Method for estimating the probability of collision between wells

A system for drilling a well, the system comprising:

• a drilling apparatus for drilling the well, the apparatus adapted for receiving directional information from a processor and adjusting drilling according to the directional information;
• the processor equipped for implementing instructions for avoiding collision during drilling of a well by performing a method comprising:
• identifying another well proximate to the well being drilled;
• collecting spatial information for at least a portion of the another well and the well being drilled;
• estimating a trajectory for at least a portion of the well being drilled and the another well;
• estimating an uncertainty in spatial information for each trajectory;
• estimating a probability of a collision with the another well during the drilling of the well by integrating a probability density function using the uncertainties and the trajectories;
• and performing the drilling in a manner that limits the probability of collision.

A method for estimating a probability of collision, P, between near-parallel wells, the method comprising:

• obtaining separation information, S0, and radius information, R0, for a given depth, L;
• and
• solving a relationship comprising:
• P
• =
• 1
• π
• ·
• sin
• -
• 1
• 
• (
• R
• 0
• S
• 0
• )
• ·
• exp
• 
• [
• -
• (
• S
• 0
• 2
• -
• R
• 0
• 2
• )
• 2
• ]
• +
• 1
• π
• ·
• ∫
• S
• 0
• -
• R
• 0
• S
• 0
• 2
• -
• R
• 0
• 2
• 
• [
• cos
• -
• 1
• 
• (
• S
• 0
• 2
• -
• R
• 0
• 2
• +
• x
• 2
• 2
• ·
• S
• 0
• ·
• x
• )
• ·
• x
• ·
• exp
• 
• (
• -
• x
• 2
• 2
• )
• ]
• 
• 
• 
• x
• ;
• where:
• x represents a distance.