One objective of the field development plan (FDP) is to optimize well patterns, that is, the number and type of well (producers or injectors) and their locations, in order to maximize net present value (NPV). Optimization cost, including reservoir simulation, is strongly needed in terms of a global solution because of countless FDP scenarios, especially robust optimization for considering geological uncertainty. To solve this problem efficiently and reliably, this study introduces a convolutional neural network (CNN)-based proxy model into particle swarm optimization (PSO). For the proxy model, three map types having the same dimension as the reservoir model were fed into the input layer, giving an NPV for a given well-pattern scenario. The first map was a well configuration map, which consists of 1, -1, and 0 for producer, injector, and no well, respectively. The second and third maps were time-of-flight (TOF) maps from producers and injectors, respectively. Because the type of input data is an image, the CNN could extract features from 3500 scenarios while training the proxy model. When the predicted NPVs from the trained CNN-based proxy model were verified for 750 test data, the coefficients of determination for the true NPVs from reservoir simulation were higher than 0.94. In addition, the proxy model was flexibly applied to various well patterns, even for different numbers of wells because it utilizes TOF maps as input data. Three points are handled in PSO-Proxy to achieve a realistic well pattern: optimization of the number of wells, well spacing constraint, and operational condition for injection wells. The optimized well pattern maximizes NPV with the optimal number of producers and injectors under the predefined maximum number of wells. In the case of well spacing, two distances, that is, the distance between the wells and the distance between a production well and reservoir boundary, are used as criteria for the solution in terms of the filter method before evaluating the NPV. For injectors, water injection is controlled by bottomhole pressure instead of a constant injection rate, which gives meaningless injection wells placed at the edge of the reservoir. When the proposed method was tested using a 2-dimensional (D) synthetic field and 3-D Egg model, its well patterns showed approximately 1.2% lower NPV than the solution from a conventional method, PSO-ECL. This was relatively small when considering that there was approximately 7.8% NPV changes in each optimization run of the PSO-ECL. In addition, PSO-Proxy required only 21% and 8.6% of the optimization cost of the PSO-ECL for the 2-D and 3-D cases, respectively. Therefore, the proposed method was found to enable reliable and efficient decision-making for FDP; further, as the reservoir complexity increases, the CNN-based proxy model should be able to reduce the optimization time dramatically.
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Jan 7, 2022
Andrea Cavaglià + 3
Open Access
