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Plastic Collapse Behaviors of Perforating Guns with Scallops
Haifeng Zhao, David Iblings, Aleksey Barykin, and Mohamed Mehdi
Schlumberger
May 10, 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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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
Phasing Density
Number of shots per foot (spf)
360/ 6 =60 phasing
1 ft
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Review: Collapse Strength of a Slick Pipe LamΓ© Thick Wall Yield Collapse Formula (Yield at Pipe ID)
API Bulletin 5C3
Tamano Ultimate Collapse Equation (SPE 48331)
ππΏπ = ππ¦π·π2 βπ·π
2
2π·π2 Open Ends
Closed Ends ππΏπ = ππ¦π·π2 β π·π
2
3π·π2
π·π = π·
π‘ =1
2π·π β π·π
π = π· π‘
ππΏπ = 2ππ¦ βπ β 1
π2
ππΏπ = 2.31 β ππ¦ βπ β 1
π2
πππ = 2ππ¦ βπ β 1
π2
Yield Collapse
ππ = ππ¦π΄
πβ π΅ β πΆ
Plastic Collapse
ππ = ππ¦πΉ
πβ πΊ
Transition Collapse
πππΈ =2πΈ
1 β π£2β
1
π π β 1 2
Elastic Collapse
ππ =1
2ππΈ + ππ β
1
4ππΈ β ππ
2 + ππΈπππ»
ππΈ = 1.08 Γ2πΈ
1 β π£2β
1
π π β 1 2
ππ = 2ππ¦ βπ β 1
π21 +
1.5
π β 1
π» = 0.071 β π’ % + 0.0022 β π % β 0.18 βππππ¦
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Ultimate Collapse Strength of Scalloped Gun Carriers
ππ = π β ππ
π β Collapse strength reduction factor due to scallops
ππ β Tamano ultimate collapse strength equation
π
ππ ππ
Definition
Slick Pipe Recessed Pipe Collapse strength
reduction factor
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Reference: Collapse Strength of Perforated Casing
π0 = 1 βπ
π
Reference: SPE 51188
π π β (1D) spacing fraction of recess
3D representation
d
s
Cross-section view
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π for Scalloped Gun Carriers
π1 = 1 βπ
πββ
π‘
π2 = 1 β ππ
π3 = 1 β πΌππ
ππ β (3D) volume fraction of recess
πΌ β fitting factor
h
t
d
Cross-section view 3D representation
s πΓβ
πΓπ‘ β (2D) area fraction of recess
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Modeling Approach Description Nonlinear post-buckling analysis using Riks method based on
arc length scheme in ABAQUS
Material model: isotropic hardening plasticity with bilinear,
power law or measured stress-strain curve
Boundary conditions: external pressure prescribed on the
exterior surface with end connection supported
Collapse Criteria 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
ma
x
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
Collapse
P1
P2
P3
Collapse pressure definition
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Test Validation of FEA
Description Test Temp
[Deg F]
D/t Tested Collapse
Pressure
[psi]
FEA
π·ππππππππ
[psi]
Difference
with 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:
β’ Detailed geometric, product name and material parameters are confidential.
β’ Stress/strain data utilized in the FEA analyses is full measured data from a test
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Case Study: π2 Expression
π2 = 1 β ππ = 1 β 90 βπ2
ππ·πββ
π‘ ππ = ππ ππ’
ππ’ = π Γπ
180ππ· Γ π‘
ππ = 2 Γ1
4ππ2β
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Case Study: Parametric Study of 7-in OD, 5-ft Length Carrier
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D [in] t [in] q [deg] S [in] w [in] d [in]
7
0.5
0.7
1.0
60 4.0 0.2 1.0
D [in] t [in] q [deg] S [in] h [in] d [in]
7 0.7
25.7
36
45
60
90
4.0 0.5 1.0
D [in] t [in] q [deg] S [in] h [in] d [in]
7 0.7 60
4.0
6.0
8.0
12.0
16.0
0.5 1.0
D [in] t [in] q [deg] S [in] h [in] d [in]
7 0.7 60 4.0
0.3
0.4
0.5
0.6
1.0
D [in] t [in] q [deg] S [in] h [in] d [in]
7 0.7 60 4.0 0.5
0.7
1.0
1.3
D [in] t [in]
7
0.5
0.7
1.0
Dimension of slick pipes
Wall Thickness, t
Angular Phasing, q
Longitudinal Spacing, S
Scallop Depth, h
Scallop Diameter, d
πFEA = πscallopFEA πpipe
FEA
Definition of βtrueβ π
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Sensitivity Study of Collapse Strength Reduction Factor
π1 = 1 βπ
πββ
π‘ π2 = 1 β 90 β
π2
ππ·πββ
π‘
[1] π· π‘ vs. π
π3 = 1 β 3 β 90 βπ2
ππ·πββ
π‘
πFEA = πscallopFEA πpipe
FEA
6 7 8 9 10 11 12 13 14 150.5
0.6
0.7
0.8
0.9
1
D/t
Coll
apse
Str
ength
Reduct
ion F
acto
r
FEA
1
2
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 S
tren
gth
Red
ucti
on F
acto
r
FEA
1
3
Collapse strength reduction factor π is linearly proportional to D/t ratio.
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Sensitivity Study of Collapse Strength Reduction Factor
π1 = 1 βπ
πββ
π‘ π2 = 1 β 90 β
π2
ππ·πββ
π‘
[2] π vs. π
π3 = 1 β 3 β 90 βπ2
ππ·πββ
π‘
πFEA = πscallopFEA πpipe
FEA
0 30 60 90 120 150 1800.5
0.6
0.7
0.8
0.9
1
q [deg]
Coll
apse
Str
ength
Reduct
ion F
acto
r
FEA
1
2
0 30 60 90 120 150 1800.5
0.6
0.7
0.8
0.9
1
q [deg]
Col
laps
e S
tren
gth
Red
ucti
on F
acto
r
FEA
1
3
Collapse strength reduction factor π is inversely proportional to π.
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Sensitivity Study of Collapse Strength Reduction Factor
π1 = 1 βπ
πββ
π‘ π2 = 1 β 90 β
π2
ππ·πββ
π‘
3 π vs. π
π3 = 1 β 3 β 90 βπ2
ππ·πββ
π‘
πFEA = πscallopFEA πpipe
FEA
2 4 6 8 10 12 14 16 18 20 22 240.5
0.6
0.7
0.8
0.9
1
S [in]
Coll
apse
Str
ength
Reduct
ion F
acto
r
FEA
1
2
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 S
tren
gth
Red
ucti
on F
acto
r
FEA
1
3
Collapse strength reduction factor π is inversely proportional to S.
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Sensitivity Study of Collapse Strength Reduction Factor
π1 = 1 βπ
πββ
π‘ π2 = 1 β 90 β
π2
ππ·πββ
π‘
[4] β vs. π
π3 = 1 β 3 β 90 βπ2
ππ·πββ
π‘
πFEA = πscallopFEA πpipe
FEA
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]
Coll
apse
Str
ength
Reduct
ion F
acto
r
FEA
1
2
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 S
tren
gth
Red
ucti
on F
acto
r
FEA
1
3
Collapse strength reduction factor π is βlinearlyβ proportional to h.
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Sensitivity Study of Collapse Strength Reduction Factor
π1 = 1 βπ
πββ
π‘ π2 = 1 β 90 β
π2
ππ·πββ
π‘
[5] π vs. π
π3 = 1 β 3 β 90 βπ2
ππ·πββ
π‘
πFEA = πscallopFEA πpipe
FEA
0 0.3 0.6 0.9 1.2 1.50.5
0.6
0.7
0.8
0.9
1
d [in]
Coll
apse
Str
ength
Reduct
ion F
acto
r
FEA
1
2
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 S
tren
gth
Red
ucti
on F
acto
r
FEA
1
3
Collapse strength reduction factor π is a quadratic function of d.
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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 β 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
β’ 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.
β’ 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