Abstract This paper compares two ensemble-based data-assimilation methods when solving the history-matching problem in reservoirsimulation models. The methods are the Ensemble Kalman Filter (EnKF) and the Ensemble Smoother (ES). EnKF has been used extensively in petroleum applications while ES is now used for the first time for history matching. ES differs from EnKF by computing a global update in the space-time domain, rather than using recursive updates in time as in EnKF. Thus, the sequential updating of the realizations with associated restarts is avoided.
EnKF and ES provide identical solutions for linear dynamical models. However, for nonlinear dynamical models, and in particular models with chaotic dynamics, EnKF is superior to ES, due to the fact that the recursive updates keep the model on track and close to the true solution. Thus, ES is not much used and EnKF has been the method of choice in most data assimilation studies where ensemble methods are used.
On the other hand, reservoir simulation models are rather diffusive systems when compared to the chaotic dynamical models that were previously used to test ES. If we can assume that the model solution is stable with respect to small perturbations in the initial conditions and the history-matching parameters, then ES should give similar results to EnKF, and ES may be a more efficient and much simpler method to implement and apply.
In this paper we compare EnKF and ES and show that ES indeed provide for an efficient ensemble-based method for history matching.
Introduction The EnKF has recently been taken into use with simulation models for oil and gas reservoirs, with the purpose of estimating poorly known parameters and to improve the predictive capability of the models (Nævdal et al., 2003). The Ensemble Kalman Filter (EnKF) was originally introduced by Evensen (1994, 2009b). A special property of the EnKF is that it considers a combined parameter- and state-estimation problem Evensen (2009a). Following the first application of EnKF with reservoir simulation models by Nævdal et al. (2003), there is now a large number of publications that address the parameter estimation in reservoir simulation models using EnKF and we refer to Evensen (2009a) and Aanonsen et al. (2009) and references therein.
Number of Pages
Looking for more?
Some of the OnePetro partner societies have developed subject- specific wikis that may help.