Retrospective Optimization of Well Controls Under Uncertainty Using Kernel Clustering

Smart field technology is an attractive research field, as it can find an optimal well control strategy to maximize the oil recovery or the net present value (NPV). As the subsurface geology is highly uncertain, the reservoir model is usually described by a set of reservoir models. In well control optimization for a reservoir described by a set of geological models, the expectation of NPV is optimized. This approach called robust optimization, entails running the reservoir simulator for all the reservoir models at each iteration of the optimization algorithm. Hence, robust optimization can be computationally very expensive when a large number of realizations are used to capture the geological uncertainty. In this work, we apply the retrospective optimization procedure to address this problem. In this approach, a sequence of optimization subproblems that contain increasing number of realizations are solved. The solution obtained at each optimization subproblem is used as the initial guess for the next stage. We use a kernel clustering technique to select a subset of reservoir models at each optimization subproblem. We present two examples that show the performance of this method. In these examples, we use the QIM-SPSA method as the optimization algorithm. The examples show that by applying the retrospective optimization approach, we can significantly reduce the computational cost, while obtaining almost the same NPV of robust optimization with including all the realizations from the beginning.