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Well Trajectory Calculation & Directional Design

This article aims to show the directional well trajectory calculation methods required for all well profile design planning, including build, hold & drop sections, and to show the utilization of trajectory and directional survey calculation methods by designing the well path of two wells. Please note that this article is one of our Directional Drilling Guide Articles.

The focus will be on is on the following items:

  • Calculate directional coordinates.
  • Calculate (TD) the total depth, (KBTVD) the true vertical depth, and vertical departure, at (EOB) interval, in a build and hold well profile.
  • Calculate directional coordinates.
  • Give formulas which are utilized in calculating the directional well trajectory for several methods: Tangential; balanced tangential; average angle; the radius of curvature; and minimum curvature.

Types of Directional well Profiles For The Trajectory Calculation

Before starting the well trajectory calculations steps for well profile design, we shall explain the different directional well planning profiles, which are mainly four types:

1) Build and Hold Directional Well Planning Profile Design

This type of directional well trajectory profile consists of:

Build Hold Directional Well planning
Directional Well Planning Build and Hold Profile Design
  • Vertical section.
  • Kickoff point.
  • Build-up section.
  • Hold section up to target. 

Consistently this type of directional well trajectory profile & calculation is used when single-completion shallow wells will be drilled.

  1. First, the wells can be vertically drilled to some point called the 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 inclination and azimuth (HOLD) until the well target.

2) Build, Hold and Drop Directional Well Planning Profile – S profile Wells Design

Build Hold and Drop Directional Well Profile - S profile Wells
Directional Well Planning Build, Hold and Drop Profile Design

This type of directional well profile consists of the following:

  • 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 the 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 that, keep holding both inclination and azimuth  (HOLD). 
  5. Further, Start dropping smoothly till well became vertical again.
  6. Finally, keep holding the angle till you reach well target.

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

Application: 

  • To hit multiple targets.
  • To decrease the inclination in a specific inter

3) Continuous Build Directional Well Planning Profile – J profile Wells Design

Build up Directional planning - J profile Wells
Directional Well Planning J profile Design (hold then build trajectory)

This type of directional well profile consists of:

  • Vertical section.
  • Kickoff point (deep). 
  • Build-up section.

They are the same as the Build and Hold Directional Well Trajectory Profile Calculation, except that the kickoff point is deeper. 

4) Horizontal Directional Well Planning Profile Design

Horizontal Directional well planning
Directional Well Planning Horizontal Profile Design

This type of directional well trajectory profile consists 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. Hence, the extra equations involved are to get the 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 productive portions of the reservoir. 
  • 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 that are not efficiently drained by vertical wells.

Planning The Well Profile

To start planning a directional well, we must design the wellbore trajectory to hit a given target. The first thing to consider is selecting the most economical design for the directional drilling trajectory profile. Of course, you shall think about which build, hold or drop trajectory calculation will be adaptable for you.

First, What Are The Parameters Which Define The Directional Well Profile | Trajectory Design

Three essential parameters shall be defined before starting any well trajectory calculation, which is as follows:

  • Kick Off Point
  • Build-Up & Drop-Off Rate
  • Tangent / Drift Angle

Kickoff Point

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 specific 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.

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

In well trajectory calculation & profile design planning, we use the term build-up and drop-off rate, which are the rates of the well deflected from zero degrees (vertical) (usually measured in degrees per 30 m or 100 ft).

The build-up rate is chosen based on 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 is a term called dogleg severity resulting from a higher build-up rate of more than 3°/100 ft. Build-up rates over 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

It is determined by one or more of the following:

  • The total depth of the well.
  • Maximum Torque and Drag limitations.
  • High dogleg severity in the build section of the well results in high torque and drag while drilling the remainder. This can be a severe limiting factor in deeper wells.
  • The formations through which the build section must pass. Higher build rates are often not possible to achieve in soft formations.
  • Mechanical limitations of the drill string or casing.
  • Mechanical limitations of logging tools and production strings.
  • Formation of “Keyseats” in the Kick-off arc ( which will result in mechanical stuck)

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 is 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 be 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 Calculations 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 (check also drilling cost per foot). 

3d plan view for directional well  planning

When planning and then starting 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. 
  1. NORTHING / LATITUDE: The horizontal distance between the target and the East/West axis in the plan view.
  1. EASTING / LONGITUDE: The horizontal distance between the target and the North/South axis in the 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. A commonly used well trajectory is the build-and-hold profile, which consists of 3 sections – vertical, build-up, and tangent.

To plot such a wellbore trajectory, we have to define the following 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);
  • The azimuth 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.

Fourth Step, What Are The Formulas To Start Your Well Trajectory Calculation

Build Up and Hold Trajectory Calculations

The following information is required For successful Well Trajectory Calculation: 

  • 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 Figure below shows a build-and-hold wellbore trajectory with the following target data :

  1. TVDAG : (KBTVD) of the target
  2. Dh: The target horizontal departure (point D).
  3. TVDAB: The kickoff point KBTVD
  4. q: build-up rate (In degrees per unit length).
Geometry  type directional  well planning for R ˃ Dh
Illustrative Diagram For Build & Hold Well Trajectory Calculation

Where:

  • KBTVD AB: Distance from the surface location to the KOP;
  • B-D: Distance from KOP to the bottom of the 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:

radius of curvature

2) Maximum inclination angle, θ:

maximum inclinations for well trajectory design and calculations

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

maximum inclinations for directional well planning

 Angle Ω can be found by considering ODC, where:

maximum inclinations for well trajectory design and calculations

Substituting OP into Equation 4 gives:

maximum inclination for well trajectory design and calculations

Now you can calculate the Maximum inclination angle, θ

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

maximum inclination for well trajectory design and calculations
The maximum inclination equation

OR

maximum inclinations for well trajectory design and calculations
The maximum inclination

3) Measured Depth of the wellbore target (MD)

The length of the arc, section BC, is:  

measued depth calculations in well trajectory design

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

measued depth calculations in well trajectory design

 The total measured depth, DM, for an actual vertical depth of TVD3 is:

measued depth calculations in well trajectory design

4) The horizontal departure GF (DE) at the end of the build can be determined by considering DCO, where:

horizontal departure calculations in well trajectory design

If it is required to calculate the 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 Well Trajectory Calculations

Build Up, Hold and Drop Off Design & Calculations
Build Up, Hold and Drop Off

 The second type of trajectory calculation is for S shape curve, which is shown 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. 

Anyway,  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 the hole (MD);
  • G-D: Deviation of the wellbore from the vertical to the end of the tangent section;
  • G-P: Deviation of the wellbore from the vertical to the end of the 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:

Build Up, Hold and Drop Off Design & Calculations
Maximum Inclination Equation
Build Up, Hold and Drop Off Design & Calculations
Maximum Inclination Equation