Multi-solution well placement optimization using ensemble learning of surrogate models

Well location optimization aims to maximize the economic profit of oil and gas field development while respecting various constraints. The limitations of the currently available well placement optimization workflows are their 1) high computational requirements, which makes them inappropriate for full-field applications where a large number of wells have to be optimized using a computationally expensive simulation model; and 2) providing a single optimal solution, whereas on-site operational problems often add unforeseen constraints that result in adjustments to this optimal, inflexible scenario degrading its value. This study presents a multi-solution, surrogate models (SMs)-assisted optimization framework to deliver diverse, close-to-optimum well placement scenarios at a reasonable computational cost. Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm is used as the optimizer while diversity in optimal solutions is achieved by multiple, parallel runs of the optimizer with different starting points. Convolutional Neural Network (CNN) is used as the SM, to partly substitute the computationally expensive reservoir model runs during the optimization process. A new, adjusted Latin Hypercube Sampling (aLHS) procedure is developed to generate initial training datasets with diverse well placement scenarios while respecting reservoir boundaries and well spacing constraints. An ensemble of CNNs is pre-trained using the generated dataset to enhance the robustness of the surrogate modeling as well as to allow estimation of the SM's prediction quality for new data points. The ensemble of CNNs is adaptively updated during the optimization process using selected new data points, to improve the SM's prediction accuracy. To the best of our knowledge, this is the first application of ensemble learning strategy to a well placement optimization problem. The added value of the framework is demonstrated by comparing three optimization approaches on the Brugge and Egg field benchmark case studies. The approaches are 1) 'no SM': using the actual reservoir model only, 2) 'Offline SM': the optimization is performed using SM-only that is pre-trained using initial training datasets generated by the actual reservoir model, and 3) 'Online SM': pre-trained CNNs are adaptively updated during the optimization process using new datasets generated using the actual reservoir model. The surrogate-assisted optimization approach substantially reduced the computation time, while a greater objective value was achieved by employing the adaptive learning strategy due to the enhanced prediction accuracy of the SMs. Multiple diverse solutions were obtained with different well locations but close-to-optimum objective values, which allows a more efficient exploration of the search space at a significantly reduced computational cost. The presented workflow integrates critical challenges that are correlated, yet often addressed independently, providing the much-required operational flexibility and computational efficiency to field operators when selecting from the optimal well placement scenarios.