Reduced-order modeling represents an attractive framework for accelerating computationally expensive reservoir simulation applications. In this paper we introduce and apply a reduced-order modeling approach for history matching. The method considered, trajectory piecewise linearization (TPWL), has been used previously for production optimization problems, where it has provided large computational speedups. The TPWL model developed here represents simulation results for new geological models in terms of a linearization around previously simulated (training) cases. The high-dimensional state space is projected into a low-dimensional subspace using proper orthogonal decomposition (POD). The geological model is represented in terms of a Karhunen-Loeve expansion of the log-transmissibility field, so both the reservoir states and geological parameters are described in a very concise way. The method is incorporated into an Ensemble Kalman Filter (EnKF) history-matching procedure. The combined technique enables EnKF to be applied using many fewer (high-fidelity) reservoir simulations than would otherwise be required to avoid ensemble collapse. More specifically, it is demonstrated that EnKF results using 50 high-fidelity simulations along with 150 TPWL simulations are much better than those using only 50 high-fidelity simulations and are, in fact, comparable to the results achieved using 200 high-fidelity simulations.

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