Dog Leg Severity (DLS) Calculator
Survey Station 1
MD at the upper survey station. Unit: feet
Angle from vertical. Unit: degrees
Compass direction from North. Unit: degrees
Survey Station 2
MD at the lower survey station. Unit: feet
Angle from vertical. Unit: degrees
Compass direction from North. Unit: degrees
Dogleg Severity
Total Dogleg Angle
Course Length
Radius of Curvature
Dogleg Severity vs. Typical Limit
| Parameter | Station 1 | Station 2 |
|---|---|---|
| Measured Depth (feet) | 5000 | 5095 |
| Inclination (°) | 10 | 12.5 |
| Azimuth (°) | 45 | 52 |
What is Dog Leg Severity (DLS)?
Dog Leg Severity (DLS) is a critical measurement in directional drilling that quantifies the total curvature of a wellbore between two points. It combines the change in both inclination (the vertical angle) and azimuth (the compass direction) into a single value, typically expressed in **degrees per 100 feet** or **degrees per 30 meters**. The term “dogleg” is an analogy for a sharp bend, similar to the shape of a dog’s hind leg.
This calculator helps drilling engineers, well planners, and geologists quickly determine the DLS, which is vital for preventing operational issues. While the prompt mentioned calculating DLS using TVD (True Vertical Depth), it’s important to clarify that DLS is calculated using data from survey stations along the **Measured Depth (MD)**, which is the actual length of the drilled wellbore. TVD is a result derived from these surveys, not a direct input for the DLS calculation itself.
Dog Leg Severity Formula and Explanation
The most widely accepted formula for calculating DLS is the Minimum Curvature method. It models the wellbore path between two survey stations as a smooth circular arc. The dogleg angle (β) is calculated first, representing the total 3D change in direction.
The formula for the dogleg angle (β) is:
β = arccos(cos(Inc₂) * cos(Inc₁) + sin(Inc₂) * sin(Inc₁) * cos(Az₂ - Az₁))
Once the dogleg angle is found, the Dog Leg Severity is calculated by normalizing this angle over a standard course length (e.g., 100 ft or 30 m).
DLS = β * (Standard Length / Course Length)
Variables Table
| Variable | Meaning | Unit (Auto-Inferred) | Typical Range |
|---|---|---|---|
| Inc₁, Inc₂ | Inclination at stations 1 and 2 | Degrees | 0° (Vertical) – 90°+ (Horizontal) |
| Az₁, Az₂ | Azimuth at stations 1 and 2 | Degrees | 0° – 360° |
| MD₁, MD₂ | Measured Depth at stations 1 and 2 | feet or meters | Depends on well depth |
| Course Length | The distance between survey stations (MD₂ – MD₁) | feet or meters | 30ft – 100ft (9m – 30m) |
Practical Examples
Example 1: Gentle Turn
Imagine a well section with a slight change in direction over a standard survey interval.
- Inputs:
- Station 1: MD = 8000 ft, Inc = 20°, Az = 150°
- Station 2: MD = 8095 ft, Inc = 21°, Az = 152°
- Calculation:
- Course Length = 95 ft
- The formula yields a total dogleg angle (β) of approximately 1.22°.
- Result: The DLS is approximately **1.28°/100 ft**, which is a low and generally acceptable value.
Example 2: Aggressive Turn
Now consider a scenario designed to build angle quickly, for instance, when kicking off from vertical.
- Inputs:
- Station 1: MD = 4500 m, Inc = 5°, Az = 90°
- Station 2: MD = 4530 m, Inc = 9°, Az = 95°
- Calculation:
- Course Length = 30 m
- The formula yields a total dogleg angle (β) of approximately 4.04°.
- Result: The DLS is **4.04°/30 m**. This is a more significant curve, and while manageable, requires careful monitoring.
How to Use This Dog Leg Severity Calculator
Using this tool is straightforward. Follow these steps for an accurate DLS calculation:
- Select Units: Start by choosing your preferred unit system, either ‘Imperial (feet)’ or ‘Metric (meters)’. This will adjust the labels and the standard length used in the calculation.
- Enter Survey Data: Input the Measured Depth (MD), Inclination (Inc), and Azimuth (Az) for two consecutive survey stations (Station 1 and Station 2).
- Calculate: Click the “Calculate” button. The calculator will instantly process the inputs.
- Interpret Results: The primary result, Dog Leg Severity, is displayed prominently. You can also review intermediate values like the total dogleg angle and the radius of curvature to better understand the wellbore’s geometry. The chart and summary table will also update with your values.
Key Factors That Affect Dog Leg Severity
Several factors influence the DLS of a wellbore. Understanding them is key to planning and drilling a successful directional well.
- Bottom Hole Assembly (BHA) Design: The type and configuration of motors, stabilizers, and bits are the primary means of controlling the well’s trajectory and the resulting DLS.
- Formation Properties: Drilling through different rock layers with varying hardness and dip angles can cause the bit to deflect, leading to unintentional changes in trajectory (and thus, DLS).
- Drilling Parameters: Weight on Bit (WOB), Rotary Speed (RPM), and mud flow rate all influence how the BHA behaves and its ability to build, drop, or turn.
- Survey Spacing: The distance between survey stations (Course Length) is critical. A shorter spacing can reveal severe, localized doglegs that might be “averaged out” and missed over a longer interval.
- Build/Drop/Turn Rates: The planned rates of change for inclination and azimuth directly determine the expected DLS. High build rates inherently lead to high DLS.
- Drill String Mechanics: The stiffness of the drill pipe and collars can resist bending, affecting the actual DLS achieved compared to what the BHA is designed for.
Frequently Asked Questions (FAQ)
1. What is considered a “high” or “bad” Dog Leg Severity?
It depends on the application. For conventional drilling, a DLS above 3-5°/100ft can increase torque, drag, and casing wear. In some specialized wells, DLS can be intentionally planned to be much higher, but this requires specific equipment designed to handle the stress.
2. Why is DLS measured per 100 ft or 30 m?
This provides a standardized unit of measurement that allows engineers to compare wellbore curvature across different wells and sections, regardless of the actual distance between surveys. It’s a normalized rate of change.
3. Can I calculate DLS directly from True Vertical Depth (TVD)?
No. DLS is a measure of the change in wellbore path along the actual drilled length, which is Measured Depth (MD). TVD is a calculated vertical component of the well path and doesn’t directly reflect the 3D curvature between two points.
4. What is the difference between Inclination and Azimuth?
Inclination is the vertical angle of the wellbore, measured in degrees from a perfectly vertical line (0° is straight down, 90° is perfectly horizontal). Azimuth is the horizontal compass direction the wellbore is pointing, measured in degrees from North (0° or 360° is North, 90° is East, 180° is South, 270° is West).
5. How does high DLS affect casing wear?
When the drill string passes through a dogleg, it exerts a lateral force on the inside of the wellbore or casing. A higher DLS means a higher force, which accelerates the wearing and grinding of the casing, potentially compromising its integrity.
6. What happens if DLS is too high?
Excessive DLS can cause many problems: high torque and drag, stuck pipe, difficulty running casing and completion equipment, and accelerated fatigue on the drill string components. It can even lead to the formation of “keyseats,” where the drill pipe wears a groove into the side of the wellbore.
7. Does this calculator work for horizontal wells?
Yes. The formula is valid for any well trajectory, including vertical, deviated, and horizontal sections. For horizontal sections, the inclination will be close to 90 degrees.
8. How accurate is this calculation?
The calculator uses the industry-standard Minimum Curvature method, which provides a very accurate approximation of the wellbore path between two survey points. The accuracy of the result is primarily dependent on the accuracy of the input survey data.