Scenario Reduction of Realizations Using Fast Marching Method in Robust Well Placement Optimization of Injectors

Choosing a representative subset of realizations can reduce significantly the number of simulations and the computational cost associated with optimization under geological uncertainty. Methods that use dynamic criteria, such as full flow simulators, can choose effectively representative realizations and reduce the number of simulations during optimization. However, these methods are expensive computationally. This study aims at investigating the effect of using diffusive time of flight (DTOF) as a feature to select a representative subset of realizations for well placement optimization under uncertainty. The proposed approach is based on the calculation of DTOF for pressure propagation in a reservoir; it was calculated using the fast marching method (FMM). To determine reservoir connectivity, a threshold was used for a number of grid blocks at specific time intervals; it can be used as a measure to evaluate and select the realizations. The proposed methodology was utilized to optimize the location of vertical injection wells on three numerical models, which are three dimensional with equally probable realizations. The optimization results of the proposed method were compared with the results of optimization using the full set and the subset realizations obtained using the K-means clustering method. In this study, 10 realizations were selected from the full set as the representative subset. The selection was based on K-means clustering and FMM. Results show that the FMM-based approach outperforms the clustering method and it can capture the uncertainty range with only a small subset of realizations with a much lower computational burden compared to the full set.