Ensemble Randomized Maximum Likelihood Method as an Iterative Ensemble Smoother

The ensemble Kalman filter (EnKF) is a sequential data assimilation method that has been demonstrated to be effective for history matching reservoir production data and seismic data. To avoid, however, the expense of repeatedly updating variables and restarting simulation runs, an ensemble smoother (ES) has recently been proposed. Like the EnKF, the ES obtains all information necessary to compute a correction to model variables directly from an ensemble of models without the need of an adjoint code. The success of both methods for history matching reservoir data without iteration is somewhat surprising since traditional gradient-based methods for history matching typically require 10 to 30 iterations to converge to an acceptable minimum. In this manuscript we describe a new iterative ensemble smoother (batch-EnRML) that assimilates all data simultaneously and compare the performance of the iterative smoother with the two non-iterative methods and the previously proposed sequential iterative ensemble filter (seq-EnRML). We discuss some aspects of the use of the ensemble estimate of sensitivity, and show that by sequentially assimilating data, the nonlinearity of the assimilation problem is substantially reduced. Although reasonably good data matches can be obtained using a non-iterative ensemble smoother, iteration was necessary to achieve results comparable to the EnKF for nonlinear problems.