Advances in Casing DesignAdvances in Casing Designwithwith

ISO DIS 10400ISO DIS 10400

ASMEASME1 December 20051 December 2005

David B. LewisDavid B. Lewis

TodayToday’’s Talks Talk

•• Strength TheoriesStrength Theories

•• Design MethodsDesign Methods

“Fears are educated into us, and can, if we wish, be educated out.”

Burst StrengthBurst Strength

•• API Internal YieldAPI Internal Yield•• VME coupled with VME coupled with LameLame’’ss EquationsEquations•• HillHill’’s Fully Plastic Burst Models Fully Plastic Burst Model•• KleverKlever--Stewart Rupture LimitStewart Rupture Limit

“Learn from mistakes of others; you can never live long enough to make them all yourself.”

The Barlow Thin Wall YieldThe Barlow Thin Wall Yield

tr

df

h

PiPi

shoopshoop

df

r

df/2

The limiting pressure is when shoop = sy, or

ODtP yBarlow

2σ=

API Internal YieldAPI Internal Yield

•• Barlow Equation (thin wall approximation).Barlow Equation (thin wall approximation).•• Uses API minimum wall (12.5% reduction on Uses API minimum wall (12.5% reduction on

nominal wall).nominal wall).•• Minimum yield strength.Minimum yield strength.•• Conservative estimate for pipe designConservative estimate for pipe design•• No consideration of tension and its impact No consideration of tension and its impact

on burston burst

ODt2

875.0 nomyAPIP

σ=

Thick Wall and VMEThick Wall and VME

•• LameLame’’ss Equation for radial and hoop stress Equation for radial and hoop stress (thick wall derivations).(thick wall derivations).

•• von Mises failure criterion.von Mises failure criterion.

( ) bio

al

rrT

σπ

σ ±−

= 22Re

axial

( )23

22

21hoopradialradialaxialhoopaxial

2radial

2hoop

2axialVME 3 τττσσσσσσσσσσ +++−−−++=

( )( )

( )( ) ⎥

⎥⎦

⎤

⎢⎢⎣

⎡

−−

+⎥⎥⎦

⎤

⎢⎢⎣

⎡

−−

= 22

22

222

22 1

io

ooii

io

iooiradial rr

rPrPrrr

PPrrσ

( )( )

( )( ) ⎥

⎦

⎤⎢⎣

⎡

−−

+⎥⎦

⎤⎢⎣

⎡

−−

−= 22

22

222

22 1

io

ooii

io

iooihoop rr

rPrPrrr

PPrrσ

Going to the Limit StateGoing to the Limit State

•• Both API and VME Both API and VME limits are limits are ““elasticelastic””limitslimits

•• Pipe still has Pipe still has capacity to capacity to withstand load withstand load beyond these limitsbeyond these limits

Pi

σyPi=PCEY

“It is not because things are difficult that we do not dare; it is because we do not dare that things are difficult.”

HillHill’’s Fully Plastic Burst Limits Fully Plastic Burst Limit

•• Based on classical mechanical analysis of Based on classical mechanical analysis of thickthick--walled cylinder walled cylinder •• ElasticElastic--perfectly plastic assumption beyond yieldperfectly plastic assumption beyond yield

•• Entire wall is plasticized based on VME Entire wall is plasticized based on VME stressstress

•• Sometimes seen with ultimate strength Sometimes seen with ultimate strength instead of yield strengthinstead of yield strength

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=nom

yHillB tODODP

2ln

32

, σ

KleverKlever--Stewart Rupture Limit Stewart Rupture Limit (ISO 10400)(ISO 10400)

•• KKnn is a correction factor for nonis a correction factor for non--elastic behavior.elastic behavior.•• KKTT is a tension correction factor.is a tension correction factor.•• ssuu is ultimate strength (for design, min UTS).is ultimate strength (for design, min UTS).•• mmff is a factor to account for process (1 for Q&T, 2 is a factor to account for process (1 for Q&T, 2

for asfor as--rolled, N and N&T).rolled, N and N&T).•• ttnn is flaw depth (for design, use max. escaping is flaw depth (for design, use max. escaping

detection)detection)

( )( )nf

nfuTnB tmtOD

tmtKKP

−−

−=

min

min2σ

nn

nK++

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎠⎞

⎜⎝⎛=

11

31

21

1000/0.000882 - 0.169n yσ=

2

1 ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

UTS

effT T

TK

•• Based on experimental and Based on experimental and theoretical work by Klevertheoretical work by Klever--Stewart selected from six Stewart selected from six different choicesdifferent choices

Collapse StrengthCollapse Strength

•• API CollapseAPI Collapse•• Tamano Collapse LimitTamano Collapse Limit•• KleverKlever--Generalized Tamano (KGT)Generalized Tamano (KGT)

API CollapseAPI Collapse•• Based on empirical collapse dataBased on empirical collapse data•• Adjusted for presence of tension, since tension Adjusted for presence of tension, since tension

reduces collapse strength reduces collapse strength •• Empirical data fitted using curveEmpirical data fitted using curve--fit over four distinct fit over four distinct

regionsregions•• Applicable region based on D/t ratio of pipe being Applicable region based on D/t ratio of pipe being

designeddesigned•• Collapse tests on 2488 specimens of K55, N80 and Collapse tests on 2488 specimens of K55, N80 and

P110 over wide range of D/t ratios. (ovality, P110 over wide range of D/t ratios. (ovality, manufacture and process tolerances, material manufacture and process tolerances, material imperfections etc. implicit)imperfections etc. implicit)

•• Regression analysis on data, fitting a 99.5% nonRegression analysis on data, fitting a 99.5% non--failure curve i.e., 0.5% probability that pipe will fail.failure curve i.e., 0.5% probability that pipe will fail.

API Collapse Derivation API Collapse Derivation --CurvesCurves

Tamano Collapse LimitTamano Collapse Limit

•• ISO DIS 10400 collapse limit is based ISO DIS 10400 collapse limit is based on a collapse limit state equation due on a collapse limit state equation due to Tamanoto Tamano

•• Interaction Equation similar to Interaction Equation similar to TimoshenkoTimoshenko

•• Ovality, eccentricity and residual stress Ovality, eccentricity and residual stress includedincluded

Tamano Collapse LimitTamano Collapse Limit( ) ( )

ultyeyeye

ultc Hpppppp

p +−

−+

=42

2

( ) ( )22 11

12080.1

−−=

mmEpe ν ⎟

⎠⎞

⎜⎝⎛

−+

−=

15.1112 2 mm

mp yey σ

rultH σεφ 18.00022.0071.0 −+=

( )avODODOD minmax100

−=φ

( )avt

tt minmax100−

=ε

y

rr σ

σσ =

m = OD/t

Klever Generalized TamanoKlever Generalized Tamano•• Derived from Derived from

TamanoTamano’’ss equationequation•• Generalizes the Generalizes the

equation for better equation for better fit over a wider fit over a wider range of D/trange of D/t

( ) ( )( )ult

ultyulteultyulteultyulteultult H

Hppppppp

−

++−+=∆

1242

( ) ( )( )22 1//1

12

−−=

aveaveaveaveelseult tDtD

Ekpν

( ) ( )⎟⎟⎠⎞

⎜⎜⎝

⎛+=

aveaveaveave

yylsyult tDtD

Skp

/211

/2

nyult hSrsH +−+= /440.00039.0127.0 εφ

Brittle BurstBrittle Burst

Based on fracture mechanicsBased on fracture mechanics

“It is clear that the future holds opportunities -- it also holds pitfalls. The trick will be to seize the opportunities, avoid the pitfalls, and get back home by six o’clock.”

Crack Propagation ModesCrack Propagation Modes

Mode 1Opening

Mode 2Sliding, or in-plane shear

Mode 3Tearing, or out-of-plane shear

Fracture ToughnessFracture ToughnessToughness is the ability to resist the propagation Toughness is the ability to resist the propagation

of a crack under load and exposure to of a crack under load and exposure to environmentenvironment

KKI –– Stress Intensity FactorStress Intensity Factor•• Several theoretical Several theoretical

models to calculate models to calculate stresses caused stresses caused near a crack due to near a crack due to a load on the a load on the structure with flawstructure with flaw

•• Usually, several Usually, several simplifications simplifications mademade

•• Shown here is an Shown here is an example for a crack example for a crack in an infinite plate in an infinite plate loaded in Mode 1loaded in Mode 1

⎟⎠⎞

⎜⎝⎛ +=

2sin1

2cos

21

1θθ

πσ

rK

⎟⎠⎞

⎜⎝⎛ −=

2sin1

2cos

21

2θθ

πσ

rK

( )213 σσνσ +=

aK πσ=1

2

21

61

yplastic

Krσπ

=

Crack GrowthCrack Growth-- The The ResistanceResistance

•• KKISSCISSC is the is the ““critical stress intensitycritical stress intensity””•• It is the resistance of material to crack It is the resistance of material to crack

propagation in environmentpropagation in environment•• It is a measurable material propertyIt is a measurable material property•• KKISSCISSC is a function ofis a function of

•• MetallurgyMetallurgy•• Environment (temperature and partial Environment (temperature and partial

pressure of Hpressure of H22S)S)

Measurement of KMeasurement of KISSCISSC•• Based on testingBased on testing

•• Dual Cantilever Beam (DCB) tests in Dual Cantilever Beam (DCB) tests in environmentenvironment

•• Several other testsSeveral other tests•• It is a direct measure of toughness, since It is a direct measure of toughness, since

it measures the it measures the ““critical stress intensitycritical stress intensity””•• It is statistical in nature, so a distribution It is statistical in nature, so a distribution

is usually sought by repeated testingis usually sought by repeated testing•• Testing should as closely reflect the Testing should as closely reflect the

environment as possibleenvironment as possible

Failure Assessment Diagram Failure Assessment Diagram (FAD)(FAD)

KKrr ==KKappliedapplied

KKII

SSrr ==PPLoad AppliedLoad Applied

PPLimitLimit

SafeSafe

FailureFailure

The RevelationThe Revelation

•• The pressure limit depends upon flaw The pressure limit depends upon flaw size, Hsize, H22S, temperature, OD, wall, and S, temperature, OD, wall, and material gradematerial grade•• Hot is goodHot is good•• Small flaws are goodSmall flaws are good•• Higher material grades are badHigher material grades are bad•• Higher HHigher H22S is badS is bad•• Lower D/t ratio is goodLower D/t ratio is good

“The man who insists upon seeing with perfect clearness before deciding never decides.”

ISO 10400 Fracture DesignISO 10400 Fracture Design

FAD diagram relationship; KFAD diagram relationship; Krr and and LLrr

Iterative solution for internal pressureIterative solution for internal pressure

( )( )⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−+

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−−

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−+⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−−

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ −−⎟

⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

=+− −

4

4

3

3

2

21022

2

65.02

2

5

2

4

2

3

2

22

22

27.03.014.016

tDaG

tDaG

tDaG

tDaGG

KtDD

aDPeL

Ieac

iFL

rr

π

⎟⎠⎞

⎜⎝⎛

−+

⎟⎟⎠

⎞⎜⎜⎝

⎛=

ataD

fpL

y

iFr

2/23

“Good people are good because they’ve come to wisdom through failure. We get very little wisdom from success, you know.”

99--5/85/8”” 53.50 lb/ft L8053.50 lb/ft L80API Internal Yield = 7,927 psiAPI Internal Yield = 7,927 psiAPI Collapse = 6,617 psiAPI Collapse = 6,617 psi

Hill = 11,103 psiHill = 11,103 psi

10400 Burst = 10,942 psi10400 Burst = 10,942 psi10400 Collapse10400 Collapse = 7,734 psi (average pipe)= 7,734 psi (average pipe)

= 9,316 psi (excellent pipe)= 9,316 psi (excellent pipe)= 4,081 psi (poor pipe)= 4,081 psi (poor pipe)

10400 Brittle Burst = 8,729 psi (average pipe K=32)10400 Brittle Burst = 8,729 psi (average pipe K=32)= 10,652 psi (excellent pipe K=50)= 10,652 psi (excellent pipe K=50)= 6,112 psi (poor pipe K=20)= 6,112 psi (poor pipe K=20)

Probability and DesignProbability and Design

“The theory of probability is at the bottom nothing but common sense reduced to calculus.”

Optimization of Cost and Reliability

INCREASING RELIABILITY

INC

REA

SIN

GC

OST

FAILURE DESIGN

OVER DESIGNEDUNDER DESIGNED

OptimizedDesign

LOW HIGH

HIGH

“The purpose of computing is insight, not numbers.”

Probabilistic Consideration of Probabilistic Consideration of StrengthStrength

•• Strength defining parameters are uncertain and Strength defining parameters are uncertain and random, butrandom, but……

•• They are pretty much the key controllable in They are pretty much the key controllable in designdesign

•• And they are measurableAnd they are measurable•• Probabilistic consideration of strength is Probabilistic consideration of strength is

therefore possibletherefore possible……•• And may be necessary in many critical well And may be necessary in many critical well

designsdesigns

“Hindsight is an exact science.”

Strength UncertaintyStrength Uncertainty

•• Controlled by Manufacturing ProcessControlled by Manufacturing Process•• Can Be Minimized But Not EliminatedCan Be Minimized But Not Eliminated•• Reflected in the distribution of Reflected in the distribution of

strengthstrength--defining parameters (yield, defining parameters (yield, OD, wall thickness, etc.)OD, wall thickness, etc.)

•• Can be measured and taken account of Can be measured and taken account of in designin design

Strength VariabilityDistribution for L-80 Yield Point

Actual Values (ksi)

70 75 80 85 90 95 100 105

RelativeFrequency

Specification Range

RelativeFrequency

Wall Thickness (Actual Wall / Nominal Wall)

Actual Thickness / Nominal Thickness - Seamless Casing

Strength Variability

0.875 0.938 1.000 1.063 1.2501.1881.125

SpecificationMinimum

Load UncertaintyLoad Uncertainty

Load uncertainty is of two typesLoad uncertainty is of two types•• Probability of occurrence of the loadProbability of occurrence of the load•• Magnitude of the load as compared to Magnitude of the load as compared to

the design loadthe design load

“Mistakes are a good investment. If you want to succeed, double your failure rate.”

Probability of Occurrence of Probability of Occurrence of the Loadthe Load

Probability of occurrence influenced byProbability of occurrence influenced by•• Operational Practice Operational Practice

•• Degree of overbalance in the case of kickDegree of overbalance in the case of kick•• Connection makeConnection make--up and corrosion up and corrosion

inhibition, testing of tubing (in the case of inhibition, testing of tubing (in the case of tubing leak)tubing leak)

•• Human ErrorHuman Error

Uncertainty of MagnitudeUncertainty of Magnitude

•• Mother NatureMother Nature•• Abnormal pressures, frac and pore Abnormal pressures, frac and pore

pressure, temperaturepressure, temperature•• Operational ProceduresOperational Procedures

•• Kill method used, contingencies in place, Kill method used, contingencies in place, planningplanning

•• Human ErrorHuman Error

Load VariabilityProbability of Kick Loading

No Kick LoadingKick Loading0

20

40

60

80

100

% P

roba

bilit

y

Load VariabilityKick Intensity

Num

ber o

f Kic

ks

Kick Intensity – Volume and Pressure

Fracture at ShoeAnd Gas to Surface

Design ApproachesDesign Approaches

•• Working Stress DesignWorking Stress Design•• Limit States DesignLimit States Design•• Reliability Based DesignReliability Based Design

•• Stochastic Strength and Deterministic Stochastic Strength and Deterministic LoadLoad

•• Stochastic Strength and Stochastic Stochastic Strength and Stochastic LoadLoad

“The man who never alters his opinion is like standing water, and breeds reptiles of the mind.”

Working Stress DesignWorking Stress Design

•• Traditional method, long historyTraditional method, long history•• Uses minimum strength Uses minimum strength •• Uses reasonable load estimate, usually at the higher Uses reasonable load estimate, usually at the higher

end (conservative load estimates)end (conservative load estimates)•• Uses elastic failure criteria (API, VME, etc.)Uses elastic failure criteria (API, VME, etc.)

•• Strength is therefore within elastic limitStrength is therefore within elastic limit•• Factor of Safety (Factor of Safety (≥≥ 1) 1) to establish a to establish a ““working stress working stress

limitlimit””--•• SF takes care of uncertainties by keeping comfortable SF takes care of uncertainties by keeping comfortable

distance between load and strengthdistance between load and strength•• Design check usually written asDesign check usually written as

•• SF x Load effect SF x Load effect ≤≤ Min StrengthMin Strength

Limitations of WSDLimitations of WSD•• SF is independent of load case SF is independent of load case –– i.e., failurei.e., failure--mode mode

consistent designs, but not riskconsistent designs, but not risk--consistent designsconsistent designs•• May be too conservative for simple wellsMay be too conservative for simple wells•• Usually does not work for complex wells (deep, Usually does not work for complex wells (deep,

HPHT, etc.)HPHT, etc.)•• SF usually empirically determined, no documented SF usually empirically determined, no documented

basisbasis•• Typically based on elasticTypically based on elastic--based limits that usually based limits that usually

do not represent true limitsdo not represent true limits•• Typically load estimates without consideration of Typically load estimates without consideration of

probability of occurrenceprobability of occurrence•• Excludes consideration of riskExcludes consideration of risk--consequence consequence

relationshiprelationship

Limit States DesignLimit States Design

•• Addresses some of the limitations of WSDAddresses some of the limitations of WSD•• Uses limitUses limit--state strength functionstate strength function

•• Ultimate limit states and serviceability limit statesUltimate limit states and serviceability limit states•• Elastic limit not always relevantElastic limit not always relevant-- load bearing limit load bearing limit

is what we are looking foris what we are looking for•• Often results in strainOften results in strain--based criteriabased criteria

•• Can be applied for deterministic or Can be applied for deterministic or probabilistic designprobabilistic design

“A theory should be as simple as possible, but no simpler.”

Deterministic Theory - WSD

LOAD RESISTANCE

Maximum Load Assumed

MinimumProperties Assumed

Factor of Safety

LOAD LOAD << RESISTANCERESISTANCE

Probabilistic Theory

RESISTANCERESISTANCERESISTANCE

RELIABILITY LEVEL

LOADLOADLOAD

LOAD < RESISTANCELOAD LOAD << RESISTANCERESISTANCE

Probabilistic Theory

RESISTANCERESISTANCE

RELIABILITY LEVEL

LOADLOAD

LOAD < RESISTANCELOAD LOAD << RESISTANCERESISTANCE

RESISTANCELOAD

Yield Point

Eccentricity

TensileStrength

Ovality

WallThickness

KickLost Returns

Running CasingCementing Casing

Tubing LeakPressure TestingShut in Pressure

Well KillStimulationOver Pull

Subsidence / CompactionSalt

Trapped Annular PressureIntentional EvacuationAccidental Evacuation

Environmental Loadings

Ductile BurstBrittle Burst

BucklingBending

SSCCSCSCC

FatigueTension Burst

TensionBrittle Tension

CollapseHigh-Strain Collapse

TorsionConnection Leak

Connection Structural

( )01

1 102 2

2

=+ +

−⎛

⎝⎜

⎞

⎠⎟ − −

P P

P P

OD kt

p py e

e yϕ τ

initial nominalexternal internal

Ψ

Collapse

( )( )T

OD OD t

p p

tOD

effective

YP

internal external

YP

0.5

π σ

σ42 2

31

1 2

12 2

2

2

− −

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

+−

−

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⎟⎟⎟

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

=

ln

Tension Burst

PorePressure

FractureGradient

KickIntensity

MudDensity

KickFrequency

Monte CarloMAISFORMSORM

SOROS

RESISTANCELOAD

Yield Point

Eccentricity

TensileStrength

Ovality

WallThickness

Yield Point

Eccentricity

TensileStrength

Ovality

WallThickness

KickLost Returns

Running CasingCementing Casing

Tubing LeakPressure TestingShut in Pressure

Well KillStimulationOver Pull

Subsidence / CompactionSalt

Trapped Annular PressureIntentional EvacuationAccidental Evacuation

Environmental Loadings

Ductile BurstBrittle Burst

BucklingBending

SSCCSCSCC

FatigueTension Burst

TensionBrittle Tension

CollapseHigh-Strain Collapse

TorsionConnection Leak

Connection Structural

( )01

1 102 2

2

=+ +

−⎛

⎝⎜

⎞

⎠⎟ − −

P P

P P

OD kt

p py e

e yϕ τ

initial nominalexternal internal

Ψ

Collapse

( )01

1 102 2

2

=+ +

−⎛

⎝⎜

⎞

⎠⎟ − −

P P

P P

OD kt

p py e

e yϕ τ

initial nominalexternal internal

Ψ ( )01

1 102 2

2

=+ +

−⎛

⎝⎜

⎞

⎠⎟ − −

P P

P P

OD kt

p py e

e yϕ τ

initial nominalexternal internal

Ψ

Collapse

( )( )T

OD OD t

p p

tOD

effective

YP

internal external

YP

0.5

π σ

σ42 2

31

1 2

12 2

2

2

− −

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

+−

−

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⎟⎟⎟

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

=

ln

Tension Burst

( )( )T

OD OD t

p p

tOD

effective

YP

internal external

YP

0.5

π σ

σ42 2

31

1 2

12 2

2

2

− −

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

+−

−

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⎟⎟⎟

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

=

ln

Tension Burst

PorePressure

FractureGradient

KickIntensity

MudDensity

KickFrequency

PorePressure

FractureGradient

KickIntensity

MudDensity

KickFrequency

Monte CarloMAISFORMSORM

SOROS

Monte CarloMAISFORMSORM

SOROS

Reliability Based DesignReliability Based Design

“The world is simple for those who understand.”

Example of RBDExample of RBDProbabilistic Strength Only (ISO/DIS 10400 Collapse)

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

4000 5000 6000 7000 8000 9000 10000 11000 12000

Collapse Strength (psi)

Pro

bab

ilit

y D

en

sity

Collapse Load KGT Collapse Strength

9 5/8" 53.5 ppf L80Load is deterministic at 6617 psiStrength uncertainty is specifiedAPI SF = 1.0KGT Design Collapse Strength = 7037 psi

Pf = 1.0E-2.9

Example of RBDExample of RBDProbabilistic Load and Strength (ISO/DIS 10400 Collapse)

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

5000 6000 7000 8000 9000 10000 11000

Collapse Strength (psi)

Pro

bab

ilit

y D

en

sity

Collapse Load KGT Collapse Strength

9 5/8" 53.5 ppf L80Load is probabilistic, Nominal value 7000 psi,P99 value of load is 7217 psiStrength uncertainty is specifiedAPI SF = 0.95KGT Design Collapse Strength = 7037 psi

Pf = 1.0E-2.3

“Lots of things can happen, but only one thing will happen.”

For an “Average” American we have:

Being injured is

Having an automobile accident is

Having a heart attack if under the age of 35 is

Fracturing your skull is

Dying (any cause) is

Dying of cancer is

Dying from stroke is

Being murdered is

Dying from a fall is

Drowning is

Being injured in a tornado is

Dying in a plane crash is

Dying in your bath tub is

Freezing to death is1 in 1,000,000 per year

1 in 20,000 per year

1 in 11,000 per year

1 in 1700 per year

1 in 500 per year

1 in 115 per year

1 in 3 per year

1 in 100 per year

1 in 77 per year

1 in 12 per year

1 in 50,000 per year

1 in 3,000,000 per year

1 in 250,000 per year

RisksRisks

1 in 200,000 per year

Design LevelsDesign LevelsDesign Level

Load

1 Deterministic

2 Deterministic

3 Deterministic

4 Deterministic

5 StochasticStochastic Strengths based on Limit State Design

Stochastic Strength based on Limit State Design

Deterministic Strength based on Limit State Design

Deterministic Working Stress based on Advanced Engineering Mechanics

Deterministic Working Stress based on API Ratings

Strength

Concluding NotesConcluding Notes•• Probabilistic design methods are standard in Probabilistic design methods are standard in

many structural design codesmany structural design codes•• They may seem complex, but in reality they are They may seem complex, but in reality they are

more rational and appealing to our sense of more rational and appealing to our sense of riskrisk--based decision makingbased decision making

•• They are unavoidable in the modern design They are unavoidable in the modern design community, with more demanding wells and community, with more demanding wells and better understanding of performance propertiesbetter understanding of performance properties

•• Properly applied, they lead to the most riskProperly applied, they lead to the most risk--consistent, optimal designsconsistent, optimal designs

•• The new design approaches are a muchThe new design approaches are a much--needed needed improvement to enable design of challenging improvement to enable design of challenging wellswells

“There are two equally dangerous extremes -- to shut reason out and to let nothing else in.”