Ensemble smoother with multiple data assimilation

In the last decade, ensemble-based methods have been widely investigated and applied for data assimilation of flow problems associated with atmospheric physics and petroleum reservoir history matching. This paper focuses entirely on the reservoir history-matching problem. Among the ensemble-based methods, the ensemble Kalman filter (EnKF) is the most popular for history-matching applications. However, the recurrent simulation restarts required in the EnKF sequential data assimilation process may prevent the use of EnKF when the objective is to incorporate the history matching in an integrated geo-modeling workflow. In this situation, the ensemble smoother (ES) is a viable alternative. However, because ES computes a single global update, it may not result in acceptable data matches; therefore, the development of efficient iterative forms of ES is highly desirable. In this paper, we propose to assimilate the same data multiple times with an inflated measurement error covariance matrix in order to improve the results obtained by ES. This method is motivated by the equivalence between single and multiple data assimilation for the linear-Gaussian case. We test the proposed method for three synthetic reservoir history-matching problems. Our results show that the proposed method provides better data matches than those obtained with standard ES and EnKF, with a computational cost comparable with the computational cost of EnKF.

[1]  G. Evensen,et al.  Data assimilation and inverse methods in terms of a probabilistic formulation , 1996 .

[2]  Dean S. Oliver,et al.  Ensemble-Based Closed-Loop Optimization Applied to Brugge Field , 2010 .

[3]  D. McLaughlin,et al.  Hydrologic Data Assimilation with the Ensemble Kalman Filter , 2002 .

[4]  Geir Evensen,et al.  Integrated Work Flow for Model Update Using Geophysical Monitoring Data , 2011 .

[5]  Geir Nævdal,et al.  History Matching Using the Ensemble Kalman Filter on a North Sea Field Case , 2008 .

[6]  G. Evensen.  Sampling strategies and square root analysis schemes for the EnKF , 2004 .

[7]  Roald Brouwer,et al.  Closed Loop Reservoir Management , 2009 .

[8]  Dean S. Oliver,et al.  Improved initial sampling for the ensemble Kalman filter , 2008 .

[9]  Yan Chen,et al.  Data assimilation for transient flow in geologic formations via ensemble Kalman filter , 2006 .

[10]  A. Reynolds,et al.  History matching time-lapse seismic data using the ensemble Kalman filter with multiple data assimilations , 2012, Computational Geosciences.

[11]  A. Reynolds,et al.  Iterative Forms of the Ensemble Kalman Filter , 2006 .

[12]  Istvan Szunyogh,et al.  Assessing a local ensemble Kalman filter: perfect model experiments with the National Centers for Environmental Prediction global model , 2005 .

[13]  Trond Mannseth,et al.  Near-Well Reservoir Monitoring Through Ensemble Kalman Filter , 2002 .

[14]  Chunhong Wang,et al.  Production Optimization in Closed-Loop Reservoir Management , 2009 .

[15]  Geert Brouwer,et al.  Results of the Brugge Benchmark Study for Flooding Optimisation and History Matching , 2010 .

[16]  Hilde Meisingset,et al.  Using the EnKF for Assisted History Matching of a North Sea Reservoir Model , 2007 .

[17]  G. Evensen.  Sequential data assimilation with a nonlinear quasi‐geostrophic model using Monte Carlo methods to forecast error statistics , 1994 .

[18]  Albert C. Reynolds,et al.  An Improved Implementation of the LBFGS Algorithm for Automatic History Matching , 2004 .

[19]  Geir Evensen,et al.  Sequential data assimilation , 2009 .

[20]  Tor Arne Johansen,et al.  Incorporating 4D Seismic Data in Reservoir Simulation Models Using Ensemble Kalman Filter , 2005 .

[21]  Chaohui Chen,et al.  Closed-loop reservoir management on the Brugge test case , 2010 .

[22]  Dean S. Oliver,et al.  An Iterative Ensemble Kalman Filter for Multiphase Fluid Flow Data Assimilation , 2007 .

[23]  G. Evensen,et al.  An ensemble Kalman smoother for nonlinear dynamics , 2000 .

[24]  Geir Nævdal,et al.  HISTORY MATCHING AND PRODUCTION FORECAST UNCERTAINTY BY MEANS OF THE ENSEMBLE KALMAN FILTER: A REAL FIELD APPLICATION , 2007 .

[25]  Albert C. Reynolds,et al.  History Matching a Field Case Using the Ensemble Kalman Filter with Covariance Localization , 2011, ANSS 2011.

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

[27]  Dean S. Oliver,et al.  Conditioning Geostatistical Models to Two-Phase Production Data , 1998 .

[28]  D. Oliver,et al.  Ensemble Randomized Maximum Likelihood Method as an Iterative Ensemble Smoother , 2011, Mathematical Geosciences.

[29]  Chunhong Wang,et al.  Production Optimization in Closed-Loop Reservoir Management , 2009 .

[30]  Christian L. Keppenne,et al.  Assimilation of temperature into an isopycnal ocean general circulation model using a parallel ensemble Kalman filter , 2003 .

[31]  Albert C. Reynolds,et al.  Results of the Brugge Benchmark Study for Flooding Optimization and History Matching , 2010 .

[32]  Dean S. Oliver,et al.  Ensemble-Based Closed-Loop Optimization Applied to Brugge Field , 2010 .

[33]  Dongxiao Zhang,et al.  Investigation of flow and transport processes at the MADE site using ensemble Kalman filter , 2008 .

[34]  P. L. Houtekamer,et al.  Ensemble Kalman filtering , 2005 .

[35]  G. Evensen,et al.  Sequential Data Assimilation Techniques in Oceanography , 2003 .

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

[37]  A. Reynolds,et al.  Estimation of Depths of Fluid Contacts by History Matching Using Iterative Ensemble-Kalman Smoothers , 2010 .

[38]  Geir Evensen,et al.  History Matching Using the Ensemble Kalman Filter on a North Sea Field Case , 2008 .

[39]  Dean S. Oliver,et al.  Conditioning Geostatistical Models to Two-Phase Production Data , 1999 .

[40]  A. Reynolds,et al.  Combining sensitivities and prior information for covariance localization in the ensemble Kalman filter for petroleum reservoir applications , 2011 .

[41]  Jan-Arild Skjervheim,et al.  An Ensemble Smoother for Assisted History Matching , 2011, ANSS 2011.

[42]  Albert Tarantola,et al.  Inverse problem theory - and methods for model parameter estimation , 2004 .

[43]  Dean S. Oliver,et al.  Memoir 71, Chapter 10: Reducing Uncertainty in Geostatistical Description with Well-Testing Pressure Data , 1997 .

[44]  A. Reynolds,et al.  Estimation of Initial Fluid Contacts by Assimilation of Production Data With EnKF , 2007 .

[45]  Istvan Szunyogh,et al.  Assessing a local ensemble Kalman filter : perfect model experiments with the National Centers for Environmental Prediction global model , 2004 .

[46]  D. Oliver,et al.  Recent progress on reservoir history matching: a review , 2011 .

[47]  J. R. Rommelse,et al.  Data assimilation in reservoir management , 2009 .

[48]  Albert C. Reynolds,et al.  Estimation of Depths of Fluid Contacts by History Matching Using Iterative Ensemble Kalman Smoothers , 2009 .