SPE

Society of Petroleum Engineers

SPE 16663

Field Comparison of 2-D and 3-D Methods for the Borehole

Friction Evaluation in Directional Wells
by E.E. Maidla and A.K. Wojtanowicz, Louisiana State U.
SPE Members

Copyright 1987, Society of Petroleum Engineers

This paper was prepared for presentation at the 62nd Annual Technical Conference and Exhibition of the Society of Petroleum Engineers held in
Dallas, TX September 27-30, 1987.

This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the·
author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the
author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers
presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Permission to copy is
restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of
where and by whom the paper is presented. Write Publications Manager, SPE, P.O. Box 833836, Richardson, TX 75083-3836. Telex, 730989 SPEDAL.

ABSTRACT design factors. Such an approach resulted in the

overestimated design and high operational
The two new general procedures for the borehole uncertainty. The example here might be reluctance
drag prediction, based on the borehole friction of many operators to reciprocate casing strings,
factor concept were compared. The procedures despite a beneficial effect of this operation on the
employed iteration over the directional survey cement bond.
stations, numerical integration between the stations
and mathematical models of the axial loads within a The knowledge of the frictional loads will
moving pipe in the borehole. The models considered improve the design criteria, and will help to
several new effects such as hydrodynamic viscous optimize the design for the minimum cost.
drag, contact surface, and the bearing angle
component of dogleg severity. In their interesting study, Johancsik et al.,
[1], developed a simplified model to predict torque
The study addressed the extent and conditions and drag for the drillstring. They also used the
under which the two-dimensional and the three- model to find the sliding friction coefficient. The
dimensional procedures diverged significantly. The model was tested in three directional wells with a
method was based on the computer calculated values significant length of the cased hole section (70%,
of the borehole friction factor from the measured 83%, and 99%). No distinction was made between
hook loads. The field data used included four cased hole friction and the open borehole friction.
casing runs from the offshore locations in the Gulf Also, the hydrodynamic effects were not considered
Coast area. In addition, the systematic theoretical which, for the drillstring movement, might have been
study was performed with over 100 computer-simulated an adequate simplification.
directional wells.
Sheppard, et al. [2] investigated the
The study revealed a good agrement between 2-D advantages of planning an undersection trajectory
and 3-D procedures for most common drilling (steady buildup) to reduce torque and drag. In the
conditions. Two 2-D model's accuracy was mostly one field case studied, they evaluated friction
affected by the bearing angle component of shallow factor values of 0.36 only within the shallow depth
doglegs. In addition, the reliability of the interval 1900 to 2400 ft.
borehole friction factor field assessment was mainly
controlled by the inclination angle and the length Bratovich, et al, [3] investigated problems of
of the slant hole section of a well. running logging tools in high-angle wells. The
field tests and the laboratory tests were performed.
For the open hole, they reported a friction factor
INTRODUCTION value 0.36 for the stand-off tool, and 0.40 for the
wireline. The open hole tests were conducted in
The complex spatial configuration of lignosulfonate water-base muds with densities
directional wells engender an additional axial load varying between 9.7 to 12.5 lbm/gal.
(drag) when pipe or bottomhole tools are run in the
boreholes. Traditionally, the frictional effects To date, very few tests have been performed
were not computed but were accounted for by the with the actual field data. The concept, that a
single value of the friction factor represents
borehole conditions has not been verified.
References and illustrations at end of paper.

125
2 FIELD COMPARISON OF 2-D AND 3-D METHODS FOR THE BOREHOLE FRICTION EVALUATION IN DIRECTIONAL WELLS SPE 16663

Furthermore the existing models are not general The calculation procedure started by assuming
since they were developed for a specific pipe type some value of the borehole friction factor and
and size. The casing problems concerning borehole recurrently calculating the axial load from the
friction have not been addressed yet. casing shoe upwards until the calculated hook load
was determined. If the calculated hook load did not
This study is a continuation of the research match the measured value, the new value was assumed
that began by considering the borehole drag impact and the procedure was repeated until the hook loads
on the casing string loads and its effect on the match occurred. The match indicated the correct
casing design criteria [4]. Later, the concept of last assumed value of the borehole friction factor.
the borehole friction factor and the field method
for its determination, based on the two-dimensional In this method, the borehole friction factor is
model, were developed [5]. Most of the early not a measured magnitude but it is calculated from
findings were in good agreement with this research. the hook load measurements. Therefore a major error
.However, the excessively high values of the can be made due to incorrect axial load predictions
calculated friction factors [5] indicated effects by the mathematical model. Consequently, it is
of some unexplained forces not included in the important to account for all possible phenomena
original two-dimensional model. which affect the borehole drag. Eventually, the
model can be simplified by ignoring those effects
The concept of the borehole friction factor which show a small impact on the borehole friction
implies its value being constant throughout the factor value.
depth of the well and independent from the wellbore
trajectory (inclination, bearing angles, doglegs). The approach used in this study was based both
It represents the mechanical frictional interaction on the computer-simulated conditions and the actual
between the pipe surface and the borehole surface field data. The simulation approach was used to
and it shall only depend upon: drilling fluid systematically investigate effects of spatial
lubricity, mud cake lubricating properities, parameters such as bit walk, bearing angle,
lithology, casing coupling size relative to borehole inclination angle and dogleg severity, including
size, pipe surface configuration (centralizers, their extreme values which were not readily
coating) and the borehole surface configuration available from the field records.
(washouts, keyseats, ledges, etc).
The collected field data were used for an
The definition of the borehole friction factor empiri~al verification of the borehole friction
is factor concept and applicability of the 2-D and 3-D
models to its determination. Unlike the simulation
study, the field verification method was based on
~B (1)
the actual directional surveys and on the on-site
record of the hook loads. To increase precision,
the hook loads were measured with the portable
The minus and the plus signs are for the equipment by-passing the existing rig
pulling-out and the running-in situations, instrumentation. The portable unit was assembled to
respectively. the deadline anchor hydraulic signal, and consisted
of a hydraulic load cell, transmitter, digitizer,
The hydrodynamic viscous drag term FD and recorder which stored the data on magnetic
represented one of the unexplained forces tape. The equipment's accuracy was 1000 lbf and the
disregarded in the previous work [5]. Other sampling rate at which the data was recorded on the
potential contributors to the error made by the two- tape was 1 sec. Before and after every rig trip,
dimensional treatment included spatial belt friction the equipment was calibrated and its readings were
effects due to the bit walk and doglegs. As a result checked for accuracy.
the new 3-D model was developed which accounted for
the above effects and for the effect of the contact The other field data regarding drilling mud
surface between pipe and borehole. properties, borehole geometry, current depth of the
casing shoe, and velocity of the pipe movement were
The main objective of this study was to verify collected or directly measured 6n the drilling
the integraty of Equ. (1), and to define an locations.
applicability of the 2-D and 3-D. treatments.
The method used for the analysis of the field
data was similar to the simulation study. The
METHOD calculated values of the borehole friction factors
were examined for their dependence upon depth, well
The calculations of the borehole friction trajectory, doglegs, and their statistical scatter.
factor were performed by the two computer programs. In all calculations, friction in the cased upper
Each program consisted of a mathematical model of section of the borehole was modelled by using
borehole drag (2-D or 3-D), and the iterative sliding friction coefficient for steel surfaces
procedure for calculating hook load. 0.25.

The input data included: drilling mud

properties, casing string composition, borehole BOREHOLE DRAG MODELS
profile (directional survey), borehole geometry,
series of measured hook loads while running The predicted hook load was calculated from the
(pulling) casing, casing string velocity, and the equation:
measured depth of the casing shoe.

126
SPE 16663 Maidla E. E. & Wojtanowicz A. K. 3

of the well trajectory.

M
The correction factor, Cs, represents an effect
FA ± .!. :E
4 m=l ( ~dd~n )m L d2
m m
(2) of the contact surface between the pipe and the
borehole. Its derivation is presented in Appendix
B. The correction factor values vary between 1 and
In Equ. (2), the plus sign is used for upward 4/TI and are dependent upon the contact surface
pipe movement and the minus sign for downward angle y as shown by the equation:
motion. The second term in this equation accounts
for hydrodynamic friction effects and is the same
for all models. The relevant c'alculations are shown
in Appendix A. (7)

3-D Model In all cases studied here, the correction

factor was always very close to unity. Therefore it
The model is based on the analytical can simply be ignored in most engineering
description of the well profile. It was derived by calculations.
analyzing forces acting on a small casing element as
shown in Fig. 1. In this study, the minimum Equation (3) does not include torsion effects
curvature method was used to interpolate a curve which might contribute to the normal force. Since
between two directional survey points. an analytical solution to equation (3) is not
In fact, the equations of the model are general generally possible, numerical integration must be
and can be used with any other interpolating scheme. used. Our calculations indicated that, when using
the classic Runge-Kutta method, only three steps are
The model considers the following effects: necessary to perform the integration.

* Spatial changes of the well direction as

measured by rates of buildup, drop-off, bit 2-D Model
walk, as well as dogleg severity and
horizontal component of the dogleg severity; This model ignores bearing angle changes and
* Buoyancy effect; the shape of the contact surface between pipe and
* One value of the borehole friction factor the borehole. In all other aspects its construction
for a well; is similar to that of the 3-D model. However, in
* Hydrodynamic friction effects calculated as the two-dimensional space, the dot product
the surge or swab pressures; expressions [5] simplify and become the explicit
* Effect of the pipe-borehole contact surface algebraic functions. Therefore, the iterative
on the drag; formula for the axial load becomes
* Torsion and spring effects are ignored.

The axial load equation is:

(3) (8)

where:
and
A
I 2 FA (R.) 2
when pulling pipe out of the well, and
qN(R.) = /[qb(R.) + [qp(R.) + R(R.) ] (I~)

where A (10)

when running pipe into the well.

The constants C1, C2 are the sign convention

constants dependent upon direction of the normal
(5) force - Table 1.

Also, for the two-dimensional borehole, the radius

q (R.) of curvature expression (6) simplifies to
p

1 1 - 11-1 R ( 11)
R= arccos[cos(0 -e )•sina •sina +cosa •cosa ( 6)
1 1- 1 1 1- 1 1 1-1]
It should be emphasized that, though
In the Equ. (3), the positive sign applies to simplified, the two-dimensional model has a strong
the upward pipe movement and the negative sign is practical appeal. From the engineering standpoint,
for the downward movement. Equations (5) describe such a model is the only solution to the problem of
projections of the distributed pipe weight on the predicting axial loads during the well planning
trihedron [11] axis associated with any given point stage. At this stage the casing string design can

127
4 FIELD COMPARISON OF 2-D AND 3-D METHODS FOR THE BOREHOLE FRICTION EVALUATION IN DIRECTIONAL WELLS SPE 16663

be achieved only by considering a simplified two- In the second part of the theoretical study we
dimensional profile of the planned well. examined the effect of doglegs on the borehole drag
models response. A single dogleg was introduced at
the end of the buildup section of the simulated
THEORETICAL STUDY wells. The dogleg was entirely confined in the
bearing angle change with no effect on the
The main objective of this study was to compare inclination. Such a configuration represented the
the two borehole drag models using wide range of the worst possible case for the two-dimensional
directional well configurations and to determine treatment since inclination was entirely unaffected
conditions under which the.models' results became by the dogleg and the 2-D model could not respond to
significantly different. The practical purpose was its value. No bit walk was assumed to eliminate
to find an error, in terms of the borehole friction other spatial effects. Buildup rate of 0.5°/100 ft
factor value, associated with using 2-dimensional and the slant hole inclination of 20° were constant
model instead of a 3-dimensional. Since the while dogleg severity (due to bearing angle changes)
available field data did not represent variety of varied from 0 to 10°/100 ft.
configurations necessary for such a study, the
directional surveys were simulated by the computer. The comparison is shown in Fig 5. The 2-D
More than 100 directional wells were generated. model responded with a maximum deviation of 34% for
Drilling mud properties, casing specification and the dogleg severity 10°/100 ft thus demonstrating
the bit size were chosen to be the same as in the its sensitivity to bearing angle doglegs. '
case history of Well 1. The final vertical depth
was simulated at approximately 8000 ft. The kick-
off point was set at 2000 ft and the directional FIELD STUDY
survey base of 100 ft was selected.
There were four field case histories considered
Computer-generated plots of the bit walk and here. All located offshore Louisiana Gulf Coast as
inclination patterns wer~ also used to provide shown in Fig. 6. The drilling fluids used in all
better understanding and visual control of the well cases were the dispersed water-base mud systems with
paths. The examples of such plots are shown in the similar mud densities.
Figs. 2 and 3 for a buildup rate of 2°/100 ft and
the inclination of 30°. Well Description and Data Acquisition Technique

Initially, a buildup rate of 2°/100 ft was Well 1 was an S-shaped well drilled to 11270 ft
assumed with the bit walk varying between 0 and -Figs. 7, 8, and Tables 4-6. Its maximum
2.4°/100 ft. Also, an inclination of the slant inclination was 39.20° at the measured depth of 5032
(sailing) portion varied from 10° to 60°. For each ft and its build-up rate averaged 2.2°/lOOft. After
well, the reference hook load was calculated using the well had been conditioned for the casing run,
the 3-D model and value of the borehole friction further side wall cores were requested from the
factor 0.4. The reference hook load was then used geology department. During that run, the cable
by the 2-D model to evaluate a new value of the tension of the side core barrel was recorded
borehole friction factor. Such a procedure provided manually using the logging unit equipment available
an easy way to compare, in dimensionless terms, on the platform. The depth was measured by the use
results between wells of different configurations. of a calibrated wheel. During the wiper trip before
In addition, the significance of the hydrodynamic the casing run the pulling out hook load for the
effects was evaluated by running the 3-D program drillstring was measured manually using our portable
with and without hydrodynamic component. unit. The casing run was also recorded using the
unit - Table 4. The measured hook load vs. time was
The comparison between 3-D and 2-D models are plotted on two 120 in. strips of paper in the form
summarized in Figs. 4 and 5. The 2-D model of logs, and the average hook loads and velocities
overestimated borehole friction factor by up to 25% were determined for 36 joints of casing. Then the
for severe doglegs, large bit walks and small slant depths were correlated with the hook loads by using
angles. The sensitivity of. the 2-D model to bearing the tally sheet with the recorded time. During
angle changes is caused by the spatial component of the casing run, the casing string was picked up at
the capstan effect which is not considered in this 4897 and 5924 ft and the two pulling hook loads were
model. recorded. The casing was equipped with rigid-type
centralizers.
The effect of the hydrodynamic friction is
shown in Table 2. The error introduced by ignoring Well 2 was a build-and-hold type well drilled
this effect was as much as 50-60% for a wide range to 9610 f t - Figs. 11, 12 and Tables 7, 8. Its
of the well buildup rates from 0.5 to 2 deg./100 ft maximum inclination was 48.30° at the measured depth
at small inclination angle of 10°. Moreover, the of 5043 ft and its build up rate averaged
hydrodynamic effect became less important with 3.3o/100ft. The rig instrumentation was used for
increasing inclination angle and for the slant holes the hook load measurements. It was equipped with a
inclined more than 60° its contribution to the load pin and three strain gauges. The hook loads
calculated value of the borehole friction factor was were recorded manually from a monitor in the mud
smaller than 17%. The reason was that in the high- logging unit. Prior to the measurements, the load
inclination holes a sliding friction dominated all sensor was calibrated. The equipment's accuracy was
other effects, particularly the effect of the swab 1000 lbf. During the wiper trip the hook load was
and surge pressures which, by their nature, were recorded while pulling out the drillstring-Table 8.
independent from the inclination angle. Total of 252 joints of casing were run in
approximately 10 hours and 151 average hook loads

128
SPE 16663 Maidla E. E. & Wojtanowicz A. K. 5

were recorded for the deeper joints. Table 7 shows Therefore, it was concluded that some effects
the selected data recorded. The pick-up attempt present while running-in casing were not active
(only pipe stretching) was made once at the total while pulling out. These effects were disregarded by
depth with the maximum pull 265,000 lbf. Forty bow- both models. One of the effects absent in the
type centralizers were installed on every joint on models was the effect of torsion (spring or
the lower sections of the casing string. unbending effect). The discrepancy between pulling
and running values of the borehole friction factor
Well 3 was a build-and-hold type well drilled cannot, however, be explained by this effect,
to 11538 ft - Figs. 15, 16 and Table 9. Its maximum because of its presence disregarding direction of
inclination was 16.35° at the measured depth of the pipe movement. Some possible explanation was
10200 ft, and its build-up rate averaged 0.5°/100ft. that ledges, washouts or bridges caused by slaughing
The rig instrumentation was similar to that of the borehole walls would work against the downward
portable unit. It consisted of a 100,000 lbf movement of the pipe. These effects constituted
capacity tensiometer placed at the dead line. The phenomenon which might be called "borehole
electronic signal from the load cell, equipped with conditions" which was not associated with mechanical
strain gauges, was digitized and stored on a friction. Though there is no phenomenological
computer hard disk. The hook load and depth were description of these effects, their contribution to
recorded every second. During the casing run the axial loads can be numerically estimated from
casing string was picked up three times. The hook pulling and running loads difference.
load was recorded for 60 joint runs. Table 8
contains some of the data recorded. After the last 2. Accuracy of the two-dimensional approach
joint was run, the casing string pick-up was
attempted (only pipe stretching) to 356,000 lbf to The values of the borehole friction factor
try and reciprocate the casing string while based on the 2-D model showed a good agreement with
cementing. Thirty bow-type centralizers were used on those from the 3-D model in Wells 1 and 2. In the
every joint on the lower section of the casing remaining two wells, however, the 2-D approach
string. overestimated the borehole friction factor by' 24
45%.
Well 4 was a build-and-hold type well drilled
to 8967 ft Figs 18, 19 and Table 10. Its maximum To improve the analysis, the overall dogleg
inclination was 52.25° at a measured depth of 6810 severity and the horizontal component of the dogleg
ft and its build-up rate averaged 2.8°/100ft. Due severity were calculated. The horizontal dogleg was
to the malfunction of the portable unit, only one an indication of the bearing angle change
hook load reading was obtained during the last joint contribution to the overall dogleg severity.
run, using the weight indicator at the driller's
console. The resolution of the equipment was 5000 The analysis revealed that the distortion of
lbf and there was no record of any previous the 2-D calculations was controlled mainly by the
calibration. After the last joint was run, the horizontal components of shallow doglegs. For
casing string was picked-up oat 270,000 lbf (only example, in Well 3 the shallow depth dogleg was
pipe stretching). Rigid-type centralizers were used. composed mainly of the bearing angle change and it
significantly contributed to the hook load. This
effect was disregarded by the 2-D model which caused
Results and Discussion an overestimation of the borehole friction factor.
Situation in Well 4 was similar with several shallow
The results are presented in Tables 3-10 and in doglegs affected mainly by the bearing angle. In
Figs. 9, 10, 11, 14, 17. The data provided Well 2, however, the large horizontal dogleg was
information on the average values of the borehole located deep in the well and did not affect 2-D
friction factor, its insensitivity to the spatial model accuracy. The depth, the magnitude and
geometry of directional wells as well as the quantity of horizontal doglegs were considered
reliability of the two-dimensional approach. Though important factors in the 2-D model applications. It
the presented results are organized on the well-by- is believed that their contribution was caused by
well basis, they will be discussed by topic rather the capstan effect which, in turn, depended upon the
than by the field case. pipe length below the dogleg.

1. Borehole friction factor values Directional survey of Well 1 did not show any
significant horizontal doglegs so the 2-D and 3-D
Similar borehole friction factors values were calculations agreed very well.
obtained for the similar mud programs, as shown in
Table 3: Apparently, the 2-D model discreaencies in
assessing the borehole friction factor were
* For all casing runs, the average borehole greatly affected by spatial irregularities within
friction factor calculated from running-in hook the shallow borehole section above the kick-off
loads were greater than those from pulling hook point. The same irregularities in the lower,
loads. directional portion of the well had negligible
* The average borehole friction factor values effect on the hook load. It seems that the main
calculated for the upward motion, in the high problem in directional drilling as far as casing
inclination wells (Wells 1 and 2) fell within design is concerned, is associated with the dogleg
range from 0.21 to .0.30. severity in the vertical hole portion of the well.
* The average borehole friction factors for wells
1, 2 and 4, calculated for running-in
conditions were from 0.38 to 0.43.

129
6 FIELD COMPARISON OF 2-D AND 3-D METHODS FOR THE BOREHOLE FRICTION EVALUATION IN DIRECTIONAL WELLS SPE 16663

3. Borehole friction factor vs depth CONCLUSIONS

The results from Wells 1, 2 and 3 proved no All the findings of this research can be
correlation between the calculated value of the summarized as follows:
borehole friction factor and depth as indicated by
the small values of the coefficients of 1. The borehole friction factor appeared fairly
determination and the regression coefficients in insensitive to measured depth, various well
Table 3, at the level of confidence 95%. Stability trajectories, size of pipe and its surface.
of the method was further supported by the low The borehole friction factor values, for most
values of standard deviations. Moreover, the cases were 0.21-0.30 for pulling conditions,
inherent scatter of the calculated values was and 0.27-0.43 for running conditions. The
largely reduced at greater depths as shown in Fig. latter were always 10-37% larger due to non-
13, for Well 2. This plot shows a convergence of the frictional phenomena resisting downward pipe
borehole friction factor values with increasing movement in the open hole. These effects have
depth. Similar plots were obtained for Wells 1 and not been yet modelled.
3.
2. The two-dimensional approach tended to
overestimate values of the borehole friction
4. Effect of well trajectories factor. When used for the running axial loads
calculations, at the well planning stage, it
The insensitivity of the borehole friction will underestimate predicted axial loads. The
factor to the well trajectory was demonstrated by 2~D model cannot be used for field assessment
similar values obtained for different wells having of the borehole friction factor unless the
various trajectories (see well descriptions and directional survey shows no shallow doglegs
Table 3). However, more field data from the same with a significant value of their bearing angle
area, and with the same drilling mud, is required to component.
come to more definite conclusion.
3. Two factors positively affect the borehole
friction assessment accuracy; the overall
5. Effect of the type of string in the well inclination, and the measured depth. Therefore
the measurements taken at shallow depths in
In Wells 1 and 2 the hook load was recorded for slightly deviated holes should not be used for
the casing, the drill string and for the wireline prediction in deeper and more inclined wells.
tool runs. Each type of string was characterized
by different surface configurations and external 4. The further investigations should provide more
diameters. Analysis of the results indicated field information from v~rious areas and
insensitivity of the borehole friction factor, drilling muds. Also a laboratory study on the
calculated from the pulling out loads to these mud cake effect on the pipe-borehole friction
differences as shown in Table 3. seems a logical next step in this research.

6. Hook load error effect ACKNOWLEDGMENTS

The theoretical effect of the measured hook The authors would like to thank Standard Oil
load on the calculated value of the borehole Production Company-Lafayette District, Exxon Company
friction factor is shown in Fig. 21. It can be USA-New Orleans, Mobil Oil Exploration and
noticed that, for low inclination wells, small Production Southeast Inc.-New Orleans, for help in
changes in the recorded hook loads may significantly recording the field data.
affect the calculated values of the borehole
friction factor. Thus the reliability of the method Grateful appreciation is given to TOTCO,
increases in more deviated holes. Also, the Martin-Decker, NCI Dillon, Ray Oil Tool Company for
importance of accurately measured hook loads is their assistance and equipment support.
further emphasized.
NOMENCLATURE

The above statement was further verified by the Unit vector in the binormal direction
field results obtained in Wells 1 and 3. In these Mud clinging constant
wells, the borehole friction factor calculated from Contact surface correction factor
the running-in loads was used to predict the pulling Measured depth, ft
loads- Figs. 10, 17. In both wells, the predicted External diameter of the pipe, in
loads were about 7% higher than the recorded ones. Borehole diameter, in
This relatively small hook load difference was Pipe deformation due to borehole
associated with some changes in the borehole reaction, in.
friction values calculated from pulling and running Modulus of elasticity, lbf/in2
conditions: for Well 1 (inclination 39°), from 0.27 Axial load, lbf
to 0.43; and for Well 3 (inclination 16°), from 0.44 Hydrodynamic viscous drag, lbf
to 0.83. Therefore, the same relative change in the Hook load, lbf
hook load implied much smaller change of the Flow friction factor
borehole friction factor in the high-inclination Consistency index, dyne.sn/100 cm2
Well 1 than in the low inclination Well 3. Pipe section length (same external
diameter), ft

130
SPE 16663 Maidla E. E. & Wojtanowicz A. K. 7

R, Length of pipe, ft 9. Bol, G. M., Effect of Mud Composition On Wear

M Number of sections of different external And Friction of Casing and Tool Joints, SPE
diameters Drilling Engineering, Oct. 1986, pp 369-376.
N Number of surveyed points
NRe Reynolds number 10. Bourgoyne, Jr., A. T., et al., Applied Drilling
n Flow-behavior index Engineering, SPE Texbook series, Vol. 2 Society
p Pressure, psi of Petroleum Engineers, Richardson, TX, 1986
dp/dt Pressure gradient due to flow friction, pp. 167' 153.
psi/ft
p Unit vector in the principal normal 11. Kreyszig E., Advanced Engineering Mathematics,
direction John Wiley and Sons, New York, 1983, p 375-376.
Q Buoyant weight, lbf
Qv Vertical projected buoyant weight of 12. Craig Jr., J. T., Randal, B. V., ''Directional
pipe, lbf Survey Calculation", Petroleum Engineering,
q Unit buoyant weight of pipe, lbf/ft March 1976. p. 38-54.
qb Unit buoyant weight projection on the
binormal direction, lbf/ft 13. "The Rheology of Oil-Well Drilling Fluids" API
qD Unit drag or rate of drag change, lbf/ft Bul. 13D, American Petroleum Institute, Dallas,
qN Unit buoyant weight projection on the TX, Aug. 1980 p.23.
principal normal direction, lbf/ft
qu Unit buoyant weight projection on the
tangent direction, lbf/ft 1\PPENDIX A
R Radius of curvature, ft
t Pipe wall thickness, in Hydrodynamic Effects
u Unit vector in the tangent direction
Vp Pipe velocity, ft/s The hydrodynamic effects are considered by
Vae Equivalent displacement velocity, ft/s calculating surge or swab pressures associated with
X X-coordinate of intersection point, in drilling mud flow, caused by pipe movement in the
y Y-coordinate of intersection point, in borehole. The pipe is assumed close~ended. The
a Inclination angle, rad calculation procedure is based on the theory of
a; Average inclination between two surveyed viscous drag for Power - Law fluids in boreholes [6]
points, rad [ 7] [ 10] [ 13] • The inertial forces and transient
s Overall angle change, rad effects are ignored. The calculation procedure
y Contact angle, rad includes:
0 Pipe-borehole ratio
e Bearing angle, rad 1. Calculation of the mud clinging constant for
p Mud density /gal the laminar flow [6],
].IB Borehole friction coefficient 2
2
o -2o lno-1
cc 2
(12)
2(1-o ) lno
REFERENCES

1. Johancsik, C. A., et. al., "Torque And Drag In and for the turbulent flow [10],
Directional Wells - Prediction And
Measurement", SPE 11380, 1983.

2. Sheppard, M. C., "Designing Well Paths

Reduce Drag And Torque", SPE 15463, 1986.
To
cc
!li-
1+o
62
(13)

3. Bratovich, et al., "Improved Techniques For

Logging High-Angle Wells", SPE 6818, 1977. where o represents a ratio of the pipe
diameter to the borehole diameter
4. Wojtanowicz, A. K., Maidla, E. E., "Minimum
Cost Casing Design for Vertical and Directional 2. Calculation of the equivalent displacement
Wells", SPE 14499, 1985. velocity [ 7] ,

5. Maidla, E. E., Wojtanowicz, A. K. ," Field 02

Method of Assessing Borehole Friction For \) \)
(14)
ae p ( 1-o + cc)
Directional Well Casing", SPE 15696, 1987.

6. Fontenot, J. E., Clark, R. K., "An Improved and the Reynolds number,
Method for Calculating Swab and Surge Pressures
and Circulating Pressure in a Drilling Well", p \) 2-n dB-d n
SPEJ, Oct 1974, p .• 451-62. 4 ae n
NRe 10.9•10 -K-- ) (15)
48 2n+l
7. Burkhardt, J. A., "Wellbore Pressure Surges
Produced by Pipe Movement", JPT, June 1961, p. 3. Calculation of the critical values of the
595-605; Trans.'· AIME, 222. Reynolds number [13],

8. Taylor, H. L., Mason, C. M., "A Systematic

Approach to Well Surveying Calculations", SPE
3362, 1971.

131
8 FIELD COMPARISON OF 2-D AND 3-D METHODS FOR THE BOREHOLE FRICTION EVALUATION IN DIRECTIONAL WELLS SPE 16663

* The contact surface is defined as shown in Fig.

20 i.e. it is controlled by the length of an
3470 - 1370 n (16) arc between interception points of the two
circles.

NRe 2 = 4270 - 1370 n (17) Initially, the circles are internally tangent
then the smaller circle is shifted by the value
4. Decision whether flow pattern is laminar, of pipe deformation ~d
transitional, or turbulent based on the
logical elimination; The approximate pipe deformation in the
direction of the applied normal force is
5. Calculation of the friction factor by
solving the Dodge and Metzner equation (23)

~=
f
4
0 • 75
log (N
Re
f1-0.5n) 0.395
- """T:"2'""
( 18 ) The distributed normal force is given by Equ. (4).
n n Let us consider Cartesian plane x-y normal to the
pipe at point i The point (0.0) i~ assumed at
6. Calculation of the frictional pressure the borehole centerline. The intersection points
losses for the laminar flow coordinates are

K 48 2n+1 ) n
(19)
d -d • n y (24)
B

or for the turbulent flow

X (25)
2
f vae P
21.1 (dB-d) (20)
Finally, the contact angie is

For the transitional flow both laminar and y larc tan ( ZX )I (26)
turbulent pressure losses are calculated and the 2Y-dB+d
larger value is chosen.

APPENDIX B

Effect of the Contact Surface

Consider a cylinder, size d, sliding in a pipe

of the same size. When applying a normal force Fn,
the resulting drag FD can be found by integrating
the small pressure area elements along the surface
of contact. The result is

(21)

In this scenario, the value of correction

factor is 4hr , which means that the actual drag is
4/n times larger than that for the flat contact
surface. In our case, the pipe diamet~r is smaller
than the borehole diameter. Thus

The contact surface correction factor C8 in equ.

(22), depends upon the contact angle y

The. following simplifying assumptions are used

to estimate the contact surface angle~

* Pipe deformation is elastic.

* Th~ contact surfac~ assumes a shape of the
borehole.
* There is a linear relation between contact
surface correctio;-u.; faetor and the contact
angle.

132
 TABLE 2 TABLE 3
TABLE
STUDY OF THE HYDRODYNAMIC FRICTION EFFECT
SIGN CONVENTION IN EQUATION 8 FIELD STUDY SUMMARY AND STATISTICS

BOREHOLE FRICTION FACTOR USING

P.s P.s Coef. of Reg.Coef. Stand.
Borehole Pipe 3-D MODEL WITHOUT HYDRODYNAMICS CONSIDERED * Well No. Remarks Model
Run. ln Pui.Out De f. 6 1 Dev.
Section
Operation
Position
c, c2 10 Ff

INCLINATION ( DEG) Casing 3-D 0.43 0.27 0.036 5 0.045-

Build-up Pulling Upper +l -I 2-D 0.44 0.28 0.078 7 0.045
BIT WALK
10 20 30
Lower +I +I ( DEG/100 FT)
I

I
Drill-
string
3-D - 0.21 - - )-
Running Upper +I +I 0 0.599 0.524 0.506
2- D - 0.24 - - -
.4 0.599 0.524 0.506
Lower +I -I
. 8 0.594 0.523 0.505
Core
Guns
3-D 0.27 0.30 - - -
Drop- off Pulling Lower -I +I 1.2 0.588 0.521 0.505
I

I
2-D 0.29 0.33 - - -
-I -I 1.6 0. 581 0.518 0.504
Running Lower
2.0 0.574 0.516 0.503 Casing
3-D 0.43 - 0.007 2 0.050
L_ - -- - -- - - L_ - - - -

2.4 0.568 0.513 0.502

2-D 0.46 - 0.006 -2 0.051
2
--·----
Dri II- 3-D - 0.25 - - -
string
*3-D Model Value = 0.40 2 -D -· 0.28 - - -
TABLE 4
3-D 0.83 0.44 0.016 12 0.183
3 Casing
WELL # 1 - CASING 2-D 1.14 0.64 0.025 -17 0.214

COMPARISON OF THE MODELS USING FIELD DATA

----------------------------------- • 4 Casing
3-D 0. 3.8 - - - -
DATA USED: .MUD DENSITY: 10.80 LBF/GAL
2-D 0.4'7 - - - -
.CONSISTENCY INDEX: 124.9 EQCP
.FLOW-BEHAVIOR INDEX: 0.781
.BIT DIAMETER: 9.875 IN
c.> .PREVIOUS CASING DIAMETER: 10.750 IN
c.>
.PREVIOUS CASING DEPTH: 3210. FT TABLE 5
.STRING BREAK DOWN:
------------------------------------ WELL # 1 - DRILLSTRING
DEPTH OD ID WEIGHT REMARK
(FT) (IN) (IN) (LB/FT) COMPARISON OF THE MODELS USING FIELD DATA TABLE 6
------ ----- ----- -------
5390. 7.625 6.875 29.70 LTC WELL # 1 - CORE GUNS
10267. 7.625 6.640 33.70 LTC DATA USED: .MUD DENSITY: 10.80 LBF/GAL
11232. 7.625 6.500 39.00 LTC .CONSISTENCY INDEX: 124.9 EQCP COMPARISON OF THE MODELS USING FIELD DATA
.FLOW-BEHAVIOR INDEX: 0.781
RESULTS: .BIT DIAMETER: 9.875 IN
------------------------------------------------- .PREVIOUS CASING DIAMETER: 10.750 IN DATA USED: .MUD DENSITY: 10.80 LBF/GAL
INPUT DATA BOR. FRIC. FACTOR • PREVIOUS CASING DEPTH: 3210. FT .CONSISTENCY INDEX: 124 •. 9 EQCP
----------------------------- ----------------- .STRING BREAK DOWN .FLOW-BEHAVIOR INDEX: 0.781
CASING MEASURED MODE PIPE 3-D 2-D .BIT DIAMETER: 9.875 IN
SHOE HOOK VELOC. MODEL MODEL DEPTH OD ID WEIGHT REMARK .PREVIOUS CASING DIAMETER: 10.750 IN
DEPTH LOAD (FT) (IN) (IN) (LB/FT) .PREVIOUS CASING DEPTH: 0. FT
(FT) (LBF) (FT/S) ------ ----- ----- ------- • STRING BREAK DOWN:
------ -------- ---- ----- ------ ---- 9646. 5.000 4.276 21.40 PIPE
ID WEIGHT REMARK
4579. 108800. IN 1.7 0.36 0.38 11166. 5.000 3.000 49.30 HWPIPE DEPTH OD
4619. 109000. IN 2.0 0.36 0.37 11270. 7.000 2.813 110.00 BHA (FT) (IN) (IN) (LB/FT)
4659. 108400. IN 2.0 0.41 0.42
4699. 114000. IN 0.5 0.31 0.32 RESULTS: 10600. 0.500 0.0 0.35 CABLE
4897. 113100. IN 2.1 0.34 0.36 10630. 3.000 0.0 16.67 C.GUNS
4897. 144100. UP 1.0 0.25 0.26 INPUT DATA BOR. FRIC. FACTOR
5135. 113500. IN 2.0 0.44 0.45 ---------------------------- ----------------- RESULTS:
5175. 114000. IN 1.5 0.47 0.48 CASING MEASURED MODE PIPE 3-D 2-D
5294. 114200. IN 2.0 0.47 0.48 SHOE HOOK VELOC. MODEL MODEL INPUT DATA BOR. FRIC. FACTOR
5371. 115100. IN 2.0 0.47 0.48 DEPTH LOAD ----------------
5407. 113900. IN 2.0 0.52 0.53 (FT) (LBF) (FT/S) CASING MEASURED MODE CABLE 3-D 2-D
5605. 115300. IN 2.0 0.54 0.55 ------ -------- ---- ----- SHOE HOOK VELOC. MODEL MODEL
5882. 128400. IN 0.1 0.42 0.43 11250. 269000. UP 4.0 0.21 0.24 DEPTH LOAD

~
5924. 130000. IN 0 .• 1 0.40 0.41 (FT) (LBF) (FT/S)
5924. 174900. UP 0.7 0.29 0.30 EQCP = DYNE.SN /lOO.CM
2 ------ -------- ---- ---- ------ -----
5924. 127000. IN 0.5 0.43 0.44 10070. 4200. UP 0.7 0.30 0.32

'"
t-'
5964.
6385.
6912.
7079.
125900.
133800.
135800.
134100.
IN
IN
IN
IN
2.0
0.5
0.6
2.2
0.38
0.39
0.46
0.43
0.39
0.41
0.47
0.44
10200.
10260.
10260.
10270.
4400.
2400.
4100.
2200.
UP
IN
UP
IN
0.7
0.7
0.7
0. 7
0.32
0.23
0.25
0.32
0.35
0.24
0.2S
0.34
0' 7157. 136800. IN 0.7 0.47 0.49 10270. 4400. UP 0.7 0.31 0.34
--------------------2 10350. 4500. UP 0.7 0.32 0.35
0' EQCP = DYNE.SN/lOO.CM -------------------
EQCP = DYNE. SN /100. C~
0"
u.a
 TABLE 7 TABLE 9
WELL # 2 - CASING WELL # 3 - CASING

COMPARISON OF THE MODELS USING FIELD DATA COMPARISON OF THE MODELS USING FIELD DATA

DATA USED: .MUD DENSITY: 10.70 LBF/GAL DATA USED: .MUD DENSITY: 9.30 LBF/GAL
.CONSISTENCY INDEX: 300.9 EQCP .CONSISTENCY INDEX: 125.7 EQCP
.FLOW-BEHAVIOR INDEX: 0.619 .FLOW-BEHAVIOR INDEX: 0.688
.BIT DIAMETER: 9.875 IN .BIT DIAMETER: 9.500 IN
.PREVIOUS CASING DIAMETER: 10.750 IN .PREVIOUS CASING DIAMETER: 10.750 IN
.PREVIOUS CASING DEPTH: 2000. FT .PREVIOUS CASING DEPTH: 3800. FT
.STRING BREAK DOWN: .STRING BREAK DOWN:

DEPTH OD ID WEIGHT REMARK DEPTH OD ID WEIGHT REMARK

(FT) (IN) (IN) (LB/FT) (FT) ('IN) ' (IN) (LB/FT)
315. 7.000 6.276 26.00 LTC 11538. 7.625 6.875 29.70 LTC
5005. 7.000 6.366 23.00 LTC
5912. 7.000 6.366 23 .. 00 LTC RESULTS:
9610. 7.000 6.276 26.00 LTC
INPUT DATA BOR. FRIC. FACTOR
RESULTS:
CASING MEASURED MODE PIPE 3-D 2-D
. INPUT DATA BOR. FRIC. FACTOR SHOE HOOK VELOC. MODEL MODEL
DEPTH LOAD
CASING MEASURED MODE PIPE 3-D 2-D (FT) (LBF) (FT/S)
SHOE HOOK VELOC. MODEL MODEL
DEPTH LOAD 5922. 132000. IN 2.0 1.03 1.47
(FT) (LBF) (FT/S) 6004. 135000. IN 2.0 0.76 1.16
6174. 137000. IN 2.0 0.91 1.30
2981. 60500. IN 2.0 0.26 0.31 6257. 140000. IN 2.0 0.69 1.05
3140. 61500. IN 2.0 0.43 0.49 6300. 139000. IN 2.0 0.93 1.31
3576. 67000. IN 2.0 0.34 0.38 6717. 148000. IN 2.0 0.72 1.04
4060. 69500. IN 2.0 0.43 0.48 7093. 154000. IN 2.0 0.75 1.05
4144. 69000. IN 2.0 0.48 0.53 7799. 166000. IN 2.0 0.72 1.00
4515. 73500. IN 2.0 0.38 0.41 7927. 174000. IN 2.0 0.39 0.63
4686. 72500. IN 2.0 0.45 0.48 9400. 192000. IN 2.0 0.68 0.93
4905. 72500. IN 2.0 0.47 0.51 9400. 277000. UP 2.0 0.38 0.58
5197. 74000. IN 2.0 0.45 0.48 9442. 192000. IN 2.0 0.70 0.96
5719. 77000. IN 2.0 0.42 0.45 9656. 192000. IN 2.0 0.81 1.08
5895. 75500. IN 2.0 0.47 0.49 9741. 195000. IN 2.0 0.75 1.01
6108. 78000. IN 2.0 0.43 0.45 9741. 294000. UP 2.0 0.49 0.70
6286. 75500. IN 2.0 0.49 0.52 9828. 192000. IN 2.0 0.89 1.17
6628. 81000. IN 2.0 0.41 0.43 9911. 192000. IN 2.0 0.93 1.21
6801. 78000. IN 2.0 0.47 0.50 10039. 195000. IN 2.0 0.88 1.16
7024. 80500. IN 2.0 0.44 0.46 10039. 302000. UP 2.0 0.45 0.65
7202. 85000. IN 2.0 0.38 0.40 10079. 194000. IN 2.0 0.93 1.22
7556. 85000. IN 2.0 0.41 0.43 10209. 194000. IN 2.0 0.98 1.27
7732. 85000. IN 2.0 0.42 0.45 10380. 198000. IN 2.0 0.93 1. 20
7909. 86000. IN 2.0 0.42 0.44 10508. 203000. IN 2.0 0.83 1.09
8081. 87500. IN 2.0 0.41 0.44 10593. 203000. IN 2.0 0.86 1.13
8258. 88000. IN 2.0 0.42 0.44 10674. 203000. IN 2.0 0.89 1.16
8432. 88000. IN 2.0 0.43 0.46 10761. 206000. IN 2.0 0.84 1.10
8592. 91500. IN 2.0 0.41 0.43 10845. 206000. IN 2.0 0.87 1.13
8808. 92000. IN 2.0 0.42 0.44 10974. 211000. IN 2.0 0.79 1.04
8985. 91000. IN 2.0 0.44 0.47 11101. 209000. IN 2.0 0.88 1.14
9161. 91000. IN 2.0 0.46 0.48 11189. 213000. IN 2.0 0.81 1.06
9205. 92500. IN 2.0 0.44 0.47
2 EQCP = DYNE. sN /100, CM2
EQCP = DYNE, SN /100. CM

TABLE 8 TABLE 10

WELL # 2 - DRILLSTRING WELL # 4 - CASING

COMPARISON OF THE MODELS USING FIELD DATA COMPARISON OF THE MODELS USING FIELD DATA

DATA USED: .MUD DENSITY: 10.70 LBF/GAL DATA USED: .MUD DENSITY: 10.20 LBF/GAL
.CONSISTENCY INDEX: 300.9 EQCP .CONSISTENCY INDEX: 143.4 EQCP
.FLOW-BEHAVIOR INDEX: 0.619 .FLOW-BEHAVIOR INDEX: 0.726
.BIT DIAMETER: 9.875 IN .BIT DIAMETER: 9.875 IN
.PREVIOUS CASING DIAMETER: 10.750 IN .PREVIOUS CASING DIAMETER: 10.750 IN
.PREVIOUS CASING DEPTH: 2000. FT .PREVIOUS CASING DEPTH: 3334. FT
.STRING BREAK DOWN: .STRING BREAK DOWN:

DEPTH OD ID WEIGHT REMARK DEPTH OD ID WEIGHT REMARK

(FT) (IN) (IN) (LB/FT) (FT) (IN) (IN) (LB/FT)

4103. 4.500 3.640 22.10 PIPE 8967. 7.625 6.625 39.00 LTC
9337. 4.500 3.826 18.40 PIPE
9610. 7.000 2.813 110.00 BHA RESULTS:

RESULTS: INPUT DATA BOR. FRIC. FACTOR

INPUT DATA BOR. FRIC. FACTOR

-----------------------------
CASING MEASURED MODE PIPE
-------------------
3-D 2-D
-----------------------------
CASING MEASURED MODE PIPE
-----------------
3-D 2-D
SHOE
DEPTH
HOOK
LOAD
VELOC. MODEL MODEL

SHOE HOOK VELOC. MODEL MODEL (FT) (LBF) (FT/S)

DEPTH LOAD --------
(FT) (LBF) (FT/S) 8967. 160000. IN 2.0 0.38 0.40
--------
9610. 194000. UP 2.0 0.25 0.28 EQCP = DYNE, SN /100, C~
2
EQCP = DYNE. SN /100. CM
134 IPE1666J
 EAST

.rz::;~~::.
VERTICAL BUILD UP RATE
DEPTH
2 DEG./IOOFT
TRIHEDRON:
u: Tangent Unit Vector
p:Principal Normal Unit Vector
b: Binormal Unit Vector

0.50

0.49

0::: 0.48
Fig. 1-Forces acting on a small casing element within the buildup section. ~
() 0.47
~
u 0.46

~ 0.45
HORIZONTAL REFERENCE, lOx FEET w
~ 0.44
~ 00 80 00 160 00 21!0 00 320 00 1!00.00
J:
~ 0.43 2.4
I I
«-"
1-
LLJ
g
---l 0
OJ 0.42 2.0
1.6 &
LLJ
LL.
·- 0.41
1.2
~
c:i"

-~
X
0.8 <::>
0 0 ~"
0 0
0.4 'V
0
~'I:('
~~~
--l-
0.0

~~
10 /..,
J:
1- 0 ~
a. 0

~- ---~~:_ ) \~~
LLJ Fig. 4-Sensltivlty of the 2·0 model to bltwalk rates and slant hole Inclinations.
0
...J
<X
u
1-
0
0
-~-----v
2.4 2.0 1.6
_J
1.2
\ "'~~
0.8 0.4 0
ll:
LLJ
> 0
0
,-------
--r--T---
BIT WALK I DEG/ 100FT I

Fig. 2-Vertical section of the computer-generated well trajectories.

0.550
BUILD-UP RATE = 0.5 deg/1 OOft
TOTAL VERTICAL DEPTH = 8000 ft
0 KOP = 2000 ft
0
EAST DEPARTURE, _10 x FEET MAX. INCLINATION = 20 deg
~.00 50.00 100 00 150 00 200 00 250.00 0::: 0.525
0
1--
u
~
0.500
z
0
i=
u
0::: 0.475
l.L
w
_j
0
:r: 0.450
w
0:::
0
m
0.425

0 2 3 4 5 6 7 8 10

f - - - - -----
DOGLEG SEVERITY, deg/1 OOft
0
0
~~--~--~--_L_ __ L_ __ L_ __ L_ __ L_ __ L_ _~--~ Fig. 5-Sensltivlty of the 2·0 model to horizontal doglegs.

Fig. 3-Horlzor\tal section of the computer-generated well trajectories.

135 SPE 16 663

 LOUISIANA

)(

I
I
\
~
I
I
I~
I
I
I
I I
I

WEL~
I
I
I

\ I
3
\I WELLS
I
I
I
I
184
I
I
I
I WEST
\ CAMERON 0
\

\
AREA
EAST
c
I CAMERON
I AREA VERMILION
I
I
AREA
E
\
\
I AREA l
,-----L_.f _____ j.. __ L..J __ lJ... _____ .l.r-I
.fJ"l._L__j SCALE:

L__ _r-"' 0 F
u L F

LOUISIANA GEOLOGICAL SURVEY

Fig. 6-Rig locations used in field study.

136
SP'E 16 6 6.3
 EAST DEPARTURE, FEET HOOK LOAD, LBF
1--LLJ
LLJ
IJ..

w
a::
-5000
-1600~--,---~~-------.~--.----.---,.---,----.----,
-3000 ·-2000 -1000 0

a
a
a
o.

N
--------1-..
1000.

I
2000.

I
1
•
3000.

Measured R~nning
' I Load
Measured Pulling Load
1--- Predicted Hook Load
I
YOOO

.
5000.

~ - 600 1----+---1 N

0::: 1--
LLJ
I I
ctLLJ
!\~:
iI !
LLJ
LL a
a ; ! !
a
0 A ::1"
!
400 :r: I

1-- i
:I:
a. ! i
1--
::::>
·o
LLJ
0
a
a
a
I \i \
\ !
I
i
I

\
CD
en 0
f\ I\ I
\ \ \lt
LLJ
0:::
Fig. 7-Well 1-horlzontal section and directional survey data. ::::> a
a
8 .;0.29
(f) a
\
"{
CD
<t I! fLa =0.• 29 \
i
LLJ \
:::!!:
HORIZONTAL DEPARTURE, FEET a
a
a 1\•\. ~
"""'
0 1000 2000 3000 4000 5000 a

fLa=O ·~~·r
a
a
a
2000 \ N

w~4
1--
LLJ
LLJ
\. /
3260
r----
.s-u-9~
()()
Fig. 10-Well1-measured and predicted hook loads for the core guns run.

IJ..
4000 ~10, I ~ll.,.
1--
EAST DEPARTURE, FEET
~, J ~~ LLJ
:I:
1-- 6340 ~~.,. LLJ
a..
LLJ 6000 ' 1'-><r-=-:.:=: IJ..

LLJ
0
~ 0:::
::::>
_J r--.... 1--
<t ~Q-
(.)
- 8000
""~ 0:::
~
1--
0:::
LLJ \ LLJ
0
>
10000
\ :I:
1--
::::>
~ 0
f T en
Fig. 11-Well 2-horizontal section and directional survey data.
12000

HORIZONTAL DEPARTURE, FEET

Fig. S-Well 1-vertical section and measured depths. 1000 2000 3000 \1000 5000.

HOOK LOAD I LBF

a
80000. 160000. 2YOOOO. 320000. YOOOOO. a
,-a
-~ I • ~easu1red R!nni nJ Loa)
.. Measured -
Pulling Load
a
a
a
'\. - - Predicted Hook Load a
a
a
N
2000

'~
N

1-- 1-- \
LLJ LLJ ~
LLJ
IJ..
a
a
a
~ LLJ
IJ..
a
a
a
\ .

~ill. ~«'
~IS\
"' \"
\~ (/~
::r
:I:
1--
:I: \.. ~
1--
a.
LLJ a
a
~\ ~ a..
LLJ
a
a
a
'\ Ia~;();.
0
~~
a 0
~\ "f: 8 =0.43
::r

~
CD

I
"" """,/
0 :• ...J
LLJ <t ~;~;.
0:::
::::> a
a
a
\ \ "I\. (.)

1--
a
a
a
.
"'
I~ '\,
(f) CD
0:::

,..
<t fLa=0.43 \
LLJ
~ \
LLJ
> ""'l'-..
"" "\
a

"" "'
a a
a
a
a
\ a
809~
~e=O
CD
'\
/
a
a
a
N
a
a
a
,....
\
\
Fig. 9-Well 1-measured and predicted hook loads for the casing run. a 96LQ \

sP·E 16 6 63
0
a ·-
CD

Fig. 12-Well 2-vertical section and measured depths.

137
 HOOK LOAD, LBF EAST DEPARTURE, FEET
8aaaa. 16aaaa. 211aooo. 32aaoo. 1100000. -80 320 720
0
I I I I I
Li J\
I
• Measured Running Load -..... 7001
Predicted Hook Load - DLS = 1.20
0 \ . ~ ~ . DLSh = 0.60

\210~
0
0

1\ \
N

1-
IJJ 400 DLS = 2.40

BOREHOLE FRIC. FACTOR

IJJ
LL
A
0
0
0
\'[\ 1--
\
DLSh=2.31

5360

'~\
:I:
::r IJJ
~.aaa a. 2aa a.11aa a. 6aa a. 8aa l. aaa
I-
IJJ
LL
DLS = 1.65
c.. DLSh = 0.53
IJJ
c ~
0
\\ IJJ
0::: 800
\"- .......... 7500 ~
I

\
\
0
0
0
c
IJJ
\ i\.,U.B = 0.43
I-
:::> DLS = 1.11
DLSh = 0.67
0:::
"' 0:::
:::> g
(f) ~
~
1\ \1\. <t
c..
IJJ
\
1\ \
1-
IJJ
IJJ
LLg
0
0
0
::r
<t
IJJ
~
0
0
0
0
,u-8=0.43
I
I JLe=O "' """ 0

:::r:
I-
:::>
0
1200

\
:I:
1-
c..
~If)

0
0
0
(\J
(f)

1600 \\ 11540
LLJo
0~
0
Fig. 14-Well 2-measured and predicted hook loads for the casing run.
"' Measured Depth, Feet
I
0 DLS : Dogleg Severity
IJJ
DLS : Bearing Angle Contribution to DLS
0:::
Co> :::>:5 2000 I I I I
CD ({);2
<X Fig. 15-Well 3-horizontal section and directional survey data.
IJJ
~
0 HORIZONTAL DEPARTUR~, FEET HOOK LOAD, LBF
0
0

"'
1100 800 120a 1600 2000. o. 8aaao. 160000. 2110000. 320000. 1,100000.
I
~
I I I I I
• Measured Running Load
J • Measured Pulling Load -
0
0
0 2100 I \ - Predicted Hook Load
L~ ~
0 0
m 0 0
0 0

~ - ~820f- ~~"9
I

\
(\J (\J

I-
I- IJJ
0
v,=-==-
~
0 IJJ IJJ
0
0 IJJ 0 LL 0
u. 0
0 ~++--,_--r--~~ +--4--~--r-- 0
0

~Q_ ~~ ~~
'

::r A
A

:I: \ :::r:
I- I-
Fig. 13-Well 2-stability of the borehole friction factor.
c..
c..
IJJ
0
0 \ lo~
~-+~~--r--r--~,- ~
IJJ 0
~~ 1\. ,u. 8 =0. 83
c ~ c ~
....I
<t
~
~
7500 -<'
~~~4-~--~
c
IJ.J
\ \'\
u 0::: ,u-8=0.83' \

·"'1\'
0
- 0 :::> g \
U) I- ~ (f)
~,
0

-o 0::: <t
.\ \
""
.rn IJJ IJJ

J--oA
>; "~
~
0
0
0
-~ ~
...
0' "~ \ \ ~ I
0' - - - 1 - + - - - ·--- !!MQJ> \
"
0
0
0 \,u.B=O
0' 0
(\J ~- I
0
0
(\J

Vol
Fig. 16-Well 3-vertical section and measured depths. Fig. 17-Well 3-measured and predicted hook loads for the casing run.
 EAST DEPARTURE, FEET
g3200 -2~00 -1600 -BOO BOO.
I I
I 11Measured Depth, Feet
D LS : Dog leg Severity
1850 I
DLS =4.74
DLsh: Bearing Angle Contribution
1- to DLS y'~ IDLSh = 1.50
LLJo
w:2 / I
LL. L
376o•
V DLS = 0.25- t - -
LLJ DLSh = 0.25
O:::o
:::>~
~ 4980
.... -
- 1 - - -1---
/ DLS = 3.09
J ~.=0.77_ r---- t--··-
v
0:::
<X
a.. 0
LLJg DLS = 0.94
0~ DLS = 0. 78
/
~
I ~~-
DLS = 4.35
DLSh = 0
0
0
~ I I
"'
"'

Fig. 18-Well 4-horizontal section and directional survey data. Fig. 20-Surface of contact between borehole and pipe.

HORIZONTAL DEPARTURE, FEET

1000 2000. 3000. 4000. 5000.
1

0
-~~700 -
I ~1.04
loo* ;
l~ I
LS= I. 4''2~--1---t---t----i
LSh=l.42
g_ i - f - ·oLSh= 1.0~~+--+--t---+--+--t----1
INCLINATION 10 20 30 40 60
1.00 (deg) 50

0.90

0.80
a:::
f2 0.70
u
~
. 0.60
u
~
_J LL. 0.50
<X La.J
() _J
0

~ 0.40
0
0
1- Ill
0::: La.J
0::
LLJ
> g 0.30
0
0
0
UJ
0.20 BUILD-UP RATE: 2 deg/1 OOft
MEASURED DEPTH: 8000 ft
KOP = 2000 ft
0
0
0.10
0
..... *Measured Depth, Feet
DLS: Dogleg Severity, 0/100 Ft
0. 00 -+-,..t.........~~-.L+-.-r"""'T""-r--r--.--..,..-,--r-r-r--r--r--.--T"'""T"-r-T"""T"-r-"1r-r-1
- DYh' erring tngle contri(utionl to oLis 160 260 360 460
0
0
0
1 HOOK LOAD, 1OOO.Ibf
OJ

Fig. 19-Well 4-vertlcal section, measured depths and directional survey data. Fig. 21-Sensltlvlty of borehole friction factor to hook loads and well Inclinations.

139
SPE 16 663