Estimation of Depths of Fluid Contacts and Relative Permeability Curves by History Matching Using Iterative Ensemble-Kalman Smoothers

With the ensemble Kalman filter (EnKF) or smoother (EnKS), it is easy to adjust a wide variety of model parameters by assimilation of dynamic data. We focus first on the case where realizations and estimates of the depths of the initial fluid contacts, as well as grid-block rock-property fields, are generated by matching production data with the EnKS. Then we add the parameters defining power law relative permeability curves to the set of parameters estimated by assimilating production data with EnKS. The efficiency of EnKF and EnKS arises because data are assimilated sequentially in time anti so history matching data requires only one forward run of the reservoir simulator for each ensemble member. For EnKS and EnKF to yield reliable characterizations of the uncertainty in model parameters and future performance predictions, the updated reservoir-simulation variables (e.g., saturations and pressures) must be statistically consistent with the realizations of these variables that would be obtained by rerunning the simulator from time zero using the updated model parameters. This statistical consistency can be established only under assumptions of Gaussianity and linearity that do not normally hold. Here, we use iterative EnKS methods that are statistically consistent, anti show that, for the problems considered here, iteration significantly improves the performance of EnKS.