Reservoir history matching by ensemble smoother with principle component and sensitivity analysis for heterogeneous formations

Ensemble-based data assimilation methods have been widely investigated and applied for inverse problems of fluid flow in porous media during the past decades. Among these methods, the ensemble Kalman filter and the ensemble smoother are probably the most popular in history-matching applications. For large-scale problems, the ensemble size is limited to the computational resources in running the forward simulation, and is usually much smaller than the total number of gridblocks. In this case, the ensemble forms a reduced-order subspace, and principle component analysis is suggested by retaining the leading eigenvectors after truncation.