A Machine Learning Approach to Reduce the Number of Simulations for Long-Term Well Control Optimization

Abstract

Abstract A long-term well control strategy is frequently selected using optimization methods applied to reservoir simulations. However, this approach usually requires a large number of simulations that can be computationally demanding. In this paper, we evaluated several machine learning (ML) techniques to reduce the number of simulations for optimizing long-term well control strategy while preserving the quality of the solution. We proposed a methodology, denoted as IDLHC–ML, which combines many ML techniques with iterative discrete Latin hypercube (IDLHC) – a gradient-free optimization algorithm that was successfully applied in previous work – to optimize the coefficients of the logistic equation that guides the well's bottom-hole pressure along the time horizon. In IDLHC-ML, we used a set of simulation runs from the first iteration to train the initial ML models. From the second iteration onwards, we employed the trained ML models to predict the net present value (NPV) and only a percentage of the scenarios, which were expected to have the best NPV, were then simulated. As we simulated new scenarios, we updated our ML models to further improve predictions. For a fair comparison, we set the same values for the optimization parameters of IDLHC to the IDLHC–ML and, then, we compared the NPV and the number of simulation runs considering different configurations of IDLHC parameters. In this paper, we evaluated a total of twelve ML regression techniques, such as Bayesian Ridge, Random Forest, and stacked ensemble learning, which consists in using the predictions from multiple ML algorithms as input to a second-level learning model. To minimize random effects, we repeatedly applied IDLHC and IDLHC–ML five times in a single reservoir model (nominal optimization). The results showed that, depending on the IDLHC optimization parameters, IDLHC-ML reduced at least 27% of simulations while keeping the equivalent NPV statistical metrics calculated in all five repetitions, when compared to IDLHC. Moreover, the best ML technique for IDLHC–ML varied with the IDLHC set of optimization parameters. To conclude, the method proposed here was able to reduce a significant amount of computational time by curtailing the total number of full-physics expensive reservoir simulations, with the help of fast and low-cost ML models. There are many published studies in well control optimization, but these generally involve high computational demand. In this sense, ML methods revealed to be an adequate and inexpensive alternative in reducing the number of simulation runs in well control optimization. The methodology is generic and it can be applied under uncertainties, and for more complex cases.