Modeling Dependence Among Geologic Risks in Sequential Exploration Decisions

Abstract

Abstract Prospects in a common basin are likely to share geologic features. For example, if hydrocarbons are found at one location, they may be more likely to be found at other nearby locations. When making drilling decisions, we should be able to exploit this dependence and use drilling results from one location to make more informed decisions about other nearby prospects. Moreover, we should consider these informational synergies when evaluating multi-prospect exploration opportunities. In this paper, we present a practical approach for modeling the dependence among prospects and determining an optimal drilling strategy that takes this dependence into account. We demonstrate this approach using an example involving five prospects. This example illustrates the value of modeling dependence among prospects and the value of learning about individual geologic risk factors when choosing a drilling strategy. Introduction When engineers and geoscientists consider a new prospect, it is important to consider its probability of success. In practice, this assessment is often decomposed into success probabilities for a number of underlying geologic factors. For example, one might consider the probabilities that the hydrocarbons were generated, whether the reservoir rocks have the appropriate porosity and permeability, and whether the identified structural trap has an appropriate seal (see, e.g., Magoon and Dow1). The overall probability of success is the product of these individual probabilities. For any single prospect, though these assessments may be difficult, the process is straightforward. However, when considering multiple prospects in a common basin or multiple targets in a single formation, in addition to considering the success of each prospect in isolation, we need to consider the dependence among prospects. For example, if hydrocarbons are found at one location, they may be much more likely to be found at another nearby location. Conversely, if hydrocarbons are not found at the first location, they may be much less likely to be found at the other. If we are making sequential drilling decisions, we should be able to exploit this dependence and use the early well results to help us make more informed decisions at other locations. When evaluating multi-prospect exploration plays, we should recognize these informational synergies, design drilling strategies that exploit these synergies and value the opportunities appropriately. Unfortunately, this can be quite challenging to do in practice. To fully model dependence among prospects, we must specify the joint probability distribution over all possible combinations of outcomes for the individual prospects. For example, if we consider five prospects where each well may be either a success (productive) or a failure (unproductive), there are 25 = 32 possible outcomes whose probabilities must be specified. Many of these probabilities will be very difficult to assess. For example, what is the chance that a well at location 5 would be productive given that 1 and 4 failed and 2 and 3 succeeded? If we have decomposed the individual risk assessments into underlying geologic factors, the task becomes even more complicated: we must assign a joint probability distribution for all of the possible combinations of outcomes of all of these factors, at each location. With three factors each of which may succeed or fail and 5 wells, there are (2´2´2)5» 33,000 different possible outcomes. Then, if we did somehow manage to specify a joint probability distribution over all possible well outcomes, it is difficult to determine an optimal drilling strategy that takes advantage of the informational synergies provided by this dependence. A traditional decision tree model would begin by considering which well to drill first, if any. We would then learn the results for that well and decide which well (if any) to drill next and so on, for all possible well outcomes and possible sequences of wells. Though conceptually straightforward, these decision trees can be quite large, even with a modest number of wells. For example with 5 wells, if we only learn whether a well failed or succeeded, the straightforward tree would include 9,496 scenarios. If we consider success or failure of three underlying geologic factors, then the decision tree would contain approximately 5 million scenarios.