Nonlinear Expectation Inference for Efficient Uncertainty Quantification and History Matching of Transient Darcy Flows in Porous Media With Random Parameters Under Distribution Uncertainty

Summary

History matching and uncertainty quantification (UQ) of Darcy flows with random parameters are important for the prediction of reservoir dynamic responses. Most existing automatic history matching (AHM) and data space inversion (DSI) methods rely on the assumption of a specific (typically Gaussian) prior probability distribution, and it remains challenging to history match strongly non-Gaussian problems without appropriate reparameterization. In the current study, we propose a new nonlinear expectation inference (NEI) method for efficient UQ accounting for distribution or Knightian uncertainty. In NEI, no prior probability distribution is assumed, but the observation data needs to be bounded by prior responses. The inferred results are not posterior realizations, but posterior subsets of realizations, such that the mean response on each subset is used for prediction. The new method is validated on synthetic and open-source realistic reservoir models. Numerical experiments show that NEI is more robust than ensemble smoother multiple data assimilation (ESMDA) and DSI on non-Gaussian cases.