History-Matching Production Data Using Ensemble Smoother with Multiple Data Assimilation: A Comparative Study
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Reservoir simulation models are generated by petroleum engineers to optimize field operation and production, thus maximizing oil recovery. History matching methods are extensively used for reservoir model calibration and petrophysical properties estimation by matching numerical simulation results with true oil production history. Sequential reservoir model updating technique Ensemble Kalman filter (EnKF) has gained popularity in automatic history matching because of simple conceptual formulation and ease of implementation. The computational cost is relatively affordable compared with other sophisticated assimilation methods. Ensemble Smoother is a viable alternative of EnKF. Unlike EnKF, Ensemble Smoother computes a global update by simultaneously assimilating all data available and provides a significant reduction in simulation time. However, Ensemble Smoother typically yields a data match significantly inferior to that obtained with EnKF. Ensemble smoother with multiple data assimilation (ES-MDA) is developed as efficient iterative forms of Ensemble Smoother to compare with conventional EnKF. For ES-MDA the same set of data is assimilated multiple times with an inflated covariance matrix of the measurement error. We apply ES-MDA and EnKF to generate multiple realizations of the permeability field by history matching production data including bottom-hole pressure, water-cut and gas-oil ratio. Both algorithms have been implemented to synthetic heterogeneous case and Goldsmith field case. Moreover, ES-MDA coupled with various covariance localization methods: Distance based, Streamline based and Hierarchical ensemble filter localization methods are compared in terms of both quality of history matching and permeability distribution.