Anti-collision and the ISCWSA error model

The Industry Steering Committee on Wellbore Survey Accuracy publishes a catalog of error terms for each directional tool type — MWD, gyro, magnetic. Each term represents a distinct physical source (accelerometer bias, uncertain magnetic declination, wireline depth error) and ships with a weighting function describing how that error propagates into North/East/Vertical position at every station.

Summing these terms is not a plain sum of variances. Systematic errors — the ones coming from a calibration bias that does not change along the well — add vectorially, fully correlated station to station. Random errors add as independent variances. That distinction, formalized by Williamson, is what separates an error model that reproduces real uncertainty from one that over- or under-states it by treating every term the same way.

The result is a 3D covariance matrix at each station — the ellipse of uncertainty — that grows with depth and shrinks wherever the tool is more precise, such as a vertical section surveyed by a well-calibrated gyro.

Having each well's ellipse of uncertainty is not enough — two ellipses, from two different wells, must be compared along the direction that actually brings them together. The ISCWSA standard rule projects the 3D covariances onto the center-to-center direction between the two trajectories and combines the two uncertainties by RSS (root sum of squares), adding the physical radii of the well and the offset casing.

This criterion — known as the pedal-curve — is less conservative than the classical definition, which sums the semi-major axes of both ellipses regardless of approach direction. The classical definition still has a role as a conservative reference, but the pedal-curve is what operators use to decide whether a well section is safe to drill as planned.

The separation factor is the ratio between the true center-to-center distance and that combined uncertainty. A factor below 1 means the ellipses touch — not that the wells necessarily cross, but that the available information cannot rule it out.

A per-station separation factor already flags where risk peaks along the well, but the operational read — the one the wellsite team uses in real time while drilling — is the travelling cylinder plot: a projection showing the offset well's relative position as if the well being drilled were a straight cylinder, viewed from above looking down-hole.

That plot's angular reference convention — high side or projected North, clockwise — follows the market standard set by Compass, which lets a reading be compared directly across different software and different operators on the same field.

Validating an anti-collision engine means reproducing the reference cases ISCWSA itself publishes — the official test well — checking variance term by term against the reference values, not just the final aggregated result.