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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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Effect of Friction (no doglegs):
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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Effect of Friction (no doglegs):
(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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Solution to Problem 3 - rotating
(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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Solution to Problem 3 - rotating
(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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Solution to Problem 3 - rotating
Solving equations (6) & (7)
(8))(tan
tan
cosIsinW
sinIsinW
N
N
1
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Solution to Problem 3 - rotating
(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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Solution to Problem 3 - rotating
Evaluating the problem at hand:
From Eq. (6),
lbf 724.59F
70.16sin*sin60*8000*30
sinIsinWF
f
f
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Solution to Problem 3 - rotating
Evaluating the problem at hand:
From Eq. (9),
lbf-ft 420,17Torque
12
1*
2
7*59,724
2
d*FT f
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Solution to Problem 3
2 (d) (ii) Alternate Solution:
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Solution to Problem 3
Taking moments about tangent point,
24
7*70.16sin*sin60*8000*30
2
dsinIsinWT
lbf-ft 420,17T
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Solution to Problem 3
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
B. Including Friction
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
B. Including Friction
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
Slide 66 of 62
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
Slide 67 of 62
Centralizer