Collision Risk Analysis: Pedal curve vs. Ellipse

Summary

1. Select wellbore locations - Not treated here (but very important!)
2. Uncertanties - From error model
3. Combine the uncertainties - 
   1. s1 and s2 on individual locations
   2. s on the distance between Cov = Cov1 + Cov2 s 2 = s1 2 + s2 2
   3. Same resulting formulas for 1) and 2)!
4. Interpretation of s
   1. Pedal point: projection from 3D (2D) onto 1D
   2. NB: Consider only ellipse/-oid (i.e., ignore pedal point) => risk cannot be quantified
5. Quantification of risk
   1. SF = D / ks
   2. Criterion: SF = 1 (for given k & given PDF
   3. Normal PDF assumed here; may be another PDF (heavier tales)

The Foundation

1. ks surfaces (in 3D) of probability density function (PDF)

Collision / Crossing Analysis: 1D Problem

1. NB: example assumes k = 2.5
2. 2.5s Ellipsoid
3. extreme 2.5s point (3D) ...
4. ... projects onto 2.5s (1D)
5. Connection between 3D, 2D, and 1D: The same k-level

Think «Inside the Box»

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Collision Risk Analysis: Pedal curve vs. Ellipse

Jon Bang, Gyrodata Ltd.

Erik Nyrnes, Statoil ASA

  

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