SPE 141967 PP Use of Reduced-order Models for Improved Data Assimilation within an EnKF Context

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. Introduction History matching is an essential component of reservoir modeling and management. It entails the updating of the reservoir model using dynamic data, e.g., production data or time-lapse seismic data. History matching can be viewed as an optimization problem in which the mismatch between observed and simulated data is minimized by modifying the parameters associated with the geological model. It typically requires large numbers of simulations, which can be extremely time consuming if high-resolution models are used. Thus, there is a significant need for efficient (proxy or surrogate) models that can predict simulation results with reasonable accuracy. Reduced-order modeling procedures, which have been applied in many application areas including reservoir simulation, represent a means for accelerating flow simulations. Many of these techniques entail the projection of the full-order (high-fidelity) numerical description into a low-dimensional subspace, which reduces the number of unknowns that must be computed at each time step. Existing approaches, applied within the context of reservoir simulation, include procedures based on proper orthogonal decomposition (Cardoso et al., 2009; Markovinović and Jansen, 2006; van Doren et al., 2006) and techniques based on trajectory piecewise linearization, TPWL (Cardoso and Durlofsky, 2010a,b; He, 2010). The target application in these studies was production optimization, and the reduced-order model was used to provide results for varying well control parameters (bottomhole pressure or flow rates).