Reduced Space Dynamics-Based Geo-Statistical Prior Sampling for Uncertainty Quantification of End Goal Decisions

The inversion of large-scale ill-posed problems introduces multiple challenges. These include, identifying appropriate noise model, prescription of suitable prior information, design of an informative experiment, uncertainty quantification, incorporation of heterogeneous sources of data, and definition of an appropriate optimization scheme. In the context of flow in porous media, subsurface parameters are inferred through the inversion of oil production data (a process called history matching). In this study, the inherent uncertainty of the problem is mitigated by devising efficient and comprehensive approaches for prior sampling. Despite meticulous efforts to minimize the variability of the solution space, the distribution of the posterior may remain intractable. In particular, geo-statisticians may often propose large sets of prior samples that regardless of their apparent geological distinction are almost entirely flow equivalent. As an antidote, a reduced space hierarchical clustering of flow relevant indicators is proposed for aggregation of these samples. The effectiveness of the method is demonstrated both with synthetic and field scale data. In addition, numerical linear algebra techniques that exploit the special structure of the underlying problems are elucidated.