Contents
- Background
- New misalignment model
- Comparison to existing models, and example calculations
- Conclusions
- Appendix: Mathematical details
Background
- Definition of tool misalignment α:
- Angle between borehole axis and survey tool axis (local, at each survey station)
- Properties:
- In general: unknown toolface
- Error propagation: random or systematic between stations
- Analogous definition for sensor misalignment in tool, and misalignment between sensor axes
- The importance of tool misalignment:
- Affects all survey tools, and all survey operations
- High relative importance in top-hole sections, i.e., typically low-inclination wellbore sections
- Significant for long survey sections with fixed toolface (sliding tool)
Introducing the new model
- Analysing misalignment in the D, I, A system (like all other error terms) is tempting, but leads to:
- One physical error source modelled by several (2-4) «sources»
- Customized or alternative solutions near vertical
- The «vertical singularity» problem: δA/δα ~ 1/sin(I)
- However, the end results are variances and co-variances in the N, E, V system:
- Can misalignment be analysed directly in N, E, V co-ordinates?
- And would this solve any of the problems above?
Starting point for new model
- The position uncertainty due to misalignment α is always perpendicular to the (local) wellbore direction.
- At each measurement, the misalignment toolface angle τ is assumed uniform on [0° ... 360°] → uncertainty «cone».
- The toolface statistics is not related to the «random» or «systematic» nature of propagation between measurements.
- Consequently, the approach should be:
- 1) Describe the uncertainty in the perpendicular plane (NEV system, and one τ).
- 2) Average over τ.
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View the entire Presentation:
A New Look at Tool Misalignment
Jon Bang, Gyrodata Inc.