How to Design Casing Strings

8/10/2019 How to Design Casing Strings

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Reprinted from

etmleum

~~NBGGPHTERNATWALecember 989

How

o Design

Casing

Strings For Horizontal

Wells

by

John

F.

Greenip

Jr.,

H y d ~ i l

ous ton

Tes.

C

wing loads in

an

extended reach well or a horizontal

tended

reach

s trings . Unders tanding these re la tion-

well

are

no different than those developed in

a

conven-

ships may simplify the design process as well as allow

tionaloilorgaswell.Thereis,however,adistinctdif- t h e e n g i n e e r t o b e t t e r t a i l o r t h e d e s i g n t o t h e

ference in

the

magnitude

of

those loads.

eciiuse

of thi s

application.

difference,

casing stri ng design for thes e applications

In e i the r

an

extende d reach well or a horizontal well,

frequently rey

uires

structural considerations such as

t h e casing s tring can be divided into

segments

for

bending

and

torque.

These

factors

may

overshadow7

analysis. F o r illustration, th ree s egm ents will be used

more traditional design

parameters of

internal yield,

(Fig. 1):

h e reach

interval, eit her horizontal or sloping;

collapse,

and

tension.

the build interval;

and t he

vertical interval. For t h e

When developing a casing design for a horizontal

exam ple well calculations, t h e build is taken to

be

con-

well. here are several points to

consider:

s tan t th roughout i t s in te rva l

and

the reach interval is

The

axial

and

torque

loads

can

be

es t imated fo r taken to have

a

constant inclination angle.

A s

with

coil

extended reach and horizorltal wells

by

analyzing the

ventional wells , the s trin g then is analyzed from t he

seaarat

e intervals. bottom up.

~ L l a t i u n s h i ~ san be deve loped for the var ious

Reach Interval

parameters

which

facilitate casing

string

design

and

unders tanding.

For the reach in te rva l , the forces on t he pipe include

The

pick

set down,

and neutral

states

a

frict ion component tha t act s

in the

opposite direction

suffiriently ifferent

load

magni tudes

to

u an.ant

to

the pipe movement.

The

incremental tension,

dF,

is

analysis

of

each separately.

dF (W)(BF){Cos8 (p )(WXBF)(Sin l

where

As

with

casing

s tring design and analysis for the

w nomin l

pipe

weiRht,ft

conventional well , re la tionships can be d e v e lo p e d

RF

buoyancy k tor

among the various param eters for horizontal and ex-

inclination angle

Point 3 surface

Vertical interval

Po~nt -

OP

Build ~nte rva l

Point

\

Reach angle

TD

coefficient of friction

Tahng t h e reach in terval to he at a constant angle,

t h e tension at t h e t o p of the interval.

F,,

will

be

F, = dFi L1

wh e re

L reach i n t e r ~ a length

If the string is being set down , the friction com-

ponent

reduces

the o~erallension:

F,

L [IW)(BF ) ICo sb - (kjIW)(BF)(Sin

d l ]

F o r t h e esamyle shown in

Fig.

KOP 4.000 f t MD

build angle 2W1100 ft

reach

angle 80

reach

i n t e n a1 length 2,000 ft

pipe

size

5%

n.

17

lblft

coefficient. of fr ictio n 0.35

mud

weight

=9.0 lblgal (buoyancy factor, B F =0.86)

F, =

2,000[(17)(0.86)(Cos 80)

0.35) 17) Oh86) Sin 0)]

-

5,000

b

Thus 5,000 lb compression must

be

applied at the top

of

t h e

reach interv al, Point 1, to push t he pipe into final

position. This force would be 0 as the pipe enters the

reach interval and increases to t he 5,000 lb compression

as the s t r ing approaches TD.

Because it is generally desirable to

pick

up t h e string

after having

reached TD, the fric t ion, again acting

Fig .

1

When

anaIyzing

a r ~ i n g

esign for

n extended

opposite to the direction of pipe movement, will in-

r e ad

or horizontal

we l l

t h e

casing

str ing

should

be

crease the

tension

load

at

Point

divided

nto three

segments:

the re rh interval either Ror-

izontal or sloping; the build

inkrcol

nnd the

uertical

F, 2,000[(17)(0.86)(Cos 80)

interual.

+

(0.35)(17)(0.86)(Sin80)]

15,200

lb



compression,

1,000

tb

Tension, 1,000b

-10 5 0 5 10 15 20 25 30

.-

B

rT

F 0.35

Build

angle

=

20 tlOO

t

Reach length 2,000

t

Reach angle 80

Fig. 2

xial

loud

versus

measured

depth.

The

maximum

Fig.

4.

Neutral

state

torque

r tio

Venus

build ang le.

The

cornpre~sionoad does

not

occur

at

P o i ~ t or 2 bu t accurrr

torque

ratio

for

each

reach

Islogth

approaches

the

aume

within the build in te rmi .

value about 1 20

EU

. .

6,000

5,000

P

4 000

3,000-

,.,*,

1,000-

0 5 10 15 20 25

30

35 40

Build

angle 1100

R

= 0.35

Reach

length

= 2,000 t

Reach angle 80

100-

Fig 3.

Bending load and

torque

versus

build

angle.

IrOrque

decreaeee an the build angle increaees while load in-

creme8

l inearly

with increasing build

angle

Keeping

the

build angle amall to reduce the loud due

to

bending

will

affect

mtation

t o q u e adversely at low

build

anghs .

4,000f i

Thus he swing between

pick

up and set

down for

t h e

reach section of

the

string

is

20 200

lb.

The

pipe will

remain stationary for any load applied to the top of

the

Teach

interval between 15,200

lb

tension and 5,000 lb

compression.

For

the neutral condition

where

there is

no

tendency toward

pipe movement,

the

friction com-

ponent is

0

and

the

tension at Point

1

is

F, 2,000[ 17) 0.86) Cos

80 ]

= 5,100

lb

Rotating during cementing

or wash-down

operations

requires that the torque

to

rotate

be estimated. This

torque

is a

function

of

the normal

force

between pipe

and

hole,

coefficient

of friction,

and

the pipe

radius.

With pipe body OD, the incremental torque, dM, is

dM (p)(W)[BF)(Sin0XOD)IZ

For the

reach

interval. the rate of

torque

increase

'

10 15 20 25 30 35 40

Build

angle, 1100

t

1,000 2,000 3,000

Aeach length,

Fig . 5.

xial load

at

KOP while

w t t i n g down caaing

string

uersu reach length. I f frequently become8 necessary to

applu

con~pres8ion t the top of

the

reach

inter~al

o ad

vance

the

pipe farther in the hok .

with length is

constant and

the

torque at the top

of

the

interval. M becomes

M

(k)(W)IBF)(Sin

0)(L)(O D)/24 ft-lb

For

the

example well

M (0.35)(17)(0.86)(Sin

80) 2,000) 5.5)/24

2,310

ft lb

This torque

must be applied at Point

1

to rotate

th t

pipe

in the reach interval. A

lower

torque could rotate

the string if the pipe were in a pick up

or

set down state

of

axial load.

However, because the axial load sta te will

cycle

during any

combined rotation-pick

up-set down

operation,

the neutral

state torque

is

used for the

reach

interval.

Build

nterval

While the

loads in

the

reach

interval change linearly



with measured dep th, th e loads in the build interval do

not, and ar e thu s more difficult to estimate. The incre-

menta l tens ion, dF t , i s a functio n of

the

normal force

which i s itself a function of the tension,

the

inclination

angle, and t he build angle:

dYt

= (W)(BF)(Cos0 ) -c

(k)(Fn)

and the normal force,

Fn, is given by

F n = {[(Ft)(da)(Sin +

[ (F t ) (dS)

-

W)(BF) (S in

8 11 0.5

with da and

do

the incrementa l

changes

in azimuth an d

inclination angles, respectively.

As

with the tension

within

the

reach in terval ,

the drag due

to friction with-

in the build inte rval

increases t h e

tension du ring pick

u p , decre ases the tension during

set

down, and has no

axial effect for

the

neutra l s tate. (While not affecting

asia l load. friction rem ains a factor for th e torq ue calcu-

lation i n the neu t ra l s t a t e . ) Tak ing the change in

azimuth angle as

0, F n reduces to

F n = [ (Ft)(d0)- W)(BF)(Sin811

The calculation of the load increase between the top

of

the

reach interval, Point

1,

and th e KOP, Point

2,

can

be determined us ing an HP-41 program. The program

considers three sta tes of pipe movem ent: pick up, set

down,

attd

the neutra l s ta te .

F o r the

example,

t h e tension at Point 2 F,,

can

be

calculated. For F,

=

15,200 lb, t h e pick

up

load,

F: is

28,100 lb.

Thus

the

build interv al, which

spans

400 ft, increases

fro m a tension load of 15,200 lb at the lower end up to

28,100 Ib at

the

K O P when

picking up

on the s tring.

This 32

lblft average

rate

of increase is considerably

higher than the

14.6

Iblft

buoyed pipe

weight

and

pro-

vides insight into t h e influence of

drag

upon t he total

load. This ra te

of

tension increase is not constant but

increases nearer

t he

KOP Fig. 2 , appro aching 50 lblft

for th is

example.

For

F,

= - ,000 Ib, the set down

load

is

F, = -4,800

lb.

In Fig. 2, th e maximum compression load does not

occur

a t

eith er Point 1o r 2 bu t occurs within th e build

interval . Fo r the example , th is maximum compression

of abo ut 5,800 lb is not high, b ut d oes identify t h e need

to

make

intermediate calculations within t h e build

interval.

For

F, =

5,100Ib,

the

neutral state load

is F2

= 9.200 lb.

Because the torque a t Point 2 also is

a

funtticm o ft he

changing

normal

force

within th e build interva l, i ts

cal-

cula t ion w a s inc luded in

the

HP-41 p rogram. The

torque value

of

primary in teres t i s tha t

when

there

is

no axial pipe movement. Th is would correspond t o

the

condition

of

rota t ing during cementing. For the neutr l

s ta te of

t h e

example, using M

=

2,310 ft-lb.

hl =

2,800 ft-lb.

Another situation

w h w e

rotation may

be

desired

is

wash-down

operations.

The torque fo r the set

down s ta te

is

M-

3.200

ft-lb.

Because the

hole

above P oint 2 is taken to be vertical,

the torque to rotate at

the

surface,

M,

= M .

A

phenom-

enon

not

addressed in the program is the mutual e ffec t

rotation

and

axial

movement

have

on

each

other. Rota-

tion will reduce the axial

drag

on the pipe and thereb y

ease

movemel~t

p or down the hole. . Th e torque calcu-

lated fo r th e pick up and se t down s ta te s is thus some-

what conservat ive , having assumed axia l drag and

rotational dr ag t o act independently of each other.

One of

the

more recognizable differences between a

highly deviated well and

a

vertical well is the potential

for significant bending load within t he build in terval.

The build angle can produce sub stantial bending loads

t o a n e x t e n t t h a t they may become

the

overr id ing

design criteria. The

bending

s t ress ,

Sb,

in the

pipe

body can

be calculated for a

given

build angle,

BA:

S b = * ZII) OD) BA)pd

This

bending stress occurs

only

a t locations within

the s t r ing where the re is a change in the

angie

of the

hole. The

reach

interva l which has been taken to

be

a t a

constant inclination has

no

associated bending load. I t

is important to remember, however, that pipe which

ends u p in the reach interval

mus t pass

th rough the

build interval thus being subjected t o the associated

bending loads.

The

bending load produces an axial tensile stress on

t h e pipe s outside

curvature

(convex surface), and

an

equal magnitude but compressive s tre ss on the inside

curva ture (concave

surface). Thus, depending on the

axial

load

state

of

the pipe,

the

added tension

and

rom-

pression created by ben ding

may

aggravate the exis t -

ing tens ion

o r

compress ion s ta te . When des igning

casing string s, i t is easier to relate loads in force rather

than

stress

because pipe body yield and joint s tre ng ths

are in force. The bending stress can be converted in to a

corresponding tension and compression load, Fb. This

is

done

by dete rmin ing the axial force which creates the

same maximum s t re s s at the pipe body

OD as

the bend-

ing load

creates

using Ap

as

th e pipe body

area:

F b

= {Sb) Ap)

The bending s t ress for the ex mple well

Sb = z

211) 5.5) 20)

= 23,200 psi

and

Fb

= ? 23,200) 4.962) = ?11.5,100 1b

Thus the

axial load

state

of

the casing

at any

location

within

the

build interval h s an additional simultaneous

115.1

kips tension and compression.

A t t h e KOP, the

net

tension load,

F,b,

is the sum of

the axial force at

Point

2 , Fi , plu the force due to

bending, Fb.

For s t r ing

pick

up

F,h

=

28,100 + 115,100

=

143,200 1b and - 7,000 Ib

or

s t r ing

set down

F,h =

-

,800 - 115,100 = 110,300 lb and

-

19,900 lb

For the neu t ra l s t a t e

F,b = 9,200 ? 115,100 = 124,300 lb a nd - 105,900

Ib

The pipe

at t h e KOP could th us ex perienc e net axial

loads ranging from 120 kips compression to 143

kips

tension. F o r this medium radius build hole, th e load

d u e

to bending contr ibutes over 75 t o t h e to ta l load.

Vertical

Interval

Once the load at Point 2 has bee11 de te rmined , the

tension

at the

surface, F,, can

be

calculated.

F or pick u p

F,

= F, + KOP) W) BF)

=

28,100

+

(4,000)(17)(0.86)

= 86 600 b

For set down

F 4 800

t 58,500

=

53,700 Ib

For

t he u e u t ~ a l t a t e

F , = 9,200 + 58,500 = 67,700 lb



Connection

Using an API L-80grade steel for the 5 +-in., 17-lb /ft

pipe and taking

the casing

connection t o

have

a tensile

efficiency of 758 , the jo in t s t ren gth , Pj, would be

Pj 10.75W4.96'7)(95,000) 354 000 b

The tension loads are highest when t he s t r i n g is

picked

up.

For t he joint

at the

surface, the tension

safety factor, SF t, is

S F t 354,000186,600 4.09

For

the joint just below the

KOP,

the tension safety

factor is

SFt 354,0001143,200 2.47

Taking the compression efficiency of

the

connection

to

be

85 , i ts compressive yield str en gth , PJC,s

Pjc (0.85)(4.9G2)(80,000)

337,000

lb

The highest compression loads are produced

when

set t ing down on the s t r ing . E'or the joint just below the

KOP, the compression safety factor, SFc, for the set

down sta te is

SFc

337,0001119,900

2.81

Fo r compression, the load a t the bottom of th e build

i n t e r v a l , F , b , a l s o s h o u l d

be

e v a l u a t e d . I n t h i s

e x a m p l e , it i s a p p r o x im a t e l y e q u a l t o t h e lo ad a t

t he KOP:

F,b -5 , 000

115,100 -120,100 Ib

and

SFc

337,000/120,100 2.81

I f the string is to be rotated, the connection must

have a yield torq ue ra t ing in excess of t he neutral s ta te

torque, 2,800 ft-lb for this example. In addit ion to i ts

basic torq ue capabil i ty , tha t pipe within th e build inter-

val

will

be subjected t o combined torqu e and bending

loads, a

dynamic

load environment general ly reserv ed

for

drill

pipe

tool joints rath ei* ha n

casing

connections.

f

the

pipe is ro t a t ed d u ri n g c e m ~ n t i n g .h e to rque

re-

quired will increase a s

the

cement fills the pipe w ithin

the reach inter\ ,al : ' This

h i g h e r

t o r q u e m i g h t b e

est imate d by using

a

heavier equivalent p i ~ ~ eeight for

the torq ue calculations.

Relationships

The example chosen used

a

build a ngle

of

20 JlOU

ft. A

diffe rent build angle

will

~)ruduce n interest ing change

in the t o rque required to ro tate .

The

torque, relatively

high for t h e very low build angles, decreases

as

t he

build angle itlcreases (Fig 3

.

At about 10"1100

f t

build,

the

torque

becon~es

early co nsta nt, increas ing slightly

with increasin g build angle. Also s h o wn in Fig. 3 i s the

ne t axial load created by the bending. This load increas -

es linearly with increasing build

angle.

A s

can be

seen

from

the two graphs, keeping

the

build angle small to

reduce the load due to bending wi l l affect rotation

to rque adversely a t t h e low build ang1c.s.

The ratio of the to rque a t Po int

2

to

tha t

at Point 1,

M,:M,, can

be

plotted against the build

angle

{Fig . 4) .

This plot is independent of coefficient of friction, pipe

OD, pipe weight, and buoyancy, assuming each s t a y s

constant throughou t t he build and reach intervals.

Ano ther relat ionship which

can

be seen from Fig.

4

is

that th e to rque rat io for

each reach

length approaches

t h e same value, about 1.20. This ra tio is depend ent on

reach angle only. Although

the

to rque rat ios are the

same, the actual torq ue values

vary

by th e rat ios of the

reach length.

F o r

a

90

reach interval , the torque rat io does not

become constan t bu t approaches

1.0.

However,

the

ratio at small build angles is higher than for th e 80"

reach angle hole and decreases more rapidly with in-

crea sing build an gle.

When running

the

string, it will

be

necessary to ap-

ply con lp re ~s ion r equent ly

at

th e to p of the reach in-

terval to advance the pipe far the r in to the

hole.

A s the

string advances, t h e load at Point

1 ,

F, , will increase

proportionallg (Fig.

5). For the example , t h e compres-

sion at Point 1 wi th 2.000 f t into t h e

reach

intervai was

calculated

t o

be 5,VOO Ib.

I f the

reach interval was

3,000h h e

compression

load upon

eaching

T D

would

be 7,500 Ib.

With

these

loads

and

using

the

set

down s t a t e

of the

HP-41 rogram, the

loads

a t the

KOP:

Point

2, are

cal-

culated. For t he example well,

t he

load at Point 2 is

about

3,000

Ib tension ivhen the bottom of the s t r i ng

enters t he reach

interval.

The load upon having3,WO ft

into the reach interval is about 8 800 Ib compression.

hus

or

the example well, th e load at Point

2

is increas-

ing faster than

the

load at Point 1. This ratio of load

change at Point

2

to load change

at

Point 1 becomes

eonsta ut beyond initial ntry into

the

re ch interval .

Also shiliru in Fig. is the load at Point 2

for

different

build angles. Each produces a separa te curve,

but

each

approaches

the

same

s lope a s th e p ipe

advances

within

the reach interval . The

ratio

of change of load, the s lope

of F1 o th e slope of F,, s independent of pipe OD and

weight

as

well as build angle. This

same

ratio also ap-

plies

t o

the s t r ing in the pick up s ta te . The ratio of

change of load is depe nd en t on th e coefficient of friction

and the reach angle.

Editor's note:

A copy of the HP-41 program can be

obtained

by

sending a sel f -addressed , s tamped en-

velope

to :

HP-41 Program, PETROLEUMN G I N E E R

IKTEHNATIONAL.

PO. 1589,

Dallas, Tex.

75221-1589.

References

1

Tolle. Glen anti Delli~igel:Thomas: "Mobil Identifies

Extenrlerl-

Reach-D~illing

dvantages,

Possibilities in N orth

Sea.

Holizon-

tal

D~ illin g echnology,Oil

LF

Gnu J . .adapted

from a

l ~ r e c e n t a t

on

to the Offshore Northern Seas Conference, Stavanger ,

Norway

( N u v e r n b ~ ~

985).

2. Johancsik. C . A . , k riesen. U . B . , Dawaon. R a p i e r To~que

nd

h a g n Ilil-ectionalM7el15-Prediction

and

Measu~ernent,

. Prt

Ttwli (June 1983)

987-99'2.

8.

Sheikholeslami, B.A.,

Schlottman,

B.W.,

Sietlel. E.4 . . Button.

D .M :

D1.illingand

P1.oduction

Aspects

of

Hol iz~)ntl

N'ella

in

t h e

Austin

Chalk, SPE papey 19X25.

3.

Gust , D.A.

and BlacDonald, R.K.:

"Rotation

of a

Long Llnrt-

111

a

Shallo\r Long-Reach

Well,

I

Pet

T ~ r l i

April lW9i 401-Wl.

N nghts reserved.No

part

o th~s

ubhcalron

may be eproduced wflhoutexpress psrrnfssfor t rhe publisher:

How to Design Casing Strings

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