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Design Guideline G22.02: Casing Hanger Load Capacity This is a step-by-step worksh eet designed to assis t in the calculations out lined in section 6.0 of Design Guideline G22.02. G22.02. The user should be able to use this wo rksheet to determine the recom recom mend ed operating range for a given slip casing hanger and a given casing type with respect to h ang load and pressure.
Step 6.1: Enter Given Data Casing Hanger: HPI or Pressure Isolation Seals being used? Casing Description:
OD (in):
C-21
No 20 OD - 106.5 LB/FT-(K55)
20 a=OD/2
ID (in):
19 b=ID/2
Minimum Yield Strength of Casing, Syp (psi): Collapse Pressure of Casing, qcollapse (psi):
b= 9.5
55000
770
Plain End Yield Strength of Casing, PEYS (lbs):
1684683
Buttress Joint Strength of Casing, BJS (lbs):
1682947
Round Joint Strength of Casing, RJS (lbs):
2361822
Joint Type:
Buttress
Modulus Of Elasticity, E (psi):
30000000
Poison's Ratio, v:
a= 10
0.292
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Step 6.2: Determine Casing Application (Thick-wall vs. Thin-wall vessel) If the mean radius of the casing divided by the wall thickness is less than or equal to 10, then the thick-wall vessel criteria applies. If the ratio is greater than 10, then the thin-wall vessel criteria applies.
ratio= Eqn.(1)
(a+b) __2__ (a-b)
ratio= 19.50
application= if (ratio >10,"thin-wall","thickwall")
application= thin-wall Step 6.3: Determine the Diametrical Deflection in the Casing That Will Cause Internal Yield Let Dyp = Diametrical Deflection that will cause internal yield in the casing (in) Let R = Mean Casing Radius (in)
R=
(a+b) 2 R= 9.75
Dyp = Eqn.(2)
2*R*Syp E
if application = "thin-wall"
2
2
2
(a+b) - v * (a - b ) Eqn.(3)
Syp*
2*a*E
otherwise
Dyp = 0.035
Step 6.4: Determine the Maximum Hang Load Capacity, P Lyield Now that the maximum diametrical deflection for th egiven casing has been determined, the hang load that will generate that same amount o fdeflection must be determined. This value will be the Maximum Hang Load Capacity for the given casing hanger and casing. Let PLyield = hang load required to generate a diametrical casing deflection equal to conditions (lbs) Let t = casing wall thickness (in) Let K = a constant based on casing hanger type 0.3 for C-21 and C-22 casing hangers 0.2 for C-29 casing hangers
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Dyp under zero pressure
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t= a-b t= 0.5
K=
0.2 if Type = "C-29" 0.3 otherwise K= 0.3
Eqn.(4)
PLyield=
Dyp*pi*t*E K*R PLyield= 5.574E+05
Step 6.5: Determine the Diametrical Deflection Due To Collapse Pressure Determine the diametrical deflection that results when the casing is subjected to its collapse pressure with no hanging load present. Let Dcollapse = Diametrical Deflection due to collapse Pressure only (in) Let f = a constant based on casing hanger type used in thin-wall cases; 3 for C-21 and C-22 casing hangers; 4 for C-29 casing hangers Let = a variable term in the equation based on R, t, and v used in thin-wall cases f=
4 if Type = "C-29" 3 otherwise f= 3
4
3* (1 v 2 ) 2
2
R * t
Eqn.(6)
= 0.583
Eqn.(5)
Eqn.(7)
Dcollapse 2 *
qcollapse * R 2 E * t
* 1 e f * * cos( f *
if application = "thin-wall"
qcollapse * a a b E
a b v
otherwise
Dcollapse = 0.010
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Step 6.6: Determine the Maximum Additional Loading at Collapse Pressure t co apse pressure, t e cas ng s a rea y e ecte ue to t e pressure. us, t e amount o e ect on t at can occur due to loading is limited since the total deflection must be less than or equal to Dyp. First calculate the amount of allowable deflection due to loading, then calculate the amount of hang load required to generate this deflection. Let Dadditional_load = Diametrical deflection due to hang load at collapse pressure (in) Let PLadditional_load = Hang load required to generate a deflection equal to Dadditional_load (lbs) Dadditional_load =
Dyp -
Dcollapse
Eqn.(8)
Dadditional_load = 2.453E-02 PL_additional_load =
Eqn.(4)
Dadditional_load * pi * t * E K*R PL_additional_load = 3.953E+05
Step 6.7 - 6.8: Graph the Recommended Operating Range The graph will have pressure (psi) on the x-axis and Hang Load (lbs) on the y-axis. Calculate the slope between the points (0 psi, 0.8*P Lyield) and (collapse pressure, PL_additional_load) slope = Eqn.(9)
PL_additional_load - 0.8*PLyield qcollapse - 0 slope = -65.72646213
Eqn.(10)
slopefactor = 0 if (HPI = "Yes") or (Type = "C-21") -1 * slope otherwise slopefactor = 0
Note: slopefactor equals zero for C-21 casing hangers and for C-22, C-29 casing hangers with HPI seals.
If Buttress Joint Strength or Round Joint Strength or 80% of Plain End Yield is less than 80% of P Lyield, then the smallest of the three values shall serve as a maximum load limit for the graph. Note that Buttress Joint Strength is not considered as a possible limit when the joint type is umknown. Determine the least of the four values, as appropriate. Limit_1 = RJS if Joint Type = "Round" BJS otherwise Limit_2 = RJS if Joint Type = "Unknown" Limit_1 otherwise Max_Limit = 0.8*PLyield 0.8*PEYS if 0.8*PEYS < 0.8*PLyield
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Max_Limit = Max_Limit Limit_1 if Limit_1 < Max_Limit Max_Limit = Max_Limit Limit_2 if Limit_2 < Max_Limit Max_Limit = 4.459E+05 The equation of the line to graph will be the Maximum Recommended Hang Load for a given casing exposed to a given pressure with the given casing hanger. This equation can be applied to the recommended pressure range which extends from 0 psi to 80% of the collapse pressure. Let TP = test pressure (psi) TP = 0,1…qcollapse
Max_Rec_Load(TP) = (0.8*PLyield) - (TP*slopefactor )
Type = C-21
Syp = 5.500E+04
0.8 * PLyield = 4.459E+05
HPI = No
qcollapse = 7.700E+02
0.8 * PEYS = 1.348E+06
OD = 20
0.8 * qcollapse = 6.160E+02
BJS = 1.683E+06
Joint Type = Buttress
RJS = 2.362E+06
ID = 19 application = thin-wall
Max_Limit = 4.459E+05
The recommended operating range is represented by the area in the 1st quadrant of the graph that is confined by: 1.) the x-axis 2.) the y-axis 3.) the line representing the Maximum Calculated Recommended Hang Load 4.) the vertical line at 80% collapse pressure 5.) the horizontal line at Max_Limit
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Recommended Operating Range 6.000E+05 5.000E+05
) s b l ( d a o L g n a H
4.000E+05 3.000E+05 2.000E+05 1.000E+05 0.000E+00 -100 0
100
200
300
400
500
600
700
800
900
-1.000E+05
Test Pressure (psi) Maximum Calculated Recommended Hang Load 80% Collapse Max_Limit
Here are some values at specific pressures to be used when graphing for reference only : Max_Rec_Load(0) = 4.459E+05 Max_Rec_Load(0.8*qcollapse) = 4.459E+05 Max_Rec_Load(q collapse) = 4.459E+05 The equation for the Maximum Calculated Recommended Hang Load can be used to calculate the maximum hang load at a given pressure less than or equal to 80% collapse pressure: Given Pressure, q given (psi) =
10000
Allowable_Load = Max_Rec_Load(qgiven) if (Max_Rec_Load(qgiven) <= Max_Limit Max_Limit otherwise Allowable_Load = Allowable_Load if (qgiven <= 0.8*qcollapse) "Pressure exceeds recommended maximum" otherwise
Allowable_Load = Pressure exceeds recommended maximum
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The equation for the Maximum Recommended Hang Load can be reversed and used to calculate the maximum pressure for a given hang load: Given Load, loadgiven (lbs) =
165000
Max_Pressure(loadgiven) = 0.8 * PLyield - loadgiven slopefactor Allowable_Pressure = Max_Pressure(loadgiven) if (Max_Pressure <= 0.8 * qcollapse) 0.8 * qcollapse otherwise Allowable_Pressure = Allowable_Pressure if loadgiven <= Max_Limit "Load exceeds recommended maximum limit." otheriwse Allowable_Pressure = #DIV/0!
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