This document summarizes key concepts from a drilling engineering course textbook. It begins by covering general casing design criteria, graphical casing design methods, and other considerations. It then discusses directional well trajectories, including the necessity of directional wells, major trajectory types, definitions, and trajectory calculations. Key points include types of basic 2D trajectories like build-and-hold and build-and-hold-and-drop trajectories. Equations are provided for calculating trajectory parameters.

1. Drilling Engineering 2 Course (2nd Ed.)

2. 1. General Casing Design Criteria
2. Graphical Method for Casing Design
3. Other Casing Design considerations

3. 1. Necessity of Directional well
2. well’s trajectory
3. Major Types of Wellbore Trajectories
4. Trajectory rule of thumbs and terms
5. Trajectory Calculation

5. Directional well
A well is declared as a directional one when it follows a
predescribed traverse or trajectory to intersect specific
targets. They can be necessary when:
Reaching a target which is below
inaccessible or restricted areas such as
a mountain, a highly populated area, a national park, etc.,
Multiple wells have to be drilled from one offshore platform
to deplete large portions of a reservoir from one structure,
Side tracking has to be done around a fish,
Fault drilling is necessary,
Salt dome drilling takes place,
Drilling a relief well to intersect a blowout well,
Sidetracking from an old well
to explore different horizons and/or directions.
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6. Directional well; schematics
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7. Directional well; schematics (Cont.)
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8. Directional well; schematics (Cont.)
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9. Directional well; schematics (Cont.)
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11. bit walk
While drilling, many factors influence
the trajectory of the bore hole.
Some of them are easy to control,
others may be difficult to estimate.
Amount the difficult ones to predict
is the so called “bit walk”
that may occur in certain formations and
does not follow a general trend.
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12. the trajectory displacement
To plan a well’s trajectory, to follow up
the drilled one as well as
to correlate its deviation from the plan,
the trajectory is generally displayed in
a horizontal view and a vertical view.
The horizontal view
projects the trajectory to a plain that has
the N-S and E-W directions as their axis and
the rotary table at its center.
The vertical or section view
shows the trajectory projected to a vertical cross-section
defined by the rotary table and the target.
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13. Definitions of trajectory
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14. Definitions of trajectory (Cont.)
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16. Target location
The first step of planning a directional well
is to identify where the target (targets)
are located in respect to the rig location.
For drilling,
the origin of the trajectory is taken from the rotary table.
Thus the location of the target,
which is mostly determined by the production
department in UTM or Lat/Long coordinates,
has to be re-calculated into
“Northing” and “Easting” in respect to the rotary table.
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17. Target depth
The depth of the target,
which can be referenced to
ground level,
mean sea level or
water table,
has to be referenced to the rotary table as well.
Note that the rotary table height
is specific to a particular rig and
when an old well has to be re-entered or sidetracks
drilled, the survey of the old well is referenced
to the rotary table height of the rig it was drilled with
which can be different from the one use later on.
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18. significant points
When these
identifications and
corrections are done,
the trajectory is planned
so that
the specified target
is reached from
the surface location.
The views of
the planned trajectory
show and
contain values for
the location of
the rotary table,
the kick of point(s),
the end of build point(s),
the drop down point(s),
the end of drop point(s)
as well as the target in
TVD (true vertical depth),
MD (measured depth),
inclination,
azimuth and
horizontal departure.
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19. Basic 2-D types of trajectories
Apart from these “significant points”
a survey is created that lists the values mentioned above
as a sequence of points that
have a constant MD difference
(or are closer when needed, e.g. at turning intervals).
Following basic, 2-D types of trajectories have been
established by the industry for practical realizations:
Build-and-hold trajectory,
Build-and-hold-and-build (double build) trajectories,
Build-and-hold-and-drop (S) trajectories,
Build-and-partial drop-and hold (modified S) trajectory.
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20. Different types of basic (2D)
trajectories
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21. type 1: Build-and-hold trajectory
At type 1 trajectories,
the well is kicked of at a specified depth,
inclination is build up until a certain amount
(end of build) and kept until the target is reached.
This type of profile is often applied
when a large horizontal displacement is required
at relatively shallow target depths.
Since there are no major changes in inclination or
azimuth after the build-up section is completed,
there are fewer directional problems with this profile,
such as dog-leg, key seats, etc..
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22. type 2: Build-and-hold-and-build
(double build) trajectories
At type 2 trajectories,
the well is kicked of at a specified depth and inclination is
build up until a certain amount (end of build).
Then this inclination is hold until a second kick of point is
reached, inclination is built up again to a certain amount
(end of build) and kept until the target is reached.
This type of trajectory is preferred for
relative large horizontal displacements
which are achieved at the first holding section.
This holding section is commonly designed with an inclination
angle of between 30 to 40◦ since within these values, close control
over the trajectory-progress is convenient.
After the second building interval
horizontal or nearly horizontal wells are often planned for.
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23. type 3: Build-and-hold-and-drop (S)
trajectories
At type 3 trajectories,
the well is kicked of at a specified depth,
inclination is build up
until a certain amount (end of build) and
kept until the drop down point is reached.
From the drop down point
until the end of drop point
the inclination is reduced to zero degrees and
the well is continued until the target is hit vertically.
Here an extra torque and drag are expected
due to the additional bend.
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24. type 3: Build-and-hold-and-drop (S)
trajectories (Cont.)
This type of profile is used
when the target is deep
but the horizontal displacement is relatively small.
It also has applications
when completing a well
that intersects multiple producing zones, or
in drilling relief-well
where it is necessary to run parallel
with the blowing well.
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25. Build-and-partial drop-and hold
(modified S) trajectory.
At type 4 trajectories,
the well is kicked of at a specified depth, inclination is
build up until a certain amount (end of build) and kept
until the drop down point.
From the drop down point until the end of drop point
the inclination is reduced but
differently to type 3 trajectories, not to zero degrees.
Then the inclination is kept
until the target is intercepted.
The applications and characteristics of this well
type are similar to the ones of type 3.
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28. Other trajectories
Along with these basic
trajectory types,
so called
catenary trajectories
(designed to minimize
torque and drag) and
general 3D trajectories
that turn in space
are common practice
today.
uncertainty ellipses along a directional well
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29. trajectory planning rule of thumbs
For the trajectory planning
itself, following
rule of thumbs
should be kept in mind:
The build-and-hold type is
the least expensive one of
all trajectory types and
easiest to drill.
For a given TVD and
horizontal departure
of a target,
the higher the kick of point,
the smaller
the slant angles,
less build up and
reduced total MD
is necessary
to reach the target.
If reasonable,
designing
the slant angle between
30◦ and 40◦
is good practice.
Slant angles smaller than
15◦ are to be avoided since
they are difficult to control.
A deep kick-off point has
certain disadvantages:
formation will probably
be harder and less
responsive to deflection,
more tripping time is
needed to change out BHAs
during side tracking,
build-up rate is more
difficult to control.
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30. Classification of build up section
according to the applied build up rate
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31. often used terms definitions
Below definitions assume the RKB position to be
at the center of the chosen coordination system.
Northing:
Horizontal distance between one survey point and
the RKB, measured to the North.
A distance to the South is generally denoted as being negative.
Easting:
Horizontal distance between one survey point and
the RKB, measured to the East.
A distance to the West is generally denoted as being negative.
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32. often used terms definitions (Cont.)
True Vertical Depth:
Vertical distance of one survey point to the RKB.
Horizontal Departure:
Horizontal distance between one survey point and
the RKB, at the level of the survey point.
Azimuth:
Horizontal angle (0 - 2.π), measured clockwise
from the true North
to the tangent of the trajectory at this survey point.
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33. often used terms definitions (Cont.)
Inclination:
Angle between the vertical component of the tangent of
the trajectory at the survey point and the vertical axis.
Thus a vertical well as an inclination of 0,
a horizontal well an inclination of π/2.
Measured Depth:
Actual length of the trajectory,
starting at the RKB up to the survey point.
Vertical Section:
Horizontal departure of the survey point projected to
the vertical view.
In this way the vertical section is always smaller or equal
to the horizontal departure.
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35. Calculations
In the following, calculations for
the radius of curvature (r1),
the maximum inclination angle (θ),
the measured depth and
horizontal departure for the buildup intervals as well as
the measured depth and
horizontal departure for the holding intervals
are presented for different basic trajectory types.
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36. Build-and-Hold Trajectory
This type of trajectory is
most common
in the industry
whenever applicable.
Figure shows this type of
trajectory where X3 < r1.
TVD and the horizontal
departure of the target
are denoted with
D3 and X3 respectively,
TVD of the kick of point is
given by D1.
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37. Calculation of r1 and θ
for Build-and-Hold Trajectory
Radius of curvature:
q [◦/ft] build up rate or inclination angle buildup
r1 [ft] radius of curvature
Maximum inclination angle (θ in [◦]):
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38. Calculation of DMi and Xi
for Build-and-Hold Trajectory
Measured depth and horizontal departure along
the buildup are computed with:
where, at the end of build
Along the holding interval, the measured depth
and horizontal departure are:
Di [ft] vertical depth at point i
along the buildup or holding interval
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39. Build-Hold-and-Drop (S) Trajectory
The maximum inclination angles can be calculated
by following equations:
for r1 + r2 > X4
and for r1 + r2 < X4:
When replacing X4 by X5 + r2.(1 − cosθ’) and D4 by
D5 + r2.sinθ’, the equations above can be used to
calculate the modified S type trajectory.
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40. 1. Dipl.-Ing. Wolfgang F. Prassl. “Drilling
Engineering.” Master of Petroleum
Engineering. Curtin University of Technology,
2001. Chapter 9

41. 1. the Survey of a Well
2. Calculating the Survey of a Well
3. Deflection Tools and Techniques
4. Hydraulic Method (Jetting)
5. Mechanical Methods