A multi-solution framework for well placement optimization using ensemble of convolutional neural networks

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. An adjusted Latin Hypercube Sampling (aLHS) procedure is developed to generate initial training datasets with diverse well placement scenarios while respecting reservoir boundaries and minimum 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. Results show that the developed framework substantially reduced the computation time, while a greater objective value was achieved employing the adaptive learning strategy due to the enhanced prediction accuracy of the SMs. Multiple solutions were obtained with different well locations and close-to-optimum objective values.