15. Torque and Drag Calculations

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PETE 661

Drilling Engineering

Lesson 15

Torque and Drag Calculations

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Torque and Drag Calculations

Friction

Logging

Hook Load

Lateral Load

Torque Requirements

Examples

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HW #8

Well Survey

due 11-04-02

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Friction - Stationary

• Horizontal surface

• No motion• No applied force

Fy = 0

N = W

N

W

N= Normal force = lateral load = contact force = reaction force

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Sliding Motion

• Horizontal surface

• Velocity, V > 0

• V = constant

• Force along surface

N = W

F = N = W

N

W

F N

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Frictionless, Inclined, Straight Wellbore:

1. Consider

a section

of pipe

in the

wellbore.

In the absence of FRICTION the forces acting on the pipe are buoyed weight, axial tension and the reaction force, N, normal to the wellbore.

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Frictionless, Inclined, Straight Wellbore:

pipe.ROTATING for used are equations

(2) : wellbore to 0

(1) : wellborealong 0

ar

These

F

F

IcosWT

IsinWN

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Effect of Friction (no doglegs):

2. Consider Effect of Friction ( no doglegs):

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Frictional Force, F = N = W sin I

where 0 < < 1 ( is the coeff. of friction)

usually 0.15 < < 0.4 in the wellbore

(a) Lowering: Friction opposes motion, so

(3)IsinWIcosWT

FIcosWT f

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(b) Raising: Friction still opposes motion,

so

IsinWIcosWT

FIcosWT f

(4)

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Problem 1

What is the maximum hole angle (inclination angle) that can be logged

without the aid of drillpipe, coiled tubing or other tubulars?

(assume =0.4)

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Solution

From Equation (3) above,

(3)

When pipe is barely sliding down the wellbore,

IsinWIcosWT

0T

IsinW4.0IcosW0

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Solution

This is the maximum hole angle (inclination) that can be logged without the aid of tubulars.

Note:

68.2I

2.5Ior tan 4.0Icot

Icot

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Problem 2

Consider a well with a long horizontal section. An 8,000-ft long string of 7” OD csg. is in the hole. Buoyed weight of pipe = 30 lbs/ft. = 0.3

(a) What force will it take to move this pipe along the horizontal section of the wellbore?

(b) What torque will it take to rotate this pipe?

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Problem 2 - Solution - Force

(a) What force will it take to move this pipe along the horizontal section of the wellbore?

F = ? F = 0N

W

N = W = 30 lb/ft * 8,000 ft = 240,000 lb

F = N = 0.3 * 240,000 lb = 72,000 lb

Force to move pipe, F = 72,000 lbf

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Problem 2 - Solution - Force

(b) What torque will it take to rotate this pipe?

As an approximation, let us

assume that the pipe lies on

the bottom of the wellbore.

Then, as before, N = W = 30 lb/ft * 8,000 ft = 240,000 lbf

Torque = F*d/2 = Nd/2 = 0.3 * 240,000 lbf * 7/(2 * 12) ft

Torque to rotate pipe, T = 21,000 ft-lbf

F

T

d/2

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Problem 2 - Equations - Horizontal

Torque, T = Wd/(24 ) = 21,000 ft-lbf

F = N T = F * dN = W

W

Force to move pipe, F = W = 72,000 lbf

An approximate equation, with W in lbf and d in inches

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Horizontal - Torque

A more accurate equation for torque in a horizontal wellbore may be obtained by taking into consideration the fact that a rotating pipe will ride up the side of the wellbore to some angle .

Taking moments about the point P:

Torque, T = W * (d/2) sin in-lbf

Where = atan = atan 0.3 = 16.70o

T = 240,000 * 7/24 * 0.2873 = 20,111 ft-lbf

FT

d/2 P

W

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Problem 3

A well with a measured depth of 10,000 ft. may be approximated as being perfectly vertical to the kick-off point at 2,000 ft. A string of 7” OD csg. is in the hole; total length is 10,000 ft. The 8,000-ft segment is inclined at 60 deg. Buoyed weight of pipe = 30 lbs/ft. = 0.3

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Problem 3

Please determine the following:

(a) Hook load when rotating off bottom

(b) Hook load when RIH

(c) Hook load when POH

(d) Torque when rotating off bottom

[ ignore effects of dogleg at 2000 ft.]

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Solution to Problem 3

(a) Hook load when rotating off bottom:

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Solution to Problem 3 - Rotating

When rotating off bottom.

lbf 120,000lbf 000,60

60cos*ft 8000*ft

lb30ft 2000*

ft

lb30

HLHLHL

5.0

80002000

lbf 000,180HL

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Solution to Problem 3 - lowering

2 (b) Hook load when RIH:

The hook load is decreased by friction in the wellbore.

In the vertical portion,

Thus, 0F

0osin*2000*30N

2000

o

NFf

0o

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Solution to Problem 3 - lowering

In the inclined section,

N = 30 * 8,000 * sin 60

= 207,846 lbf

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Solution to Problem 3 - Lowering

HL = We,2000 + We,8000 - F2000 - F8000

= 60,000 + 120,000 - 0 - 62,354

Thus, F8000 = N = 0.3 * 207,846 = 62,352 lbf

HL = 117,646 lbf while RIH

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Solution to Problem 3 - Raising

2(c) Hood Load when POH:

HL = We,2000 + We,8000 + F2000 + F8000

= 60,000 + 120,000 + 0 + 62,354

HL = 242,354 lbf POH

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Solution to Problem 3 - Summary

MDft

RIHROT

POH

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Solution to Problem 3 - rotating

2(d) Torque when rotating off bottom:In the Inclined Section:

NF

IsinWN

2

d*F

Arm*Force

Torque

f

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(i) As a first approximation, assume the pipe lies at lowest point of hole:

12

1*

2

7*60sin*8000*30*3.0

2

dIsinW

2

dN

2

dFTorque f

lbf-ft 187,18Torque

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(ii) More accurate evaluation:Note that, in the above figure, forces are not balanced; there is no force to balance the friction force Ff.

The pipe will tend to climb up the side of the wellbore…as it rotates

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Solution to Problem 3 - Rotating

Assume “Equilibrium”

at angle as shown.

sinIsinWFF fTangentAlong 0

cosIsinWNF Tangentto.Perpend 0

…… (7)

sinIsinWN …… (6)

cosIsinWN

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Solving equations (6) & (7)

(8))(tan

tan

cosIsinW

sinIsinW

N

N

1

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(ii) continued

Taking moments about the center of the pipe:

Evaluating the problem at hand:

From Eq. (8),

2

d*FT f

70.16

)3.0(tan)(tan 11

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From Eq. (6),

lbf 724.59F

70.16sin*sin60*8000*30

sinIsinWF

f

f

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From Eq. (9),

lbf-ft 420,17Torque

12

1*

2

7*59,724

2

d*FT f

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2 (d) (ii) Alternate Solution:

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Taking moments about tangent point,

24

7*70.16sin*sin60*8000*30

2

dsinIsinWT

lbf-ft 420,17T

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Note that the answers in parts (i) & (ii) differ by a factor of cos

(i) T = 18,187

(ii) T = 17,420

cos = cos 16.70 = 0.9578

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Effect of Doglegs

(1) Dropoff Wellbore angle dogleg

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Effect of Doglegs

A. Neglecting Axial Friction (e.g. pipe rotating)

0N2

sinT2

sinsTIsinW

0N2

sinT2

sin)TT(IsinW:F normal along

(10) 2

sinT2IsinWN

W sin I + 2T

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Effect of Doglegs

A. Neglecting Axial Friction

(11) 12

cos

IcosW2

cosT

02

cosTIcosW2

cos)TT(:F tangentalong

I cos W T

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Effect of Doglegs

B. Including Friction (Dropoff Wellbore)

While pipe is rotating

(10)&(11)

WcosIT

2sinT2IsinWN

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Effect of Doglegs

B. Including Friction

While lowering pipe (RIH)

(as above)

i.e. (12)

2sinT2IsinWN

NIcosWT

)2

sinT2IsinW(IcosWT

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Effect of Doglegs


While raising pipe (POH)

(13)

(14)

NIcosWT

)2

sinT2IsinW(IcosWT

)2

sinT2IsinW(2

d

2

dNTorque

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Effect of Doglegs

(2) Buildup Wellbore angle dogleg

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Effect of Doglegs

A. Neglecting Friction

(e.g. pipe rotating)

0N2

sinT2

sinTTIsinW:F normalalong

2sinT2IsinWN

0N2

sinT2

sinT2IsinW

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Effect of Doglegs

A. Neglecting Axial Friction

(16) 12

cos

IcosW2

cosT

02

cosTIcosW2

cos)TT(:F tangentalong

I cos W T

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Effect of Doglegs

B. Including Friction (Buildup Wellbore)

When pipe is rotating

(15)&(16)

WcosIT

2sinT2IsinWN

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Effect of Doglegs


While lowering pipe (RIH)

(15)

(17)2sinT2IsinWIcosWT

NIcosWT

2sinT2IsinWN

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Effect of Doglegs

While raising pipe (POH)

(18)

(19)2sinT2IsinW

2

d

2

dNTorque

22Tsin-WsinIWcosIT .e.i

NIcosWT

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Problem #4 - Curved Wellbore with Friction

In a section of our well, hole angle drops at the rate of 8 degrees per 100 ft.

The axial tension is 100,000 lbf at the location where the hole angle is 60 degrees.

Buoyed weight of pipe = 30 lbm/ft

= 0.25

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Problem # 4

- Curved Wellbore

with Friction

T = 100,000 lbf

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Evaluate the Following:

(a) What is the axial tension in the pipe 100 ft. up the hole if the pipe is rotating?

(b) What is the axial tension in the pipe 100 ft up the hole if the pipe is being lowered into the hole?

(c) What is the axial tension in the pipe 100 ft up the hole if the pipe is being pulled out of the hole?

(d) What is the lateral load on a centralizer at incl.=64 if the centralizer spacing is 40 ft?

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Solution 4(a) - Rotating

Axial tension 100 ft up hole when pipe is rotating :

Pipe is rotating so frictional effect on axial load may be neglected.

2

6860IAVG

oAVG 64I

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Solution 4(a) - Rotating

From equation (11),

315,1000,100T

lbf 1,315

64cos*ft100*ft

lb30

IcosWT

68

rotating lbf 315,101T68

T60 = 100,000 lbf

T68 = 101,315 lbf

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Solution 4 (b)

(b) Tension in pipe 100 ft Up-Hole when Pipe is being lowered:

From equation (10):

lbf 16,648N

13,9512,696

4sin*000,100*264sin*100*30N

2sinT2IsinWN

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Solution 4 (b)

From equation 10,

From equation 12,

NIcosWT

lbf 162,4F

16,648*0.25NForceFriction

f

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Solution 4(b) - Lowering

From equation 12,

T)(T 867,2000,100T68

lbf 153,97T68

-2,847

162,4)64cos*100*30(T

T60 = 100,000 lbf

T68 = 97,153 lbf

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Solution 4 (c)

(c) Tension in Pipe 100 ft Up-Hole when pipe is being raised:

From equation (10),

lbf 16,648N

13,9512,696

4sin*000,100*264sin*100*30N

2sinT2IsinWN

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Solution 4 (c)

lbf 162,4F

16,648*0.25NForceFriction

f

From equation 12,

NIcosWT

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Solution 4(c) - Raising

From equation 12,

T)(T 5477000,100T

lbf 5477

162,4)64cos*100*30(T

68

lbf 477,105T68

T60 = 100,000 lbf

T68 = 105,477 lbf

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Solution 4(a, b and c)SUMMARY

Rot 100,000 101,315

RIH 100,000 97,153

POH 100,000 104,477

T60 T68

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Solution 4 (d)

(d) Lateral load on centralizer if spacing = 40 ft. (after pipe has been rotated):

From above,

This is for 100 ft distance

lbf 648,16N

64 at

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Solution 4 (d)

for 40 ft distance,

i.e., Lateral load on centralizer,

lbf 6,659 100

40*648,16N .centr

lbf 1200ft

lb30*pipe offt 40 :Note

lbf 659,6N .centr

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Alternate Approach

(d) Lateral load on centralizer if spacing = 40 ft. (after pipe has been rotated)

From above,

From above,

So, 30 ft up-hole,

lbf 101,315T ,68at lbf 100,000T ,60 at

lbf 395,100Tlbf )100/30(*315,1000,100T

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Alternate Approach

From Eq. (10),

for 40 ft centralizer spacing,

lbf 6,685N

5,6061,079 40/100}*{4

)6.1sin(*395,100*264sin*40*30N2

sinT2IsinWN

lbf 685,6N .centr

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Centralizer

15. Torque and Drag Calculations

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