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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.”