Trajectory: geometry, curvature and data quality

MD, TVD and segment projections

MD describes along-hole length from a chosen origin; TVD is vertical depth from an agreed datum. Check reference origins before comparison. Values with different datums cannot be treated as competing estimates of the same depth. An MD/TVD pair does not determine plan position or reconstruct the complete trajectory.

For an ideal straight segment at constant inclination I from vertical, ΔTVD = ΔMD cos I and horizontal displacement = ΔMD sin I. This is local learning geometry, not a universal survey-processing method. If inclination and azimuth change between stations, interpolation choice affects coordinates.

Check limiting cases: I = 0° is vertical; I = 90° has zero vertical increment. Software trigonometric functions generally use radians, so degree conversion must be explicit. Azimuth is needed to split horizontal displacement into directions; without it this simple model gives only horizontal projection length.

Walkthrough

A straight 100 m segment at I = 60° has ΔTVD = 50 m and horizontal projection ≈86.603 m. These are increments, not total depth or distance from the wellhead.

Independent task

A straight segment is 200 m at I = 30°. Find vertical and horizontal increments. What remains unknown without azimuth and starting coordinates?

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Spatial angle and DLS

Inclination change is not total spatial direction change when azimuth changes too. For directions I1, I2 and A1, A2, their angle β follows the dot product: cos β = cos I1 cos I2 + sin I1 sin I2 cos(A2−A1). Use consistent angular units inside the calculation.

The learning DLS estimate normalises β by station separation: DLS = β/ΔMD × 30 when β is in degrees and the result is °/30 m. It is an interval-average characteristic under the selected model, not a measurement of maximum local curvature between stations. Short spacing and measurement errors can materially affect the value.

Numerical checks include positive ΔMD, finite inputs and a cosine within the arccos domain, allowing for rounding. The calculation does not prescribe allowable curvature for a string, casing or BHA. Such assessment requires the design, equipment properties, chosen method and uncertainty analysis.

Walkthrough

With unchanged azimuth, inclination rises from 20° to 23° over 30 m: β = 3° and DLS = 3°/30 m. The same angle over 60 m gives 1.5°/30 m.

Independent task

Both inclinations are 60°, azimuth difference is 10° and ΔMD = 30 m. Calculate β and DLS. Why is the answer neither zero nor necessarily 10°/30 m?

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Survey quality and inference limits

Coordinates depend on measured angles, starting point, azimuth reference, depth matching and processing method. True, magnetic and grid north are different references. Do not compare azimuth datasets until their bases and previously applied conversions are known.

Use a survey passport: instrument, time, MD stations, inclination, azimuth, units, datum, north reference, corrections, method and quality information. A missing item may not invalidate every use but must limit inference. Individual values on a shared scale might be comparable while precise relative well position remains unsupported with unknown coordinate systems.

Distinguish record differences from physical well changes. Reprocessing or correction can move calculated coordinates without new drilling. Distance between nominal centre lines alone does not establish safe separation. Actual assessment requires uncertainty models and an approved trajectory-management process; this chapter does not replace it.

Walkthrough

Two reports give azimuth 90°, one magnetic and one grid referenced. Equal numbers do not establish equal direction. The required conversion is unknown without further data.

Independent task

Two datasets share MD and inclination values, but one lacks datum and azimuth reference. Which comparisons are conditionally possible and which conclusions must be deferred?

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Capstone: reviewing a trajectory report

A learning straight segment is 100 m long at 60° from vertical. In a separate interval, two stations differ in inclination by 3° at unchanged azimuth over ΔMD = 60 m. Two reports list equal azimuth values, but one lacks a north reference.

Check local geometry and DLS normalisation, then bound report comparison. Do not combine independent examples into an actual trajectory. These calculations establish neither equipment compatibility nor safe well separation.

Walkthrough

Separate straight-segment projections, interval direction change and report metadata.

Independent task

Calculate projections and DLS. What evidence is needed to compare spatial position?

Attempt in the interactive worksheet →