/100

ft .

4

5730

12

. r

•

Fcb

V Rcb =

2

E • I

16 5730

W

m

. sin 9

2

Fcb

.

. • . A-IS)

and

the corresponding hole curvature

is :

• A-17

[

E I W . 9]

1/2

F

b.

[ - fJ .

_·

__

·_m=-·_S_ln_

12

• r

e

can also estimate the effect of

lateral

hole

curvature on the critical buckling force.

This

form

of analysis suggests that

small

values

of lateral hole curvature should not alter the

magnitude

of the critical buckl ing force. How-

ever, fo r high curvatures, buckling can be

prevented.

e

have derived a relationship that defines the

minimum

late ra l hole curvature that will prevent

buckling. The critical

lateral

curvature that

will prevent buckling

is

depicted

in

Fig.

25. The

critical condition occurs when the radial clear

ance equals the radial offset

caused by

the

later

al

hole curvature. This occurs

when:

409


8/16

8

CRITICAL BUCKLING

FORCE

AND STRESSES FOR

PIPE

IN INCLINED

CURVED

BOREHOLES

SPEjlADC 2

VBRcb - C ri tical vertical build

rate

hole

curvature for buckling, degjl00 ft .

The

angl e ;

is

re1ated to hole curvature b

the following:

APPENDIX

B

Since the bending stress is

b • L • F • j

M

m

-

2 . sin Uj2)

9

• Buoyant weight of pipe, lbjft .

- Change in radial clearance due to hole

curvature;

+

for positive curvature,

- for negative curvature, in. .

•

Net

pipe deflection for

critically

dropping hole curvature, in. .

- C ri ti ca l Ar that prevents buckling

in a dropping inter val,

in. .

-

Hole

angle

from

vertical, deg).

b • L

-

2

and

• • • • • • • • • • • • • • B-5

• • • • • • • • . • B-6

Bending Stresses

The

maximum

bending st re sse s in buckled pipe can

be determi

ned from

the expected curvature of the

helically buckled pipe and the additional bending

induced by the flex of the pipe body between the

tool

joints.

API

has published

5

equations for

computing

the

maximum bending s tr es se s of

drill

pipe in tension

in

curved

boreholes.

These

equations are based

on beam column

equations

that neglect gravity loads. We have developed

similar equations for bending s tres ses of drill

pi pe in curved boreholes

under compress

ive loads.

Roark has deriv ed

the

appropriate basic beam

column equations

that

apply to the problem of

drillpipe

under compressive loads

in

a

curved

bore

hole. Roark s equations are for a simply support

ed

beam

column to

which

are applied equal

and

opposite

bending

moments at the ends.

The

rele

vant equations are:

H1

; - ----- tan Uj2)

B-1

F • j

. . • . . • . . . . . .

B-3

Substituting

B-5

into B-I0):

. . . . . . . . .

B-8

• • • • . . • • • • . . B-7

• • . . .

•

B-9

b . E . U . 00

S

m

sin Uj2)

M 00

S =

_ 1

__

m

I 2

; L

a • - . - • •• B-I0)

2 2

the

maximum

bending stress for drillpipe und

compressive load in a curved borehole

becomes:

y = a + rc

from the geometry

The

above equation only

appl

ies if the center

the pipe span does not touch the wall of th

hole.

The

limiting condition

is

depicted

Fig.

18

where the center of the pipe just touch

the wall of the hole. For curvatures or load

greater than indicated, some portion of the pip

body would be in contract with the hole.

For

cu

vatures or loads

equal

to or 1ess than depi cte

the pipe

body

would

not

be

supported

by

the

wa

of the hole

and

the

stress Eq. B-8 would

appl

When the pipe

body

just touches at the center

the span

• . • • . • . B-2

[

1 -

cos Uj2 ]

-

F

cos Uj2

H1

M

m

=

cos Uj2

and B -ll) into

B-9

gives:

These

equations can

be

adapted to the problem of

drillpipe in a curved borehole by equating the

pos

it

i

on

of the

ends

of the beam column to the

ends of the pipe at the tool

joints. See

Fig.

17. Equating the unknown end moments M

1

in

Eq.

B-1

and B-3 gives the following equation

for the maximum moment:

b • L2

a=

8

•••••••••••••

B-11

; • F • j

M

m

=

•• ••• •••••

B-4

sin Uj2)

b • L2

Y -

+ rc • ••••• • B-12

8

410


9/16

SPE/IADC 21942

FR NK J . SCHUH

9

Combining Eq. B-1 and B-2 and

solving for y gives:

y • j . . tan U/4

Equating

B-12) and

B-13)

. . • • . . . •

B-13)

4.

If

there

is

pipe body contact, determine

by

trial and error a pipe joint length that

would just

touch the wall of the hole

and

use this pipe length in Eq. B-8 to calculate

the maximum bending

stress.

The curvature produced

by buckl

i

ng has been

de

fined

by lubinski s

equation

45:

4 . 1 2 • r

bb • • . . . . . . . B-17)

p2

+

4 1 2 r

2

• B-14)

2

j . b . l tan U/4

•

l2

rc •

8

This simplifies to :

Substituting Eq.

A-3

for P and simplifying gives:

3. If there is no pipe body contact, use Eq.

B-8 to calculate the bending stress using

the

buckl

i

ng

curvature in place of the hole

curvature in Eq.

B-8.

Eq.

B-15 defines the hole curvature where the pipe

body just

touches in the center of the

span as

well as the

maximum

hole curvature for

which

Eq.

B-8

defines the maximum bending stress.

The maximum

bending stress for drillpipe for

which

a portion of the pipe body touches the wall of the

hole can be calculated

by:

1

Solving Eq.

B-15

by trial

and error for a

pipe length that

would

just touch the

wall of the hole for the defined parame

ters. The best form for

an

i terati

ve

solution

of l i s :

2.

Using

that

length solve Eq.

B-8

for the

maximum bending

stress.

In this case, the maximum

bending

stress would

occur at the two points in the pipe

body just

be

yond the portion touching the wall of the hole.

The

bending

stresses on

buckled pipe can be deter

mined

by

the following steps:

1. Determine the maximum curvature of the heli-

cally

buckled pipe.

2. Determine the pipe body is touching the

wall of the hole

when

subjected to a hole

curvature equivalent to the curvature of the

helix.

2 .

rc

. .

B-21)

• . . . . . . . B-20)

. . . . . . . . . B-18)

• • B-19)

r

+

jArl . F

2 • E I

r F

bb -

2 • E • I

r F I 1 2 V R I

bbm =

2

E ·

I

8 · 5730

.

12

1

2 . E • I

+

r

bb

r .

F

2 E I

and

since

»r

r .

F

2 .

rc

b

c

= . . . .

B-22)

j . l . [tan U/4 - U/4]

In

a curved borehole with buckled pipe, the effec

tive radial clearance will range from r

+ Ar

to r - Ar. The highest helical curvatures and

bending stresses

will occur in the portion of the

curved hole where th e radial clearance

is

r Ar. The maximum curvature will therefore

be:

The

maximum curvature that will not allow pipe

body contact

becomes:

If bm

is

1es s than be. th e maximum

bending

stress is

calculated directlY from Eq.

B-8.

If b

c

is less than

bbm

then Eq.

B-22

must be

so

1

vea by tri

a1 and

error

for a value of l

that

makes

b

c

= bbm

This value of l

must be used

in Eq.

B-8 to calculate

th e maximum

bending

stress.

B-15)

. . . . . •

B-16)

tan U/4

2 . rc · U

b •

j

4

b

=

j . l . [tan U/4 - U/4]

l

411


10/16

10

CRITICAL BUCKLING FORCE AND

STRESSES

FOR

PIPE IN INCLINED CURVED BOREHOLES

SPE/IADC

21

APPENDIX C

NOMENCLATURE

APPENDIX B

M

m

=

Maximum moment in the center of the span,

in.

lbf).

rc = Radial clearance between the tool joint and

pipe

body

of

drillpipe,

in.).

Sm

= Maximum

bending s tr es s, p si ).

U

=

L/j

. . . .

C-2)

r F

2 • E

R =

1. The lateral contact force of buckled pipe

the

wall

of the hole just

at

the critica

buckl i

ng

force.

2. The net

lateral

contact force considerin

the

effect

of the gravity force on the pip

between the pipe

and

the hole

at

the top

the arch of the buckled pipe.

3. The

ratio

of the frictional drag betwe

buckled

pipe and nonbuckled pipe that occu

at the critical buckling force.

F

Lcf = • • • • • • • • • • • C-3)

2 R· 12

You will note

that

the Cheatham equation

diffe

from

the Pasley equation by the square root

two. Cheatham presents some impressive eviden

supporting its applicability.

These

include:

That Pasl ey and Dawson

merely

defined t

axial force at which the pipe would beg

snaking across the bottom of an inclin

hole r athe r than the force required to rai

the pipe

up

into a full helix.

2.

It matches

test

data collected

by

Lubins

and Woods and an

equation a ttribu ted

Lubinski from unpublished works.

3.

It

is reasonably close to an empirical form

la first published

by

Dellinger of Mobil.

il e the author is ne i th er inc 1i ned

nor

probab

capable of critically reviewing the derivation

we

have

combined the two

critical

buckl ing

equ

tions with other publ ished relationships that r

late to buckled pipe and derived some significa

factors

that we believe strongly supports t

Pasley Dawson equation as the appropriate val

for

critical

buckl

ing.

The

key

equations are t

Lubinski equations that define the curvature

buckled pipe and

Mitchell s

equation

6

th

defines the

lateral

contact force between the pi

and the wall in

th e

hole fo r buckled pip

Lubi

nski s equation for the curvature of

buckl

pipe is

as

follows:

and Mitchell s equation for the

lateral

conta

force of buckled pipe on the wall of the hole

as

follows:

If we look at the case for buckled pipe in a hor

zontal hole just at the critical buckling force

defi ned

by

the two authors, we can

combi

ne th

equations for

critical

buckling force, bucklin

curvature and lateral contact force to define:

. . C-l)

s; n

B]

[

S E · rI

Fcc =

a • The deflection of the center of a circular

arc as indicated in Fig. IS.

b • hole curvature, rad/in.).

Bb

• Curvature of a he lica l buckle, rad/in.).

Bbm

=

Maximum

curvature of helically buckled

pipe in curved borehole, rad/in.).

b

c

• Curvature that

just

allows pipe body

contact at center of span,

rad/in.).

E •

Young s modulus

29.6 x

10

6

for

steel,

psi).

F • Axial load

at

end of

beam,

lbf).

=

Moment of inertia for pipe

body,

in.

4

j = • I/F)

1/2,

i n . ) .

L = Length of

beam

column one joint of drill

pipe or the distance

from

a tool

joint

to

the center support pad of Heviwate pipe),

in.).

Ml • Moment applied

at

each end of the

beam,

in.

1bs) .

00 = Outside diameter of pipe

body,

in.).

r =

Radial

clearance between tool joints and

ho1

e

ID, i

n . ) .

y = Deflection

at

cente r of the span, in.).

VBR· Vertical hole curvature, deg/l00

ft.) .

= Deflection angle at the end of the

beams,

rad).

Critical Byckling for Straight Inclined Holes

One

of the

dilemmas

facing a

high

angle or horizon-

ta l

well

designer

is

the selection of the

critical

buckling equation for straight inclined holes.

The two most prominent choices are the Pasley/

Dawson equation see Eq. 1) which has been select-

ed

by the author and the Cheatham, Chen and Lin

equation given below.

412


11/16

SPE/IADC

21942

FRANK

J.

SCHUH

The results of

this

evaluation are included in

Table C-1.

Comparison of Critical

Buckling Force

Equations

Cheatham

Chen Lin

Combining

the equations

shows

that the

lateral

contact force generated by the buckled pipe using

the

Pasley/Dawson

equation is numerically

equal

to

the

weight

per foot of the subject pipe.

If

the

Cheatham

equation is used, one determines that the

lateral contact force at the critical buckling

force is equal to two times the

buoyant

weight of

the pipe. In a horizontal hole, the net contact

force

between

the pipe and the

wall

of the hole

is

the vector sum of the 1atera1 contact forces due

to buckling and the gravity forces. See Fig. 26.

Si

nee

the 1atera1 contact forces due to

buckl

ing

are

always

exerted

on

the pipe in a direction per-

pendicular to the wall of the hole and the gravity

forces act

vertically

downward the net force is

the radial vector

component

of these two direction-

al

forces.

At

the very top of the hole

where

the

buckled pipe

has

been pushed up to contact the

wa of the hole, the net force

is

the numeri ca1

difference between the lateral contact and the

buoyant weight

of the pipe. If the

Pasley/Dawson

equation is

used

to define buckling, the net con

tact force at the critical buckling load

is

found

to

be

exactly zero. With the Cheatham relation-

ship, we find that there

is

a large net force

which is numerically equal to one times the buoy

ant weight per foot of the pipe.

The most

import

comparison of the

two

equations is

in the defini tion of the net contact force between

the critically buckled pipe and the

wall

of the

hole at

the

crest

of the arch described by a

helical buckle in a horizontal hole.

The

Pasley/

Dawson equation suggests that the critical buck

ling force

pushes

the pipe up to the top of the

hole with

positive net forces

along al l

of the

arch

except at the very top where the pipe just

barely contacts the top of the hole. It seems

reasonable that a decrease below the critical

buckling force would tend to drop the pipe away

from the top of the hole and

an

increase would

merely

cause the contact force to increase. The

Cheatham equation suggests that there

is

a very

large contact force

between

the pipe at the top of

the arch

when

the pipe

is

under the Cheatham

Lateral contact force of

buckled pipe at the critical

buckling force, lbf/ft

Net lateral contact force

between the pipe and hole

at

the top of the arch of the

buckle, lbf/ft

Ratio of frictional drag

between

buckled pipe and

nonbuckled

pipe at the

critical

buckling force

T ab le C -l

o

1 2

413

critical buckl ing load.

It

would appear that

one

would have

to significantly decrease the axial

force below

Cheatham s critical

buckling

force.

before the net forces

would

permit the pipe to

begin to

fall

away from the top of the hole.

This

is contrary to the concept of a critical load.

The

frictional force of moving buckled pipe is

equa1 to the net 1atera1 contact force of the

buckled

pipe

on

the

wall

of the hole times the

coefficient of friction. For nonbuckled pipe, the

frictional force is

equal

to the coefficient of

frict ion times the buoyant weight per foot of the

pipe. Since the

lateral

contact force is exerted

outward on the hole and the gravity force

is

always downward can be deduced that the

decrease in net force

on

the top half of the hole

due to the gravity force

is

exactly offset

by

the

increase in the net contact force in the

bottom

half of the hole.

Thus

the frictional force for

buckled pipe is simply the lateral contact force

due to buckling times the coefficient of fric-

t ion.

We

can, therefore, compute the

change

in

frictional force when pipe just buckles by compar

ing the lateral contact force of the

buckled

pipe

to the

buoyant

weight per foot of the pipe.

If

the Pasley/Dawson equation

is

used to represent

the critical buckling force, we find that the fric-

tional force to move buckled pipe at the critical

buckling force is exactly the

same as

the

friction-

al

force of

nonbuckled

pipe at that

same

load con

dition.

With

the Cheatham equation, we find that

the frictional force for the

buckled

pipe would

be

twice as large as the frict ional force for nonbuck

led pipe at

this same

loading condition.

The field observations of wells subjected to

buck

ling loads,

though somewhat

limited, suggests that

there are no noticeable surface effects when

one

exceeds the critical buckl ing force. Since the

surface measurements would only be effected by

friction forces,

we

believe that the field observa-

tion

is better supported

by

the

Pasley/Dawson

equation than by the Cheatham equation where a

significant

change in

frictional

loads

should

occur.

NOMENCLATURE

APPENDIX

C

E = Young s

modulus

29.6 x 10

6

psi for

steel, psi .

Fcc =

Cheatham derived critical buckling

force,

bf).

I Moment of

inertia

of pipe body in.

4

Lcf

=

Lateral contact force

between

pipe or

buckled pipe and wall of the hole,

lbf/ft .

r = Radial clearance between the tool joints

and

wall

of the hole, in. .

R

= Radius

of curvature of

buckled

pipe, in. .

W

m

=

Buoyant weight of pipe,

lb/ft .


12/16

2

CRITICAL

BUCKLING

FORCE N STRESSES FOR

PIPE

IN INCLINED CURVED BOREHOLES

SPE IADC

/BOREHOLE

/ NON BUCIQ ED P I P ~ _

NON BUClQ ED

PIPE

- I I I I ' ~ B ~ O R ~ E ~ H O L ~ E ~ - - - - - -

Fig

5

- NON BUCKLED PIPE

IN

DROPPING CURVE AT LOW LOADS

Fig

1

NON-BUCKLED PIPE

IN BUILD CURVE

-;::z

BOREHOLE

BOREHOLE

BUC= ;

Fig 6. - PIPE BUCKLED

IN

A

DROPPING

CURVE

Fig 2

- PIPE BUCKLED

IN

A BUILD CURVE

BOREHOLE

-

NON BUCIQ ED

PIPE

ig NON-BUCKLED PIPE IN DROPPING CURVE

AT

HIGH LOAD

Fig 3. - COMPARISON BUCKLED PIPE IN CURVED WITH STRAIGHT HOLE

EQUIVALENT

/ SIZED

STRAIGHT

BOREHOlE

Fig 8 - BUCKLING IN A DROPPING INTERVAL

R

~

Fig

4 - BUCKLING IN A BUILD INTERVAL

~

borehol

Fig 9. -

HOLE

CURVATURE

THAT

PREVENTS

BUCKLING

414


13/16

SPE/IADC 21942

FRANK J

SCHUH

13

\

\

\

I

BU

;{

1/

\

1/

\

j .

\

1/

/

V

II:IU

ueg

8.5

in .

e

10

IPPi

Mtd

j

IoRI

l L

]

~ I P E

IN01

BI

CKl

ED

0

20

90

CRITICAL BUCKLING IN CURVED

BOREHOLES

4.5 in 16.6

Ib f t

Grade E DRILL PIPE

Range 2

Pipe

with 6 1 4

in . Tooljoints

100

o

-12-10

8 6 4 2

0 2 4 6 8 10

VERTICAL

BOLE CURVATURE del 100 ft

Fig

12. - BUCKLING OF 4.5 in DRILLPIPE

ti 80

:2

8 70

60

m 50

I 40

30

\

II

\

~ U C

a Et

: 1:1

/

1/

1/

/

V

1:11

ae

~ : :

gle

p il l

Ie

pp

RM

Ild

I1RTI.

Pl PF

BUI

KLEp

0

90

20

CRITICAL BUCKLING IN

CURVED BOREHOLES

5 in 19.5 Ib/f t . Grade E DRILL PIPE

Range 2 Pipe

with 6 3 8

in . Tooljoint.s

100

80

8

70

o

-10

8 6 4 2

0 2 4 6 8 10

VElmCAL

BOLE CURVATURE

del 100 ft.

Fig

10. - BUCKLING OF 5 in . DRILLPIPE

60

m

50

I

40

30

,

II

\

/

~

B

~

r;{ ,

/

\

/

\

V

I

\

\

If

V

9

_ ~ e ~

AI

2:

1

;

V

D

1m

r

NI)T B1

C

LEP

CRITICAL BUCKLING IN CURVED BOREHOLES

3.5 in 13.3 lb f t

Grade

E DRILL PIPE

Range 2

Pipe

with

4 3 4

in . TooIjoints

100

o

-1 1 12-10-8-6-4-20 2 4 6 8 101214

VElmCAL BOLE CURVATURE

del 100 fl

Fig

13. - BUCKLING OF 3.5

in

DRILLPIPE

90

ti

80

:2

g

70

60

m

50

In

=

40

8

30

20

10

~ U C

t

1:1

i

stl

j

1

~

1/

:0

/

I ~

/

V

Ih/

in he

11 pp

g M

lid

IRTI

P1PF.

{OT

BU


14/16

\

/

HE

~

~

\

BU

\

\

\

1

/

/

V

aeg AD

~

in .

Ho e

10

ppg MlJd

NOT Bt

CKI

ED

o

-12-10

8 6 4 2 0 2 4 6 8 10

VERTICAL

BOLE

CURVATURE

de./l00

It

Fig 16. BUCK JNG

OF

3.5 in

HEVlWATE

90

. ;

80

:2

0

70

0

60

50

I

40

u

30

20

10

P

[PE

/

BU

/

/

/

:II

~ ~

fie

tc

pp

I

M

ild

BU<

KLED

0

o

-10 8 6 4 2 0 2 4 6 8 10

Vl:RTICAL BOLE

CURVATURE

de./l00

ft

Fig 14. -jBUCKUNG

OF

5

in HEVlWATE

20

90

80

8 70

CRITICAL BUCKLING FORCE ND STRESSES FOR

14 PIPE IN INCLINED CURVED BOREHOLES SPE/IADC 21

CRITICAL

BUCKUNG

IN

CURVED BOREHOLES CRITICAL

BUCKUNG

IN

CURVED BOREHOLES

5 in

49.3 Ib/f t

HEVlWATE DRILL

PIPE 3.5

in 25.3

Ib/f t

HEVlWATE DRILL

PIPE

Range 2

Pipe

with 6 1/2 in . Tooljoints Range 2 P ip e w ith 4 3/4 in Tooljoints

100 100

I

L 2 l · ~ 1

fig 17

- MAXIMUM BENDING STRESS WITH COMPRESSIVE AXIAL LOAD

Fig 18. -

CENTER OF

PIPE BODY JUST TOUCHING

~ V

~

r

/

Buc

/

1/

/

/

5

riB:

:fie

l

pp

g

M

BU

KLED

90

10

20

R I T I ~ e K U N IN CURVED

BOREHOLES

4.5 in 4 UJ lb/ft HEVIWATE DRILL PIPE

Ranle 2 c ~ l p e

with 6 1/4

in. Too ljoint s

100

o

-10

8 6 4 2 0 2 4 6 8 10

VERTICAL HOLE CURVATURE de./l00 ft.

Fig 15. BUCKUNG

OF

4.5 in HEVlWATE

80

§ 70

416


15/16

SPE/IADC 21942

FRANK

J. SCHUH

15

MAX BENDING STRESS IN CURVED BOREHOLES

3.5

in

13.3 Ib/f t

Grade E

DRILL

PIPE

Range 2 Pipe

with

4 3 4 in .

Tooljoints

2 5 - r - - - - r - ~ 7 t - - - . - . . . . . - - - .

.

MAX

BENDING STRESS IN CURVED

BOREHOLES

5

in

19.5 Ib/ft Grade E DRIlL PIPE

Range

2 Pipe

with

6 3 8 in .

Tooljoints

25 ... .... . . ... ...

. . _

In

15.

rn

15

n

rn

E

E

u

u

I

is

10

=

10

II

III

I

I

5

5

°1

90

6.125

. ole

10

pIlg

Mud

0

1

30

40

50 60

0

10

20

30

40

AXIAL COMPRESSIVE

LOAD

1

lb

AXIAL

COMPRESSIVE LOAD

1

lb

Fig

19. STRESSES

ON

5 in DRILlPIPE

Fig

21. STRESSES ON

3.5

in DRIIJ..PIPE

Iii

20

+ - ~ ~ ~ ~ ~ - - : = . . . . . . . . : J . . . . . ~ - l - - - ; - - - : : : : - I

Po

g

o

6000

0

0

0

ft..

8

de,. 1

....

ST luTED

FATI 11:

bo ft..

14

deg/

1

10

deg/

1

bo ft..

a

lieg/

1O

b ft..

on

.

.

8.5 .

o

10 I

IPg

Mu

+l2

or

deg/

00

ft.

o

o

5

:MAX BENDING STRESS IN CURVED BOREHOLES

5 in

49.3

lb/ft HEVlWATE DRILL PIPE

Range 2 Pipe

with

6 1 2 in.

Tooljoints

25

Iii

20

Po

g

500

0

0

0

MAX BENDING STRESS IN CURVED BOREHOLES

4.5

in 16.6

Ib/f t

Grade E

DRILL

PIPE

Range

2 Pi pe w ith

6 1 4

in .

Tooljoints

25

- r - - - ~ - - ~ - ~ : f - - - , , . . . -

.

, .

t 20

g

o

AXIAL

COMPRESSIVE LOAD

1 lb

Fig 20. STRESSES

ON

4.5

in

DRILlPIPE

XI L

COMPRESSIVE LOAD

1 lb

Fig 22. STRESSES ON 5

in.

HEVIWATE

417


16/16

16

CRITICAL BUCKLING FORCE

ND STRESSES FOR

PIPE IN INCLINED

CURVED

BOREHOLES

SPE IADC

2

net cont ct force

uckling

cont ct

for

HALF PITCH L N G T H ~

uckling nd gr vity vectors

Fig

25

LATERAL HOLE CURVATURE THAT PREVENTS BUCKL

50

0

0

0

0

1 0

0

f t

. - -

15\ deg

. .

ESTIlot

T1i n

I

MIT

I1nn

ft

1 4

L .

eg/

1OO

ft..

10

6

d

g/100

t..

2

AI

gle

1

ppg

M

Id

2

pr 2

eg/l00

ft .

o

o

MAX BENDING STRESS

IN

CURVED BOREHOLES

4.5 in 41.0

Ib/f t

HEVIWATE

DRILL

PIPE

Range

2

P ipe w ith

6 1/4

in TooIjoints

25

AXIAL COMPRESSIVE LOAD 1000

lb

Fig 23 STRESSES ON 4.5

in

HEVIWATE

ii

20

c

c

c

III

15

III

CI

i

10

EI

i

5

MAX

BENDING STRESS

IN

CURVED BOREHOLES

3.5

in

25.3 Ib/f t

HEVIWATE

DRILL PIPE

Range 2

P ip e w it h

4 3 /4

in. TooIjoints

25

_r_ r r . . . .. __.

Fig 26 HORIZONTAL BUCKLING

FORCES

PASLEY DAWSON

CRITICAL

FOR

i

20

c

g

I

10

- f - - - - := : I ; ; ;ooo-=-; - - - -+=_ 1

2

0 2

deg/ 00 ft .

40

0

00

o - . . . . . ~ . . . . . _ r ~ . . . . . . . . . - I o ~ . . . . . . . . . . . . - . . . . . . . . . . . . . . . . . . . . 4

o

AXIAL COMPRESSIVE LOAD

1000

lb

Fig 24 STRESSES ON 3.5

in HEVIWATE

spe 21942critical buckling inclined ms

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