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Well placement optimization aims to determine optimal well locations so that the economic benefit from oil production can be maximized. Geological uncertainty has a significant impact on the optimal well placement plan and therefore has to be considered in the well placement optimization problem. A geological realization reduction framework for well placement under geological uncertainty is proposed in this work. The objective is to optimally select a small subset of realizations and incorporate them into the well placement optimization problem, so as to reduce the computational efforts. A reservoir case study demonstrates that the selected smaller subset of realizations is a very good representation of a larger superset of realizations and can significantly decrease the computational time associated with the well placement optimization problem.

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Summary History matching of a steam-assisted-gravity-drainage (SAGD) reservoir requires a large ensemble size for proper uncertainty assessment, which ultimately results in high computational cost. Therefore, it is necessary to reduce the number of realizations for SAGD-reservoir simulation purposes. In this paper, a novel sampling method (based on the probability-distance-minimization method) to generate an initial ensemble of reduced size is discussed. This method considers multiple static measurements and geological properties and uses Kantorovich distance to quantify the probability distance between the original ensemble and the reduced ensemble, which is later optimized by use of the mixed-integer linear-optimization (MILP) technique. To show the effectiveness of the method, we have shown history matching of an SAGD reservoir using the smaller size initial ensemble derived from the proposed method and compared with the original ensemble. For history matching, the ensemble Kalman filter (EnKF) has been used because of its ability to assimilate data for large-scale nonlinear systems. Results are compared with several other methods, such as importance sampling, kernel K-means clustering, and sampling by use of orthogonal ensemble members. The robustness and usefulness of each method for generating an improved initial ensemble of reduced size are analyzed on the basis of two criteria: (1) Does the smaller ensemble retain the same statistical distribution characteristics as the original ensemble, and (2) does the smaller ensemble improve the performance of history matching? In general, we conclude that the improved, smaller initial ensemble created by use of the proposed method retains the best statistical characteristics of the original ensemble. Also, it provides better performance compared with other ranking methods in sampling and history matching using EnKF. Finally, the proposed method can reduce the computing cost significantly without compromising uncertainty in the forecast model, which allows for real-time updating at smaller time intervals.

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