Ma, Xiang (ExxonMobil Upstream Research Company) | Hetz, Gill (Texas A&M University) | Wang, Xiaochen (ExxonMobil Upstream Research Company) | Bi, Linfeng (ExxonMobil Upstream Research Company) | Stern, Dave (ExxonMobil Upstream Research Company) | Hoda, Nazish (ExxonMobil Upstream Research Company)
Many recent developments in generating history matched reservoir models that approximately characterize subsurface uncertainty are associated with the ensemble smoother (ES) method. It is much better suited for practical history matching applications because it does not require updating of the dynamical variables and thus the frequent simulation restarts required by ensemble kalman filter (EnKF) are avoided. However, the performance of original single update scheme of ES is poor for strongly nonlinear problems and therefore iterations may be needed. Several iterative forms of ES were proposed in the past few years, most of which combine ideas from random maximum likelihood (RML) and ensemble-based techniques. Unlike previous implementations, we pose the history matching problem as a full nonlinear least squares optimization problem and classical Levenberg-Marquardt (LM) algorithm is used as the optimization solver. By showing the that solution of the linearized least squares subproblems arising from each iteration has similar structure to that of standard ES update equation, we propose to use ES as the linear least squares solver to avoid the expensive adjoint calculation. In this way, the proposed algorithm can be considered as an iterative ES and the regularization parameter can be updated following the standard LM rule. Furthermore, because it is casted as an optimization problem, it is straightforward to extend it to robust nonlinear least squares method that can automatically estimate the measurement noise level and reduce the effect of outliers in the data that is essential for field applications. Two synthetic reservoir models are used to showcase the effectiveness and robustness of the newly developed algorithm.