Measured Depth (MD) Calculator
Calculate Measured Depth (MD) and Horizontal Displacement (HD) based on True Vertical Depth (TVD) and the wellbore's angle of inclination from vertical.
Understanding Measured Depth (MD) in Drilling
In the oil and gas industry, and other geotechnical applications, understanding the precise location of a wellbore is critical. Two fundamental measurements used to describe a well's position are True Vertical Depth (TVD) and Measured Depth (MD). While they sound similar, they represent distinct aspects of a well's trajectory.
What is True Vertical Depth (TVD)?
True Vertical Depth (TVD) is the vertical distance from a reference point (usually the surface or Kelly Bushing) straight down to a point in the wellbore. It represents how deep the well is directly below the surface, regardless of any horizontal deviation. If you were to drop a plumb line from the surface, TVD would be the length of that line to the point of interest in the well.
What is Measured Depth (MD)?
Measured Depth (MD) is the actual length of the wellbore from the surface reference point, following the path of the drill bit. If you were to unroll the wellbore and measure its total length, that would be the MD. For a perfectly vertical well, MD and TVD are identical. However, for deviated or horizontal wells, MD will always be greater than or equal to TVD because the wellbore travels a longer path to reach a certain vertical depth.
What is Angle of Inclination?
The Angle of Inclination, often simply called "inclination" or "deviation angle," is the angle at which the wellbore deviates from the true vertical. An angle of 0 degrees indicates a perfectly vertical well, while an angle of 90 degrees indicates a perfectly horizontal well. This angle is crucial for understanding the well's trajectory and calculating its true path.
The Relationship Between MD, TVD, and Inclination
For a simplified, straight inclined section of a wellbore, the relationship between MD, TVD, and the angle of inclination can be described using basic trigonometry. Imagine a right-angled triangle where:
- The vertical side is the True Vertical Depth (TVD).
- The hypotenuse is the Measured Depth (MD).
- The horizontal side is the Horizontal Displacement (HD).
- The angle between the TVD and MD is the Angle of Inclination.
Using these relationships, we can derive the following formulas:
- Measured Depth (MD) = TVD / cos(Angle of Inclination)
- Horizontal Displacement (HD) = TVD * tan(Angle of Inclination)
It's important to note that these formulas apply to a single, straight inclined section. Real-world wellbores often have complex trajectories with multiple curves and changes in inclination and azimuth, requiring more sophisticated survey calculations (e.g., Tangential, Minimum Curvature methods).
Why are these calculations important?
Accurate calculation of MD, TVD, and HD is vital for:
- Well Planning: Designing the trajectory to reach target reservoirs efficiently.
- Drilling Operations: Monitoring the drill bit's position, preventing collisions with other wells, and ensuring the well stays within its geological target.
- Reservoir Engineering: Understanding the true thickness of a reservoir intersected by the well.
- Production Optimization: Placing perforations and completion equipment at the correct depths.
- Cost Estimation: Longer MDs generally mean higher drilling costs.
Example Calculation:
Let's say a well has reached a True Vertical Depth (TVD) of 5,000 feet, and the wellbore is inclined at an angle of 45 degrees from vertical.
- TVD = 5,000 feet
- Angle of Inclination = 45 degrees
Using the formulas:
- MD = 5,000 / cos(45°) = 5,000 / 0.70710678 ≈ 7,071.07 feet
- HD = 5,000 * tan(45°) = 5,000 * 1 ≈ 5,000.00 feet
This means the drill bit has traveled approximately 7,071.07 feet along its path to reach a point that is 5,000 feet directly below the surface, and it has also moved 5,000 feet horizontally from the surface location.