... Abstract Ensemble Kalman filtering (EnKF) is an effective method for reservoir history matching. The underlying principle is that an initial ensemble of stochastic models can be progressively updated to reflect the measured values as they become available. However, the ensemble Kalman filter...

... assimilation for the linear-Gaussian case and an approximate relationship between ES and one iteration of the Gauss-Newton method. ES-MDA is easy to combine with any commercial simulator, in fact, much easier than it is to couple the ensemble Kalman filter (EnKF) with a commercial simulator. Here, we apply...

... Abstract Although the EnKF has many advantages, such as ease of implementation and efficient uncertainty quantification, it suffers from a few key issues that limit its application to large-scale simulation models of real fields. Among these key issues is the well known problem of ensemble...

... lead to shrinkage of off-diagonal elements. Abstract Using a small ensemble size with the ensemble Kalman filter (EnKF) to update numerical reservoir models has proved to be an efficient method of reservoir history matching but, unless some type of localization is used, the standard EnKF update...

... Abstract The standard formulation of the ensemble Kalman filter (EnKF) does not take into account the physical constraints on state variables during the data assimilation step so constraint violations are often handled heuristically. The physical constraints often contain valuable information...

... and water cut. In the EnKF, the state vector y is represented by an ensemble of realizations. The EnKF involves a forecast (prediction) step and an update step. The forecast step is represented by the following equation, Introduction Sequential data assimilation with continuous production data...

... Abstract Although there is intense interest in employing the ensemble Kalman filter (EnKF) for assisted history matching, it is well known that the approximation of covariance matrices from a finite ensemble of states and a finite ensemble of predicted data vectors can lead to a large...

... for Variable Geological Parameters This paper proceeds as follows. We first describe the TPWL representation of flow solutions on new geological models and evaluate TPWL performance for an example case. We then give a brief overview of EnKF and describe the combined EnKF-TPWL workflow. The proposed...

... ES is an alternative data assimilation method that differs from EnKF by computing the global update in one go 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. ES is otherwise...

... time. It is clear from Equation (6) that the updated state vectors are linear combinations of the forecasted state vectors. Further, because the EnKF only uses the covariance of the forecasted state vectors, it is technically appropriate only for multi-Gaussian random fields. In other words...

... and frequency of use of the ensemble Kalman filter (EnKF) as an assisted history matching technique has increased significantly. As EnKF generates multiple history-matched models, it conceptually allows one to characterize the uncertainty in reservoir description and future performance predictions. However...

... Abstract The EnKF has become increasingly popular for updating and history matching reservoir simulation models. Originally the filter was developed for sequential conditioning of state variables to dynamic data. It was later extended to solve the combined state and parameter estimation problem...

... of the model. In practice, it is hardly known with certainty and it is important to account for this uncertainty in the modeling and history matching phases. The ensemble Kalman filter (EnKF), when modified appropriately, to account for non-linearity and non-Gaussianity, is quite robust for automatic history...

... the reservoir model if used wisely. In this study, the Ensemble Kalman filter (EnKF) approach is used to estimate reservoir flow and material properties by jointly assimilating dynamic flow and geomechanics observations. The resulting model can be used for managing and optimizing production operations...

... a two-stage Ensemble Kalman Filter (EnKF) that utilizes the tracer data in conjunction with coarse-scale saturation constraints to identify the fine-scale saturation distribution and associated uncertainties. The coarse-scale saturation distribution can be conveniently obtained via an inversion...

... Abstract This paper demonstrates the potential and advantages of the Ensemble Kalman filter (EnKF) as a tool for assisted history matching, based on its sequential processing of measurements, its capability of handling large parameter sets, and on the fact that it solves the combined state...

... approach receiving the most attention to date is the ensemble Kalman filter (EnKF). Although the EnKF has many advantages such as ease of implementation and efficient uncertainty quantification, it is technically appropriate only for random fields (e.g., permeability) characterized by two-point...

... coefficients and heterogeneities can be estimated using ensemble Kalman filter (EnKF) for history matching. Hierarchical or multi-scale heterogeneities are generally poorly represented, especially in deepwater reservoirs. We developed a hierarchical description of heterogeneities that introduced new variables...

... convergence ensemble realization EnKF ensemble Kalman filter matrix reservoir simulation covariance matrix application singular evolutive interpolated kalman filter Kalman Filter forecast modeling & simulation permeability field waterflooding assimilation fluid dynamics enhanced recovery...

.... Gao , G. , Zafari , M. , and Reynolds , A.C. : " Quantifying Uncertainties for the PUNQ-S3 Problem in a Bayesian Setting With RML EnKF ," paper SPE 93324 presented at the 2002 Improved Oil Recovery Symposium , Tulsa, Oklahoma 13-17 April . 8. Zafari , M. , Reynolds , A.C...