Sequential field development plan through robust optimization coupling with CNN and LSTM-based proxy models

Abstract

Well operation optimization is vital in maximizing the net present value (NPV) of the field development plan (FDP). As well operation is a time-series scenario, this problem contains numerous parameters to be optimized and countless solutions. This results in huge optimization time to evaluate each scenario using the reservoir simulator, especially with robust optimization. In this study, particle swarm optimization is coupled with the deep learning-based proxy model to solve such problems in the 2D synthetic and 3D Egg cases. First, the long short-term memory (LSTM) proxy model is developed to estimate the reservoir response to the well operation scenario instead of reservoir simulation. When the drilling and bottomhole pressure (BHP) schedules are entered into the input layer for the proxy model, the average cumulative field oil and water productions and field water injection from the multiple reservoir models are obtained in the output layer. In case of well pattern, the optimized scenario of the location and type of wells in Kim et al. (2021a) was fixed in this study. After the LSTM proxy model fits with the training data pair of time-series BHP schedule and corresponding the responses obtained by ECLIPSE (ECL), it can predict the time-series field response for given BHP scenario. When the calculated NPV from the LSTM is compared with the true NPV from ECL, the coefficient of determination for the validation and test datasets is higher than 0.97, solving the overfitting problem of the simple neural network (NN) proxy model. It is critical to select a proper deep learning algorithm according to the characteristics of the input and output data. While the convolutional NN (CNN) is proper to make a proxy model for well pattern scenario, which consists of the static images with the same dimension in Kim et al. (2021a), the LSTM is suitable for well operation scenario, which changes over time. Second, the drilling and BHP schedules are optimized under the constraint of the maximum available rig. Also, to reduce these high-dimensional optimization variables, we define the BHP schedule as a cosine function instead of the stepwise approach. It reduces the number of training data required for the proxy model. Third, optimization strategies are reviewed for both the well pattern and well operation. The sequential proxy, CNN-LSTM, shows similar NPVs with the results of the sequential ECL-ECL. However, CNN-LSTM requires only 12% of optimization time compared to ECL-ECL for the 3D case. Therefore, CNN-LSTM is proposed as the reasonable solution for reliable decision-making for the FDP in a short time.