# DIRECTIONAL DRILLING TRAJECTORY DESIGN AND CALCULATIONS

## DIRECTIONAL DRILLING PLANNING - WELLS TRAJECTORY DESIGN AND CALCULATIONS

### Our Objective

The target of this article is to show the directional well trajectory calculations methods required for well path design and to show the utilization of trajectory and directional survey calculation methods by designing the well path of two wells. The focus will be on is on the below items:
• Calculate directional coordinates.
• Calculate (TD) the total depth , (KBTVD) the true vertical depth, vertical departure, at (EOB) interval, in a build and hold well profile.
• Calculate directional coordinates.
• Give formulas which is utilized in calculating the directional well trajectory for several methods: Tangential; balanced tangential; average angle; radius of curvature; and minimum curvature.

### 4 Major Types of Directional well Profiles

#### 1) Build and Hold Directional Well Profile

This type of directional well profile consist of:
• Vertical section.
• Kickoff point.
• Build-up section.
• Hold section up to target.
Always this type of directional well trajectory profile is used when single completion shallow wells will be drilled.
1. First, the wells can be vertically drilled to some point called  kick-off point (shallow depth).
2. Then, the well is deflected smoothly until a maximum inclination angle with the desired azimuth.
3. After that, it is preferred to run casing if this is applicable.
4. Finally, keep holding both inclination and azimuth  (HOLD) till the well target.

#### 2) Build, Hold and Drop Directional Well Profile - S profile Wells

This type of directional well profile consist of:
• Vertical section.
• Kickoff point.
• Build up section.
• Hold section.
• Drop off section.
• Hold section up to target.

The drilling of such type will be with the following sequence:

1. First, the wells can be vertically drilled to some point called  kick-off point (shallow depth).
2. Then, the well is deflected smoothly until a maximum inclination angle with the desired azimuth.
3. Then, it is preferred to run casing if this is applicable.
4. After than, keep holding both inclination and azimuth  (HOLD).
5. Further, Start dropping smoothly till well became vertical again.
6. Finally, keep holding the angle till reach well target.

This type of Directional well trajectory profile has a disadvantage which is it will produce higher torque and drag for the same horizontal departure.

Application:
•  For sidetracking.
• To avoid faults.
• To hit multiple targets.
• To decrease the inclination in a certain inter

#### 3) Continuous Build Directional Well Profile - J profile Wells

This type of directional well profile consist of:
• Vertical section.
• Kickoff point (deep).
• Build-up section.
They are same as to the Build and Hold Directional Well Profile except that the kickoff point is at a deeper depth.

#### 4) Horizontal Directional Well Drilling

This type of directional well trajectory profile is consist of anyone of the above profiles in addition to a horizontal section within the required target interval.

The horizontal section is usually drilled at 90 degrees so the extra equations involved is to get length of the horizontal section to calculate the total well departure and total measured depth.

The hole total KBTVD usually remains the same as the KBTVD of the well at the start of the horizontal section as there are no dip variations within the reservoir.

Applications:
• To connect the portions of the reservoir that are productive.
• To increase productivity from low permeability reservoirs by increasing the amount of formation exposed to the wellbore.
• To produce thin oil zones with water or gas coning problems.
• To maximize production from reservoirs which are not being efficiently drained by vertical wells.

### Planning The Well Profile

To start planning a directional well, we have to design the wellbore trajectory, to hit a given target. The first thing to consider is selecting the most economical wise design for directional drilling trajectory profile.

#### A) Kickoff Point

Definitions:
Which is the MD at which the well is planned to be deflected from vertical, a change in inclination is started and the well is oriented with certain azimuth (in terms of north, south, east and west).

Simple Hints:
1. The shallowest KOPs will result in a decrease in the tangent section inclination. Also it will be more difficult to kick off well on deeper formations
2. Starting kick-off the well should happen on more stable formations.

#### B) Build-up and drop off rate (in degrees of inclination)

Definition:
Which are the rates at which the well is deflected from the zero degree (vertical) (usually measured in degrees per 30 m or 100 ft).

How to select the Build up or the drop off
The build up rate is chosen on the basis of previous field experience, offset wells and the available tools, but rates between 1° and 3° per 100 ft are commonly used in conventional drilling. Since Build up rate and drop off rate are constant, these sections of the well, form the arc of a circle.

(DLS)
There are an a term called dogleg severity which is a result of a higher build up rate more than 3°/100 ft
Build up rates in excess of 3°/30 m are likely to cause doglegs when drilling conventional deviated
wells with conventional drilling equipment. The build-up rate is often termed the dogleg severity

#### C) Tangent angle | drift angle

Which is the inclination (in degrees from the vertical) after the BU section of the directional well. This section of the well is termed the tangent section because it much like a tangent to the end of the arc formed by the BU section of the directional well. The tangent angle range is preferred to be (10° and 60°) as it will difficult to control the trajectory of the well at angles below 10° and also  to run WL logging into directional wells at higher inclinations values (more than 60°).

#### Second Step, Start Your Trajectory Design By Collecting Well Data (Target And Geography).

The trajectory of a directional well must be carefully planned considering that the most effective trajectory is utilized to drill between the rig surface location and the target location with the lowest costs.

When planning, and then started drilling the well, the location of all points along the well-path trajectory is considered in three dimensions which are: -
1. KBTVD : The vertical depth of the point below a particular reference point.
2. NORTHING / LATITUDE: The horizontal distance between the target and the East/West axis in plan view.
3. EASTING / LONGITUDE: The horizontal distance between the target and the North/South axis in plan view.

#### Third Step, How To Define The Oil / Gas Wells Trajectory

Now let’s understand how to plan the geometrical profile of the oil / gas wells to reach the target. Commonly used well trajectory is the build and hold profile, which consists of 3 sections - vertical, build-up and tangent.

To plot such wellbore trajectory, we have to define below points:
• KOP kick-off point.
• KBTVD and horizontal displacement for the final point of the build-up section.
• KBTVD and horizontal displacement of the target (defined by surface and target coordinates).
As the driller will only be able to determine the long hole depth of the well, the following information will also be required:
• MD at the KOP (same as KBTVD of KOP);
• Build up rate for the build-up section (selected by engineer);
• The azimuth which is the direction in which the well is to be drilled in degrees from north (defined by surface and target coordinates);
• MD at (EOB)
• MD of the target.

#### Forth Step, What Is The Formulas To Start Your Well Profile Calculations

Build Up and Hold Design And Calculations

The following information is required:
• Surface (slots) coordinates.
• Target coordinates (Selected by the geologist).
• Target KBTVD (Selected by the geologist).
• KOP KBTVD (Selected by the directional Engineer).
• Build Up Rate (Selected by the directional Engineer).

The two Figures below show a build-and-hold wellbore trajectory with the following target data :
1. TVD3 : (KBTVD) of the target
2. Dh: The target  horizontal departure (point D).
3. TVD1: The kickoff point KBTVD
4. q : build up rate (In degrees per unit length).
Where:
• KBTVD AB: Distance from the surface location to the KOP;
• B-D: Distance from KOP to the bottom of hole;
• Dh : Deviation of the wellbore from the vertical (Horizontal displacement);
• KBTVD AG: True vertical depth;
• MD (A-D): Well measured depth; and
• q: Build up rate (°/30 m).

For the following formula, note that KBTVD3 =TVDAG, KBTVD2 =TVDAC, KBTVD1 =TVDAB.

1) The radius of curvature, R:

2) Maximum inclination angle, θ:

The angle τ can be found by considering the triangle OPD, where (case R ˃ Dh):
Angle Ω can be found by considering ODC, where:

Substituting OP into Equation 4 gives:

Now you can calculate Maximum inclination angle, θ

The maximum inclination angle, θ, for the build-and-hold case where Dh less than R is:

 The maximum inclination equation

OR

 The maximum inclination
3) Measured Depth of the wellbore target (MD)
The length of the arc, section BC, is:

The length of the trajectory path, CD, can be determined from triangle DCO as:

The total measured depth, DM, for a true vertical depth of TVD3 is:
4) The horizontal departure GF (DE) at the end of the build can be determined by considering DCO, where:

If it is required to calculate measured depth and horizontal departure at any point in the build section, consider the intermediate inclination angle θ’, the inclination angle at C’, which will yield a new horizontal departure, Dn.
Build Up, Hold and Drop Off Design And Calculations

 Build Up, Hold and Drop Off
The second type of trajectory is S shape curve, which is showed above, There are two cases:
1. R less than Dh and R+R1 more than Dt
2. R less than Dh and R+R1 less than Dt.

Any way,  the maximum inclination is reduced to zero at Dt with drop radius R1, which is derived in the same manner as the build radius, R.

KBTVD BG: Distance from the surface location to the KOP;
KBTVD AG: True vertical depth of well (KBTVD);
B-D: Distance from KOP to the bottom of hole (MD);
G-D: Deviation of the wellbore from the vertical to the end of tangent section;
G-P: Deviation of the wellbore from the vertical to the end of drop section;
A-G: True vertical depth;
A-P:Measured depth; and
D: End of tangent section

The following equations are used to calculate the maximum inclination angles for R+R1 more than Dt  and  R+R1 less than Dt:

 Maximum Inclination Equation
 Maximum Inclination Equation