Directional survey quality: magnetic corrections, sag and gross errors

Every position in a well file, every target hit and every anti-collision scan rests on the survey, and an MWD survey is only as good as its magnetic reference and its corrections. This article works through survey quality on a horizontal well near the equator: the corrections from magnetic to grid north, the field checks every station should pass, drill-string interference and sag, and the gross errors that no tolerance band catches.

Where survey error comes from

An MWD tool carries three accelerometers and three magnetometers. From the gravity vector it gets inclination and toolface; from the magnetic field, projected on the horizontal plane, it gets the azimuth from magnetic north. Each step adds error.

The reference. Magnetic north is turned to grid north with a declination from a model of the earth's field, which drifts year by year and does not see local magnetism in the crust.

The drill string. Steel above and below the non-magnetic collars magnetises along the string, so the axial magnetometer reads a field that is not the earth's. This axial bias is the largest single error in most MWD surveys.

The BHA. The sensor's collar bends under its own weight, so in a high-angle hole its axis points slightly below the hole's and it reads a lower inclination. This is sag.

People and files. A declination applied with the wrong sign, a mistyped inclination, a mixed-up north reference. Rare, and large when they happen.

The ISCWSA error models describe the first three as ellipses (see anti-collision: separation factor, ellipses and travelling cylinder). Survey QC checks that each real station behaves as the model assumes, and corrects what can be corrected.

From magnetic north to grid north

The tool measures an azimuth from magnetic north. Well plans and maps are in grid north. The conversion has two terms:

D

magnetic declination, east positive, from a field model on the survey date

γ

grid convergence: the angle between grid north and true north at the well

Δλ, φ

longitude from the UTM zone's central meridian, and latitude

Near the equator the two terms behave very differently. Convergence scales with sin φ, so at 4.3° N it is small: +0.195° at the example well, in UTM zone 18. Declination there is large and moving. The World Magnetic Model 2025 gives −9.77° (west) on the example's survey date, changing by −0.18° a year. A reference computed when the well was planned, more than a year before it was drilled, is already a fifth of a degree out.

The field checks: gravity, total field and dip

Each MWD station measures the full gravity and magnetic vectors, so it can be checked against what the earth should give at that place and date. Three numbers are compared:

• G total, the length of the gravity vector, against 1 g. Typical tolerance ±0.0025 g.
• B total, the length of the magnetic vector, against the model's total field. Typical tolerance ±300 nT.
• Dip, the angle of the magnetic vector below horizontal, against the model's dip. Typical tolerance ±0.45°.

A station outside a band is suspect: a sensor fault, steel nearby, or a reading taken while the string was moving. The trap is the reverse. A station inside every band can still carry a large azimuth error, because an axial bias changes the azimuth far more than it changes B total or dip in some directions. The azimuth error from an axial bias ΔB_z is, to first order:

ΔB_z

axial magnetic bias from the drill string (nT)

I, A_m

inclination and magnetic azimuth of the station

B, δ

total field and dip; B cos δ is the horizontal field the compass works from

The error is largest in a horizontal hole running magnetic east or west, and smallest where the horizontal field is strong. That second factor is where the region comes in.

The example well

The example is a horizontal producer in a sandstone reservoir, set in typical conditions of the Llanos foreland of eastern Colombia: flat ground, a rotary table 260 m above sea level, the reservoir at about 2,340 m TVD and a 1,000 m lateral heading east-north-east. The top hole is gyro-surveyed; the 12¼″ and 8½″ sections are surveyed by MWD every stand.

The raw readings were built with the module's own forward model from a known hole, so every error can be measured against the truth, then run through the same QC and corrections as a real survey.

A hand check of the lateral

1. Azimuth error per station. In the lateral, 320 nT × sin 90° × sin 75° / 26,795 nT = 0.0115 rad, or 0.66°. The engine measures a mean of −0.66° across the lateral's stations.
2. Sideways drift of the lateral. 1,000 m × 0.0115 = 11.5 m. The build adds about 2.5 m: 180 nT gives 0.0065 rad at 90°, weighted by sin²I, which averages 0.5 over the 771 m build. Together about 14.0 m to the left.
3. Sag. 0.20° is 0.00349 rad, so 1,000 m of lateral read 0.20° low puts TD 3.49 m too deep. The build adds 771 m × 0.5 × 0.00175 = 0.67 m. Together 4.16 m.
4. An old reference. The declination 14 months earlier was −9.56°, 0.21° from the survey date's value. Over the well's 1,491 m horizontal departure that is 1,491 × 0.00365 = 5.4 m.

The engine, running minimum curvature on every station, gives 13.96 m left, 4.13 m deep and 5.47 m. These are not ellipse sizes. They are systematic errors: every station shares them, so they add up along the hole instead of averaging out.

What the station checks show

Two of 102 stations fail. The first lateral station, 19 m below the 9⅝″ shoe, reads B total 347 nT low: casing steel close to the sensor. Its azimuth is 3.4° off. It is rejected and the next station carries the survey on.

Every other lateral station passes, between +3 and +143 nT. Yet each of them is 0.66° off in azimuth. Heading 075° magnetic, the tool's axis sits almost square to the earth's field, so a bias along it barely changes the field's length. A total-field check cannot see an axial bias in an east-west lateral.

The dip chart shows the other side. In the vertical hole, 630–1,850 m, the dip reads 0.29° high on average and one station fails at +0.46°. There the tool's axis is vertical and the earth's field only 25° below horizontal, so an axial bias tilts the field and moves the dip. Near the equator a bias in vertical hole shows in the dip; at high latitudes it shows in B total. In the lateral the dip moves less than 0.3° and every station passes.

After multi-station analysis, below, both checks tighten around zero: the run-1 RMS falls from 103 nT and 0.23° to 37 nT and 0.07°, and run 2 from 86 nT and 0.12° to 39 nT and 0.08°.

Why the latitude matters

The same 300 nT axial bias, in a horizontal hole on the same 065° grid heading, gives different errors in different fields. Each column below is DrillIQ's engine evaluating the station in WMM2025 at that place.

Low dip helps: most of the field is horizontal, which is what the compass uses. At 60° N only 15,244 nT is horizontal and the same bias costs 0.99°. But the field over this part of South America is weak overall, so the Llanos has less horizontal field than North Oman. And with a 9.8° west declination, a lateral that looks north-east on the map runs closer to magnetic east than its grid heading suggests. Check every lateral's magnetic azimuth.

Correcting the survey

Multi-station analysis (MSA). All the stations of one run share the same sensor and the same drill string, so they share the same biases. MSA finds the bias vector that brings every station's B total and dip closest to the reference, by least squares weighted by the tolerances, then recomputes each azimuth from the corrected field. With five or more stations at toolfaces spread over at least 90°, the cross-axial biases can be solved too; otherwise only the axial one. On the example, run 1's 25 stations give an axial bias of 200.6 nT, run 2's 34 stations 336.0 nT, against 180 and 320 nT put in. The cross-axial terms come out under 10 nT. The lateral's mean azimuth error falls from −0.66° to +0.03°.

Single-station axial correction. The alternative distrusts the axial magnetometer at each station and solves its value from the reference field alone. It needs no run of stations, but it fails where the axial reading cannot be told from the field: near horizontal and near magnetic east-west. Its conditioning is √(cos²I + sin²I cos²A_m), and DrillIQ leaves stations below 0.2 uncorrected and flags them. This lateral averages 0.26: usable, but only just. On a lateral turned 10° further east, MSA with spread toolfaces would be the only magnetic correction left.

Sag. The sensor reads the inclination low by the sag angle times sin I. The angle comes from a BHA deflection model for the actual collar sizes, stabilisers and weight on bit; DrillIQ applies it per run. On the example the lateral's inclination error falls from −0.197° to +0.003°.

In-field referencing (IFR). A local survey of the earth's field replaces the global model's values with measured ones. It removes the crustal part of the declination error and tightens the B total and dip tolerances. For small targets or close offsets, IFR with MSA is the usual combination.

The chart shows each correction left out in turn, with the others applied. The drill-string bias is the largest: 14.0 m to the left at TD, growing from the landing, invisible to the total-field check. Sag puts the lateral 4.1 m deeper than it is, which matters in a thin reservoir and for the TVD of the next well's target. A reference 14 months old puts it 6.4 m right: the 5.5 m of the declination change plus the 0.9 m the fully corrected survey still carries from sensor noise and the residual bias.

Gross errors: the checks no tolerance band makes

Gross errors happen after the measurement, so the field checks never see them.

The declination's sign. Applied as +9.77° instead of −9.77°, every azimuth turns 19.5°. The example's TD moves 508 m. B total and dip are unchanged. DrillIQ recomputes each station's azimuth from its raw readings and the run's own reference and flags any that differ from the recorded value by more than 0.5°, so a wrong sign fails every station at once: all 59 above 3° in the example.

A mistyped station. An inclination of 89.56° keyed as 98.56° at 3,000 m reads as 8.86°/30 m into the station and 9.07°/30 m out of it. The dogleg check against the well's 6°/30 m limit flags both intervals. A single spike in DLS, up and back down, is almost always a typing error rather than the hole.

A north reference mixed up. When the positions in a file were computed from true azimuths and the azimuths are stored in grid, each horizontal step is turned by the convergence. The survey QC compares the stored steps with its own minimum-curvature steps and reports a constant +0.195° turn from 1,860 m, and says it matches the grid convergence. Near the equator that turn is small. At 60° N, 3° from the central meridian, the same formula gives 2.6°.

Independent checks. Compare the MWD with a gyro run where one is run, and the lateral's landing TVD with the log's marker depths. Two independent surveys disagreeing by more than their ellipses allow is the strongest gross-error test there is.

A checklist for the rig team

• Compute the magnetic reference for the survey date, not the planning date; the declination here moves 0.18° a year.
• Check the declination's sign and the north reference of every survey file on its first station.
• QC every station's G total, B total and dip, and reject stations near casing shoes or fish.
• Know each lateral's magnetic azimuth; near east-west, passing B total says little about azimuth.
• Run MSA per run once it has five or more stations at spread toolfaces, and watch the run's RMS fall.
• Apply a sag correction from a BHA model in every high-angle run.
• Treat a DLS spike that goes up and straight back down as a typing error until shown otherwise.
• Compare MWD with a gyro or with log markers wherever the target is tight.

How DrillIQ handles it

DrillIQ's Directional & Surveys module takes each run's magnetic reference from WMM2025 on the run's date, an IFR set or a typed value, and converts between magnetic, true and grid north. Every station with raw readings gets the gravity, total-field and dip checks against its tool's tolerances, and its recomputed angles are compared with those recorded. Corrections are kept per run beside the recorded values: sag, multi-station analysis or the single-station axial correction with its conditioning. Positions, reports and anti-collision scans all use the corrected survey, and imported files are checked for depth order, doglegs, gaps, position jumps and north-reference rotations. Everything above was worked out with the same engines.

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References

1. Williamson, H.S. Accuracy Prediction for Directional Measurement While Drilling. SPE 67616, SPE Drilling & Completion, 2000.
2. Russell, A.W. and Roesler, R.F. Reduction of Nonmagnetic Drill Collar Length Through Magnetic Azimuth Correction Technique. SPE/IADC 13476, 1985.
3. Ekseth, R. et al. The Reliability Problem Related to Directional Survey Data. IADC/SPE 103734, 2006.
4. Wolff, C.J.M. and de Wardt, J.P. Borehole Position Uncertainty: Analysis of Measuring Methods and Derivation of Systematic Error Model. SPE 9223, Journal of Petroleum Technology, 1981.
5. Chulliat, A. et al. The US/UK World Magnetic Model for 2025–2030: Technical Report.

About this example. The well in this article is a representative scenario set in typical Llanos Basin, Colombia conditions and worked through with DrillIQ's engines. It is not a client's well, and its figures are not field results.