Unintentional collision between two wellbores may have serious economic and health, safety, and environmental consequences. It is therefore important to evaluate the probability of such an event in the well-planning phase and at critical stages during the drilling phase.

A commonly used approach is to analyze the collision probability between two points, one in each wellbore, which are determined from geometric criteria only. This procedure may ignore point pairs with higher collision probabilities, and thereby lead to overoptimistic conclusions. Typically, the results from such methods will be accurate only for simple wellbore geometries, such as straight sections, and for position uncertainties that are highly symmetrical with respect to the wellbores. More advanced methods that overcome such limitations are impractical for general application because of high conceptual or computational complexity.

This paper proposes novel analytic methods that may potentially overcome these problems. Formulae are derived for two important situations: the direct-hit (DH) and the unintentional-crossing (UC) scenarios. In both cases, the spatial region of interest is divided into carefully designed segments, such that the collision probability can be accurately evaluated for each segment. The total collision probability is then found by summing the results over all segments. The main advantage of this approach is that it gives accurate results for arbitrary well geometries and uncertainty-ellipsoid orientations.

The algorithms can easily be integrated in existing software for wellbore-anticollision analysis. The paper shows examples of results that are all in good agreement with control calculations. Compared with existing methods, the proposed methods are therefore believed to represent an improvement to quantitative collision-probability analysis for both the wellbore-planning and the drilling phases.

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