Probability Estimates for Petroleum Drilling Decisions

Abstract

Here are general procedures for estimating probabilities in several exploratory and development drilling situations. The methods are based on Bayesian analysis of statistical samples, indirect probability estimation from random variables, and traditional probability principles. Introduction Modem drilling decisions are based on criteria that reflect not only the potential value of a venture but also its uncertainty. The criterion most commonly computed is the expected discounted value. Economic calculations used to obtain drilling decision criteria vary from one-page worksheets to comprehensive computer models. Irrespective of the method of calculation, estimates of the probability for a dry hole and the complementary probability for a producer have critical effects on the resulting decision. Estimating probabilities for events that do not follow a definite mathematical law is one of the most difficult tasks imaginable. Drilling decision problems have their own special complications that often preclude using traditional probability estimation preclude using traditional probability estimation methods. Most probability estimation procedures are based on a statistical sample; however, the sample must be random, the sample observations must be independent, and the sample must be sufficiently large. In the drilling decision problem, a formal sampling program generally is not economically feasible, and program generally is not economically feasible, and the estimator must base his probabilities only on the data available and on his subjective assessments. Two general methods are developed here for estimating probabilities. One is based on variations of the traditional probability estimate from a statistical sample. These variations allow for the inclusion of a subjective probability estimate with the small sample characteristic of many drilling decision problems. The second procedure allows for the calculation of a probability from the cumulative distribution function of probability from the cumulative distribution function of a subjectively defined random variable that determines whether the well will produce. This indirect method of computing a probability from estimates on a random variable generally is easier than estimating the probability directly. probability directly. In addition to the discussion of the two general methods described above, applications to the most common exploratory and development drilling problems are presented here. These applications include problems are presented here. These applications include the following:Exploratory drilling on a structural prospect,Exploratory drilling on a stratigraphic prospect,Development drilling in a reservoir with pay discontinuities,Development drilling in a zone with a water contact,Development drilling in a zone containing a barrier, andProbabilities for a dual development well. Each section is illustrated with an example problem containing data that would be available in a typical drilling situation. Both probability trees and formulas are given for most of the examples. Since the formulas usually define only the dry-hole probability or its complement, they are not so useful in computing decision criteria as the probability trees, which give a more detailed description of the events associated with the venture. JPT P. 687