Estimation of Relative Permeability and Capillary Pressure for PUNQ-S3 Model Using a Modified Iterative Ensemble Smoother

The iterative ensemble smoother (IES) algorithm has been extensively used to implicitly and inversely determine model parameters by assimilating measured/reference production profiles. The performance of the IES algorithms is usually challenged due to the simultaneous assimilation of all production data and the multiple iterations required for handling the inherent nonlinearity between production profiles and model parameters. In this paper, a modified IES algorithm has been proposed and validated to improve the efficiency and accuracy of the IES algorithm with the standard test model (i.e., PUNQ-S3 model). More specifically, a recursive approach is utilized to optimize the screening process of damping factor for improving the efficiency of the IES algorithm without compromising of history matching performance because an inappropriate damping factor potentially yields more iterations and significantly increased computational expenses. In addition, a normalization method is proposed to revamp the sensitivity matrix by minimizing the data heterogeneity associated with the model parameter matrix and production data matrix in updating processes of the IES algorithm. The coefficients of relative permeability and capillary pressure are included in the model parameter matrix that is to be iteratively estimated by assimilating the reference production data (i.e., well bottomhole pressure (WBHP), gas-oil ratio, and water cut) of five production wells. Three scenarios are designed to separately demonstrate the competence of the modified IES algorithm by comparing the objective function reduction, history-matched production profile convergence, model parameters variance reduction, and the relative permeability and capillary pressure of each scenario. It has been found from the PUNQ-S3 model that the computational expenses can be reduced by 50% while comparing the modified and original IES algorithm. Also, the enlarged objective function reduction, improved history-matched production profile, and decreased model parameter variance have been achieved by using the modified IES algorithm, resulting in a further reduced deviation between the reference and the estimated relative permeability and capillary pressure in comparison to those obtained from the original IES algorithm. Consequently, the modified IES algorithm integrated with the recursive approach and normalization method has been substantiated to be robust and pragmatic for improving the performance of the IES algorithms in terms of reducing the computational expenses and improving the accuracy.