Efficient Implementation of an Iterative Ensemble Smoother for Data Assimilation and Reservoir History Matching

Abstract

Raanes et al. [1] revised the iterative ensemble smoother of Chen and Oliver [2, 3], denoted Ensemble Randomized Maximum Likelihood (EnRML), using the property that the EnRML solution is contained in the ensemble subspace. They analyzed EnRML and demonstrated how to implement the method without the use of expensive and potentially unstable pseudo inversions of the low-rank state covariance matrix or the ensemble-anomaly matrix. The new algorithm produces the same result, realization by realization, as the original EnRML method. However, the new formulation is simpler to implement, numerically stable, and computationally more efficient. The purpose of this document is to present a simple derivation of the new algorithm and demonstrate its practical implementation and use for reservoir history matching. An additional focus is to customize the algorithm to be suitable for big-data assimilation of measurements with correlated errors. We demonstrate that the computational cost of the resulting “ensemble sub-space” algorithm is linear in the number of measurements, also when the measurements have correlated errors, as well as the state-space dimension. The final algorithm is implemented in the Ensemble Reservoir Tool (ERT) for running and conditioning ensembles of reservoir models. Several verification experiments are presented.