Casing Hanger Calculation PDF

My Calculation
Page 1 of 3
Engineering Calculation Sheet Calculation No 002 rev-1
Subject Casing Slip Hanging Capacity Determination Prepared By YUDHI Date 21-Jul-13
attach on 9-5/8" #47.0 L-80 casing
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 radial deflection (positive - outward)
σ1 axial membranne stress
σ2 hoop stress / circumferential membranne stress (positive - tensile hoop stress)
F radial load
HC axial load / casing slip capacity / slip hanging capacity
P downhole pressure
PANNULUS annulus pressure
Known Slip Data
l 4.00 [inch] slip length

α 15 [°] taper slip angle
µ 0.280 [-] friction coefficient
E 30,000,000 [PSI] modulus Young
ν 0.3 [-] Poisson Ratio
PANNULUS 5,000 [PSI] annulus pressure (between casing and slip)
Known Casing Data

OD 9.625 [inch] casing outer diameter
ID 8.681 [inch] casing inner diameter
IDDRIFT 8.525 [inch] casing inner drift ID (taken from API SPEC 5CT or API 5L)
t 0.472 [inch] thickness
RMEAN 4.577 [inch] mean radius
ppf 47.0 [lbf/ft] casing poundage
σy 80,000 [PSI] casing yield strength
PCOLLAPSE 4,750 [PSI] casing collapse (calculation based on API TR 5C3)
Friction Angle Foundation Modulus

2
θ = atan(µ) k = (E.t)/(RMEAN )
= 15.64 [°] = 676,077 [PSI/inch]
Flexural Rigidity Cylinder Constant
D = (E.t3) / 12 (1-ν2) λ = 4√k/(4.D)
= 288,885 [lbf.ft] = 0.875 [inch-3/4.ft-1/4]
My Calculation
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Free body diagram determination

F+R1+R2+HC = 0
HC = R2.sin α + R1.cos α … for ΣFY = 0
R2.cos α = F + R1.sin α … for ΣFX = 0
R1 = R2.μ …
F = P.(2π.l.t) …
F = R2.cos α - R1.sin α R2 = F / (cos α - μ.sin α)

F = R2.cos α - R2.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 = 0 [PSI] ωMAX = [-PANNULUS/(4.D.λ4)].[1 - e-(λ.l/2).cos (λ.l/2)]

= -0.0061 [inch]
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] ... Slip capacity without annulus pressure load
HC_ANN = (σTOTAL . (2π.l.t)) / cot (α+θ)

= 280,727 [lbf] ... Slip capacity with annulus pressure load
My Calculation
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Trigonometric proof for transverse load factor from pipe load to slip
cot (α+θ) = [cot α . cot θ -1] / [cot θ + cot α] … taken from [4]
cot (α+θ) = [(cos α/sin α).1/μ -1] / [1/μ + (cos α/sin α)]
cot (α+θ) = [(cos α/μ.sin α) - (μ.sin α/μ.sin α)] / [(sin α/μ.sin α) + (μ.cos α/μ.sin α)]
cot (α+θ) = [cos α - μ.sin α] / [sin α + μ.cos α]
Reference:
[1] Oil and Gas Well Casing Suspension Assemblies, Rhodes & Wilhoit
[2] A Re-examination fo Drillpipe/Slip Mechanism, SPE99074
TH
[3] Roark's Formula for Stress and Strain, 7 Edition, page 607, Table 13.2 case 17
TH
[4] Machinery Handbook, 27 Edition, page 90 & 157
[5] Private discussion with colleagues

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My Calculation

Known Slip Data

l 4.00 [inch] slip length

Known Casing Data

Friction Angle Foundation Modulus

Free body diagram determination

F = R2.cos α - R1.sin α R2 = F / (cos α - μ.sin α)

Stress Resultant Determination due to Annulus Pressure [3]

σ1 = 0 [PSI] ωMAX = [-PANNULUS/(4.D.λ4)].[1 - e-(λ.l/2).cos (λ.l/2)]

Casing Slip Capacity Determination [1]

HC = (σy . (2π.l.t)) / cot (α+θ)

HC_ANN = (σTOTAL . (2π.l.t)) / cot (α+θ)

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