A drilling string is experiencing a release in tension load from hoisting system

Question

A drilling string is experiencing a release in tension load from hoisting system to increase the weight on bit (WOB) by 25,000 lb. For the given well information: String pipe: dry unit weight 20 lb/ft OD-4.5 in ID-3.64 in Density (ps)-65 ppg Material modulus of elasticity (E) = 30,000 ksi: (1 ks 1000 psi) .Mud density (Pm) 10 ppg. String inclination angle ()-30 deg. .Bore Hole inner diameter (Dhole)- 8 in Will the string pipe undergo buckling? If yes, which mode of buckling it will experience (sinusoidal or helical)? Note:- Show your work to prove your answer Consider the buoyed unit weight of the pipe in your calculations; i.e., the considered unit weight shall be accounting for buoyancy effect. Ensure units consistency in your calculations; i.e., do necessary unit conversions in your calculations; do

Explanation / Answer

The buoyed weight of the tubing per unit length in a wellbore which was calculated as follows:

Wi= MWi*Ai/231,.

Wi= MWo*Ao/231

Ws= The weight of the steel or pipe per unit length,20 Ib/ft.

We=Ws+Wi-Wo

We= buoyed pipe weight of per unit length,

We=Ws+0.0408((MwoXDo2-MwiXDi2))

       Consider Pipe Ht 196 Inch.

Density of Mud =65 ppg.

Mwi= initial mud weight inside the tubing,

Mwo= final mud weight outside the tubing,

Desity= mass/Volume of pipie

Masss of Pipe= (65 PpgX 2038 Inch3)

1 inch3= 0.004 gal

Mass of Pipe= 572ib/gal

Same calculated for Mass of Tube = 876.2 ib/gal.

So,We=20+0.0408((876.2*8*8)-(572*3.64*3.64))

            =1998.7 Ib/in

Fb= Paslay buckling force, , E = Young's modulus

Helical Bucking force=3.66 *SQRt((EIWeSinQ)/Rc)).

Lateral Bucking Force=5.66 *SQRt((EIWeSinQ)/Rc)).

Rc=0.5(OD-ID)

   =0.5*(8-4.5)

   =1.75 in

I=3.14(Do^4-Di^4)/64

= 3.14*((8^4)-(3.64^4))

=192.10 inch4.

So ,Helical Buckilng Load=1814111.9

      Lateral Load= 10267873.3

SqRt2* Fp<fb<Sq2*Fp-------lateral 0r Buclikng

No, lateral or Buckling Load.

2 X SqRt2 X Fp<Fb----------Buckling Load.

No buckling Load.

So there will be no sinusoidal Load or Buckling Load .

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