-
Torque and Drag in Directional Wells-Prediction and Measurement
C.A. Johancsik, * SPE, Exxon Production Research CO. D.B. Friesen,
** Exxon Production Research Co. Rapier Dawson, SPE, Exxon
Production Research Co.
Summary A computer model has been developed to predict
drill-string torque and drag, and a versatile rotary torque meter
has been built to use in calibrating the model. The principle of
the predictive model is that torque and drag forces in a
directional wellbore are primarily caused by sliding friction.
Sliding friction force is calculated by multiplying the sidewall
contact force by a friction coefficient.
Realistic sliding friction coefficients were determined from
field data by using the same predictive computer model. These field
data were gathered using novel torque and hookload indicators that
are accurate, por-table, and easily installed. Good agreement
between fric-tion coefficients calculated from different loads in
the same well, as well as agreement between those for dif-ferent
wells, indicates the validity of the predictive drillstring model.
Sliding friction is concluded to be the major source of torque and
drag in directional wells. For waterbase mud systems, typical
friction coefficients range from 0.25 to 0.40.
Introduction Drillstring drag is the incremental force required
to move the pipe up or down in the hole; torque is the moment
re-quired to rotate the pipe. Drag forces usually are given
relative to the string weight measured with the string rotating but
not reciprocating. Measured from the rotating string weight, the
pickup drag usually is slightly greater than the slack-off drag.
The magnitudes of torque and drag are related in any particular
well; high drag forces and excessive torque loads normally occur
together.
There are a number of causes for excessive torque and drag,
including tight hole conditions, sloughing hole, keyseats,
differential sticking, cuttings buildup caused by poor hole
cleaning, and sliding wellbore friction. With the exception of
sliding friction, these causes are associated with problem
conditions in the wellbore. Con-versely, in wells with good hole
conditions, the primary source of torque and drag is sliding
friction.
Torque and drag from any source tend to be more troublesome in
directional holes. In very deep, highly deviated wells overcoming
torque and drag can be critical to the successful well
completion.
The capability to predict frictional loads on drill pipe
Now with Esso Resources Canada Ltd. "Now with Esso E&P
Norway Inc.
01492136/84/0061-1380$00.25 Copyright 1984 Society of Petroleum
Engineers of AIME
JUNE 1984
has two main benefits. First, deep, highly deviated wells can be
planned to minimize torque and drag. Use of torque and drag as
criteria to select the most appropriate well path will help ensure
successful drilling operations to total depth. Second, more
complete knowledge of drillstring loading allows use of improved
drill string design techniques. Drillstring components can be
chosen by using a systematic approach that considers the extra
forces involved.
Torque and Drag Prediction Technique Mathematical Model. A
lumped-parameter model pro-vides the basis for the prediction of
torque and drag. Both torque and drag are assumed to be caused
entirely by sliding friction forces that result from contact of the
drill string with the wellbore. Other less important sources of
torque and drag are not considered in this model.
Two factors affect sliding wellbore friction-the nor-mal contact
force and the coefficient of friction between the contact surfaces.
The product of these two factors represents the magnitude of the
sliding friction force.
The normal contact force between the pipe and hole wall depends
on several factors. This paper considers on-ly two contributions to
normal force-the effects of gravity on the pipe and the effects of
tension acting through curvatures in the wellbore. These forces,
and their contributions to normal force, are shown schematically in
Fig. 1. Other factors such as pipe bend-ing may contribute small
normal forces but are not con-sidered here.
The sliding friction coefficient is the ratio of the fric-tion
force to the normal contact force. In reality, this value depends
on specific contacting materials and on the degree of lubrication
at various places in the wellbore. However, in this paper all these
effects are ex-pressed as a single characteristic friction
coefficient representing average conditions in a particular
wellbore. Determination of this lumped-parameter coefficient is
fundamental to practical application of this model. Computer
Calculations. The following paragraphs describe the calculation of
torque and/or drag forces when the sliding friction coefficient is
given. This calculation is made directly. The reverse calculation,
where a friction coefficient is determined from given torque or
drag data, is done by assuming a friction coef-ficient and
iterating to match the data. In either case, drill string
description and wellbore survey data are required.
987
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Fig.1-Force balance on drillstring element illustrating sources
of normal force.
Once the drillstring description, sUlVey data, and fric-tion
coefficient are specified, the calculation starts at the bottom of
the drill string and proceeds stepwise upward. Each short element
of the drill string contributes small in-crements of axial and
torsional load to running totals in the control program.
Calculation of these load in-crements is the heart of the whole
calculation.
Calculation of the normal force is the first step in calculating
the load increments for an element of the drillstring. Fig. 2 shows
the forces acting on a short, slightly cUlVed element. The net
normal force, F n' is the negative vector sum of normal components
from the weight, W, and from the two tension forces, Ft and F t
+f1Ft . Even though the axis of the element is as-sumed to be an
arc of a circle, this circle is not usually vertical and therefore
the net normal force is not usually in the vertical plane.
Fortunately, the friction calculation requires only the magnitude
of the normal force, not its direction. The magnitude of the normal
force is
The equation for normal force leads immediately to equations for
the tension increment:
f1Fr=Wcos8 pPn , ....................... (2)
and for the torsion increment: f1M=JkFn r. .
............................. (3)
In Eq. 2, the plus or minus sign allows for pipe motion either
up or down; the plus sign is for upward motion where friction adds
to the axial load and the minus sign is for downward motion where
the opposite is the case. In presenting data, this sign often is
carried with the friction coefficient, so that a negative value
identifies coeffi-cients calculated from slack-off drag
measurements.
Eqs. 1 through 3 would be exact if applied to in-finitesimal
elements of the drillstring. Use of longer
988
Fig. 2-Forces acting on drillstring element during pickup.
elements introduces small errors caused by neglecting
second-order terms. For example, Eq. 1 uses the tension at the
bottom of the element and assumes that tension does not change over
the length of the element. First-order approximations are
appropriate here because the underlying problem is complex.
Predicting drill string drag is a three-dimensional belt friction
problem with gravity; no closed-form solution for this problem
exists except for special cases where f1a=O or W=O.
The errors introduced by Eqs. 1 through 3 are small if the
CUlVature of each drillstring element is small. In test
calculations with typical sUlVey data, changing from I-to 100-ft
[0.3- to 30.S-m] elements produced only about a 1 % change in the
overall results. All the calculations discussed in this paper were
made with the drill string divided into roughly 100-ft [30.S-m]
elements.
The best way to choose drill string element lengths is to use
the basic sUlVey data stations to establish the calcula-tion
intelVals. When intermediate calculation points are desired-for
example, at a change in drill string proper-ties-a linear
interpolation can be made. With this ap-proach, sUlVey inaccuracy
probably contributes more er-ror to the results than approximations
in the computer model.
Calibration of the Model. Before being used for torque and drag
prediction, the computer model must be calibrated. Specifically,
calibration involves a realistic determination of typical average
sliding wellbore friction coefficients.
Realistic friction coefficients can be calculated from actual
drilling situations by using the computer program with drillstring
surface loads as input data to calculate the friction coefficient
for a particular well geometry and drillstring. Input data include
pickup weight, slack-off weight, and torque readings, each of which
can produce an independent friction coefficient. Agreement among
the three coefficients from one well not only lends credibility to
the model but also provides confidence in
JOURNAL OF PETROLEUM TECHNOLOGY
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the friction coefficient for its use in prediction of torque and
drag when subsequent wells are planned.
It is believed that friction coefficients will depend largely on
mud type and whether a hole is predominantly cased or open. Thus,
friction coefficients from a number of similar wells must be
compared to verify useful values for prediction use. This requires
collection of a signifi-cant amount of field data for statistical
comparison.
Field readings, to be reduced to wellbore friction
coef-ficients, must be accurate and in useful units. This in-cludes
both torque and drag data; torque must be in foot-pounds force or
Newton-meters rather than in amperes or percent. Also, the friction
calculation is enhanced by the use of accurate survey data. The
directional well descrip-tion and the drillstring configuration are
obtained easi-ly-accurate surface loads are not. Field Measurement
of Torque and Drag The ability to obtain accurate field readings of
drill string loads depends largely on the accuracy of the
measure-ment equipment. Most rigs are well equipped to measure
weights; few are capable of accurately measuring rotating
torque.
To ensure high-quality field data, two special tools have been
designed and built, one for tension and one for torque. Both
devices can be used for direct measurement or as calibration
instruments to verify rig torque and drag readings accurately. Drag
Measurements. Almost all drilling rigs have a weight indicator to
provide the operator with string weight, weight on bit (WOB) , and
drag and overpull forces. The weight indicator normally is both
accurate and repeatable. However, the force is sensed at the
drill-ing line and includes the weight of the traveling equip-ment
and the kelly. To analyze drag forces, the tensions at the top of
the drill pipe , below the kelly, are required. Thus, it is
necessary to subtract the weight of the travel-ing equipment when
string weights are recorded.
There are several potential sources of error in rig drag
readings. Zero offset in the instrument and inaccurate knowledge of
total traveling equipment weights are two sources. The best way to
eliminate these errors is to calibrate the weight indicator with a
load cell placed below the kelly and traveling equipment. Weight
Indicator Calibration Sub. A short drill collar sub was machined,
instrumented, and calibrated to pro-vide accurate tensile readings
over the range of to 500,000 lbf [0 to 2 224 kN] with less than
0.5% error. The sub is 30 in. [76.2 cm] long with NC50 connections.
A machined-down area in the center is instrumented with strain
gauges in a conventional four-arm, 350-ohm Wheatstone bridge
arrangement. A protector cover, at-tached only above the gauge
area, protects the gauges and houses a plug-in-type connector.
Strain readings are monitored using conventional strain readout
equipment. The sub was calibrated on an accurate tensile testing
machine to 500,000 lbf [2 224 kN]. The weight in-dicator
calibration sub is shown in Fig. 3.
Use of this device involves making up the sub between the kelly
saver sub and the top joint of drillpipe. With slips set on the
drillpipe, the blocks are hoisted in small weight increments up to
full string weight. Readings from both the weight indicator and the
calibration sub are recorded and plotted to produce a calibration
curve. This
JUNE 1984
Fig. 3-Weight indicator calibration sub.
calibration relates weight indicator readings to actual tension
at the top of the drillstring.
Drillstring pickup drag readings are taken by hoisting the
string slowly and recording the weight indicator reading.
Similarly, slack-off drag is recorded while run-ning in slowly, and
the rotating string weight is recorded while rotating without
reciprocating the pipe. These readings then are adjusted according
to the calibration curve to give actual loads at the top of the
drill string for use in the computer program.
Torque Measurements. Measurement of rotary drilling torque
presents a problem, primarily because it is dif-ficult to sense and
communicate torque from a rotating piece of machinery. Most
drilling rigs are equipped with some simple method for indicating
torque. However, few of these techniques are accurate, and most
devices are not calibrated to provide readings in useful torque
units.
A few drilling rigs in the world are equipped with calibrated
rotary torque indicators. Even when they work well, these devices
lack portability. A portable torque meter can be taken from rig to
rig as needed and can be easily returned to a shop for
recalibration or repair. 1
Portable Torque Meter Design. To collect torque data from
several rigs, it was necessary to design a portable device to
measure torque in absolute torque units with a range up to 50,000
ft-Ibf [67 kN m]. An important con-sideration was the ease of
installation without customiz-ing conventional rig components.
Also, the device had to withstand the rugged working
environment.
The concept of a portable torque-measuring device in-volved
choice of a placement location in the torque path, a method for
sensing torque, and a technique to com-municate readings in a
suitable readout display. These problems were solved in the
following way. The torque meter is designed to fit in the torque
path between the rotary table and the kelly bushing (KB). Torque is
con-tinuously sensed internally with strain gauges, and the data
are communicated by a frequency-modulated (FM) datal ink to a
receiver and display unit.
The prototype torque meter is designed to adapt to a 27V2-in.
[70-cm] pin drive system. Its configuration is
989
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Fig. 4-Rotary torque meter.
that of a 4 V2-in. [11.4-cm] thick, ring-shaped spacer plate
located between the rotary table and the drive bushing. Pins on the
torque meter fit into the rotary table, and holes in the torque
meter accept the drive pins from the KB. Fig. 4 shows the prototype
torque meter.
The body of the torque meter was machined from steel. Kelly
drive pins were attached using the same pro-cedure used in the
manufacture of drive bushings. Holes to accept Kelly drive pins
were bored and fitted with wear bushings.
The torque path within the torque meter is from the four drive
pins to the four wear bushings. Within the steel body, compressive
and tensile forces are generated in front of and behind the drive
pins, respectively. Strain in the steel resulting from these forces
can be measured with strain gauges.
To increase strain to measurable levels, eight load-bearing webs
were created within the solid steel struc-ture. These eight webs
are oriented between drive pins and wear bushings. Two strain
gauges are used on each web, top and bottom, and are connected in
parallel. Each parallel pair is wired in series with the pair
situated diametrically opposite to create one ann of the 350-ohm
Wheatstone bridge. This strain-gauge bridge design is a
conventional four-ann circuit with alternating tension and
compression anns.
The net effect of this bridge arrangement is that web tension
and compression are additive. When torque is applied, a signal is
generated proportional to the torque. Because of the symmetrical
arrangement of tension and compression gauges, the bridge negates
side loads and reacts only to torque.
Telemetering the data is accomplished using an FM radio
transmitter in conjunction with a custom-built radio frequency
amplifier. Change in the strain signal is con-verted to a change in
a subcarrier frequency. This infor-mation is transmitted through
three radial antennas that are imbedded in fiberglass around the
circumference of the torque meter. Transmission (carrier) frequency
on the prototype torque meter is approximately 100 MHz [1 X 108
cycles/sec).
A dipole receiving antenna and an FM radio receiver receive and
demodulate the signal. Output from the receiver is a direct current
voltage that is proportional to torque. A strip-chart recorder
provides a pennanent trace of the torque signal. The torque
transducer is protected by a %-in. [1.9-cm] thick steel plate on
top and a S-in. [0.9-cm] thick steel plate on bottom. Removable
cover plates provide access to the battery power supply and to the
transmitter package where the on/off switch is located. 990
Calibration of the instrument is accomplished using a special
calibration frame capable of applying 50,000 ft-lbf [67 kN m] of
known torque. Hydraulic cylinders are used with load cells to apply
and measure the force at a known moment-ann length. This device
allows easy recalibration to verify continued accuracy of torque
readings. Field Use of Torque Meter. The torque meter is in-stalled
between the table and drive bushing during a con-nection. The slips
will fit through the center ofthe torque meter, and subsequent
connections can be made with the torque meter in place. Drilling,
working pipe, washing the floor, etc., can all be done virtually
ignoring the presence of the torque meter.
Static and dynamic torque data are recorded on a strip-chart
recorder with a pennanent tract for a given period of drilling
activity. As expected, the typical torque trace is not constant
during drilling but rather includes oscilla-tions at various
frequencies. In this paper, these oscilla-tions are ignored; all
torque readings are average values.
Torque readings are taken at a variety of drilling con-ditions
with various rotary speeds and WOB's. Changes in rotary speed have
only a minor effect on mean torque values. WOB, particularly in
deeper, deviated wells, also tends to have a small effect on torque
levels. This may result from the counteracting effects of increased
bit torque and decreased string weight (and thus decreased
friction) when WOB is increased. Friction Coefficients From Field
Data Three examples are given that show the calculated fric-tion
coefficients from accurate surface torque and drag data. Table 1
shows tabulated infonnation about each well, including details of
the drill string and the direc-tional profile, as well as measured
loads and calculated friction coefficients. Example 1. Well No.1
was drilling at 9,790 ft [2984 m] when torque and drag readings
were taken. The well configuration was a 32 0 [0.56-rad] average
angle build-and-hold profile with the kickoff point at 1,000 ft
[305 m). A seawater-base drilling fluid of 11.6 Ibm/gal [1389
kg/m3] was used. Seventy percent of the hole was cased.
Pickup drag was 49,000 lbf [218 kN] over the rotating string
weight of 153,000 lbf [681 kN]. Slack-off drag was 31,000 lbf [138
kN] less than string weight. Using the computer program, these
loads reduced to a friction coefficient of 0.28 for pickup and
-0.27 for slack-off.
Torque readings both on and off bottom oscillated
in-tennittently with a mean value of 15,900 ft-Ibf [21 KN . m]. The
detennination of a friction coefficient from this torque is
complicated by the presence of drillpipe rubbers in the cased
section of the hole. The characteristic radius of the drill pipe
was increased in consideration of these rubbers to a value slightly
greater than that for 4 V2-in. [11.4-cm] drillpipe with 6S-in.
[16.2-cm] tool joints. The resulting sliding friction coef-ficient
was calculated to be 0.27. Example 2. Well No.2 was a deep,
relatively low-angle well. When readings were taken, an 8V2-in.
[21.6-cm] hole was being drilled at 15,573 ft [4746 m], below
12,900 ft [3932 m] of9Ys-in. [24.4-cm] casing. The hole was kicked
off at 3,000 ft [914 m] to a build-and-hold well profile with 24 0
[0.42-rad] average angle. This par-ticular hole was relatively free
of doglegs.
JOURNAL OF PETROLEUM TECHNOLOGY
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TABLE 1-FRICTION COEFFICIENTS FROM FIELD DATA
Well No.1 Depth, ft 9,790 Percent of hole cased, % 70
Drillstring 124 ft of 73f4-in. DC
990 ft of 41J2-in. HW 8,676 ft of 41f2-in. DP
Well profile build and hold Kick-off paint, ft 1,000 Average
angle, degrees 32 Maximum angle, degrees 37 Mud weight, Ibm/gal
11.6 Rotating string weight, Ibf 153,000 Pickup weight, Ibf 202,000
Slack-off weight, Ibf 122,000 Rotating torque, ft-Ibf 15,900
Pickup 0.28 Slack-off -0.27 Rotating 0.27
The pickup weight of 377,000 lbf [1676 kN] was reduced to a
friction coefficient of 0.31 using the com-puter program. A
slack-off string tension of 232,000 lbf [1031 kN] produced a
coefficient of -0.3L
Torque readings, both on and off bottom, were ap-proximately
18,300 ft-Ibf [25 kN m]. Torque was fairly constant with only small
oscillations synchronous with rotary speed. Drillpipe rubbers were
used in the cased portion of the hole with greater frequency of use
near surface. If the extra effective radius was considered, the
torque reading produced a sliding friction coefficient of 0.29.
Example 3. Well No.3 was a case in which high torque and drag
were experienced during and after drilling out a 9Ys-in. [24.4-cm]
casing shoe at 12,100 ft [3688 m]. The
2000
4000
t; ~ 6000 UJ Cl Cl UJ a: ~ 8000 UJ :;:
10.000
1~IW ANGLE
I HEAVY -WEIGHT PIPE AND
\ DRILL COLLARS
PICK-UP
WELL No.3
14.0000'-------1-oo---~2DO----300----4DO-----.J500
TENSION IN DRILL STRING Ix 1000 LBS'
Fig. 5-Drillstring tension vs. depth from Well No.3.
JUNE 1984
Well No.2 Well No.3 15,573 12,200
83 99 458 ft of 63i4-in. DC 372 ft of 61f2-in. DC 15,115 ft of
5-in. DP 840 ft of 5-in. HW
10,988 ft of 5-in. DP build and hold build and hold
3,000 2,400 24 44 27 49
12.5 9.8 290,000 218,000 377,000 376,000 232,000 141,000 18,300
24,500
0.31 0.40 -0.31 -0.40
0.29 0.39
build-and-hold well profile was kicked off at 2,400 ft [731.5 m]
to an average angle of 44 [0.77 rad]. The well had several severe
doglegs of 4 and 6 per 100 ft
[0~07 and 0.1 rad per 30.5 m] in the lower portion of the build
zone.
Initially an attempt had been made to drill out the shoe while
drillpipe rubbers were used to protect the casing and drillstring.
However, the torque required to rotate was found to be more than
35,000 ft-Ibf [47 kNm]. This was beyond the capability of the rig
rotary drive.
After the pipe was tripped to remove rubbers, the string could
be rotated but only when surface tension was slacked off. Without
WOB, rotation was impossible. With approximately 38,000 lbf [169
kN] on the bit, the string could be rotated with a mean rotating
torque of 24,500 ft-Ibf [33 kN m]. With an estimated 2,000
ft-Ibf
0
2000
BUILD 4DOO ANGLE
t; ~6IJXl UJ Cl Cl UJ a:
~1IIlOO :;:
10.000
12.000 2000 FT -LBS ESTIMATED
BIT TORQUE
WELL No.3
14,0000'---------5000---10..-'..000---15,-00-0
--2-0.o-oo--2-5,00-0--30--',lIXl TORQUE IN DRILL STRING 1FT
-LBI
Fig. 6-Drillstring torque vs. depth from Well No.3.
991
-
[2.7 kN m] bit torque, the remaining 22,500 ft-lbf [30 kN'm]
resulting from friction was reduced to a sliding friction
coefficient of 0.39.
Without drillpipe rubbers, the radius of the drillpipe for use
in the program was determined to be two-thirds of the distance
between pipe body radius and tool joint radius. This is a
reasonable assumption when based on the hypothesis that two-thirds
of the side load is sup-ported at the tool joints.
Like torque values, the pickup and slack-off drag values were
very large. Pickup weight was 376,000 Ibf [1672 kN], which was
158,000 Ibf [702 kN] more than the calculated rotating string
weight of 218,000 ft-lbf [295 kN m]. Rotating string weight was not
recorded as it was impossible to rotate without WOB. The pickup
weight value produced a friction coefficient of 0.40. Slack-off
weight of 141,000 Ibf [620 kN] produced to a coefficient of
-0.40.
Torque and Drag Profiles. Once a friction coefficient has been
determined, it is interesting to use the computer model to
calculate the load profiles along the length of the drillstring.
Fig. 5 illustrates tension in the drill string as a function of
depth for Well No.3. Three cases shown are pickup, rotating off
bottom, and slack-off of the drillstring.
The tension profile while rotating off bottom (no axial
movement) is a smooth curve. The slope of this curve at any point
represents the product of the buoyed drill string weight per foot
and the cosine of the hole inclination angle.
Axial movement of the pipe produces marked changes in drill
string tension. The most notable changes occur in the build zone
between 2,400 and 4,800 ft [731.5 and 1463 m] where noticeable
doglegs are present. In par-ticular, the lower part of the build
zone had extreme doglegs of up to 61100 ft [0.1 rad/30.5 m]. Rapid
changes in tension occur in this area in both pickup and slack-off
tension.
Because friction acts in an upward direction during slack-off,
the slope of this curve illustrates the relative effects of
friction and weight on the string tension. Be-tween 4,000 and 4,600
ft [1219 and 1403 m], because of the extreme doglegs, the upward
friction force is greater than the increments of pipe weight, and
the string tension actually decreases over this interval.
A torque profile during drilling is shown in Fig. 6 for the same
well. Torque changes in the vertical section of the hole (0 to
2,400 ft [0 to 731.5 m]) are shown to be small because of small
side forces. As with tension, torque changes are rapid in the angle
build zone and more gradual in the hold-angle zone. The
2,000-ft-lbf [2.7 kN] bit torque shown is assumed.
Conclusions 1. Drillstring torque and drag are primarily caused
by
simple sliding friction between the drill string and the wall of
the hole.
2. The computer model presented in this paper is realistic.
3. Sliding friction coefficients in seawater-base mud typically
lie between 0.25 and 0.40.
992
Acknowledgments
We thank Exxon Production Research Co. for permis-sion to
publish this paper and Exxon Co. U.S.A. for their continued support
and cooperation in collecting field data. Special thanks are
extended to Lisa A. Beaudry, Hubert L. Morehead, and Paul H. La
Marche for their contributions in developing this technique.
Both the torque meter and the hookload indicator were fabricated
by Brewer Eng. Laboratories of Marion, MA; LaVerne F. Wallace and
Roger W. Masson were the principal Brewer participants in this
project and did most of the design work on both devices.
Reference
1. Dyer, N.D.: "Rotary Torque Indicator for Well Drilling
Ap-paratus," U.S. Patent No. 3,664,184 (1972).
Nomenclature
Ff = sliding friction force acting on element, Ibf [N]
F n = net normal force acting on element, Ibf [N] Ft = axial
tension acting at lower end of
element, Ibf [N] tJ.Ft = increase in tension over length of
element,
Ibf [N] M = torsion at the lower end of element, ft-lbf
[Nm] tJ.M = increase in torsion over length of element,
ft-lbf [Nm] r = characteristic radius of drill string element,
ft
[m] W = buoyed weight of drill string element, Ibf
[N] ex = azimuth angle at lower end of drill string
element, degrees [rad] tJ.ex = increase in azimuth angle over
length of
element, degrees [rad] 8 = inclination angle at lower end of
drill string
element, degrees [rad] tJ.8 = increase in inclination angle over
length of
element, degrees [rad] if = average inclination angle of
element,
degrees [rad] p, = sliding friction coefficient between
drill string and well bore
SI Metric Conversion Factors ft x 3.048*
Ibf x 4.448 222
"-Conversion factor is exact.
E-Ol E+OO
m N
JPT
Original manuscripl received in Society of Petroleum Engineers
office Jan. 25, 1983. Paper accepted for publication July 2, 1983.
Revised manuscript received Jan. 3, t 984. Paper (SPE 11380) first
presented at the 1983 IADCISPE Drilling Conference held in New
Orleans Feb. 20-23.
JOURNAL OF PETROLEUM TECHNOLOGY