Ensemble Kalman filter method for Gaussian and non-Gaussian priors

The objective of this work is to find an efficient and robust way to implement the ensemble Kalman filter (EnKF) to assimilate production and seismic data for both Gaussian and truncated pluri-Gaussian geological models.; Truncated pluri-Gaussian models have proven to be useful for generating realistic geological models of facies distributions. In this work, we will specifically test a new idea for modeling of a channelized reservoir (fluvial system with two fades, channel facies and non-channel facies). EnKF is used to adjust the facies distribution (e.g. channel and non-channel fades) as well as the porosity and permeability of each fades to match production data and seismic data. For two and three-dimensional pluri-Gaussian models, we present a new procedure to ensure that facies observations at wells are honored at each data assimilation step.; As the erroneous saturation distribution obtained with EnKF may result from nonlinearity or the failure of the assumption that the ensemble of predictions is approximately Gaussian, we investigate the application of a global and local normal score transform to transform water saturation to a Gaussian variables before applying the EnKF analysis step. We also apply an iterative EnKF scheme to obtain more plausible saturations distributions. To improve water cut data matches, we consider matching breakthrough times directly before matching watercut data.; The integration of seismic data poses problems because of the large number of data that are assimilated. With a global assimilation procedure based on subspace projection, filter divergence becomes severe. On the other hand, our implementation of a local updating method to reduce filter divergence results in an unrealistic rough facies map. We introduce a projection method to obtain a more realistic map of the facies distribution, which retains the inherent smoothness of the underlying geological model.; The characterization of measurement error is important if one uses a Bayesian approach to condition reservoir models to dynamic data. We use Savitzky-Golay smoother and wavelet smoother to estimate the measurement error in the production data, and use a modified EM (Expectation-Maximization) algorithm combined with a quadratic fitting to estimate the measurement error in the 4-D seismic data.