THE ROLE OF CHANCE IN EXPLORATION

Abstract

In the early stages of speculative mining ventures, when extrapolation of scanty data is unavoidable, the role of chance can be at least as important as that of professional skills.

Having drilled n consecutive successful wells without a failure, at what point can it be said that the chances of ultimate failure of the venture are negligible?

Conversely, having drilled n consecutive failures, at what point can it be said that the chances of ultimate success are unacceptably remote?

Having estimated the area required to be underlain by hydrocarbons for a venture to be profitable, how many wells should one be prepared to drill to ensure at least one success with a specified probability?

Defining Relative Area as the area underlain by what is sought, expressed as a fraction of the total area of interest, the probability of success in a well drilled at random is precisely this Relative Area.

Drilling may be regarded as random if the outcome of a well cannot be predicted. When the goal of the geologist — the construction of a deterministic model — has been achieved, the drilling is not random and the methods of this paper are not valid.

When all n wells drilled so far have been successful, the minimum-likely Relative Area is given by

where p is the probability of success and also the Relative Area (0 ≤ P ≤ 1); P is the degree of confidence required (0 < P < 1); and n is the number of wells drilled.

When all n wells have been failures, the maximum-likely Relative Area is given by

If a specified Relative Area p' exists, the minimum number of wells required to ensure at least one success is given by the nearest integer n that satisfies the inequality

When some wells have been successful and others failures, the probability of exactly r successes (irrespective of order) in a total of n wells is

This may be of little value when n is small. But when n is large (say 20 or more), and when 'success' refers to the finding of something that did not influence the siting of the wells (such as the presence or absense of a particular facies), then the probable range of the Relative Area is given by

where z may be taken as 1.6 for 90 percent confidence, and 2.0 for 95 percent confidence.

These relationships are aids to geological judgement, not substitutes for it.