Using Value-of-Information with Continuous Distributions to Optimize Appraisal Well Locations

Patrick Leach
Decision Strategies, Missouri City, TX

An approach to optimizing appraisal well effectiveness by choosing the location that reduces uncertainty by the greatest amount has been suggested (Haskett, SPE paper 84241, 2003). A challenge remains, however. Haskett's method currently assumes perfect information from the map and wells regarding areal extent. Information is almost always imperfect and requires a Bayesian analysis. This involves approximating the continuous uncertainty distribution with several discrete values (usually the P10/P50/P90). The Bayesian process generates posterior probabilities for these values, but it does not generate new P10/P50/P90 values. Hence, one cannot derive the P10–P90 uncertainty ranges required by Haskett's method while accommodating the imperfect nature of the information.

The author has developed a Bayesian methodology using continuous distributions throughout the analysis (rather than discretizing). Three “daughter” distributions are calculated with means equal to the P10/P50/P90 of the parent. The standard deviations of the daughters are automatically optimized and appropriate weighting factors are calculated such that when the three daughters are combined stochastically, the original parent is very closely approximated. These weighting factors are, by definition, the a priori probabilities for the Bayesian analysis.

The Bayesian transformation is then performed stochastically, creating three new continuous distributions which represent the posterior scenarios (the “interpreted” small, medium, and large cases). The P10–P90 ranges can easily be taken off these distributions and the posterior probabilities applied to them so as to generate the uncertainty ranges required by Haskett's method.

The author sees additional potential uses for this methodology in value-of-information analyses in which the decision criterion is a statistic other than the mean.