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Advances in Casing Design with ISO DIS 10400

ASME 1 December 2005 David B. Lewis

Today’s Talk • Strength Theories • Design Methods

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

Burst Strength • • • •

API Internal Yield VME coupled with Lame’s Equations Hill’s Fully Plastic Burst Model Klever-Stewart Rupture Limit

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

The Barlow Thin Wall Yield h

r Pi

shoop

df

t

df/2

shoop Pi

r

df

The limiting pressure is when shoop = sy, or

PBarlow

2t =σy OD

API Internal Yield • Barlow Equation (thin wall approximation). • Uses API minimum wall (12.5% reduction on nominal wall). • Minimum yield strength. • Conservative estimate for pipe design • No consideration of tension and its impact on burst

PAPI = 0.875

σ y 2 t nom OD

Thick Wall and VME • Lame’s Equation for radial and hoop stress (thick wall derivations). • von Mises failure criterion. σ VME = σ axial 2 + σ hoop 2 + σ radial 2 −σ axialσ hoop −σ axialσ radial −σ radialσ hoop + 3(τ12 +τ 22 +τ 32 ) σ axial =

(

TRe al

π ro 2 − ri 2

)

±σb

(

)

⎡ ri 2ro 2 (Po − Pi ) ⎤ 1 ⎡ Pi ri 2 − Poro 2 ⎤ σ hoop = −⎢ ⎥ 2 +⎢ ⎥ 2 2 2 2 r − − r r r r ⎣ o i ⎦ ⎣ o i ⎦

(

σ radial

)

(

(

)

⎡ ri 2 ro 2 (Po − Pi )⎤ 1 ⎡ Pi ri 2 − Po ro 2 =⎢ ⎥ 2 +⎢ 2 2 2 2 ⎢⎣ ro − ri ⎥⎦ r ⎢⎣ ro − ri

(

)

(

)

)⎤⎥ ⎥⎦

Going to the Limit State • Both API and VME limits are “elastic” limits • Pipe still has capacity to withstand load beyond these limits

Pi=PCEY

σy

Pi

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

Hill’s Fully Plastic Burst Limit • Based on classical mechanical analysis of thick-walled cylinder • Elastic-perfectly plastic assumption beyond yield

• Entire wall is plasticized based on VME stress • Sometimes seen with ultimate strength instead of yield strength

PB , Hill

⎛ OD = σ y ln⎜⎜ 3 ⎝ OD − 2t nom 2

⎞ ⎟⎟ ⎠

Klever-Stewart Rupture Limit (ISO 10400) 2(t min − m f t n )

PB = K n K T σ u 1+ n

⎛1⎞ Kn = ⎜ ⎟ ⎝2⎠

OD − (t min − m f t n ) 1+ n

⎛ 1 ⎞ ⎟⎟ + ⎜⎜ ⎝ 3⎠

⎛ Teff K T = 1 − ⎜⎜ ⎝ TUTS

⎞ ⎟⎟ ⎠

2

• Based on experimental and theoretical work by KleverStewart selected from six different choices

n = 0.169 - 0.000882 σ y / 1000

• • • •

Kn is a correction factor for non-elastic behavior. KT is a tension correction factor. su is ultimate strength (for design, min UTS). mf is a factor to account for process (1 for Q&T, 2 for as-rolled, N and N&T). • tn is flaw depth (for design, use max. escaping detection)

Collapse Strength • • •

API Collapse Tamano Collapse Limit Klever-Generalized Tamano (KGT)

API Collapse • Based on empirical collapse data • Adjusted for presence of tension, since tension reduces collapse strength • Empirical data fitted using curve-fit over four distinct regions • Applicable region based on D/t ratio of pipe being designed • Collapse tests on 2488 specimens of K55, N80 and P110 over wide range of D/t ratios. (ovality, manufacture and process tolerances, material imperfections etc. implicit) • Regression analysis on data, fitting a 99.5% nonfailure curve i.e., 0.5% probability that pipe will fail.

API Collapse Derivation Curves

Tamano Collapse Limit • ISO DIS 10400 collapse limit is based on a collapse limit state equation due to Tamano • Interaction Equation similar to Timoshenko • Ovality, eccentricity and residual stress included

Tamano Collapse Limit pc ult

p e = 1.080

(p =

e + py )

2

−

(p

2E 1 1 − ν 2 m(m − 1)2

(

)

H ult = 0.071φ + 0.0022ε − 0.18σ r φ = 100

ε = 100

(ODmax

− OD min ) OD av

(t max

− t min ) t av

e − py )

2

4

+ pe p y H ult

p y = 2σ ye

1.5 ⎞ m −1⎛ 1 + ⎜ ⎟ 2 m − 1⎠ m ⎝

σr =

σr σy

m = OD/t

Klever Generalized Tamano ∆pult =

(p

eult

+ p yult ) −

(p

+ p yult ) + 4 peult p yult H ult 2

eult

2(1 − H ult )

peult = kels

2E 1 (1 − ν 2 ) (Dave / tave )(Dave / tave − 1)2

p yult = k yls

⎛ ⎞ 1 ⎜⎜1 + ⎟⎟ (Dave / tave ) ⎝ 2(Dave / tave ) ⎠ 2S y

H ult = 0.127φ + 0.0039ε − 0.440rs / S y + hn

• Derived from Tamano’s equation • Generalizes the equation for better fit over a wider range of D/t

Brittle Burst Based 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 Modes

Mode 1 Opening

Mode 2 Sliding, or in-plane shear

Mode 3 Tearing, or out-of-plane shear

Fracture Toughness Toughness is the ability to resist the propagation of a crack under load and exposure to environment

K – Stress Intensity Factor I

K 1 = σ πa σ1 =

K1

σ2 =

K1

2πr

cos

θ⎛

θ⎞ ⎜1 + sin ⎟ 2⎝ 2⎠

θ⎛ θ⎞ cos ⎜ 1 − sin ⎟ 2⎝ 2⎠ 2πr

σ 3 = ν (σ 1 + σ 2 ) rplastic

1 K 12 = 6π σ 2y

• Several theoretical models to calculate stresses caused near a crack due to a load on the structure with flaw • Usually, several simplifications made • Shown here is an example for a crack in an infinite plate loaded in Mode 1

Crack Growth- The Resistance • KISSC is the “critical stress intensity” • It is the resistance of material to crack propagation in environment • It is a measurable material property • KISSC is a function of • Metallurgy • Environment (temperature and partial pressure of H2S)

Measurement of KISSC • Based on testing • Dual Cantilever Beam (DCB) tests in environment • Several other tests

• It is a direct measure of toughness, since it measures the “critical stress intensity” • It is statistical in nature, so a distribution is usually sought by repeated testing • Testing should as closely reflect the environment as possible

Failure Assessment Diagram (FAD) Failure Kr =

Kapplied KI Safe

Sr =

PLoad Applied PLimit

The Revelation • The pressure limit depends upon flaw size, H2S, temperature, OD, wall, and material grade • • • • •

Hot is good Small flaws are good Higher material grades are bad Higher H2S is bad Lower D/t ratio is good

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

ISO 10400 Fracture Design FAD diagram relationship; Kr and Lr 2 3 4 ⎛ ⎞ ⎛ D⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ PiF ⎜ ⎟ πa ⎜ ⎟ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ a a a a 2 ⎝ ⎠ ⎜ 2G − 2G ⎜ ⎟ ⎟ ⎟ + 5G4 ⎜ ⎟ − 4G3 ⎜ ⎟ + 3G2 ⎜ = 0 1 ⎜ ⎜D ⎟ ⎟ ⎜D ⎟ ⎜D ⎟ ⎜D ⎟ ⎛⎛ D ⎞2 ⎛ D ⎞2 ⎞ t t t − − − ⎜ −t ⎟ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜⎜ ⎟ − ⎜ − t ⎟ ⎟KIeac ⎜ ⎝2 ⎠ ⎠ ⎝2 ⎠ ⎝2 ⎠ ⎝2 ⎠ ⎜⎝ 2 ⎠ ⎝ 2 ⎠ ⎟ ⎝ ⎠ ⎝ 2

(1− 0.14L )(0.3 + 0.7e 2 r

−0.65L6r

)

3 ⎛⎜ piF ⎞⎟ ⎛ D / 2 + a ⎞ Lr = ⎜ ⎟ 2 ⎜⎝ f y ⎟⎠ ⎝ t − a ⎠

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

9-5/8” 53.50 lb/ft L80 API Internal Yield = 7,927 psi API Collapse = 6,617 psi Hill = 11,103 psi 10400 Burst = 10,942 psi 10400 Collapse = 7,734 psi (average pipe) = 9,316 psi (excellent pipe) = 4,081 psi (poor pipe) 10400 Brittle Burst = 8,729 psi (average pipe K=32) = 10,652 psi (excellent pipe K=50) = 6,112 psi (poor pipe K=20)

Probability and Design

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

Optimization of Cost and Reliability HIGH DESIGN

INCREASING COST

FAILURE

Optimized Design UNDER DESIGNED

LOW

OVER DESIGNED

INCREASING RELIABILITY

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

HIGH

Probabilistic Consideration of Strength • Strength defining parameters are uncertain and random, but… • They are pretty much the key controllable in design • And they are measurable • Probabilistic consideration of strength is therefore possible… • And may be necessary in many critical well designs “Hindsight is an exact science.”

Strength Uncertainty • • •

Controlled by Manufacturing Process Can Be Minimized But Not Eliminated Reflected in the distribution of strength-defining parameters (yield, OD, wall thickness, etc.) • Can be measured and taken account of in design

Strength Variability Distribution for L-80 Yield Point Specification Range

Relative Frequency

70

75

80

85

90

Actual Values (ksi)

95

100

105

Strength Variability Actual Thickness / Nominal Thickness - Seamless Casing

Relative Frequency

Specification Minimum

0.875

0.938

1.000

1.063

1.125

1.188

Wall Thickness (Actual Wall / Nominal Wall)

1.250

Load Uncertainty Load uncertainty is of two types • Probability of occurrence of the load • Magnitude of the load as compared to the design load

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

Probability of Occurrence of the Load Probability of occurrence influenced by • Operational Practice • Degree of overbalance in the case of kick • Connection make-up and corrosion inhibition, testing of tubing (in the case of tubing leak)

• Human Error

Uncertainty of Magnitude • Mother Nature • Abnormal pressures, frac and pore pressure, temperature

• Operational Procedures • Kill method used, contingencies in place, planning

• Human Error

Load Variability Probability of Kick Loading 100

% Probability

80

60

40

20

0

Kick Loading

No Kick Loading

Load Variability

Number of Kicks

Kick Intensity

Fracture at Shoe And Gas to Surface

Kick Intensity – Volume and Pressure

Design Approaches • • •

Working Stress Design Limit States Design Reliability Based Design • Stochastic Strength and Deterministic Load • Stochastic Strength and Stochastic Load

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

Working Stress Design • • •

Traditional method, long history Uses minimum strength Uses reasonable load estimate, usually at the higher end (conservative load estimates) • Uses elastic failure criteria (API, VME, etc.) • Strength is therefore within elastic limit

• Factor of Safety (≥ 1) to establish a “working stress limit”• SF takes care of uncertainties by keeping comfortable distance between load and strength • Design check usually written as • SF x Load effect ≤ Min Strength

Limitations of WSD • SF is independent of load case – i.e., failure-mode consistent designs, but not risk-consistent designs • May be too conservative for simple wells • Usually does not work for complex wells (deep, HPHT, etc.) • SF usually empirically determined, no documented basis • Typically based on elastic-based limits that usually do not represent true limits • Typically load estimates without consideration of probability of occurrence • Excludes consideration of risk-consequence relationship

Limit States Design • •

Addresses some of the limitations of WSD Uses limit-state strength function • Ultimate limit states and serviceability limit states • Elastic limit not always relevant- load bearing limit is what we are looking for • Often results in strain-based criteria

• Can be applied for deterministic or probabilistic design

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

Deterministic Theory - WSD LOAD < RESISTANCE LOAD

RESISTANCE

Factor of Safety

Maximum Load Assumed

Minimum Properties Assumed

Probabilistic Theory LOAD < RESISTANCE LOAD LOAD

RESISTANCE RESISTANCE

RELIABILITY LEVEL

Probabilistic Theory LOAD < RESISTANCE LOAD

RESISTANCE

RELIABILITY LEVEL

Reliability Based Design Ductile Burst Brittle Burst Buckling Bending SSC CSC SCC Fatigue Tension Burst Tension Brittle Tension Collapse High-Strain Collapse Torsion Connection Leak Connection Structural

Kick Lost Returns Running Casing Cementing Casing Tubing Leak Pressure Testing Shut in Pressure Well Kill Stimulation Over Pull Subsidence / Compaction Salt Trapped Annular Pressure Intentional Evacuation Accidental Evacuation Environmental Loadings

Pore Pressure

Fracture Gradient

Kick Intensity

LOAD

Yield Point

Wall Thickness

Ovality

RESISTANCE Tensile Strength

Mud Density

Kick Frequency

Eccentricity

Collapse

0=

Tension Burst

⎛ OD 2k ⎞ 1 − ⎜ ⎟ Ψ − (p external − p internal) Pe2 + Py2 ⎝ 1 + 10ϕ initial t nominalτ ⎠ Py Pe

Monte Carlo MAIS FORM SORM SOROS

⎡ ⎛ ⎢ ⎜ ⎢ ⎜ 2 ⎢⎛ ⎜ ⎞ ⎟ ⎢⎜ ⎜ Teffective p internal − p external ⎟ ⎜ + ⎢ ⎜ ⎛ ⎢ ⎜⎜ π OD 2 − (OD − 2t ) 2 σ ⎟⎟ ⎜ YP ⎜ ⎠ ⎢⎝ 4 1 ⎜ 2 σ YP ln ⎜ ⎢ ⎜ 2t ⎜ 3 ⎢ ⎜ 1− ⎜ ⎝ ⎝ OD ⎢⎣

(

)

“The world is simple for those who understand.”

⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎞⎟ ⎟⎟ ⎟⎟ ⎟⎟ ⎟ ⎠⎠

2

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦

0.5

=1

Example of RBD Probabilistic Strength Only (ISO/DIS 10400 Collapse) Collapse Load

KGT Collapse Strength

0.001 0.0009 9 5/8" 53.5 ppf L80 Load is deterministic at 6617 psi Strength uncertainty is specified API SF = 1.0 KGT Design Collapse Strength = 7037 psi

0.0008

Probability Density

0.0007 0.0006 0.0005 0.0004 0.0003

Pf = 1.0E-2.9 0.0002 0.0001 0 4000

5000

6000

7000

8000 Collapse Strength (psi)

9000

10000

11000

12000

Example of RBD Probabilistic Load and Strength (ISO/DIS 10400 Collapse) Collapse Load

KGT Collapse Strength

0.002 0.0018

9 5/8" 53.5 ppf L80 Load is probabilistic, Nominal value 7000 psi, P99 value of load is 7217 psi Strength uncertainty is specified API SF = 0.95 KGT Design Collapse Strength = 7037 psi

0.0016

Probability Density

0.0014 0.0012 0.001 0.0008

Pf = 1.0E-2.3

0.0006 0.0004 0.0002 0 5000

6000

7000

8000

9000

10000

Collapse Strength (psi)

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

11000

Risks For an “Average” American we have:

Being injured is

1 in 3 per year

Having an automobile accident is

1 in 12 per year

Having a heart attack if under the age of 35 is

1 in 77 per year

Fracturing your skull is

1 in 100 per year

Dying (any cause) is

1 in 115 per year

Dying of cancer is

1 in 500 per year

Dying from stroke is

1 in 1700 per year

Being murdered is

1 in 11,000 per year

Dying from a fall is

1 in 20,000 per year

Drowning is

1 in 50,000 per year

Being injured in a tornado is

1 in 200,000 per year

Dying in a plane crash is

1 in 250,000 per year

Dying in your bath tub is

1 in 1,000,000 per year

Freezing to death is

1 in 3,000,000 per year

Design Levels Design

Strength

Level 1

Deterministic Working Stress based on API Ratings

Load

Deterministic

Deterministic Working Stress 2

based on Advanced

Deterministic

Engineering Mechanics 3

4

Deterministic Strength based on Limit State Design Stochastic Strength based on Limit State Design

Deterministic

Deterministic

Stochastic Strengths based 5

on Limit State Design

Stochastic

Concluding Notes • Probabilistic design methods are standard in many structural design codes • They may seem complex, but in reality they are more rational and appealing to our sense of risk-based decision making • They are unavoidable in the modern design community, with more demanding wells and better understanding of performance properties • Properly applied, they lead to the most riskconsistent, optimal designs • The new design approaches are a much-needed improvement to enable design of challenging wells “There are two equally dangerous extremes -- to shut reason out and to let nothing else in.”