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20.7 Acceptable Risk of Collision
A key barrier to adopting probability based rules is defining what number represents an acceptable risk. Until industry standards are developed (currently under consideration in the ISCWSA) clients are unlikely to require reporting based on probability based rules.
20.8 A simplified Calculation of Probability of Collision
A second key barrier to adopting probability based rules is that calculating the actual probability of collision is a difficult problem that requires a huge ‘Monte Carlo’ analysis that would tax the capabilities of standard computing systems.
This is a further advantage of the scalar factor method for calculating separation factor. It can translate easily into a close approximation of the probability of intersection (actual collision) using the following process:
1.
Calculate the Radius Factor for the two wells a. Rf1 = semi-major axis 1 x semi-minor axis 1 / hole 1 radius squared b. Rf2 = semi-major axis 2 x semi-minor axis 2 / hole 2 radius squared c. RF = square root of (RF1 x RF2) Calculate the number of standard deviations at which the ellipses touch a. If the SF by expansion was based on 1 sigma then T = SF b. If the SF by Expansion was based on n sigma then T = n x SF
2.
3.
Calculate the following simple components a. S = T x 30
S is an angle in degrees that can be used in the following fit model
b. Index = 7 x (1 + Cos (S)) c. CR = e ^ Index
E is the base for natural logarithms (2.718282)
d. Collision Risk per million is CR / RF
Warning: This formula only gives a good estimate of collision risk in the range from SF = 0 to SF = 3 at 2 sigma. Collisions are very rare indeed beyond this (6 standard deviations apart). Do not use this formula outside this range or collision risk will be over-estimated.
It should be noted that this calculation is the probability of the centre points of the ellipses colliding. It does not represent the complex probabilities of two curved well paths colliding in 3D space but serves as a useful guide.
The table on the following page gives an idea of what you could expect to see.
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