Dogleg Severity (DLS) & TVD Calculator
An engineering tool to calculate dogleg severity for directional drilling based on survey data, and its effect on True Vertical Depth (TVD).
Select the measurement system for depth values.
Survey Station 1 (Upper)
feet
Degrees (°)
Degrees (°)
feet
Survey Station 2 (Lower)
feet
Degrees (°)
Degrees (°)
Well Path Visualization
Simplified 2D representation of the change in inclination. Not to scale.
What is Dogleg Severity (DLS)?
Dogleg Severity (DLS) is a critical measurement in the directional drilling industry, quantifying the total curvature of a wellbore between two points. It is typically expressed in degrees per 100 feet (°/100 ft) or degrees per 30 meters (°/30 m). This metric combines the change in both inclination (the vertical angle) and azimuth (the horizontal direction) into a single value representing the wellbore’s tortuosity or bend. A high DLS indicates a sharp turn, while a low DLS signifies a more gradual change in direction. The ability to accurately calculate dogleg severity using TVD related data is fundamental for well planning and execution.
Directional drillers, well planners, and drilling engineers use DLS calculations to ensure the well path stays within design limits. Excessive dogleg severity can lead to serious operational problems, including increased torque and drag on the drill string, premature wear on casing and drill pipe, and difficulties running logging tools or completing the well. Therefore, managing and predicting DLS is essential for drilling efficiency, safety, and cost-effectiveness.
Dogleg Severity Formula and Explanation
The most widely accepted method for DLS calculation is the Radius of Curvature method. This formula models the wellbore path between two survey stations as a smooth circular arc, providing a more accurate representation than simpler tangential methods. The ability to calculate dogleg severity using TVD and survey data is built upon this principle.
The core formula is:
Dogleg Angle (β) = arccos(cos(Inc₂) * cos(Inc₁) + sin(Inc₂) * sin(Inc₁) * cos(Az₂ - Az₁))
DLS = Dogleg Angle (β) * (Reference Length / Course Length)
Where Course Length = MD₂ - MD₁ and the reference length is typically 100 ft or 30 m.
Variables Table
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| MD₁, MD₂ | Measured Depth at survey stations 1 and 2 | feet / meters | 0 – 30,000+ |
| Inc₁, Inc₂ | Wellbore Inclination at stations 1 and 2 | Degrees (°) | 0 – 90+ |
| Az₁, Az₂ | Wellbore Azimuth at stations 1 and 2 | Degrees (°) | 0 – 360 |
| TVD₁, TVD₂ | True Vertical Depth at stations 1 and 2 | feet / meters | 0 – 30,000+ |
| DLS | Dogleg Severity | °/100 ft or °/30 m | 0 – 20+ |
Practical Examples
Example 1: Standard Build Section
Consider a typical build section in a well where both inclination and azimuth are changing over a standard survey interval.
- Inputs (Imperial):
- MD₁: 8200 ft, Inc₁: 15.0°, Az₁: 120.0°
- MD₂: 8300 ft, Inc₂: 17.5°, Az₂: 124.0°
- TVD₁: 8050 ft
- Results:
- Course Length: 100.0 ft
- Dogleg Angle: 2.85°
- Dogleg Severity (DLS): 2.85 °/100 ft
- Change in TVD: 97.02 ft
- Final TVD₂: 8147.02 ft
Example 2: High Dogleg Turn
This example shows a more aggressive turn, resulting in a higher DLS, which might be found in a horizontal well section.
- Inputs (Metric):
- MD₁: 2500 m, Inc₁: 85.0°, Az₁: 90.0°
- MD₂: 2530 m, Inc₂: 88.0°, Az₂: 105.0°
- TVD₁: 1200 m
- Results:
- Course Length: 30.0 m
- Dogleg Angle: 15.22°
- Dogleg Severity (DLS): 15.22 °/30 m
- Change in TVD: 1.95 m
- Final TVD₂: 1201.95 m
How to Use This Dogleg Severity Calculator
- Select Units: Start by choosing between ‘Imperial (feet)’ and ‘Metric (meters)’. This sets the standard for all depth inputs and the DLS output.
- Enter Survey Station 1 Data: Input the Measured Depth (MD1), Inclination (Inc1), Azimuth (Az1), and True Vertical Depth (TVD1) for the upper survey station.
- Enter Survey Station 2 Data: Input the Measured Depth (MD2), Inclination (Inc2), and Azimuth (Az2) for the lower survey station.
- Calculate: Click the “Calculate” button. The calculator automatically updates if you change any input value.
- Review Results: The primary result, Dogleg Severity, is prominently displayed. You can also view intermediate values like Course Length, total Dogleg Angle, and the calculated change in True Vertical Depth (ΔTVD). The final TVD at station 2 is also shown.
Key Factors That Affect Dogleg Severity
- Well Plan Design: The planned trajectory is the primary determinant. Aggressive build or turn rates designed into the plan will naturally result in higher DLS.
- Bottom Hole Assembly (BHA): The design of the BHA, including the type of mud motor, stabilizers, and bit, heavily influences its directional tendencies and ability to follow the planned path.
- Drilling Parameters: Weight-on-bit (WOB), rotary speed (RPM), and flow rate can be adjusted by the directional driller to control the BHA’s behavior and manage the DLS.
- Formation Characteristics: The type of rock being drilled (hard, soft, laminated) can cause the BHA to deviate from the planned path, leading to unintentional changes in DLS.
- Survey Interval Length: The distance between survey stations (e.g., 100 ft vs. 30 ft) can affect the calculated DLS. Shorter intervals provide a higher-resolution view of the wellbore’s curvature. A sharp bend over 10 feet will be averaged out over a 100-foot survey, showing a lower DLS than is actually present.
- Driller Skill and Experience: An experienced directional driller can anticipate trends and make subtle adjustments to keep the well on track, minimizing unwanted doglegs.
Frequently Asked Questions (FAQ)
- What is considered a high Dogleg Severity?
- This is relative, but generally, DLS above 3-5°/100ft is considered potentially problematic for standard drilling and casing runs. High-build “curve” sections in horizontal wells can be intentionally designed with DLS of 8-20°/100ft or more, requiring specialized equipment.
- How does TVD relate to Dogleg Severity?
- While DLS is a measure of curvature along the measured depth, this curvature directly impacts the rate of TVD change. In a build section (increasing inclination), higher DLS slows the rate of TVD increase. The ability to calculate dogleg severity using TVD as a reference helps in understanding the well’s vertical progress relative to its tortuosity.
- Why is the Radius of Curvature method preferred?
- It treats the well path as a smooth arc between survey points, which is a more realistic physical model than assuming straight-line segments (Tangential method) or simply averaging angles. This leads to more accurate DLS and positional calculations.
- Can DLS be negative?
- No. DLS is a scalar magnitude representing the total change in angle. It is always a positive value.
- What is the difference between Dogleg Severity and Build/Turn Rate?
- Build Rate is the change in inclination only. Turn Rate is the change in azimuth only. Dogleg Severity is a composite measure that combines both changes into a single value representing the total 3D curvature.
- How does changing the unit system affect the calculation?
- The core formula for the dogleg *angle* is the same. However, the final DLS value is normalized to a reference length. The calculator automatically switches this reference from 100 feet (Imperial) to 30 meters (Metric) to provide the correct industry-standard output for the selected unit system.
- What happens if my survey interval is not exactly 100 ft or 30 m?
- The calculator handles this automatically. It calculates the actual dogleg angle over your specific course length (MD₂ – MD₁) and then scales that result to the standard reference length (100 ft or 30 m).
- What causes keyseating?
- Keyseating is directly related to dogleg severity. The side force of the drill pipe against the wellbore at the inside of a bend can wear a groove (a “keyseat”) into the formation. High DLS creates higher side forces, accelerating this process and increasing the risk of getting stuck.