DIRECTIONAL DRILLING

Dr.Eng: Taher Elfakharany

Done By:
Abdelrahman Khaled 20192265
Amr Khaled 20190242
Marco Khair 20194745
Habiba Ali 20193224
Roaa Ahmed Morsi 20193631
 Directional Drilling
Table of Contents
Introduction ..................................................................................................................................... 1
Azimuth ........................................................................................................................................... 1
Directional Well Planning ............................................................................................................... 2
Types of well profiles ...................................................................................................................... 2
Build-up & Hold design (Type Ⅰ) ................................................................................................ 3
'S' Type well design (Type Ⅱ) ...................................................................................................... 5
Type III (Deep Kick-off and Build) ............................................................................................. 7
Deflection Tools and Techniques..................................................................................................... 8
Whipstocks .................................................................................................................................. 8
Jetting Bit .................................................................................................................................. 10
Rebel Tool ................................................................................................................................. 11
Mud Motors ............................................................................................................................... 12
Specialized Deflection Techniques ................................................................................................ 13
Curved Conductors .................................................................................................................... 14
Slant Hole Drilling .................................................................................................................... 14
Toolface Setting ............................................................................................................................. 15
Graphical Methods .................................................................................................................... 15
Ragland diagram.................................................................................................................... 15
Ouija board ............................................................................................................................ 16
Calculations ............................................................................................................................... 16
Bottom Hole Assemblies (BHA) ................................................................................................... 17
Pendulum Principle ................................................................................................................... 17
Fulcrum Principle ...................................................................................................................... 18
Packed Hole Stabilization Principle .......................................................................................... 18
Trajectory Calculations.................................................................................................................. 19
Radius of curvature Method ...................................................................................................... 20
Minimum Curvature Method ..................................................................................................... 21
Projecting Ahead ....................................................................................................................... 22
References ..................................................................................................................................... 23
FIGURE 1 DEFINITION OF AZIMUTH ......................................................................................................................... 1
FIGURE 2 TYPES OF WELL PROFILES.......................................................................................................................... 2
FIGURE 3 TYPE 1 PROFILE ..................................................................................................................................... 3
FIGURE 4 TYPE 2 PROFILE ...................................................................................................................................... 5
FIGURE 5 TYPE III PROFILE. .................................................................................................................................... 7
FIGURE 6 WHIPSTOCK TYPES ................................................................................................................................. 9
FIGURE 7 CIRCULATING WHIPSTOCK ........................................................................................................................ 9
FIGURE 8 JETTING BIT ........................................................................................................................................ 10
FIGURE 9 REBEL TOOL ........................................................................................................................................ 11
FIGURE 10 OPERATION PRINCIPLES OF TURBINE AND PDM ........................................................................................ 12
FIGURE 11 BENT SUB. ........................................................................................................................................ 12
FIGURE 12 FIXED PLATFORM USING CURVED CONDUCTOR .......................................................................................... 14
FIGURE 13 FIXED PLATFORM USING SLANT RIG......................................................................................................... 14
FIGURE 14 RAGLAND DIAGRAM ........................................................................................................................... 15
FIGURE 15 OUIJA BOARD .................................................................................................................................... 16
FIGURE 16 PENDULUM PRINCIPLE ......................................................................................................................... 17
FIGURE 17 FULCRUM PRINCIPLE ........................................................................................................................... 18
FIGURE 18 BOTTOM HOLE ASSEMBLIES. ................................................................................................................. 18
FIGURE 19 PACKED BHA PRINCIPLE ...................................................................................................................... 18
FIGURE 20 BHA CONFIGURATIONS ....................................................................................................................... 19
FIGURE 21 RADIUS OF CURVATURE ........................................................................................................................ 20
FIGURE 22 MINIMUM CURVATURE METHOD ........................................................................................................... 21
FIGURE 23 BIT WALK.......................................................................................................................................... 22
Introduction
Controlled directional drilling is a technique for directing a well along a predetermined course to
a bottom hole target located at a certain distance and direction from a surface location.
There are many reasons for drilling a directional well, including:
1. Side-tracking existing wells (because of hole problems or fish or reaching new targets).
2. Restricted surface locations.
3. To reach multiple targets.
4. To reduce number of offshore platforms.
5. Horizontal Drilling.
6. To reach thin reservoirs (using horizontal or multilateral drilling).
7. Environmental footprint.
8. Salt dome drilling (direct the well away from the salt dome to avoid casing collapse
9. problems).
10. Geological requirements.
11. To avoid gas or water coning problems.
12. For intersecting fractures.
13. For re-entering existing wells.

Azimuth
The azimuth of a wellbore at any point is defined as the direction of the wellbore on a horizontal
plane measured clockwise from a north reference. Azimuths are usually expressed in angles from
0-360, measured from zero north. 135°, Azimuths can also be expressed in a quadrant system
from 0-90 measured from north in the northern quadrants and from south in the southern
quadrants. The azimuth reading of 135 equates to S45 E in quadrant readings, see Figure1.

Figure 1 Definition of azimuth

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Directional Well Planning
The planning of a directional well requires the following information:
1. Surface and Target Co-ordinates: UTM, Lambert or geographical.
2. Size of and shape target(s).
3. Local Reference Co-ordinates: For multi-well sites, these must include template, platform
center and slot location.
4. Required well inclination when entering the target horizon.
5. Prognosed Lithology: including formation types, TVD of formation tops, formation dip
and direction.
6. Offset well bit and BHA data: Required for bit walk, building tendencies of BHA’s.
7. Casing program and drilling fluid types.
8. Details of all potential hole problems which may impact the directional well plan or
surveying requirements.
9. A listing of definitive survey data of all near-by wells which may cause a collision risk.
For offshore drilling, this listing should include all wells drilled from the same. platform
template or near-by platforms and all abandoned wells in the vicinity of the new wells.

Types of well profiles

If the position of the surface location is known and given the location of the target, its TVD, and
rectangular coordinates, it is possible to calculate the best well profile that fits the coordinates of
the surface and the bottom hole target that fit this data. The well profile is plotted in the vertical
plane as shown in Figure 2. This figure also describes the various sections of a directional well.

Figure 2 Types of well profiles

There are three basic well profiles which include the design of most directional wells:
Type one: Build and hold trajectory. This is made up of a kickoff point, one build up section and
a tangent section to target.

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Type two: S -Shape trajectory. This is made up of a vertical section, kick- off point, build-up
section, tangent section, drop-off section and a hold section to target.
Type three: Deep Kick off trajectory. This is made up of a vertical section, a deep kick off and a
build up to target.
Another secondary type is horizontal wells. A horizontal well is a well which can have any one
of the above profiles plus a horizontal section within the reservoir. The horizontal section is
usually drilled at 90 degrees and therefore the extra math involved is quite simple as we only
need the measured length of the horizontal section to calculate the total well departure and total
measured depth. The hole total TVD usually remains the same as the TVD of the well at the start
of the horizontal section. However, if the horizontal section is not drilled at 90 degrees or there
are dip variations within the reservoir, then the total hole TVD will be the sum of the TVD of the
horizontal section and the TVD of the rest of the well.

Build-up & Hold design (Type Ⅰ)

To carry out the geometric planning for a Type I well, Figure 3, the following information is
required:
▪ Surface Coordinates
▪ Target Coordinates
▪ TVD of target
▪ TVD to KOP
▪ Build-up rate

Figure 3 Type 1 Profile

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Using the detailed trigonometry shown in Figure 3, the maximum inclination angle αmax for type
I trajectory can be calculated for two cases:
First Case R > D2
The maximum inclination angle αmax for type I trajectory is given by:

Second Case R < D2

The maximum inclination angle αmax is given by:

➢ Build- up Section
1. Radius of curvature (R) of build-up section:
360 × 100
R=
2𝜋 × 𝐵𝑈𝑅
Where: BUR = build-up rate, degrees/100ft.
2. Measured length of build-up section:
𝛼1 × 100
MD2 =
BUR
3. Vertical length of build-up section:

𝑉2 − 𝑉1 = 𝑅1 × sin 𝛼

4. Horizontal displacement (departure) at end of build-up section:

D1 = R1 x (1 - cos α)
➢ Tangent Section
5. Measured length of tangent section:
𝑉3 − 𝑉2
𝑀𝐷3 =
cos 𝛼
6. Vertical length of tangent section:
V3 - V2 = MD3 x cos α
7. Horizontal displacement at end of tangent section:
D2 = D1 + MD3 x sin α
8. Total measured depth for type I wells:
TMD= MD1 + MD2 + MD3

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'S' Type well design (Type Ⅱ)
To carry out the geometric planning for a type II well the following information is required:
▪ Surface Coordinates.
▪ Target Coordinates.
▪ TVD of target.
▪ TVD at end of drop-off (usually end of well).
▪ TVD to KOP.
▪ Build-up rate.
▪ drop-off rate.
▪ Final angle of inclination through target.

Figure 4 Type 2 profile

1. Radius of curvature (R1) of build-up section:

360 × 100
R1 =
2𝜋 × 𝐵𝑈𝑅

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 2. Radius of curvature of drop-off section:

360 × 100
R2 =
2𝜋 × 𝐷𝑂𝑅
𝛼1 = 𝑋 + 𝑌
𝑂𝑄 𝑄𝑆
tan 𝑋 = 𝑂𝑃 and tan 𝑌 = 𝑃𝑆

𝑂𝑄 = 𝐻𝑡 − 𝑅1 − 𝑅2 cos 𝛼2 − (𝑉𝑡 − 𝑉𝑒) tan 𝛼2

𝑂𝑃 = (𝑉𝐸 − 𝑉𝑏) + 𝑅2 sin 𝛼2
𝑄𝑆 = 𝑅1 + 𝑅2
1 1
𝑃𝑆 = (𝑃𝑄 2 − 𝑄𝑆 2 )2 where 𝑃𝑄 = (𝑂𝑃2 − 𝑂𝑄 2 )2
At point C:
𝑉𝑐 = 𝑉𝑏 + 𝑅1 sin 𝛼1
𝐻𝑐 = 𝑅1 − 𝑅2 cos 𝛼2
100𝛼1
𝑀𝐷𝑐 = 𝑀𝐷𝑏 +
𝜙1
At point D:
𝑉𝑑 = 𝑉𝑐 + 𝑃𝑆 cos 𝛼1
𝐻𝑑 = 𝐻𝑐 + 𝑃𝑆 sin 𝛼1
𝑀𝐷𝑑 = 𝑀𝐷𝑐 + 𝑃𝑆
At point E:
VE is known.
𝐻𝑒 = 𝐻𝑑 + 𝑅2(cos 𝛼2 − cos 𝛼1)
100(𝛼1 − 𝛼2)
𝑀𝐷𝑒 = 𝑀𝐷𝑑 +
𝜙2
At point T:
100(𝑉𝑡 − 𝑉𝑒)
𝑀𝐷𝑡 = 𝑀𝐷𝑒 +
cos 𝛼2

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Type III (Deep Kick-off and Build)
This profile is only used in particular situations such as salt dome drilling or side tracking.
A deep KOP has certain disadvantages:
1. Formation will probably be harder and less responsive to deflection.
2. More tripping time is required to change out BHAs while deflecting.
3. BUR is more difficult to control.
The following information is required:
1. Surface (slot) coordinates.
2. Target coordinates (by geologist).
3. one further parameter from
▪ i)- vertical depth at KOP,
▪ ii) - build-up rate (φ),
▪ iii) – maximum angle of inclination.
4. If any one of the parameters (i), (ii),or (iii) is known the others can be determined.

Figure 5 Type III profile.

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 𝐻𝑡
𝛼2 = 2 tan−1
𝑉𝑡 − 𝑉𝑏
𝑉𝑡 − 𝑉𝑏
𝑅=
sin 𝛼2
2𝜋(𝑉𝑡 − 𝑉𝑏)𝛼2
𝐵𝑇 =
360 × sin 𝛼2
𝛼2 180(sin 𝛼2) × 100
𝐵𝑈𝑅 (𝜙) = =
𝐵𝑇 𝜋(𝑉𝑡 − 𝑉𝑏)

18000
OR 𝜙= 𝜋𝑅

Deflection Tools and Techniques

Whipstocks
The whipstock is widely used as a deflecting medium for drilling multilateral wells. It consists of
a long inverted steel wedge which is concave on one side to hold and guide a deflecting drilling
or milling assembly. It is also provided with a chisel point at the bottom to prevent the tool from
turning, and a heavy collar at the top to withdraw the tool from the hole.
Today, whipstocks are mainly used to mill casing windows for sidetracking existing wells.
1) A removable whipstock
can be used to initiate deflection in open hole, or straighten vertical wells that have become
crooked. The whipstock consists of a steel wedge with a chisel-shaped point at the bottom to
prevent movement once drilling begins. The tapered concave section has hard facing to
reduce wear. At the top of the whipstock is a collar that is used to withdraw the tool after the
first section of hole has been drilled. The whipstock is attached to the drill string by means of
a shear pin. Having run into the hole, the drill string is rotated until the toolface of the
whipstock is correctly positioned. By applying weight from surface, the chisel point is set
firmly into the formation or cement plug. The retaining pin is sheared off and drilling can
begin. A small-diameter pilot hole is drilled to a depth of about 15 ft below the toe of the
whipstock. After this rathole has been surveyed, the bit and whipstock are tripped out. A hole
opener is then run to ream out the rathole to full size. Once the deflected section of hole has
been started, a rotary building assembly can be run to continue the sidetrack. If there is a
build-up of cuttings at the bottom of the hole, it may be difficult to position the whipstock.
This led to the introduction of the "circulating whipstock", which contains a passageway to
allow mud to wash out these cuttings or fill from the bottom of the hole.

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 2) A permanent whipstock
Is used mainly in cased hole for sidetracking around a fish or by-passing collapsed casing. A
casing packer is set at the kick-off point to provide a base for the whipstock. The whipstock is run
with a mill that will cut a "window" in the casing. After setting the whipstock in the required
direction and shearing the retaining pin, the milling operation begins. Once the window has been
cut, the mill is replaced by a small diameter pilot bit. The pilot hole is subsequently reamed out to
full size. If the whipstock is used correctly, it can be considered as a reliable and effective
deflecting tool. It can provide a controlled and gradual buildup of angle.

Figure 6 Whipstock Types

Figure 7 Circulating Whipstock

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 There are however several disadvantages:
1. The rathole that is drilled initially must be reamed out, requiring a new BHA to be run.
2. While drilling, the whipstock may rotate, deflecting the bit away from its intended
direction.
3. As the bit drills off the whipstock, some drop in inclination may occur.
4. When using a permanent whipstock to mill a window in the casing, the window itself is
often too small.
It may be advisable to use a section mill to cut out a larger length of casing, then set a cement
plug and deflect the wellbore with a mud motor and bent sub.

Jetting Bit
Jet deflection is a technique best suited to soft-medium
formations in which the compressive strength is relatively
low. The hydraulic power of the drilling fluid is used to
wash away a pocket of the formation and initiate
deflection. A specially modified bit must be used that has
one nozzle much larger than the other two. The bit is run
on an assembly which includes an orienting sub and a
full-gauge stabilizer near the bit. Once on bottom, the
large nozzle is oriented in the required direction.
Maximum circulation rate is used to begin washing
without rotating the drill string. The pipe is worked up
and down while jetting continues, until a pocket is
washed away. At this stage the drill string can be rotated
to ream out the pocket and continue building angle as
more WOB is applied. Surveys must be taken frequently
to ensure the inclination and direction are correct. If it is
found that the deflected section of the well is not
following the planned trajectory, the large nozzle can be Figure 8 Jetting Bit
reoriented, and jetting can be repeated.
Advantages:
1. A full gauge hole can be drilled from the beginning (although a pilot hole may be
necessary in some cases).
2. Several attempts can be made to initiate deflection without pulling out of the hole.
Disadvantages:
1. The technique is limited to soft-medium formations (in very soft rocks too much erosion
will cause problems).
2. Severe doglegs can occur if the jetting is not carefully controlled (if the drilling is fast,
surveys must be taken at close intervals).
3. On smaller rigs there may not be enough pump capacity to wash away the formation.

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Rebel Tool
The "rebel tool" is primarily used to
change the azimuth of the trajectory. It
is normally run in the tangential
section of the hole to correct the
tendency of the bit to walk to the left
or right. The rebel tool is run with a
conventional rotary assembly and
should be placed immediately above
the bit for maximum effect. The body
of the tool is similar to a short drill
collar 8-16 ft long. The tool is
available in diameters ranging from 4
13/16" to 8 7/8”. The lower end of the
tool has a box connection looking
down so that it can be made up
directly on top of the bit. Along the
length of the collar is a recess that
accommodates a shaft or torsion rod.
At each end of the shaft is a curved
paddle, and it is this mechanism that
deflects the bit. While drilling a
directional well, the top paddle rotates
to the low side of the hole and is
forced into the recess. This causes the
shaft to turn and forces the lower
paddle against the borehole, exerting a
lateral force on the bit. The paddles
can be fitted to provide a left- or right- Figure 9 Rebel Tool
hand turn at the bit. The paddles have
tungsten carbide hard facing to ensure
high wear resistance. Surveys should be taken at close intervals to monitor direction.
Advantages:
1. It saves time, since no orientation is required, and only minor changes to drilling
parameters are necessary (rpm reduced to give more torque at the paddles; circulation
rate increased to clean paddles).
2. It is much cheaper to run than a downhole motor and bent sub.
3. The rebel tool will provide a gradual change in direction (0.5-2.5 per 100 ft), but it
requires a gauge hole to work properly.

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Mud Motors
There are two types of mud motors,
Figure 10:
1. Turbines.
2. Positive displacement motors
(PDM).

1. Turbines:
The turbine motor consists of a
multistage blade- type rotor and stator
sections, a thrust bearing section and a
drive shaft. The number of rotor/stator
sections can vary from 25 to 50. The Figure 10 Operation principles of turbine and PDM
rotor blades are connected to the drive
shaft and are rotated by mud pumped under high pressure. The stator deflects the mud onto the
rotor blades. Rotation of the rotor is transmitted to the drive shaft and drillbit. Turbines were
widely used in the past, however, recent improvements in PDM design have relegated the use the
turbines to special drilling applications.
2. PDM:
A positive displacement motor (PDM) consists of (Figure 10):
▪ Power section (rotor and stator).
▪ By-pass valve.
▪ Universal joint.
▪ Bearing assembly

Down hole Motor and Bent Sub.

(DHM) like positive displacement motor are the most common
types which are used to drive the bit without rotating the drill
string. The deflection is provided by a special sub placed above
the motor to create a side force at the bit. The bent sub is a
short length of drill collar usually about 2 ft long. The axis of
the lower (pin) connection is machined slightly off vertical.
The amount of offset angle can vary between 0.5 (for very
gradual changes of trajectory) and 3° (for very rapid changes).
The bent sub forces the bit and motor to drill in a specific
direction that is determined by the tool face. The tool face is
indicated by a scribe line marked on the inside of the bend in
the sub. The amount of deflection is a function of the offset.
Once the assembly is run to bottom, the orientation of the bent Figure 11 Bent Sub.
sub can be measured by surveying tools. The bent sub itself

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 may contain an orienting sleeve, or a separate orienting sub may be run immediately above
the bent sub.
The advantages of using a bent sub or bent housing with a mud motors:
▪ For difficult deflections (deflecting through a casing window) a bent housing can
be installed within the motor itself. This is a special device that is placed between
the stator and bearing assembly to give a slight bend of (1- 1.5) °/100 ft. This
means that a bent housing will provide a larger turn than a bent sub of similar
size.

The advantages of using a bent sub or bent housing with a mud motor:
▪ Full –gauge hole can be drilled
▪ gives a smooth curvature with less risk of severe doglegs. This technique can be used
to build or drop inclination, and to steer the bit to the left or right. When a very rapid
change of angle is required, a bent sub can be used together with a bent housing.

A down hole turbine can be used in the same way as PDM motor to deflect the wellbore.
The shorter length of the PDM, however, gives a greater advantage over the turbine for kicking-
off and sidetracking operations.
In the long tangential section of the directional well, however, turbines may be more cost-
effective than conventional rotary methods.
It is possible to steer the turbine over this section by means of an offset stabilizer. The offset
stabilizer can be oriented in the required direction, the drill string is not rotated, and the turbine
drives the bit along the desired course. then DS is rotated by offset

Specialized Deflection Techniques

When the reservoir is relatively shallow and covers a wide area, this method requires a very high
angle of inclination to reach the target. The angle could be reduced by selecting a shallower KOP,
but this is not always possible, because of softer formations nearer the surface. An alternative
approach is to eliminate the vertical part of the trajectory completely by introducing deflection at
the surface. By doing this, the problems of building and maintaining inclination are reduced, and
a larger area of the field can be covered from one central platform.
There are two techniques have been proved successful:

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Curved Conductors
In offshore areas such as the Gulf of Mexico there are
oil and gas reservoirs situated at depths of 3000-6000 ft
below the seabed. Large fixed platforms are required to
develop these fields in water depths up to 450 ft.
Conventional directional wells from these platforms
cannot, however, cover the entire area and so several
platforms are required, increasing the cost of the
development by a substantial amount. The curvature of
the conductors (1970) is 3-6° per 100 ft and they are
driven 150-200 ft into the seabed. The conductors can
be oriented towards the target as they are being driven,
so that horizontal corrections for azimuth are reduced.
The initial deflection at the seabed is already 10-20°of
inclination. Drilling problems with the curved
conductors have proved to be no more serious than in
previous directional wells. Figure 12 Fixed platform using curved conductor

Slant Hole Drilling

Another technique for drilling an inclined hole starting
from the surface is to mount the rig at some angle to
the vertical. The hole is spudded at this angle and
drilling continues in the conventional manner. It is
theoretically possible to orient the rig such that the hole
is drilled directly to the target. For some land-based
operations, the derrick has been tilted at 45° to the
vertical.
To adapt a standard drilling rig for slant hole drilling,
certain modifications must be made:
1. The rotary table must be inclined so that it is
perpendicular to the axis of the derrick. (A
power swivel may be used as an alternative.)
2. The travelling block and hook must be run on
guide rails up inside the derrick.
3. The BOP stack must be mounted on a frame
that can be tilted to the required angle. Figure 13 Fixed platform using slant rig.
4. A hydraulic pipe racking system makes the
handling of drill pipe much easier.

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Toolface Setting
To set the toolface properly the directional driller must have certain information:
1. The present inclination and azimuth of the hole.
2. The required change in inclination or azimuth to correct the trajectory or kick off the
well.
3. The expected rate of change (Le. the dogleg) that the deflecting tool can provide.

Graphical Methods
Ragland diagram

Figure 14 Ragland Diagram

The solution can be represented on a Ragland diagram:

▪ The line OA represents the present direction (050°).
▪ Along this line the current inclination (8°) is scaled off.
▪ This fixes the position P. At this point a circle representing the expected change of angle
(1.5 degree) is drawn.
▪ The line OB represents the new. direction (060°) which cuts the circle at 2 points X and
Y. The angle APY gives the orientation angle. Toolface settings are usually given in terms
of degrees left or right from the High Side of the hole. In this case the required toolface
heading (APY) is 75° right of High Side in order to change the azimuth to 060°.
▪ Notice also that this will result in a slight increase in inclination (OY represents about 8.5
degree). If the orientation angle were chosen as APX, the result would be a direction of
060°, but a drop in angle to about7.5°.

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Ouija board
On the rig, the directional driller may use a "Ouija board" This involves a similar technique to
that described for the Ragland diagram but is much quicker since no diagrams need be drawn.

Figure 15 Ouija board

Calculations
Alternatively, a series of equations can be derived to calculate the necessary angles directly.
To calculate the change in azimuth for a given toolface heading, dog-leg angle and inclination:

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Bottom Hole Assemblies (BHA)
The bottom hole assembly refers to the drill collars, HWDP, stabilizers and other accessories used
in the drill string. All wells whether vertical or deviated require careful design of the bottom hole
assembly (BHA) to control the direction of the well in order to achieve the target objectives.
Stabilizers and drill collars are the main components used to control hole inclination.
There are three ways in which the BHA may be used for directional control:
1. Pendulum Principle.
2. Fulcrum principle.
3. Packed hole stabilization principle.

Pendulum Principle
The pendulum technique (Figure 16) is used to
drop angle especially on high angle wells where it
is usually very easy to drop angle. The pendulum
technique relies on the principle that the force of
gravity can be used to deflect the hole back to
vertical. The force of gravity is related to the
length of drill collars between the drill bit and the
first point of tangency between the drill collars
and hole. This length is called the active length of
drill collars and can be resolved into two forces:
one perpendicular to the axis of the wellbore and
is called the side force and one acts along the
hole. Increasing the active length of drill collars
causes the side force to increase more rapidly than
the along hole component. The side force is the
force that brings about the deflection of the hole
Figure 16 Pendulum principle
back to the vertical. Some pendulum assemblies
may also use an under gauge near-bit stabilizer to
moderate the drop rate. High WOB’s used with a pendulum assembly may bend the BHA and
cause the hole angle to build instead of drop. Also, pendulum assemblies have a tendency to walk
to the right depending on the type of bit used and since they are flexible, they will follow the
natural walk of the drill bit.

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Fulcrum Principle
This is used to build angle (or increase hole
inclination) by utilizing a near bit stabilizer to
act as a pivot or a fulcrum of a lever, Figure
17. The lever is the length of the drill collars
from their point of contact with the low side
of the hole and top of the stabilizer. The drill
bit is pressed to the high side of the hole
causing angle to be built as drilling ahead
progresses. Since the drill collars bend more
as more WOB is applied, the rate of angle
build will also increase with WOB.

The build rate also increases with:

1. distance from near bit stabilizer to
2. first stabilizer in the BHA
3. reduction in RPM Figure 17 Fulcrum Principle
4. increase in hole angle.
5. reduction in drill collar diameter

Packed Hole Stabilization Principle

This is used to hold or maintain hole inclination and direction
and are typically used to drill the tangent section of a well. The
packed BHA relies on the principle that two points will contact
and follow a sharp curve, while three points will follow a
straight line, Figure 18. Packed BHA has several full gauge
stabilizers in the lowest portion of the BHA, typically three or
four stabilizers. This makes the BHA stiff and hence it tends to
maintain hole angle and direction.
Figure 19 Packed BHA principle

Figure 18 Bottom hole assemblies.

Page | 18
Figure 20 BHA Configurations

Trajectory Calculations
At the end of each successful survey (e.g. single-shot, multi-shot, steering tool, surface readout
gyro, MWD) the following data is measured:
▪ survey measured depth.
▪ wellbore inclination.
▪ wellbore azimuth (corrected to relevant North).
The above data will then enable the bottom hole location at the last survey point to be calculated
accurately in terms of:
• TVD
• Northing
• Easting
• Vertical section
• dog-leg severity
The calculated data is then plotted on the directional well plot (TVD vs vertical section on the
vertical plot, N/S vs E/W rectangular coordinates on horizontal plot).
There are several methods used for survey calculations. However, only the two most widely used
methods will be presented here:
1. radius of curvature method.
2. minimum curvature method.

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Radius of curvature Method
The radius of curvature method (Figure 21) uses the top and bottom angles to generate a space
curve having a spherical arc shape which passes through the two stations. Each course length is
assumed to be a circular arc in both the vertical and horizontal planes.
Increment of true vertical depth (∆ΤVD):

Where:
∆MD = increment of course length
Ⅰ1, Ⅰ2 = inclination angles at stations 1 and 2 respectively
Increment of northing co-ordinate (∆N):

Increment of easting co-ordinate (∆E):

Where: A1, A2 = azimuth angles at stations 1 and 2 respectively

Note: If the azimuth and inclination angles remain unchanged between survey points then these
equations are no longer applicable because of the resulting division by a zero term.

Figure 21 Radius of curvature

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Minimum Curvature Method
The minimum curvature method (Figure 22) uses the principle of minimizing the total curvature
within the constraints of the wellbore in order to produce a smooth circular arc. The surveys at the
two stations define vectors which are tangent to the wellbore at the survey points. A ratio factor
(RF) is used to smooth the vectors on to the wellbore curve.

Figure 22 Minimum curvature method

First calculate the ratio factor (RF):

Where:
RF = Ratio Factor.
DL = dogleg angle in degrees.

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Projecting Ahead
Once the location of the last survey point is calculated, it is also necessary to calculate the future
course of the well to see whether the well is on course to hit the target.If the well is off course,
then a correction may be required.
In the horizontal plane:

Total walk needed = 2 Z

Where: Z= difference between the present direction and direction to target from the present
location

Figure 23 Bit walk

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References
• Williamson H.S. (2000) "Accuracy prediction for directional measurement while drilling"
SPE drilling & Completion 15 (4), December.
• Wolff, C and de Wardt, J (1981) "Borehole Positional uncertainty - analysis of measuring
methods and derivation of systematic error model" JPT, Dec.,2339
• API RP 7G (1981). Drillstem Design and Operating Limited. API Publications.
• Eastman Whipstock. Introduction to directional drilling. Eastman Whipstock Publication.

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