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A Data-Space Approach For Well Control Optimization Under Uncertainty

Data-space inversion (DSI) methods provide posterior (history-matched) predictions for quantities of interest, along with uncertainty quantification, without constructing posterior models. Rather, predictions are generated directly from a large set of prior-model simulations and observed data. In this work we develop a data-space inversion with variable controls (DSIVC) procedure that enables forecasting with user-specified well controls in the prediction period. In DSIVC, flow simulations on all prior realizations, with randomly sampled well controls, are first performed. User-specified controls are treated as additional observations to be matched in posterior predictions. Posterior data samples are generated using a randomized maximum likelihood procedure, with some algorithmic treatments applied to improve performance. Results are presented for a channelized system. For any well control specification, posterior predictions can be generated in seconds or minutes. Posterior predictions from DSIVC are compared to reference DSI results. DSI requires prior models to be re-simulated using the specified controls, while DSIVC requires only one set of prior simulations. Substantial uncertainty reduction is achieved through data-space inversion, and reasonable agreement between DSIVC and DSI results is consistently observed. DSIVC is applied for data assimilation combined with production optimization under uncertainty, and clear improvement in the objective function is attained.