Hybrid Ensemble Kalman Filter With Coarse-Scale Constraint for Nonlinear Dynamics
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This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 124826, A Hybrid Ensemble Kalman Filter With Coarse-Scale Constraint for Nonlinear Dynamics, by Shingo Watanabe, SPE, Akhil Datta-Gupta, SPE, and Yalchin Efendiev, SPE, Texas A&M University, and Deepak Devegowda, SPE, University of Oklahoma, prepared for the 2009 SPE Annual Technical Conference and Exhibition, New Orleans, 4-7 October.Interest in ensemble Kalman filters (EnKFs) is driven by the need for continuous reservoir-model updating and uncertainty assessments based on dynamic data. The EnKF approach relies on sample-based statistics derived from an ensemble of reservoir-model realizations. Sampling error in these statistics, particularly with the use of modest ensemble sizes, can degrade EnKF performance severely, leading to parameter overshoots and filter divergence. The proposed hybrid-multiscale EnKF improved operational-data assimilation and helped overcome many limitations associated with the classical EnKF implementation.IntroductionA primary motivation for history matching is to construct reliable predictive models and then to quantify the uncertainties in forecasting. Traditional history matching applies local and regional changes by use of multipliers to reservoir properties to calibrate the reservoir model with production data. However, this approach often creates artificial discontinuities that lessen geologic realism in the updated model. The manpower and time required to achieve a satisfactory history match render the manual process inefficient for assessing multiple-model realizations. Automated methods that use inverse theory or stochastic approaches to minimize appropriately defined misfit functions have received increased attention along with development of robust history-matching algorithms and enhancements in computational capabilities.With modern field-monitoring technology, such as permanent well monitors and intelligent-completion technology, production data often are incorporated into the reservoir model upon availability. Recognizing under-lying uncertainties in the geologic model, it is desirable to generate a suite of plausible model realizations rather than a single best-history-matched model. The EnKF combines these capabilities for the purposes of reservoir characterization and uncertainty assessment. In the EnKF framework, an ensemble of model realizations is updated progressively as the data become available by use of an assimilation sequence that contains a forecast step that propagates the ensemble forward in time and an update step that modifies the reservoir variables to match the current observation.
