Summary

When preparing a field–development plan, the forecast value of the development can be sensitive to the order in which the wells are drilled. Determining the optimal drilling sequence generally requires many simulation runs. In this paper, we formulate the sequential decision problem of a drilling schedule as one of finding a path in a decision tree that is most likely to generate the highest net present value (NPV). A nonparametric online–learning methodology is developed to efficiently compute the sequence of drilling wells that is optimal or near optimal. The main ideas behind the approach are that heuristics from relaxed problems can be used to estimate the maximum value of complete drilling sequences constrained to previous wells, and that multiple online–learning techniques can be used to improve the accuracy of the estimated values. The performance of various heuristic methods is studied in a model for which uncertainty in properties is neglected. The initial heuristic used in this work generates a higher estimated NPV than the actual maximum NPV. Although such a heuristic is guaranteed to find the true optimal drilling order when used in the A* informed-search algorithm method, the cost of the search can be prohibitive unless the initial heuristic is highly accurate. For the variants of heuristic search methods with weighting parameters, the results show that it might not be possible to identify parameters that can be used to find a solution quickly without sacrificing the accuracy of the estimated NPV in this drilling–sequence problem. In contrast, the online learned heuristics derived from observations from previous drilling steps are shown to outperform the other variants of heuristic methods in terms of running time, accuracy of the estimated value, and solution quality. Multilearned heuristic search (MLHS) with space reduction (MLHS–SR) is an efficient and fast method to find a solution with high value. Continuing the search with space restoration is guaranteed to improve the solution quality or find the same solution as the MLHS without any space reduction.

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