A Unified Framework for a Class of Ensemble Data Assimilation Algorithms in Reservoir History Matching Problems

In recent years ensemble data assimilation (EnDA) algorithms, such as the ensemble Kalman filter, the ensemble smoother and their iterative counterparts have received considerable attention from researchers and practitioners in petroleum engineering, due to their relative simplicity in implementations, reasonable computational costs and reliable performance. The main goal of this paper is to extract some common structures among a class of EnDA algorithms, and establish a mathematical framework that can not only be used to analyze these existing methods in a unified way, but also entails new algorithm developments in the future. For illustration, in an example demonstrated in the paper, we transplant a deterministic inversion algorithm into the proposed framework, and derive from it an EnDA algorithm that has been applied to the Brugge field case study. The new EnDA algorithm tends to converge faster than the original inversion algorithm itself. In addition, instead of obtaining a single solution as the original inversion algorithm does, the new EnDA algorithm provides an ensemble of solutions that lays the ground for uncertainty quantification. On top of this example, we believe that one may also incorporate other deterministic inversion/optimization methods into the proposed framework and gain similar benefits.