schuh1989 (1)

SPE. 20150

NEW MEXICO TECH CENTENNIAL SYMPOSIUM

Horizontal Well Planning-Build Curve Design

Frank J. Schuh, Drilling Technology, Inc.

Copyright 1989, Society of Petroleum Engineers, Inc.

This ·paper was prepared for presentation at the Centennial Symposium Petroleum Technology Into the Second Century at New Mexico Tech, Socorro, NM, October 16-19, 1989.

This paper was s~lected for present~tion by the N~w Mexico Tech Centennial Symposium Committee. Contents of the paper, as presented, have not been reviewed by the Society

?f Pe~roleum Engineers and are ~UbJect to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers,

~ts oH1~ers, or members. If submitted for publication, this paper is subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Permission to copy IS restncted 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

The goa 1 of most hori zonta 1 drilling projects is to place a long horizontal hole in a narrow verti- cal target. To accomplish this objective in the most economical manner, requires a build design that will hit the target without numerous bottom hole assembly changes and a rig that can handle the torque and drag 1 oads produced by the dri 11- string in the horizontal hole. This paper de·- scribes several methods for designing the build curve that offer improved methods for hitting a small horizontal target while using a single bot- tom hole assembly for the angle building portions of the ho 1 e. The paper a 1 so presents a nove 1 method for estimating the torque and drag forces for typical drillstrings in a horizontal hole.

Introduction

The two characteristics that most clearly differen- tiate horizontal drilling from conventional direc- tional drilling are the use of angle-build motors and specialized build curve designs. A good build curve design is nearly as important as selecting the best directional drilling contractor.

The optimum length for a horizontal hole is reached when . the incrementa 1 cost of addi t i ana 1 length is greater than the value of the production from the additional length. Since the productive performance cant i nues to increase with increasing length, the optimum is probably close to the maxi- mum 1 ength that can be successfully drilled. The mechanical limits for horizontal holes are primari- ly related to torque and drag 1 imits for the rig and dri 11 string equipment. To reach the maximum possible length, one needs to minimize the torque and drag forces. Since buckling and gravity References and illustrations at end of paper.

forces dominate the torque and drag effects in the horizontal hole, the optimum design requires the selection of the lightest possible dril1string components that wi 11 not be buckled during dri 1- ling operations.

Build Curve Design

The simplest possible build curve design is a single uniform curve that begins at the near verti- cal kickoff point and reaches go• at the end of the curve in a single continuous arc. If the variability of the performance of the angle-build motor provides an error in the vertical depth at the end of the curve that is less than the allow- ab 1 e to 1 e ranee of the hori zonta 1 target, this build curve design is in fact the optimum design.

Unfortunately, the variability and uncertainty of performance of most angle-build motors greatly exceeds the allowable tolerance of the hori zonta 1 targets. It, therefore, becomes necessary to design adjustment intervals in the build curve to compensate for these uncertainties.

Build curve design begins with a definition of the horizontal target. There are basically two types of horizontal targets:

a A defined vertical depth target a A defined structural position in a

reservoir

For horizontal wells in gas and/or water coning applications, it may be most effective to drill a truly horizontal hole in a TVD target that is 1 ocated a fixed distance from the gas/oil and/or water/oil contacts. For this type horizontal well the target angle will be go·.

2

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HORIZONTAL WELL PLANNING - BUILD CURVE DESIGN NMTECH 890008

The most common type horizontal target is not necessarily horizontal but is a lateral path _that tracks a specific structural position in the reservoir. For coning applications, this may be either the top or bottom of the reservoir. It also might be a specific position that has been selected to assure full communication with the reservoir from hydraulic fractures initiated at that depth. "Hori zonta 1" targets in these cases will not be hori zonta 1 but will attempt to track the selected structural position or be drilled a 1 ong a path that is expected to track the structural position. The allowable height of this path represents the target tolerance.

The purpose of the build curve design is to provide the operator with an efficient method of hitting the horizontal target within the pre- scribed to 1 erance without utilizing numerous BHA changes. The build curve design must provide a balance between the following considerations:

o Avoid problem formations.

o Minimize the displacement of the end of the curve.

o Minimize the drilled length of the build curve.

0

0

0 0

0

Provide an adjustment interval for han- dling other than the ideal build rate.

Allow the utilization of structural mark- ers encountered in the bu i 1 d i nterva 1 to adjust the final target depth.

Meet the target tolerance limits.

Provide a curve that will allow a full length horizontal hole to be drilled.

Provide a completable hole that will permit the use of all necessary production tools and equipment.

The optimum build rate for a specific horizontal hole must both provide the directional control needed to hit the target as well as a build curve height that avoids including troublesome forma- tions in the build interval. If, for example, an especially troublesome formation is located 850 ft above the horizontal target, one would probably select a kickoff point below that formation and use the remaining height to dictate the required build rate curvatures.

If one only considers the requirements of drilling the build curve, the best design will use the highest curvature rate that can be obtained.

Since the build curvature also affects all subse- quent operations, one needs to ba 1 ance the advan- tage of high curvature with the impact of that curvature on the future operations. Table I 1 i sts several of the curvature limits that should be considered.

If one p 1 ans to steer the entire hori zonta 1 sec- t ion and no production equipment or too 1 s wi 11 be run through the curve, the optimum build curve

will use the maximum available build rate. If the hori zonta 1 section is to be drilled with surface rotation, one should 1 imit the hole curvature to the curvature limit of the drill string compo- nents. Another important consideration is to provide a curvature that will not inhibit the selection of ordinary conventional production too 1 s during the comp 1 et ion and future production operations.

The following sections will cover three build curve types which we have identified as:

1. The simple tangent build curve;

2. The complex tangent build curve;

3. The ideal build curve.

The dimensions of these build curves can be calcu- lated from the geometric relationships of straight lines and circular arcs. For the simple tangent bu i 1 d curve where we intend to keep the too 1 face of the bent housing motor pointed up and maximize the angle building rate of the tool, the path can be described as a circular arc in a vertical plane. See Figure 1. The key equations for calculating the height, displacement and length of a vertical circular arc are:

R

v

H

L

5730 8

. . . • . . ( 1)

. . . ( 2)

R · (cos h - cos I 2) . . . (3)

100 · (I ^{2 -} h) 8 . . . ( 4)

For the complex and ideal build curves that uti- lize build and turn segments, the path can be approximated by the geometry of circular arcs projected to the vertical plane. See Figure 2. The key equations for the geometry of the build turn segments are: 5730 . . . ( 5)

. . . ( 6)

H . . . (7)

L . . . • . (8)

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NMTECH 890008 FRANK J. SCHUH

DL

=

(lz - l1) · BT . . . (9) .

cos DL - cos l1 · cos lz

. . (10) cos AAz

sin l1 sin lz

cos;=--Bv . . • . . • • • . . • . (11) BT

Lastly, the appropriate equations for the straight adjustment intervals are:

V = L · cos (12)

H = L · sin (13)

The Simple Tangent Build Curve

The oldest and most widely used build curve design is the simple tangent build curve. Figure 3 is a sketch of a typical simple tangent build curve.

The simp 1 e tangent build curve divides the build arc into two segments that are separated by a straight "tangent" adjustment interval. It is generally assumed that both build curve segments will be drilled with the same angl e-bui 1 d motor assembly and that the rate of bui 1 d in the second build will also equal the rate of build experi- enced while drilling the first build segment.

The concept for the simple tangent build curve comes from the observations that an angle-build motor will give highly consistent curvature perfor- mance on a given well in a specific area, even though its performance may vary significantly between wells with different target formations or in other areas. With this design, the operator utilizes the observed build curvature in the first build to calculate the most likely height of the second build and from that the required length of the tangent interval and depth of the second kick- off point. This reduces the error in hitting the end of curve target to the relatively small differ- ence between the actual and predicted heights of the second build curve. To be successful with this technique, it is essential that the kickoff point and the planned build curve be designed using the lowest possible build rate for the se- lected angle-build motor assembly.

Table 2 shows the step by step calculations re- quired to calculate the dimensions of the build curve design shown in Figure 3. The key decisions required of the designer are the curvature rates, the angle of the tangent i nterva 1 and the 1 ength of the tangent interval. The design build rate must be no greater than the minimum expected build rate for the angle-build motor selected.

If the actual build rate in the field exceeds the planned (minimum) rate, the length of the tangent

interval is adjusted so that the second build curve reaches the target if it builds at the same rate as the first curve. This limits the error in hitting the target to the difference between the actual second build and the adjusted planned sec- ond build. If the first build curvature on our example were actually 8.6./100 ft the planned second build height would be 155.9 ft. If the second build actually builds at 8.3./100 ft, the actual second build height would be 161.5 ft, which is 5.6 ft lower than planned. If a single curve without a tangent had been used, an error of .3°/100 ft would have missed the target by 26 feet.

Se 1 ect i ng the appropriate tangent 1 ength is very important because few of the tangent drilling assemblies actually drill at constant angles.

Fortunately, it is not necessary to drill a tan- gent interval at a constant angle provided one has a good judgement of the final angle at the bit.

The minimum recommended length of the tangent interval is 120ft. This is based on the typical MWD survey spacing and the desirability of minimiz- ing the tangent length. With a typical steerable MWD package used for dri 11 i ng the tangent inter- val, the MWD inclination sensor will be positioned about 60 ft above the bit. Assuming one . takes surveys at 30 ft spacing, the survey of the first 30ft of the tangent interval is not available until 90 ft of the tangent section has been drilled. At this point only one third of the tangent i nterva 1 has been surveyed and that por- tion will also include any transition affects caused by placing the angle-holding steerable motor assembly in the bottom of the highly curved angle-build portion of the hole. After drilling 120 ft of section, the deepest MWD survey will provide data on the first half of the 120 ft inter- val. Since we must predict the angle at the bit in order to correctly judge the depth at which to start the second build interval, we must extrapo- late the performance measured above the MWD sensor to the bit.

The final selection in a simple tangent build-- curve design is the angle for the tangent inter- val. One of the most common choices is 45°.

With the tangent at 45 o, the end of the curve falls at the same position regardless of the curvature of the angle build portions of the hole.

Increasing the tangent angle lowers both the height and the magnitude of the potential error in the second build. The height of the second build decreases rapidly as you increase the angle above 45•. For example, the height of a second build at 8°/100 ft decreases from 209 ft for a 45° tangent to 96 ft with a 60° tangent.

Placing the tangents at angles greater than 45• increases the length of the hole and the displacement of the end of the curve. It also makes the length and displacement sensitive to the actua 1 curvatures in the first and second bui 1 d.

These considerations make tangent angles above 60. unacceptable. One other consideration in choosing the position of the tangent interval is to provide the ability to intersect any critical structural markers in the tangent interval so that one can adjust the second build kickoff point 3

4 HORIZONTAL WELL PLANNING - BUILD CURVE DESIGN NMTECH 890008 based on the actual observed position in the stra-

tigraphic column.

A Complex Tangent Build Curve

The complex tangent build curve provides the next logical step in controlling the accuracy of hit- ting a small TVD target. A typical complex tangent build curve design is shown in Figure 4.

The design calculations for the example are included in Table 3. For this build curve design, one utilizes the first build interval to establish the performance levels of the angle-build motor selected for the job just as is done with the simple tangent method. However, instead of using this same curvature in selecting the kickoff point for the second build curve, the concept is to use a lower design rate than was actually experienced in the upper part of the hole.

In the ex amp 1 e case, we have designed the first build at the expected minimum rate of 8°/100 ft and designed the second build with a build rate that is 1.5°/100 ft less than the first build rate or 6-1/2°/100 ft. One of the key concepts of this technique is that the 1 ower design rate for the second build can be obtained using the same angle-build motor as the first build by orienting the too 1 face to the right or left of vertical. The 6-1/2°/100 ft vertical build rate can be obtained from the 8°/100 ft angle-build tool used in the first build by turn-

; ng the too 1 face of the angl e-bu i 1 d motor to 35° left or right of vertical.

The well could be designed to p 1 ace all of the turn in one direction if that were desired.

However, in most situations it is better to turn the well to either the 1 eft or right for about half of the second build and then in the opposite direction- for the final half. In our example we chose to turn the well left for the first half and right for the second half. This strategy produces a change in azimuth of 16.8• to the left fol- lowed by a turn to the right of 14.7°. The approximate vertical section and other key dimen- sions of the second bu i 1 d can be computed using the build turn equations 5 through 11.

The comp 1 ex · bu i 1 d curve design is not intended to produce a straight well bore path but to provide the driller with the ability to adjust the curva- ture rate both upward and downward while drilling the second build curve. Comparing this example with the example of the simple tangent build curve shows some of the advantages and disadvantages of this design. The greatest disadvantage of this design is that the length, height and displacement of the second bu i 1 d are increased The 1 ength of the second build is increased from 500 ft to 615 ft. The height is increased from 168 ft to 206 ft, and the di sp 1 a cement 1 ength is increased from 460 ft to 567 ft. The principal advantage of . this design is that the actual height of the second build curve can be adjusted both up and down. The maximum vertical-adjustment is as much as 38 ft upward if the change is known at the beginning of the second build curve. This would provide a maximum height adjustment of 18% of the

rema1n1ng height. The build turn interval also has a greater total curvature than the build of a simple tangent design, however, the increase is not large. For the example case, the total dogleg in the build curve is only 10% larger than for a completing simple tangent design.

This design has its greatest application for hori- zontal holes that are drilled to a structural target. It is quite useful when the final target position is defined by the tops of formations that are located within the second build curve.

Although one can certainly not make 1 arge correc- tions, the size of the adjustment can be signifi- cant. For example, in our 6-1/2°/100 ft design build case, we will reach 70° when we are 53 ft above the hori zonta 1 target. At that point, it is possible to reach the horizontal target with our maximum 8°/100 ft build rate in a vertical height of only 43 ft by turning the toolface straight up. This would allow a 10 ft upward vertical adjustment from only 53 ft above the target. It is also possible to achieve down- ward target adjustments by· increasing the toolface angle.

The complex build curve provides a trade-off be- tween target TVD accuracy and target position and direction. Table 4 summarizes the effect of the trade-offs. To use this design most effectively, the well designer needs to establish a greater latitude in end of curve displacement and direc- tion to maximize the control of the vertical target.

The Ideal Build Curve

The ideal build curve is shown in Figure 5. It is simply a complex build curve without a tangent interval. It could therefore be drilled with a single angle-build motor run unless limited by the bit life. Obviously this would provide the lowest cost method for drilling a build curve. It would a 1 so require that the expected range of perfor- mance of the angle-build tool would be less than could be absorbed by the adjustment of too 1 face angle while drilling the second build and turn section. Although we can probably not predict the build rate performance of angle-build motors pre- cisely enough to use the Ideal build curve on the first we 11 in an area, it should be considered. for the second or third well in an area.

Torgue and Drag

After one has designed the optimum build curve for the well, one of the next questions is how far can you drill horizontally. The problem now shifts from directional control to torque and drag. In a given hole, the maximum horizontal length is reached or perhaps exceeded when you can no longer rotate the pipe or sufficiently load the bit to drill. Table 5 1 ists the current record horizon- tal lengths as a function of hole size and build curvature rates. Although we do not know how close these record 1 engths were to the 1 imi ts, it is assuring to realize that the 1 imit is not less than these 1 engths. The well designer needs to

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NMTECH 8g0008 FRANK J. SCHUH 5

understand the torque and drag consequences of his alternate design choices.

One so 1 uti on adopted by many operators on their first attempt is to plan for a horizontal length on the 1 ow side of the spectrum. That concept will probably generate 500 ft as super safe, 1,000 ft as reasonable, 2,000 ft as (lggressive, and 4,000 ft would equal the record. If one stays under the 2,000 ft mark, it is unlikely that true torque and drag limits will be reached. Operation- al problems with torque or drag in this length would indicate some other problem such as cuttings accumulation or wall sticking. However, to opt i- mi ze the cost of hori zonta 1 ho 1 es, one must come to grips with the true limits. Table 6 lists the most important factors affecting the torque and drag 1 imits.

To plan for 2,000 ft horizontal well length, it is probably necessary to consider the torque and drag. The torque and drag analysis must include predictions of the torque and drag while rotating off bottom, drilling with surface rotation, drill- ing while steering a down hole motor, and the drag forces while tripping. It is also important to know the stresses on the dri 11 string components due to the curvature of the hole and these loads.

There are a number of proprietary and commercia 1 torque and drag computer models that can be used to prepare the best pass i bl e estimates of torque and drag for a horizontal hole. If the well course is quite complex or if the well is a combi- nation directional well with a shallow kickoff point and a 1 ong tangent section, these programs offer the only reasonable method for analyzing the problem. However, for a typical on-shore horizon- tal hole that uses a deep kickoff point and a relatively compact build curve, it is possible to estimate the torque and drag using some relatively simple approximations. If one assumes that:

o The build curve can be represented by a simple goo arc.

o The same size and weight of pipe are used throughout the build curve.

o The hole is approximately horizontal.

o None of the pipe in the horizontal hole is buckled. (See Appendix ^2).

o The coefficient of friction is equal to .33.

The torque and drag rel at i onshi ps can be reason- ably approximated by the following relationships.

Torque for the pipe in the horizontal hole is:

00 • Wm · L Th ^{= - - - -}

72

. (14) The torque for rotating pipe in the goo build depends on the magnitude of the ax i a 1 force ap- plied to the end of the curve. While drilling a hori zonta 1 ho 1 e with surface rotation, the a xi a 1

force at the end of the curve is equa 1 to the weight on the bit.

For WOB < .33 · Wm · R:

OD · Wm · R Tb = - - - -

72

. . . ( 15)

For WOB > .33 · Wm · R:

OD · Wm · R 00 · WOB Tb = - - - - - + - - -

144 46 . . . . ( 16) For example, lets consider a horizontal hole with a build curve radius of 850 ft and a hori zonta 1 1 ength of 1, 000 ft. What is the torque whi 1 e rotating off bottom with 30,000 lb on the bit?

Assuming that we are using g,2 1b/gal mud and 5 in. Heviwate drillpipe throughout the build curve and horizontal interval, the buoyant weight of the pipe is Wm = • 86 · SO 1 b/ft. The torque in the horizontal part of the hole would be:

6. 5 . ( . 86 . so) . 1000 Th = - - - -

72

Th

=

3,882 ft-lbf.

The torque in the bu i 1 d curve wh i 1 e rotating off bottom when WOB = 0 is ca 1 cul a ted from equation 15.

6.5 . (.86 . 50) . 850 Tb = - - - -

144 Tb

=

1650 ft-lbf.

The total torque rotating off bottom is:

T = Th + Tb . . . (17)

T = 3882 + 1650

=

5532 ft-lbf

With 30,000 lb on the bit, the force at the end of the curve exceeds . 33 · Wm · R and the torque in the build curve is calculated from equation 16.

6.5 . (.86 . 50) . 850 6.5 . 30,000

Tb = + - - - - -

144 46

Tb

=

5,88g ft-lbf.

6

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HORIZONTAL WELL PLANNING - BUILD CURVE DESIGN NMTECH 890008 The tot a 1 torque rotating with 30,000 1 b on the

bit is:

T = Th + Tb

T = 3,882 + .5,889 = 9,771 ft-lbf

The axial drag while lowering the pipe on a trip or while steering with a downhole motor can be calculated from the following approximations. For the pipe in the horizontal hole, the axial drag is given by:

. . ( 18) The drag for the· pipe in the build curve is a function of the axial force on the pipe at the end of the curve as it enters the hori zonta 1 ho 1 e.

This force is equal to the weight on the bit plus the drag of the pipe in the hori zonta 1 . If the bottom hole assembly is expected to provide signif- icant stabilizer drag, this force should be included in the end of curve force. This force at the end of the curve is given by:

F₀ = Dh + WOB + BHA . ( 19) The drag for the pipe in the build curve is depen- dent on the magnitude of the a xi a 1 force at the end of the curve.

If F₀ ^< .25 · Wm · R:

Db = .4 ·

wm ·

^R . . . (20) If F₀ > .25 Wm · R:

. . . . (21) The drag for the example well described above while drilling with 30,000 lb bit load in the steering mode is calculated as follows:

(.86 . 50) . 1000 3

Dh = 14,333 lb F₀ = 14,333 + 30,000 F₀ = 44,333 lb

.25 · Wm · R = .~5 · (.86 · 50) · 850 .25 · Wm · R = 9,138 lb

Therefore: F₀ > .25 · Wm · R

( . 86 . 50) . 850

D b = - - - + .69 · 44,333 4

Db= 9,137 + 30,390 Db= 39,727 lb The total drag is:

D = 14,333 + 39,727 D = 54,060 lb

. . . (22)

To drill with 30,000 lb, it will be necessary to slack off the bit load plus the drag or 84,060 lb in this example.

To calculate the hoisting drag, the steps are quite similar. The drag in the horizontal portion of the hole is given by:

. . . (18)

The tensile drag in the build interval is a func- tion of the tensile load on the pipe at the end of the curve. This force is equa 1 to the friction a 1 drag for the pipe in the hori zonta 1 i nterva 1 p 1 us any nongravity frictional loads such as might be caused by stabilizer hanging or other such af- fects. The drag around the build curve is calcu- lated as follows:

If F₀t < .85 · Wm · R Dbt = .33 Wm R If F₀t > .85 · Wm · R

. . . (23)

. . . (24)

Dbt = .69 · F₀t - .25 · Wm · R . . . (25) These relationships can be used to estimate the magnitude of torque and drag for most hori zonta 1 well designs. When these evaluations are coupled with an analysis of the critical buckling force included in Appendix B, it is possible to evaluate the affect on torque and drag by changing compo- nents in the horizontal drillstring. Reducing the weight of the pipe in the horizontal will decrease torque and compressive drag as long as the lighter pipe does not buckle. If conditions dictate that buckling will occur, the analysis need go well beyond these simple relationships.

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NMTECH 8g0008 FRANK J. SCHUH

Nomenclature

BHA

DL

H

Build Rate {⁰/100 ft).

Total curvature for build-turn segment,

{

0/100 ft).

Vertical build rate for build-turn seg- ment, {⁰/100 ft).

Nongravi ty induced axi a 1 friction a 1 force in the bottom hole assembly, {lbf).

Total drag {lbf).

Compressive Drag in the build curve, { 1 bf).

Tensile drag in the build, {lbf).

Axi a 1 drag wh i 1 e pulling or 1 oweri ng the pipe in the horizontal portion of the hole without rotation, {lbf).

Total dogleg in a build-turn segment, {deg).

The axial compressive force on the pipe at the end of the curve, (lbf).

Axial tension at the end of the curve, ( 1 bf) .

Displacement, (ft).

b Initial inclination angle, (deg).

L OD R

v

Final inclination angle, (deg).

Length of hole or pipe segment, (ft).

Outside diameter of the tool joints, (in).

Build radius of a segment or the overall build curve radius for torque and drag estimate, (ft).

Vertical build radius, (ft).

Total torque (ftOlbf).

Rotating torque in the build curve, (ft-lbf)

Rotating torque for pipe in a hori zonta 1 portion of the hole, (ft. lbf).

Vertical height, (ft).

The average buoyant weight of the pipe (1 bm/ft).

WOB Weight on bit, {lbf).

Azimuth change, (deg).

¢

Toolface angle, (deg).

References

1. Dawson, Rapier; Exxon Production Research Co., and Pas 1 ay, P. P . ; Cons u 1 tan t : .. Dr i 11 i p e Buckling in Inclined Holes, .. JPT, {Oct. 1g84).

2. Morites, Guntes: ¹¹Worldwide Horizontal Drilling Surges, .. Oil & Gas Journal, {Feb. 27, 1g8g), APPENDIX A

Torque and Drag Approximations for A Uniform Build Curve

Let: D =Tool joint OD, {in.).

F = Axial force on the pipe at any point in the curve.

f = Coefficient of friction.

= Angle of hole above horizontal.

I= 0 at end of curve, {horizontal).

I = goo at KOP in radius.

R =Radius of build curve, (ft).

T = Torque in the build curve.

w =Unit buoyant weight of the pipe in the curve, (lb/ft).

Fe = Lateral contact force in curve, (lb/ft).

F₀ = Axial compressive force on the pipe at the EOC.

OD =Tool joint ODin build curve, (ft).

AT = Torque produced along a AQ length element of pipe, (ft lb).

For these derivations it is more useful to define the coordinate system for angle as beginning with zero at the hori zonta 1 end of curve position and goo as the angle for the vertical kickoff point.

The torque produced a 1 ong an e 1 ementa 1 1 ength of pipe in a circular build curve is given by:

. . . (A-1)

The force at any point a 1 ong the build curve is given by:

F = F_{0 -} w sin . . . (A-2) Combining A-1 and A-2:

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HORIZONTAL WELL PLANNING - BUILD CURVE DESIGN NMTECH 890008

AT

=

f ; ABS[:o - w sin I + w cos 1)

A~

. . . . . {A-3}

For a circular build arc:

At = R · AI · · . . . {A-4}

Substituting A-4 in A-3 and rearranging to a dimen- sionless form:

I::.T = :

ABS[~

^{- sin} + cos I) !::.I

f · D • w · R 2 w · R

. . . • . (A-5) T

f · D • w · R

I=1r/2 I [ Fa )

r -

ABS - - - - sin I + cos I AI I=O 2 w · R

. (A-6) Using an iterative numerical procedure, we solved equation A-6 in terms of (F₀/wR) and plotted the results in Fig. 5.

In light of the significant uncertainty in the magnitude of the friction factor and radius, we believe that these results can be adequately approximated by the two straight dashed lines shown on the figure. The resulting approximation in equation form is given by:

For F₀ < w · R/3

T ⁼ (f · D · w • R)/2 . . . (A-7)

F₀ > w R/3

T = ( f · OD · w • R) /4 + [ 1r . F ⁰ ] • • (A- 8) 4 · w · R

In oil field units for f = .33 and WOB = F₀ these become:

WOB < .33 · Wm · R

00 • Wm · R

Tb = - - - -

72 • • . . . • (A-9}

WOB > .33 · Wm · R

OD · w · R OD · WOB Tb = - - - - + · - - -

144 46 . . . . {A-10}

Compressive Drag, while drilling in the steering mode or while lowering the pipe in the hole:

let Ft = force at the top of the curve.

The change in axial force along the sliding pipe in a circular build curve is given by:

AF = f ^o ABS[:i + w cos

J)A~

- w (sin I) ^o At

. . . (A-ll)

The axial force at any point in the build curve is also affected by the axial drag below that point:

Fi = Fi-1 + AF . . . (A-12) At the bottom of the curve where I = 0 the axial force is:

• • • • • • • • . . . • (A-13}

Substituting for At and dividing to make the form dimensionless gives:

~

^{= f ·}

ABS[~

^{+ cos}

1)

AI - (sin I) · AI

w • R w • R

. . . (A-14) Ft I=1r/2 [ F.

- - - = ~ ^{_1 _ _} + w • R 1=0 w • R

f o

ABS[wF~

R + cos 1) AI - (sin I) o AI]

• • • . • (A-15)

The drag force Of in the build curve is given by:

Of= Ft- F₀ + w · R ... (A-16) Dividing by w · R to make the solution dimensionless:

SPE 2 0 1 50

NMTECH 890008 FRANK J. SCHUH

Of Ft Fo

- - = - - - + 1 • . . . (A-17)

w . R w . R w · R

Using an iterative numerical procedure, we pre pared the plot of (Df/wR) versus (F₀/wR) for f = .33 shown in Fig. 7.

The approximation shown by the dashed lines in Fig. 7 is oilfield units for f = .33 is:

For F₀t < .25 · Wm · R:

Df = .4 · Wm · R . . . (A-18) For F₀ > .25 . Wm . R:

Df

=

.25 · Wm · R + .69 · F₀ . . . (A-19) To solve for the tensile drag (pulling out of hole):

let F₀ = tensile force at end of curve~

AF • f o ABS[:i - w cos 1) ^o A£ + w (sin I) ^o A£

(A-20)

~

^{= f ·}

ABS[~

- cos I] · AI + (sin I) · AI

w • R w • R

Fi = Fi-1 + AF Fi=O = Fo

Ft I=w/2 [ F·

- - = ~

_,_+

w · R I=O w · R

(A-21) . . . . (A-22)

. (A-23)

f ·

ABS[~

^{- cos I] AI + (sin I) o All}

w • R J

. (A-24) The tensile drag force Of is given by:

. . . . (A-25) In dimensionless form it becomes:

Df Ft Fo

- - = - - - -

. . . . (A-26) w · R w . R w . R

The . numerical solution for the tensile drag is shown in Fig 8 for f = .33.

The approximation for tensile drag is shown by the dashed lines in Fib. 8 and in oilfield units is:

for Fot < .85 . Wm . R~

Dbt = .33 · Wm · R . . . (A-27) For F₀ > .85 . w . R:

Dbt = .69 · Fot - .25 . Wm . R . . (A-28) Appendix B

Torque and drag force approximations for the hori- zontal portion of a hole assume that none of the pipe is buckled.

Critical buckling force for a pipe in horizontal hole was derived by Dawsonl.

[

E ·

I ·

^{Wm sin}

8]

¹¹²

Fe

=

2

12 . r . . . ( B-1)

Fe= critical buckling force, (lb).

Where:

E = 29.6 · 10⁶ psi steel.

I = moment of inertia, (in 4) •

Wm =buoyant weight of pipe, (lb/ft).

[

65. 5 - MW]

Wm

=

Wa 65.5 . . . (B-2)

Wa = average weight of pipe and tool joints·

· in air, ( ¹ b/ft) . MW =Mud density, (lb/gal).

r = radial clearance between pipe and hole, (in).

There has been considerable concern over the appro- priate radial clearance to use with coupled or tool jointed pipe. If the pitch of the buckled pipe is large compared to the distance between

9

10

SPE 2 015 0

HORIZONTAL WELL PLANNING - BUILD CURVE DESIGN NMTECH 8g0008 tool joints the radial clearance is defined by the

tool joint OD rather than the OD of the pipe body. Since this is generally the case for ·hori- zonta 1 drill i ng app 1 i cations we define the rad i a 1 clearance as:

r = (Dh - Dtj)/2 ... (B-3) 8 = hole angle go• for horizontal hole Dh =diameter of hole, (in).

Dtj =diameter of tool joint, (in.).

In oilfield units for a horizontal hole:

[

I · Wa · (65.5 - MW)]¹¹²

Fe = 550 · . . . (B-4)

Dh - Dtj

Torque for rotating nonbuckled pipe in a straight inclined hole:

OD · Wm · L · f sin 8

T = - - - . . ; . . (B-5) 24

T =torque, (ft lbs).

In oilfield units with f = .33 and for a horizontal hole:

OD · Wm · L

T

= - - - -

. . . (B-6) 72

Axial drag for pulling or pushing nonbuckled pipe in a straight inclined hole:

D

=

Wm · L · f · sin 8 . . . (B-7)

Where:

D =drag force, (lb).

In oilfield units for a horizontal hole with

f = .33:

. . . (B-8)

TABLE 1 CURVATURE LIMITS

o Rotate conventional steering tools 3-4./100 ft o Rotate nonmag drill collars 6-7./100 ft o Use conventional production tools 10./100 ft o Rotate 5" Heviwate drill pipe 12-15./100 ft o Motor drilling without rotation 30+./100 ft

TABLE 2 SIMPLE TANGENT EXAMPLE Given:

Expected angle bu i 1 d performance, 8• to 9.5./100 ft.

Minimum tangent length, 120 ft.

Tangent angle, so·.

Target angle go• at gooo ft TVD.

Solution:

Use the minimum expected build rate to plan the build curve.

Use the same build rate for first build and second build intervals.

5730 5730

Build radius: R = - - ^{= - -} = 716 ft

B 8

Height first build:

V = R · (sin I2 - sin I1)

V = 716 · (sin 50 - sin 0) = 54g ft Height of tangent:

V = L · cos I

v

= 120 . cos (50) = 77 ft Height of second build:

V = 716 · ( s i n go - s i n 50) ·= 168 ft KOP = gooo - 54g - 77 - 168 = 8,206 ft

SPE 2 015 0

NMTECH 890008 FRANK J. SCHUH

Displacement, first build:

H = R · (cos I 1 - cos I 2)

H

=

716 · (cos 0 - cos 50)

=

256 ft Displacement of tangent:

H

=

L · sin I

H

=

120 · sin 50

=

92 ft Displacement of second build:

H

=

716 · (cos 50 - cos 90)

=

460 ft Length of first build:

100 . (I 2 - h) L = - - - -

B

100 . (50 - 0)

L = = 625 ft

8

Length of second build:

100 . (90 - 50)

L

= =

500 ft

8 Measured Depths:

At end of first build: 8206 + 625 = 8831 ft At end of tangent: 8831 + 120

=

8951 ft At end of second build: 8951 + 500

=

9451 ft If build rate is 9.5./100 ft, how long is the tangent section?

5730

Build radius: R = - - = 603 ft 9.5

Height first build:

603 (sin 50 - sin 0)

=

462 ft Height second build:

603 (sin 90 - sin 50)

=

141 ft Total 603 ft

Planned height of build curve:

549 + 77 + 168

=

794 ft Required Tangent Height:

794 - 603

=

191 ft Length of Tangent:

v

191

L = - - = - - = 297 ft cos I cos 50

TABLE 3

COMPLEX TANGENT EXAMPLE PROBLEM GIVEN:

Expected angle build performance 8 to 9.5./100 ft.

Minimum tangent length - 120 ft.

Tangent angle-

so•.

Target angle go• at 9,000 ft.

S e c o n d b u i 1 d 1 . 5 •

I

1 00 f t 1 e s s t h an the first build

SOLUTION:

Use the 8 • /100 ft m1 n 1 mum expected build rate for the first build.

Use 8 - 1.5

=

6.5./100 ft for second build.

First build radius:

5730 5730

R1 = - = - = 716 ft

B 8

5730 5730

R2 = - = - - = 882 ft

B 6.5

Height first build:

V

=

R · (sin I2 - sin I1)

V = 716 · (sin 50 - sin 0) = 549 ft Height of tangent:

V

=

L · cos I

=

120 · cos 50

=

77 ft

11

12

SPE 2 015 0

HORIZONTAL WELL PLANNING - BUILD CURVE DESIGN NMTECH 890008 Height of second build:

V

=

882 · (sin 90 - sin 50)

=

206 ft KOP

=

9,000 - 549 - 77 - 206 = 8,168 ft Displacement first build:

H = R · (cos h - cos I 2)

H

=

716 · (cos 0 - cos 50)

=

256 ft Displacement tangent:

H

=

L · sin I

=

120 · sin 50 = 92 ft Displacement of second Build:

H = 882 · (cos 50 - cos 90) = 567 ft Length of first build:

L

=

L

=

100 . ( I2 - h) B

100 . (50 - 0)

8

=

625 ft Length tangent: L

=

120 ft Length of second build:

100 . (90 - 50)

L

= =

615 ft

6.5

r

^6.

s l

Toolface angle 2nd build = arc cosl---J= 35.r 8.0

Azimuth change in second build.

Total dogleg in second build is:

DL

=---

BT (I2 - l1) Bv

8.0

DL

= ---

(90 - 50)

=

49.23°

6.5

If all turn is in the same direction the azimuth change is:

cos DL - cos I1 · cos I2 cos AAz = - - - -

sin It sin I2

AAz

=

arc cos cos 49.23 - cos

so

x cos 90

=

_{31 5•}

sin 50

x

sin 90 · Azimuth change if first half of second build is turned left and second half is turned right.

First half: I1

= so·

^I2

=

^10•

Total dogleg: DL

= ---

8.0 (70 - 50)

=

24.62•

6.5

cos 24.62 - cos 50 . cos 70 Cos AAz = - - - -

sin 50 · sin 70 AAz =arc cos (.96)

=

16.76• left Second half: I1

=

10· I2

=

go•

8.0

DL

= ---

(90·70)

=

24.62•

6.5

[

cos 24.62 - cos 70 · cos-90]

arc cos

sin 70 · sin 90

.96

= 14.65• right Total direction change in second build:

Az =

-16.76• (left) + 14.65° (right)

= -2 . 11 • ( 1 eft) TABLE 4

HORIZONTAL TARGET TRADE-OFFS

1. Target TVD vs. position and direction of the end of curve

2. EOC positiion vs. EOC direction.

3. Target TVD, eoc position and direction accuracy vs. cost.

NMTECH 890008 FRANK J. ·SCHUH TABLE 5

RECORD HORIZONTAL WELL LENGTHS

Type Size Radius Length

i.h_ _ f L _ f L

Short 4-3/4 30 425

6 35 889

Medium 4-1/2 300 1,300

6 300 2,200

8-1/2 400-800 3,350 Long 8-1/2 1,000-2,500 4,000 12-1/4 2,300 1,000

TABLE 6

HORIZONTAL TARGET TRADE-OFFS

1. Target TVD vs. position and direction of the end of curve.

2. EOC position vs. EOC direction.

3. Target TVD, EOC position and direction accuracy vs. cost.

TABLE 7

FACTORS AFFECTING TORQUE AND DRAG LIMITS o Length of Horizontal Hole

o Drillstring Design - Heviwate

- Drillpipe in horizontal hole - Required bit loads

o Coefficient of Friction - Mud type

o Rig Capacity - Torque - Axial - Top drive

o Horizontal Drilling Technique - Surface rotation

- Steering mode

SPE 2 015 0

13

14

SPE 2 015 0

HORIZONTAL WELL PLANNING - BUILD CURVE DESIGN NMTECH 890008

VERTICAL SECTION

VIEW 1 2

PLAN H

Fig. 1-Basic build curve geometry.

PLAN VIEW

VERTICAL SECTION

Fig. 2-Build and turn geometry.

_ _ KOP 716'

549'

77' 168'

460'

B deg/100 ft Build rate 50 deg Tangent angle 120 ft Tangent length

716'

Fig. 3-Simple tangent build curve.

549'

77' 206

716'

PLAN VIEW

8 deg/100 ft •otor build rate

6.5 deg/100' 2nd build rate

120 ft tangent at 50 deg angle

Fig. 4-Complex tangent build curve.

SPE 2 015 0

NMTECH 890008 FRANK J. SCHUH

3.00

2.50 ,-...

0::

*

_{~ 2.00}

0

0

*

~1.50 '+-

' w :::>

0

0:: 1.00 I-0

0.50

PLAN VIEW

8 deg/100 ft Total curvature rate 8 deg/100 ft Firat build rate 6.5 deg/100 ft 2nd build rate

Fig. 5-Ideal build rate.

:

.

: : : : :

~

: : ^A

. ;

:

I'

: ^:

~

:

I

.

: _:

)

¹⁷

: A

:

1/

.

:

/

: : :

A

.

: : : :

.

I T T - . I I I I I I I o

u

~

_o o I o o o o o

0.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00

EOC FORCE/(w•R)

Fig.

6-

Torque in the build curve.

3.00

: : : :

2.50

.

: :

/

: :

.

:

v

: :

: /

.

:

v

: :

/

:

.

:

V'

: :

:

.

~

=v

:

0.50

: :

.

I I o I o o o

.

^{I o o o}

..

-.--.--.--.- 0.00

0.0 0.5 1.0 1.5 2.0 2.5 3.0

EOC FORCE/(w•R)

Fig. 7 -Compressive drag in build cuNe.

3.00

2.50

,-...2.00 0::

*

:t

~

'.1.50 (.!)

<(

0::

c

1.00

0.50

0.00

: : : :

.

: : : :

.

: :

/

: :

. .

v

: :

: :

/

:

v

: :

/

:

.

: ~,.

·----

: :

.

-.-

...

^{o o I I I o o I I I I I I I .-.--.--.-}

0.0 0.5 1.0 1.5 2.0 2.5 3.0

EOC FORCE/(w•R)

Fig. 8-Tensile drag in build curve.

15