My Calculation
1
Page
Calculation No
Engineering Calculation Sheet
Subject
Casing Slip Hanging Capacity Determination
attach on 9-5/8" #47.0 L-80 casing
Prepared By
YUDHI
of
3
002 rev-1
Date
21-Jul-13
This calculation was conducted in order to determine casing slip capacity. Initial load comes from downhole pressure (P)
uniformly distributed to casing and (PANNULUS) which act between outer side of casing and wellhead inner profile.
P will be transfer to casing slip through casing. It will create radial load (F) as it will be translated to casing slip
in terms of axial load for braking movement (HC).
In the picture below, PANNULUS being visualize act upward, while in practice its exerted to casing in all direction,
especially in a band of uniform pressure where casing slip directly bite the casing outer profile.
Nomenclature
ω
σ1
σ2
F
HC
P
PANNULUS
radial deflection (positive - outward)
axial membranne stress
hoop stress / circumferential membranne stress (positive - tensile hoop stress)
radial load
axial load / casing slip capacity / slip hanging capacity
downhole pressure
annulus pressure
Known Slip Data
l
α
µ
E
ν
PANNULUS
Known Casing Data
OD
ID
IDDRIFT
t
RMEAN
ppf
σy
PCOLLAPSE
4.00
15
0.280
30,000,000
0.3
5,000
[inch]
[°]
[-]
[PSI]
[-]
[PSI]
slip length
taper slip angle
friction coefficient
modulus Young
Poisson Ratio
annulus pressure (between casing and slip)
9.625
8.681
8.525
0.472
4.577
47.0
80,000
[inch]
[inch]
[inch]
[inch]
[inch]
[lbf/ft]
[PSI]
casing outer diameter
casing inner diameter
casing inner drift ID (taken from API SPEC 5CT or API 5L)
thickness
mean radius
casing poundage
casing yield strength
4,750
[PSI]
casing collapse (calculation based on API TR 5C3)
Friction Angle
θ = atan(µ)
=
15.64 [°]
Foundation Modulus
2
k = (E.t)/(RMEAN )
= 676,077 [PSI/inch]
Flexural Rigidity
D = (E.t3) / 12 (1-ν2)
=
288,885 [lbf.ft]
Cylinder Constant
λ = 4√k/(4.D)
0.875 [inch-3/4.ft-1/4]
=
My Calculation
Page
2
Calculation No
Engineering Calculation Sheet
Prepared By
Subject Casing Slip Hanging Capacity Determination
YUDHI
of
3
002 rev-1
Date
21-Jul-13
attach on 9-5/8" #47.0 L-80 casing
Free body diagram determination
F+R1+R2+HC = 0
HC = R2.sin α + R1.cos α
R2.cos α = F + R1.sin α
R1 = R2.μ
F = P.(2π.l.t)
F = R2.cos α - R1.sin α
F = R2.cos α - R2.μ.sin α
…
for ΣFY = 0
…
for ΣFX = 0
…
…
R2 = F / (cos α - μ.sin α)
R2 = P.(2π.l.t) / (cos α - μ.sin α)
F = R2.(cos α - μ.sin α)
HC = R2.sin α + R1.cos α
HC = R2.sin α + (R2.μ).cos α
HC = R2.(sin α + μ.cos α)
HC = [P.(2π.l.t) / (cos α - μ.sin α)].(sin α + μ.cos α)
HC = P.(2π.l.t).[(sin α + μ.cos α)/(cos α - μ.sin α)]
HC = P.(2π.l.t) / cot (α+θ)
…
cot (α+θ) known as transverse factor
from pipe load to slip [2]
Stress Resultant Determination due to Annulus Pressure [3]
σ1 and σ2 consider only stress in certain direction due to uniform pressure loading over a band of annulus pressure
while σTOTAL account remaining stress exerted to casing before casing yield occur
Remind that PANNULUS always act in all direction (in this case its being visualized as a band of uniform radial loading)
σ1 =
ωMAX = [-PANNULUS/(4.D.λ4)].[1 - e-(λ.l/2).cos (λ.l/2)]
=
-0.0061 [inch]
0 [PSI]
σ2 = (ωMAX.E/RMEAN)+(ωMAX.σ1)
=
-40,052 [PSI]
… compressive hoop stress
σTOTAL = σy - σ2
=
39,948 [PSI]
Casing Slip Capacity Determination [1]
Casing slip capacity was determine by using σy as a limit to prevent plastic deformation on casing
HC = (σy . (2π.l.t)) / cot (α+θ)
=
562,189 [lbf]
HC_ANN = (σTOTAL . (2π.l.t)) / cot (α+θ)
=
280,727 [lbf]
... Slip capacity without annulus pressure load
... Slip capacity with annulus pressure load
My Calculation
3
Page
Calculation No
Engineering Calculation Sheet
Subject Casing Slip Hanging Capacity Determination
Prepared By
attach on 9-5/8" #47.0 L-80 casing
Trigonometric proof for transverse load factor from pipe load to slip
cot
cot
cot
cot
(α+θ) =
(α+θ) =
(α+θ) =
(α+θ) =
[1]
[2]
[3]
[4]
[5]
… taken from [4]
[cot α . cot θ -1] / [cot θ + cot α]
[(cos α/sin α).1/μ -1] / [1/μ + (cos α/sin α)]
[(cos α/μ.sin α) - (μ.sin α/μ.sin α)] / [(sin α/μ.sin α) + (μ.cos α/μ.sin α)]
[cos α - μ.sin α] / [sin α + μ.cos α]
Reference:
Oil and Gas Well Casing Suspension Assemblies, Rhodes & Wilhoit
A Re-examination fo Drillpipe/Slip Mechanism, SPE99074
TH
Roark's Formula for Stress and Strain, 7 Edition, page 607, Table 13.2 case 17
TH
Machinery Handbook, 27 Edition, page 90 & 157
Private discussion with colleagues
YUDHI
of
3
002 rev-1
Date
21-Jul-13