ips-16-39-plastic collapse behaviors of perforating guns ... · pdf file12 modeling approach...
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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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I. Introduction to Perforating Gun and Conveyance Systems
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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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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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II. Ultimate Collapse Strength for Recessed Tubulars
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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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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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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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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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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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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