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

The uncertainty quantification of Darcy flows using history matching is important for the evaluation and prediction of subsurface reservoir performance. Conventional methods aim to obtain the maximum a posterior or maximum likelihood estimate (MLE) using gradient-based, heuristic or ensemble-based methods. These methods can be computationally expensive for high-dimensional problems since forward simulation needs to be run iteratively as physical parameters are updated. In the current study, we propose a nonlinear expectation inference (NEI) method for efficient history matching and uncertainty quantification accounting for distribution or Knightian uncertainty. Forward simulation runs are conducted on prior realisations once, and then a range of expectations are computed in the data space based on subsets of prior realisations with no repetitive forward runs required. In NEI, no prior probability distribution for data is assumed. Instead, the probability distribution is assumed to be uncertain with prior and posterior uncertainty quantified by nonlinear expectations. The inferred result of NEI is the posterior subsets on which the expected flow rates are consistent with observation. The accuracy and efficiency of the new method are validated using single- and two-phase Darcy flows in 2D and 3D heterogeneous reservoirs.