A data-space inversion procedure for well control optimization and closed-loop reservoir management

  • Su JiangEmail author
  • Wenyue Sun
  • Louis J. Durlofsky
Original Paper


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 control (DSIVC) procedure that enables forecasting with user-specified well controls in the post-history-match 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 a gradient-based optimizer. For prescribed post-history-match well control settings, posterior predictions can be generated in seconds or minutes. Results are presented for a channelized system, and posterior predictions from DSIVC are compared with those from the standard DSI method. Standard 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 generally observed. DSIVC is then applied for data assimilation combined with production optimization under uncertainty, as well as for closed-loop reservoir management, which entails a sequence of data assimilation and optimization steps. Clear improvement in the objective function is attained in these examples.


History matching Reservoir simulation Data-space inversion Uncertainty quantification Optimization under uncertainty 


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Funding information

The authors received partial funding from Chevron Energy Technology Company and the Stanford Smart Fields Consortium.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Energy Resources EngineeringStanford UniversityStanfordUSA

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