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Plastic Collapse Behaviors of Perforating Guns with ScallopsHaifeng Zhao, David Iblings, Aleksey Barykin, and Mohamed MehdiSchlumbergerMay 9-11, 2016, Galveston, TX

2016 International Perforating Symposium (IPS) IPS-16-39

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Outline

I. Introduction to Perforating Gun and Conveyance Systems

II. Ultimate Collapse Strength for Recessed Tubulars

III. Finite Element Analysis (FEA) and Test Validation

IV. Conclusions and Future Work

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33

I. Introduction to Perforating Gun and Conveyance Systems

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44

Slickline Coiled Tubing

Wireline Tubing-Conveyed Perforating (TCP): Completions and Drillstem testing

Open-string TCP system

Perforating Gun and Conveyance Systems

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55

Density and Phasing

Distance (in degrees) between charges

PhasingDensity

Number of shots per foot (spf)

360°/ 6 =60° phasing

1 ft

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66

II. Ultimate Collapse Strength for Recessed Tubulars

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77

Review: Collapse Strength of a Slick Pipe§ Lamé Thick Wall Yield Collapse Formula (Yield at Pipe ID)

§ API Bulletin 5C3

§ Tamano Ultimate Collapse Equation (SPE 48331)

𝑃"# = 𝜎&𝐷() − 𝐷+

)

2𝐷()Open Ends

Closed Ends 𝑃"# = 𝜎&𝐷() − 𝐷+

)

3𝐷()

𝐷( = 𝐷

𝑡 =12𝐷( − 𝐷+

𝑘 = 𝐷 𝑡⁄

𝑃"# = 2𝜎& 2𝑘 − 1𝑘)

𝑃"# = 2.31 2 𝜎& 2𝑘 − 1𝑘)

𝑃45 = 2𝜎& 2𝑘 − 1𝑘)

Yield Collapse

𝑃6 = 𝜎&𝐴𝑘 −𝐵 −𝐶

Plastic Collapse

𝑃: = 𝜎&𝐹𝑘 −𝐺

Transition Collapse

𝑃:= =2𝐸

1− 𝑣) 21

𝑘 𝑘 − 1 )

Elastic Collapse

𝑃: =12 𝑃= +𝑃4 −

14 𝑃= −𝑃4 )+ 𝑃=𝑃4𝐻

𝑃= = 1.08×2𝐸

1 − 𝑣)2

1𝑘 𝑘 −1 )

𝑃4 = 2𝜎& 2𝑘 − 1𝑘)

1 +1.5𝑘 −1

𝐻 = 0.071 2 𝑢 % + 0.0022 2 𝑒 % − 0.18 2𝜎K𝜎&

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88

Ultimate Collapse Strength of Scalloped Gun Carriers

𝑃# = 𝜇 2 𝑃:𝜇 – Collapse strength reduction factor due to scallops𝑃: – Tamano ultimate collapse strength equation

𝝁𝑃:𝑃#

Definition

Slick PipeRecessed PipeCollapse strength reduction factor

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Reference: Collapse Strength of Perforated Casing

𝜇N = 1 −𝑑𝑆

Reference: SPE 51188

𝑑 𝑆⁄ – (1D) spacing fraction of recess3D representation

d

s

Cross-section view

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1010

𝜇 for Scalloped Gun Carriers

𝜇Q = 1−𝑑𝑆 2ℎ𝑡

𝜇) = 1 − 𝑓K

𝜇T = 1 −𝛼𝑓K

𝑓K – (3D) volume fraction of recess𝛼 – fitting factor

h

td

Cross-section view 3D representation

sV×WX×Y

– (2D) area fraction of recess

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1111

III. FEA and Test Validation

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Modeling ApproachDescriptionØ Nonlinear post-buckling analysis using Riks method based on

arc length scheme in ABAQUSØ Material model: isotropic hardening plasticity with bilinear,

power law or measured stress-strain curveØ Boundary conditions: external pressure prescribed on the

exterior surface with end connection supported

Collapse CriteriaØ When the collapse pressure is reached, the structure will deform dramatically and lose pressure-bearing

capacity.

Local Yielding

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Physical Understanding of Collapse (Post-buckling)

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

1.2

U/D

P/P m

ax

Collapse

P3

P1

P2

-3 -2 -1 0 1 2 30

0.05

0.1

0.15

0.2

0.25

0.3

x/S

U/D

CollapseP1P2P3

Collapse pressure definition

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Example: Collapse Animation of 15SPF 5 FT

Deformation Scale Factor = 1

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Test Validation of FEA

Description Test Temp [Deg F]

D/t Tested Collapse Pressure

[psi]

FEA𝑷𝒄𝒐𝒍𝒍𝒂𝒑𝒔𝒆

[psi]

Differencewith Tests [%]

Test 1 368 9.4 32,250 30,660 -4.9%Test 2 318 10.7 22,500 22,831 +1.5%Test 3 250 10.7 24,263 23,651 -2.5%Test 4 250 14.0 18,329 18,633 +1.7%Test 5 400 11.6 22,745 23,311 +2.4%

Note: • Detailed geometric, product name and material parameters are confidential.• Stress/strain data utilized in the FEA analyses is full measured data from a test

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Case Study: 𝜇) Expression

𝜇) = 1 − 𝑓K = 1 − 90 2𝑑)

𝑆𝐷𝜃 2ℎ𝑡

𝑓K = 𝑉5 𝑉e⁄𝑉e = 𝑆×

𝜋180𝜃𝐷×𝑡

𝑉5 = 2×14𝜋𝑑

)ℎ

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Case Study: Parametric Study of 7-in OD, 5-ft Length Carrier

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D [in] t [in] θ [deg] S [in] w [in] d [in]

70.50.71.0

60 4.0 0.2 1.0

D [in] t [in] θ [deg] S [in] h [in] d [in]

7 0.7

25.736456090

4.0 0.5 1.0

D [in] t [in] θ [deg] S [in] h [in] d [in]

7 0.7 60

4.06.08.012.016.0

0.5 1.0

D [in] t [in] θ [deg] S [in] h [in] d [in]

7 0.7 60 4.0

0.30.40.50.6

1.0

D [in] t [in] θ [deg] S [in] h [in] d [in]

7 0.7 60 4.0 0.50.71.01.3

D [in] t [in]

70.50.71.0

Dimension of slick pipes

Wall Thickness, t

Angular Phasing, θ

Longitudinal Spacing, S

Scallop Depth,h

Scallop Diameter, d

𝜇ghi = 𝑃jklmmnoghi 𝑃opoqghir

Definition of “true” 𝝁

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Sensitivity Study of Collapse Strength Reduction Factor

𝜇Q = 1 −𝑑𝑆 2

ℎ𝑡

𝜇) = 1 − 90 2𝑑)

𝑆𝐷𝜃 2ℎ𝑡

[1]  𝐷 𝑡⁄ vs. 𝜇

𝜇T = 1 − 3 2 90 2𝑑)

𝑆𝐷𝜃 2ℎ𝑡

𝜇ghi = 𝑃jklmmnoghi 𝑃opoqghir

6 7 8 9 10 11 12 13 14 150.5

0.6

0.7

0.8

0.9

1

D/t

Col

laps

e St

reng

th R

educ

tion

Fact

or µ

µFEA

µ1

µ2

6 7 8 9 10 11 12 13 14 150.5

0.6

0.7

0.8

0.9

1

D/t

Colla

pse S

treng

th Re

ducti

on F

actor

µ

µFEA

µ1

µ3

Collapse strength reduction factor 𝜇 is linearly proportional to D/t ratio.

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Sensitivity Study of Collapse Strength Reduction Factor

𝜇Q = 1 −𝑑𝑆 2

ℎ𝑡

𝜇) = 1 − 90 2𝑑)

𝑆𝐷𝜃 2ℎ𝑡

[2] 𝜃 vs. 𝜇

𝜇T = 1 − 3 2 90 2𝑑)

𝑆𝐷𝜃 2ℎ𝑡

𝜇ghi = 𝑃jklmmnoghi 𝑃opoqghir

0 30 60 90 120 150 1800.5

0.6

0.7

0.8

0.9

1

θ [deg]

Col

laps

e St

reng

th R

educ

tion

Fact

or µ

µFEA

µ1

µ2

0 30 60 90 120 150 1800.5

0.6

0.7

0.8

0.9

1

θ [deg]

Colla

pse S

treng

th Re

ducti

on F

actor

µ

µFEA

µ1

µ3

Collapse strength reduction factor 𝜇 is inversely proportional to 𝜃.

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Sensitivity Study of Collapse Strength Reduction Factor

𝜇Q = 1 −𝑑𝑆 2

ℎ𝑡

𝜇) = 1 − 90 2𝑑)

𝑆𝐷𝜃 2ℎ𝑡

3  𝑆 vs. 𝜇

𝜇T = 1 − 3 2 90 2𝑑)

𝑆𝐷𝜃 2ℎ𝑡

𝜇ghi = 𝑃jklmmnoghi 𝑃opoqghir

2 4 6 8 10 12 14 16 18 20 22 240.5

0.6

0.7

0.8

0.9

1

S [in]

Col

laps

e St

reng

th R

educ

tion

Fact

or µ

µFEA

µ1

µ2

2 4 6 8 10 12 14 16 18 20 22 240.5

0.6

0.7

0.8

0.9

1

S [in]

Colla

pse S

treng

th Re

ducti

on F

actor

µ

µFEA

µ1

µ3

Collapse strength reduction factor 𝜇 is inversely proportional to S.

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2121

Sensitivity Study of Collapse Strength Reduction Factor

𝜇Q = 1 −𝑑𝑆 2

ℎ𝑡

𝜇) = 1 − 90 2𝑑)

𝑆𝐷𝜃 2ℎ𝑡

[4] ℎ vs. 𝜇

𝜇T = 1 − 3 2 90 2𝑑)

𝑆𝐷𝜃 2ℎ𝑡

𝜇ghi = 𝑃jklmmnoghi 𝑃opoqghir

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.5

0.6

0.7

0.8

0.9

1

h [in]

Col

laps

e St

reng

th R

educ

tion

Fact

or µ

µFEA

µ1

µ2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.5

0.6

0.7

0.8

0.9

1

h [in]

Colla

pse S

treng

th Re

ducti

on F

actor

µ

µFEA

µ1

µ3

Collapse strength reduction factor 𝜇 is “linearly” proportional to h.

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2222

Sensitivity Study of Collapse Strength Reduction Factor

𝜇Q = 1 −𝑑𝑆 2

ℎ𝑡

𝜇) = 1 − 90 2𝑑)

𝑆𝐷𝜃 2ℎ𝑡

[5] 𝑑 vs. 𝜇

𝜇T = 1 − 3 2 90 2𝑑)

𝑆𝐷𝜃 2ℎ𝑡

𝜇ghi = 𝑃jklmmnoghi 𝑃opoqghir

0 0.3 0.6 0.9 1.2 1.50.5

0.6

0.7

0.8

0.9

1

d [in]

Col

laps

e St

reng

th R

educ

tion

Fact

or µ

µFEA

µ1

µ2

0 0.3 0.6 0.9 1.2 1.50.5

0.6

0.7

0.8

0.9

1

d [in]

Colla

pse S

treng

th Re

ducti

on F

actor

µ

µFEA

µ1

µ3

Collapse strength reduction factor 𝜇 is a quadratic function of d.

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IV. Conclusions and Future Work

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Conclusions and Future Work§ An analytical collapse strength equation based on Tamano formula was proposed for scalloped

perforating guns.

§ The proposed equation was thoroughly validated with the aid of FEA in a multivariable parametric space – an analysis hardly affordable with the use of physical tests.

§ An FEA method used to validate the proposed equation showed strong agreement with the test data giving collapse predictions for scalloped tubulars within 5% of the test results.

§ The method applied to scalloped perforating guns can also be used for any tubulars with patterned cutouts or recesses, such as prepacked sand screens, perforated or slotted liners, etc.

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Questions?

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Publications

• Zhao,  H.,  Iblings,  D.,  Barykin,  A.,  and  Mehdi,  M.,  2015,  Plastic  Collapse  Behaviors  of  Tubulars  with  Recess  Patterns,  Proceedings  of  ASME  International  Mechanical  Engineering  Congress  &  Exposition,   IMECE2015-­‐50204,  Houston,  TX.

• Zhao,  H.,  Iblings,  D.,  Barykin,  A.,  and  Mehdi,  M.,  2016,  Plastic  Collapse  Behaviors  of  Tubulars  with  Recess  Patterns,    ASCE-­‐ASME  Journal  of  Risk  and  Uncertainty  in  Engineering  Systems,  Part  B:  Mechanical  Engineering  ,  Accepted.

IPS-16-39