Casing Hanger Calculation

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