Comparing the adaptive Gaussian mixture filter with the ensemble Kalman filter on synthetic reservoir models

Over the last years, the ensemble Kalman filter (EnKF) has become a very popular tool for history matching petroleum reservoirs. EnKF is an alternative to more traditional history matching techniques as it is computationally fast and easy to implement. Instead of seeking one best model estimate, EnKF is a Monte Carlo method that represents the solution with an ensemble of state vectors. Lately, several ensemble-based methods have been proposed to improve upon the solution produced by EnKF. In this paper, we compare EnKF with one of the most recently proposed methods, the adaptive Gaussian mixture filter (AGM), on a 2D synthetic reservoir and the Punq-S3 test case. AGM was introduced to loosen up the requirement of a Gaussian prior distribution as implicitly formulated in EnKF. By combining ideas from particle filters with EnKF, AGM extends the low-rank kernel particle Kalman filter. The simulation study shows that while both methods match the historical data well, AGM is better at preserving the geostatistics of the prior distribution. Further, AGM also produces estimated fields that have a higher empirical correlation with the reference field than the corresponding fields obtained with EnKF.

[1]  Andreas Størksen Stordal,et al.  Sequential Data Assimilation in High Dimensional Nonlinear Systems , 2011 .

[2]  T. Bengtsson,et al.  Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants , 2007 .

[3]  Dinh-Tuan Pham,et al.  A New Approximate Solution of the Optimal Nonlinear Filter for Data Assimilation in Meteorology and Oceanography , 2008 .

[4]  Henning Omre,et al.  Hierarchical Ensemble Kalman Filter , 2010 .

[5]  Rolf Johan Lorentzen,et al.  Analysis of the ensemble Kalman filter for estimation of permeability and porosity in reservoir models , 2005 .

[6]  A. Stordal,et al.  Bridging the ensemble Kalman filter and particle filters: the adaptive Gaussian mixture filter , 2011 .

[7]  Chris Snyder,et al.  Toward a nonlinear ensemble filter for high‐dimensional systems , 2003 .

[8]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[9]  Jianlin Fu,et al.  A markov chain monte carlo method for inverse stochastic modeling and uncertainty assessment , 2008 .

[10]  Dean S. Oliver,et al.  THE ENSEMBLE KALMAN FILTER IN RESERVOIR ENGINEERING-A REVIEW , 2009 .

[11]  Jonathan D. Beezley,et al.  An Ensemble Kalman-Particle Predictor-Corrector Filter for Non-Gaussian Data Assimilation , 2008, ICCS.

[12]  Neil J. Gordon,et al.  Editors: Sequential Monte Carlo Methods in Practice , 2001 .

[13]  A. Stuart,et al.  Sampling the posterior: An approach to non-Gaussian data assimilation , 2007 .

[14]  Simon J. Godsill,et al.  On sequential Monte Carlo sampling methods for Bayesian filtering , 2000, Stat. Comput..

[15]  Jun S. Liu,et al.  Sequential Imputations and Bayesian Missing Data Problems , 1994 .

[16]  P. Bickel,et al.  Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems , 2008, 0805.3034.

[17]  Dean S. Oliver,et al.  Improving the Ensemble Estimate of the Kalman Gain by Bootstrap Sampling , 2010 .

[18]  G. Evensen Data Assimilation: The Ensemble Kalman Filter , 2006 .

[19]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[20]  Jeffrey L. Anderson EXPLORING THE NEED FOR LOCALIZATION IN ENSEMBLE DATA ASSIMILATION USING A HIERARCHICAL ENSEMBLE FILTER , 2007 .

[21]  A. R. Syversveen,et al.  Methods for quantifying the uncertainty of production forecasts: a comparative study , 2001, Petroleum Geoscience.

[22]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .