Quantifying the Benefit of Ensemble Selection for Optimization Under Uncertainty

Due to significant uncertainty in reservoir parameters, maximizing reservoir potential is an extremely difficult task. To be able to make decisions that maximize the reservoir potential, knowledge of possible ranges of reservoir parameters and production optimization are critical. The closed-loop reservoir management approach enables the petroleum industry to understand possible ranges of reservoir parameters and optimize production strategy accordingly. Closed-loop reservoir management can also be used to quantify uncertainty in reservoir parameters and take into account during reservoir management process accordingly. An ensemble of reservoir realizations can be incorporated in the workflow to probabilistically forecast production and an optimum production strategy for the overall ensemble can be obtained using robust optimization concepts,. However, robust optimization involves optimizing every realization which requires significant computational cost. Thus, careful consideration is required of the trade-off between the number of models optimized and the computational cost.

This thesis aims to investigate the benefit of optimizing production strategy with different ensemble sizes. Two-phase reservoir modeling of waterflooding is used in this study. Markov Chain Monte Carlo (MCMC) is used in the history matching process to investigate probability distributions of uncertain reservoir parameters. The Minimax approach which aims to maximize spread in input uncertainty space will be used in selecting representative models for different ensemble sizes. Simultaneous Perturbation Stochastic Approximation (SPSA) is applied to each ensemble to optimize production strategy. The study compared the resulting NPVs using optimized production strategies from different ensemble sizes.

Results show that increasing ensemble size leads to a better development strategy. However, the incremental benefit decreases with increasing ensemble size. The study indicated that the development strategy that is based on multiple realizations is better than development strategy that was developed based on single realization even though the multiple realizations case did not include all possible realizations. The study also demonstrates a systematic methodology for investigating the benefit of using multiple models for optimization vs. a single realization.