casing burst strength after casing wear.pdf

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Copyright 2005, Society of Petroleum Engineers

This paper was prepared for presentation at the 2005 SPE Production and OperationsSymposium held in Oklahoma City, OK, U.S.A., 17 19 April 2005.

This paper was selected for presentation by an SPE Program Committee following review ofinformation contained in a proposal submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Society of Petroleum Engineers and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers presented atSPE meetings are subject to publication review by Editorial Committees of the Society ofPetroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the Society of Petroleum Engineers isprohibited. Permission to reproduce in print is restricted to a proposal of not more than 300words; illustrations may not be copied. The proposal must contain conspicuousacknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

AbstractCasing wear by drillstring results in a thinner portion of casing

wall and a reduction on casing burst strength (the ability to

hold internal pressure). How to estimate the reduced casing

burst strength on such a crescent-worn casing has been an

important issue in oil and gas industry, as it is directly related

to how to safely design casing strings. A common approach is

to estimate the reduction of casing burst strength of such worn

casing from API burst strength equation with a linear

reduction by the remaining wall thickness or the wear

percentage, equivalent to a uniform-worn casing model,

despite a question on whether such a linear reduction of casing

burst strength is over-conservative and may result in a higher

casing cost.

This paper presents a further study on hoop stress and

deformation of such a crescent-worn casing and discusses

the reduction of casing burst strength. The hoop stress in the

thinner portion of such a crescent-worn casing is found

close to that from a uniform-worn casing, when local

bending in the thinner portion of crescent-worn casing is

ignored. The reduction of burst strength of casing worn by

drillstring may still be estimated from casing yield or rupture

burst strength with a linear reduction by wear percentage for

sweet service well conditions, while more and non-linearreduction of burst strength of casing worn by drillstring may

be needed for sour service well conditions, to prevent an

earlier casing burst onsulfide stress cracking.

Introduction

Casing wear by drillstring is an increasing problem for drilling

deep wells and/or extended-reach wells. Such casing wear

develops from a long time exposure of the casing to a rotating

drillstring in the drilling process, with large contact forces

between drillstring and casing when casing is bent (Fig. 1),

which results from setting casing in a dogleg well section or

due to casing buckling under large axial compressive l

The casing burst strength (the ability to hold internal press

will be reduced due to the wear of casing. The more wea

casing the more reduction on casing burst strength. A h

could even be worn out on a casing string resulting in a t

casing failure.

Figure 2 shows the measured and predicted casing wear on

top 2500 m of 13 3/8 casing installed at 2508 meters MD

an inclination of 68 degrees in Gullfaks Well A-42 at N

Sea.2Casing wear was measured by an ultrasonic imager

and the maximum wear was indicated about 35% of the ca

nominal wall thickness at 480 meters MD. The casing w

was due to drilling and back-reaming the next open hol

5334 MD, with high drillstring tension load and casing dog

severity of 2.9 degree per 30 m.

The reduction of casing burst strength on such worn ca

needs to be correctly estimated in order to do a safe ca

design, as well as to decide whether an additional casing ne

to be set to cover a worn casing before further dril

operations. Although there have been some studies

modeling worn casing burst strength,3, 4a common approacstill to use API burst strength with a linear reduction by

remaining wall thickness or the wear percentage, despi

question on whether the linear reduction on worn casing b

strength is over-conservative and may result in a higher cas

cost. This paper is to present a further study on this issue

discuss the reduced casing burst strength on such worn cas

Casing Burst Strength

1. Casing without WearFor a casing without wear and subjected to an inte

pressure (Pi) and external pressure (Po), as shown in Fig.

the induced casing hoop stress () can be expressed by

Lame equation:5

222

22

22

221)(

rrr

rrpp

rr

rprp

io

oioi

io

ooii = { }o, rrr iThe casing hoop stress is a tensile stress on casing burst

(high internal pressure), and it is higher at the casing in

diameter fiber and lower at the casing outer diameter fibe

shown in a half-ring cut-off illustration (Fig. 3b). The hig

the internal pressure (Pi), the higher the tensile hoop stress

till the casing material yields. The casing hoop stress is

always balancing with the casing internal and exte

SPE 94304

Casing Burst Strength After Casing WearJ. Wu, ChevronTexaco, and M.G. Zhang, LGMZ Inc.


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2 SPE 94

pressures acting on the casing inner and outer diameter

surfaces:

oi

r

r

ooii drrPrP

22 (2)

API (American Petroleum Institute) has adopted the Balow

equation to represent casing burst strength,6 with an

approximation of casing yield under internal pressure, andcalled it as internal yield pressure (the maximum pressure

differential of internal pressure minus external pressure to start

at casing material yield):

D

tP

y

API

2875.0 (3)

The factor of 0.875 in the above equation is to account for the

API pipe wall thickness tolerance of 12.5% less than the

nominal wall thickness. It is seen that the thicker the casing

wall (t) the higher the API casing burst strength. Fig. 4 shows

a casing burst sample from a previous casing burst test.7

Other casing burst strength equations include initial yield burst

equation, the full-yield burst equation, and the casing ruptureburst equation, from casing triaxial stresses analysis.7, 8 The

initial yield burst equation is based on more accurate

derivation of casing initial yield at the casing inner diameter

fiber. The full-yield burst equation is based on the casing yield

across the entire wall thickness. The casing rupture burst

equation is based on casing ductile tensile failure. Under the

casing capped-ends condition (internal pressure will exert on

the closed casing ends and produce a tension load), they are

written as (0.875 factor is included to account for the API pipe

wall thickness tolerance of 12.5% less than the nominal wall

thickness):

D

t

D

tP

y

IY1

2

3

2875.0

(4)

D

t

D

tP

y

FY1

2

3

2875.0

(5)

tD

tP ult

DR 2

875.0 (6)

Figure 5 shows the calculated casing burst strengths for a 9

5/8 P-110 casing (casing material yield strength 110,000 psi,

casing tensile strength 140,000 psi) of different wall thickness

(equivalent to different casing weight) under casing capped-

ends condition. They all demonstrate a linear or near-linear

reduction as the casing wall thickness (equivalent to different

casing weight) reduces. The API burst strength gives thelowest value among them.

2. Casing with WearFor casing with wear by drillstring and subjected to internal

pressure (Fig. 5, only internal pressure is shown to represent

the pressure differential of internal pressure minus external

pressure from now on), the casing hoop stress () on the

remaining wall section of casing will increase, comparing with

casing without wear (Fig. 6), in order to balance with the

casing internal pressure acting on the casing inner diameter

surface, as a result of the loss of hoop stress on the worn-out

wall portion.

A slotted ring model is used to calculate the casing h

stress increase in the remaining wall section of worn ca

(Fig. 7), where W represents the casing wear depth. The

of hoop stress plus the exposure of internal pressure on

worn-out wall portion of a worn casing, comparing wit

casing without wear, would be equivalent to a hoop force F

wrr

i

i

i

drPF )(

)(*

)(22

22

22

22

wrr

w

rr

rrppw

rr

rprpwpF

iiio

oioi

io

ooii

i The casing hoop stress increase () in the remaining wa

worm casing is then calculated as:

)( wt

F

In fact, in addition to the hoop stress increase in the remainwall of worn casing, there would also be an induced bend

moment in the remaining wall to maintain a force-mom

balance, as shown in Fig. 8. With ignoring casing deformat

this bending moment would be:

2)

2()

2)((

FtwrF

wtrwtM

io =

This bending moment would produce a bending hoop stres

the remaining wall of worn casing, which is a tensile h

stress at inner diameter location and compressive hoop st

at outer diameter location:

3,)(

)2(3)

2(

wt

wrrrFt

I

rwrrMio

oi

m =

=

{ }o

, rwrri

By comparing with FEA modeling results of worn ca

stress, the worn casing hoop stress in the remaining w

section can be finalized by including the two hoop stincreases due to casing wear. A correlation factor of 0.6

W/t) is also added to the bending hoop stress to account

the effect of actual wear shape and worn casing deformatio

2222

22

22

22

,)(

2(95.11)(wt

rrrFwt

Frrr

rrpprrrprp io

io

oioi

io

ooiiw =

{ }o

, rwrri

Figure 9 shows the calculated casing hoop stress (maxim

average, and minimum) in the remaining wall section for

5/8 53.5# T-95 casing, from the above derived worn ca

hoop stress equation (Eq. 12), under 1000 psi internal press

and zero external pressure, by comparing with FEA mode

results. The maximum hoop stress is at the inner diam

fiber of the remaining wall section, the minimum hoop st


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SPE 94304

is at the outer diameter fiber of the remaining wall section, and

the average hoop stress is at the middle of the remaining wall

section. The average and maximum hoop stresses increases as

the casing wear increases, but the minimum hoop stress

decreases as the casing wear increases due to bending.

Figure 10 shows a comparison of the derived maximum hoop

stress of the worm casing by drillstring with the maximumhoop stress by a uniform wear model (calculated from

Equation 1, with new casing inner diameter = ri + w after

wear), on a 9 5/8 53.5# T-95 casing. It is shown that without

including the local bending stress the maximum hoop stress at

the remaining wall of worm casing by drillstring is almost the

same as the maximum hoop stress calculated by uniform-

worn model. With considering the local bending, the

maximum hoop stress at the remaining wall of worm casing

by drillstring can become very high for large casing wear

cases.

The Finite Element Analysis (FEA) is conducted to model 9

5/8, 53.5#, T-95 casing with wear by drillpipe tool-joint(6.5/8 OD). The casing wear depth and wear angle are

calculated based on the wear percentage, as listed in Fig. 11.

Figure 12 shows the FEA modeling result on a 30% wear case

for 1000 psi casing internal pressure and zero external

pressure. The maximum hoop stress occurs at the inner

diameter fiber of the worn section is about 21,000 psi, and the

minimum hoop stress about 2,800 psi at the outer diameter

fiber of the worn section.

The worn casing deformation is also studied by FEA modeling

on the 9 5/8, 53.5#, T-95 worn casing. For a 50% wear casing

and under 1000 psi internal pressure and zero external

pressure, the original round shape of casing at zero internal

pressure will be deformed into a slightly oval shape as

shown in Fig. 13, due to a weaker worn section under higher

tension and bending loads (the shown deformation is 50 times

larger than actual for easy observation).

Based on the above analysis and derivation, the worn casing

burst strength could be defined when the casing yields or

ruptures in the remaining wall section of worn casing. The

worn casing yield burst strength can be determined through

the von Mises yield criterion for casing triaxial stresses

condition:

yarawrwarw

=2222

,

22

,

222

, (13)

When considering only casing hoop stress and 100% wall

thickness casing, the worn casing burst strength could be

calculated as follows.

1. Worn casing initial yield burst strength, when the maximum

hoop stress at the inner diameter fiber of the remaining wall of

worn casing reaches the casing material yield strength:

yiw wrr

=

, (14)

2. Worn casing full yield burst strength, when the aver

hoop stress in the middle of the remaining wall of worn cas

reaches the casing material yield strength:

y

oi

w

rwrr

=

=

2,

3. Worn casing ductile tensile rupture burst strength, when

average hoop stress in the middle of the remaining wal

worn casing reaches the casing material tensile strength:

ult

oi

w

rwrr

=

=

2,

(

Figure 14 shows the calculated worn casing burst stren

from the above equations 14 to 16, for a 9 7/8 casing (ac

wall thickness 0.619, yield strength 134,880 psi, ten

strength 155,185 psi,), comparing with the previo

published worn casing burst test data on the same casing.6

full yield and rupture burst strengths reduce linearly as cawear increases, but the initial yield burst strength redu

more and non-linearly due to the local bending at the w

section. The rupture burst strength is seen very close to

previously published worn casing burst test data.6

Figure 15 shows the initial yield burst strength of

crescent-worn casing by drillstring (with and with

considering the local bending at the worn casing secti

comparing with the initial yield burst strength from

uniform-worn casing model (calculated from Equation

with new casing inner diameter = ri + w after wear), and

well as the API casing burst strength linearly-reduced

casing wear (it is also a uniform wear model). It is seen the initial yield burst strength of crescent-worn ca

without considering the local bending is almost the same

that from the uniform-worn casing model. The API b

strength (87.5% min. wall) further reduced by linear reduc

(uniform-worn casing model) gives a safe prediction

the initial yield burst strength of crescent-worn casing w

the local bending being considered on low casing w

condition (about less than 20% wear).

Conclusions1. Analytic and Finite Element Analysis (FEA) modelin

conducted to develop a hoop stress equation for

thinner portion of crescent-worn casing by drillstrwhich gives a hoop stress similar to that from a unifo

worn model when local bending at the worn sectio

ignored, but a higher max. hoop stress than that fro

uniform-worn model when local bending is consider

2. Casing burst strength can be estimated by a linreduction starting from casing full-yield or rupture b

strength by the wear percentage for casing worn

drillstring under sweet service condition, which giv

reduced casing burst strength higher than that from

linear reduction starting from API burst strength.

3. For sour service condition, casing burst strength of wcasing by drillstring may be reduced more by a non-lin


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4 SPE 94

reduction to prevent an earlier casing burst from sulfide

stress cracking.

4. The linear reduction starting from API burst strength(87.5% min. wall) may be used to estimate the worn

casing burst strength under sour service condition, on low

wear conditions (about less than 20% wear).

5. Further study on the local bending at the worn section of

crescent-worn casing and the worn casing burst strengthunder sour service condition may still be needed.

NomenclatureD: casing outer diameter, in.

F: hoop force loss due to casing wear, lb

I: moment of inertia of worn section, in.4

M: bending moment at the worn section, lb-in.

r: casing radial coordinate, in.

ri: casing inner radius, in.

ro: casing outer radius, in.

PAPI: API burst strength, psi

PIY: casing initial burst strength, psi

PFY: casing full-yield burst strength, psiPDR: casing rupture burst strength, psi

Pi: casing internal pressure, psi

Po: casing external pressure, psi

t: casing wall thickness, in.

w: casing wear depth, in.

a: casing axial stress, psi

r: casing radial stress, psi

: casing hoop stress, psi

,w: casing hoop stress at worn section, psi

y: casing material yield strength, psi

: casing hoop stress increase due to hoop force, psi

,m: casing hoop stress increase due to bending, psi

AcknowledgmentsThe authors wish to thank ChevronTexaco for permission t

publish this paper.

References

1. Maurer Engineering: Improved Casing and Riser WTechnology, DEA-42 Phase V Proposal, 1997.

2. M.H.steb, et al: Casing Wear in Horizontal WelField Case Histories, IADC Well Control Confere

1996

3. Song, J.S., et al: The Internal Oressure CapacityCrescent-Shaped Wear Casing, IADC/SPE 23

IADC/SPE Drilling Conference held in New Orle

Louisiana, February v1992

4. Klever, F.J. AND Stewart, G. : Analytical Burst StrenPrediction of OCTG With and Without Defects,

48329, SPE Applied Technology Workshop on R

Based Design of Well Casing and Tubing, May 1998.

5. Flugge, W.: Handbook of Engineering MechaniMcGraw-Hill Book Company, 1962.

6. Bulletin on Formulas and Calculations for CasTubing, Drill Pipe, and Line Pipes Properties,

Bulletin 5C3, Six Edition, American Petroleum Instit

Washington, D.C., Oct. 1994.

7. Paslay, P.R., et al: Burst Pressure Prediction of TWalled, Ductile Tubulars Subjected to Axial Load,

48327, SPE Applied Technology Workshop on R

Based Design of Well Casing and Tubing, May 1998.

8. Wu, Jiang: Casing Design Criteria, ChevronTexTech Memo 2002-#24, July 2002.


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SPE 94304

Fig. 1 Casing wear by drillstring rotation.1

Fig. 2 Casing wear measurement and prediction example.2

iiDPt=2

iP

or ir

oP

iiDPt=2

iP

or ir

oP

(a) (b)

Fig. 3 Casing hoop stress and internal pressure balance on casing without wear.


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6 SPE 94

Fig. 6 Casing burst sample.7

9 5/8" P-110 Casing Burst Strength

0

5000

10000

15000

20000

25000

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Casing wall thickness, in.

Casing

burststrength,p

si

API Burst

Initial-yield Burst

Full-yield Burst

Ductile Burst

Fig. 4 Casing burst strengths for casing without wear.

(a) (b)

Fig. 5 Casing hoop stress balances with internal pressure on worn casing.


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SPE 94304

(a) (b)

Fig. 6 Casing hoop stress balances with internal pressure on casing without wear.

t

w

ri ro

iP

FF

t

w

ri ro

iP

=

Fig. 7 Casing wear slotted ring model on hoop stress pressure balance.

t

w

ro

iP

FF

M

t

w

ri

ro

iP

FF

M

ri

Fig. 8 Casing wear slotted ring model on force and moment balance.


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9 5/8 53.5# T-95 Casing Hoop Stress

-5000

0

5000

10000

15000

20000

25000

30000

35000

40000

0 10 20 30 40 50 60

Casing Wear, %

CasingHoopS

tress.psi

Max. analytic Max . FEAMean analy tic Mean FEAMin. analytic Min. FEA

Figure 9 Worn casing hoop stress in the remaining wall section.

9 5/8 53.5# T-95 Casing Hoop Stress

5000

10000

15000

20000

25000

30000

35000

0 10 20 30 40 50 60

Casing Wear, %

Casing

Hoop

Stress.psi

Max. hoop stress w ith bendingMax. hoop stress w ithout bendingMax. hopp stress, uniform w ear model

Figure 10 Comparison of max. hoop stress.

9 5/8" 53.50#/ft, T-95 Casing Wear Modeling

Ro = 4.8125 (in.) Casing OD radius

Ri = 4.2675 (in.) Casing ID radius

t = 0.545 (in.) Casing wall thickness

Rt = 3.3125 (in.) Drillpipe tool-joint OD radius

B

A

CRi

Rt

Ro

Casing

Drillpipe tool-joint

Pi (internal pressure)

Po (external pressure) =0

Casing A B C

Wear Wear Depth Eccentricity Wear angle

(%) (in.) (in.) (deg.)

0 0 0.955 0

5 0.0273 0.982 23.77

10 0.0545 1.010 33.15

20 0.1090 1.064 45.62

30 0.1635 1.119 54.4240 0.2180 1.173 61.26

50 0.2725 1.228 66.82

60 0.3270 1.282 71.46

70 0.3815 1.337 75.41

80 0.4360 1.391 78.80

90 0.4905 1.446 81.76

100 0.5450 1.500 84.34

Figure 11 Worn casing geometry for FEA modeling.


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SPE 94304

1

MN

MX

2809

48376866

889510923

1295214980

1700919037

21066

APR 4 2004

13:36:50

NODAL SOLUTION

STEP=1

SUB =10

TIME=1

S1 (AVG)

DMX =.004864

SMN =2809

SMX =21066

Figure 12 Worn casing stress from FEA modeling.

Fig. 13 Worn casing deformation under internal pressure.

9 7/8" Casing Burst Strength (0.619" wall, 134,880 psi yield

strength, 155,185 psi tensile strength)

5,000

8,000

11,000

14,000

17,000

20,000

23,000

0 10 20 30 40 50 60

Casing w ear, %

Casing

burststrength,psi

Initial yield (100% wall)

Full yield (100% wall)

Rupture (100% wall)

Shell burst test data (100% wall)

Fig. 14 Worn casing burst strength prediction and comparison.


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9 7/8" Casing Burst Strength (0.619" wall, 134,880 psi yield

strength, 155,185 psi tensile strength)

5,000

8,000

11,000

14,000

17,000

20,000

0 10 20 30 40 50 60

Casing wear, %

Casingburststrength

,psi

Initial yield (100% wall)

Initial yield (100%wall) without bending

Initial yield (100% wall) with uniform wear

API burst, 87.5% min. wall

API burst, 100% wall

Fig. 15 Worn casing initial yield burst strength comparison.

casing burst strength after casing wear.pdf

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