Risk Analysis in Drilling Investment Decisions
Authors: Newendorp Paul D. , Root Paul J. 
Published: December 2007

Abstract
A method of assessing and describing the degree of uncertainty involved in the dedication of capital for drilling an oil or gas well is presented. The problem involves associating probabilities with the range of profitabilities that might result from a particular drilling prospect.
This method of risk analysis recognizes the probabilistic nature of the variables affecting profitability. The method systematically combines the distributions of each variable into a final distribution of ultimate profitability. The entire range and distribution of financial outcomes that might occur from the drilling of the prospect and their related probabilities of occurrence are provided. A numerical example is given to illustrate the use of the method.

Introduction
The dedication of capital for drilling an oil or gas well is a classic example of a decision made under uncertainty. The decision maker must consider the chances that the well will be dry, the chances of recovering the amount of reserves needed to make a certain profit, and the effects of uncertain economic factors such as allowable trends and fluctuations in crude price. To incorporate simultaneously all factors into a sound decision is a difficult task. Consequently there has been growing emphasis in recent years on the use of formal decision theory techniques as a guide for management decisions. These techniques require precise estimates of risk, and the success of their application is dependent on the accuracy of the risk analysis.
Historically the problem has been handled more or less informally. The risk analysis of a drilling prospect was presented to management using descriptions such as:
We have a good shot at the Morrow. Control is fair. It is a sure thing. This well is pretty risky.
From these descriptions the decision maker, relying on his experience, intuition, judgment, and perhaps luck, was expected to reach some sort of decision. The use of modern decision theory techniques requires a more precise and objective assessment of risk. Specifically, the petroleum engineer and geologist must portray risk in terms of numerical probabilities.
A method of risk analysis that has not been applied previously to drilling investment decisions is presented. This approach explicitly recognizes the probabilistic nature of each variable affecting ultimate profitability. An example is given to illustrate the technique. Finally, the compatibility of this method of risk analysis with utility theory is discussed.

The Problem
The problem can be stated simply when a drilling prospect is being considered. What is the probability of drilling a dry hole, of finding sufficient reserves to pay out the well, of realizing a net profit of $200,000, etc.?
Definition of the basic process that generated the distribution of possible outcomes is the first step in applying probability theory. For example, consider the operation of a machine that cuts threads on carriage bolts. Suppose the shop foreman observes that the machine produces defective bolts at a consistent rate of 0.1 percent of total output, and that there is no pattern to the occurrences of defective bolts. He may then ask the question-"What is the probability of three defective bolts in a batch of 1,000?" If his observations are correct, the operation of the machine can be classified as a Bernoulli process, and he may reasonably expect that the theory of probability will provide an answer to his question. For this type of process the shop foreman could use the equation of binomial probability to compute the probabilities of any possible number of defective bolts in a given batch.
Now the question arises - "What is the basic process that generated the distribution of oil and gas accumulations?" Formal probability theory can be applied to our analysis of risk if the process can be defined. The petroleum explorationist, however, is not so fortunate as the shop foreman. Despite the wealth of modern petroleum technology, a complete description of the accumulation processes is not possible. Hence, the first restriction in the approach to the problem of risk analysis has been noted: the basic process that generated the distribution of petroleum accumulations is not known.
Another complicating factor is that the probabilities (assuming they could be calculated) of encountering specific amounts of petroleum change with time, i.e., with the information that is available. In the sequential development of a geologic province, the large geologic structures and fields usually are drilled first. Consequently, the probability of finding additional fields of equivalent size gradually decreases.
In most instances, the outcome of the next well drilled is not independent of all previous outcomes.
JPT
P. 579ˆ