EnKF-MCMC

Abstract

Abstract The ensemble Kalman filter (EnKF) has recently become a popular history-matching tool largely because of its computational efficiency and ease of implementation. While EnKF has improved a previous history match obtained manually in several field cases, and often appears to give reasonable results for realistic synthetic history matching problems, one cannot theoretically establish that EnKF samples correctly the posterior probability distribution for the reservoir model parameters or correctly assesses the uncertainty in the production forecast unless strong assumptions of Gaussianity and linearity apply. In multiphase flow problems, the relationship between data and reservoir model parameters and the primary simulation variables is highly nonlinear, so the theoretical justification for obtaining a correct assessment of the uncertainty in model parameters and future performance predictions does not hold. On the other hand, it is well known that the Markov chain Monte Carlo (MCMC) method sample correctly in the limit. However its direct application to reservoir problems can be prohibitively expensive computationally. Here we use a variant of EnKF, the ensemble square root filter (EnSRF), to provide an initial sample of the posterior pdf and to propose transitions for the MCMC method. We present a synthetic reservoir case and show that the combined application of EnSRF and MCMC provides improved history-matching results and a better characterization of uncertainty in the predicted reservoir performance.