drilling · directional
Minimum Curvature Survey Calculation
RF = (2/β)tan(β/2); ΔTVD = (ΔMD/2)(cosI₁+cosI₂)RF; ΔN = (ΔMD/2)(sinI₁cosA₁+sinI₂cosA₂)RF; ΔE = (ΔMD/2)(sinI₁sinA₁+sinI₂sinA₂)RF
click formula to derive ↑
Inputs
°
°
°
°
ft
ft
Description
Converts two adjacent MD/Inclination/Azimuth survey stations into a 3D wellbore position increment (TVD, Northing, Easting) using the minimum curvature method — the industry-standard technique for building a wellpath from raw survey data.
Variables
| Symbol | Unit | Description |
|---|---|---|
| ΔTVD | ft | TVD Increment |
| ΔN | ft | Northing Increment |
| ΔE | ft | Easting Increment |
| I₁ | ° | Inclination at the upper (shallower) survey station. |
| A₁ | ° | Azimuth at the upper survey station, measured clockwise from north. |
| I₂ | ° | Inclination at the lower (deeper) survey station. |
| A₂ | ° | Azimuth at the lower survey station, measured clockwise from north. |
| MD₁ | ft | Measured depth of the upper survey station. |
| MD₂ | ft | Measured depth of the lower survey station. Must exceed MD₁. |
Assumptions
- Survey stations are accurate and properly spaced (gyro or corrected MWD)
- The wellbore follows a smooth circular arc between the two stations (minimum curvature assumption)
- Magnetic declination and grid convergence corrections have already been applied to azimuth values before input
Limitations
- Accumulates error over many stations if individual surveys carry systematic bias — always reconcile against gyro check surveys at casing points
- Treats the path between stations as a single circular arc — cannot capture multiple curvature changes between two widely spaced stations
- Position uncertainty grows with measured depth; this calculation does not itself provide an error ellipse (use dedicated survey QC software for that)
Use Cases
- → Wellpath construction: Build a full 3D wellbore trajectory station-by-station from raw directional survey data for well planning and as-drilled documentation.
- → Anti-collision analysis: Compute as-drilled position to compare against offset wellbores and maintain separation in multi-well pad development.
- → Target verification: Confirm the wellbore has reached the planned subsurface target location (TVD, N, E) within an acceptable tolerance.
Related Calculations
Region Notes
Permian Basin
Multi-well pad development in the Delaware/Midland Basins relies on minimum curvature surveys at every joint to maintain anti-collision separation across densely spaced laterals (often <10 ft apart at landing depth).
Bakken
Closely spaced multi-well pads require frequent gyro check-surveys reconciled against MWD minimum-curvature positions to manage collision risk in the Middle Bakken/Three Forks interval.
Global
Minimum curvature is the de facto industry standard wellpath method, having replaced older tangential and balanced-angle methods in essentially all modern directional drilling software.
References
Primary source
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