Multi-level Optimization of Reservoir Scheduling Using Multi-resolution Wavelet-Based Up-scaled Models

This paper presents a multi-level procedure for production and injection scheduling through a numerical model-based optimization of well control variables. To calculate the net present value (NPV), the objective function of optimization, this procedure uses a number of discretized systems for a reservoir model with different degrees of up-scaling prepared according to a multi-resolution wavelet technique. These up-scaled models were incorporated into optimization based on a probability function. In early optimization iterations, due to the necessity to explore the search space quickly, the coarsest grid model has a higher chance for selection than the others; however, by a selection (with a low probability) of the finest up-scaled grid model in these iterations, solutions and objective function were tuned. In the later iterations of optimization, the finest up-scaled grid model probability was the highest in order to ensure the reliability of the final solution. The optimization algorithm is an adaptive simulated annealing algorithm coupled with a polytope. This procedure was evaluated in two case studies. The first case study was a horizontal 2D oil model with water flooding. The second case study was a vertical 2D oil model with gas injection. The results show that the proposed optimization procedure provides approximately the same accuracy compared to the situation in which the fine grid model is used for all the optimization iterations. Also, the run-time for the proposed optimization procedure is comparable to the run-time of the optimization in which only the coarsest grid model is used to calculate objective function. Moreover, the superiority of the wavelet-based up-scaling over an analogous multiple grid system optimization using uniformly up-scaled models is presented.