History matching of channel reservoirs using ensemble Kalman filter with continuous update of channel information

Abstract

Ensemble Kalman filter (EnKF) has been widely studied due to its excellent recursive data processing, dependable uncertainty quantification, and real-time update. However, many previous works have shown poor characterization results on channel reservoirs with non-Gaussian permeability distribution, which do not satisfy the Gaussian assumption of EnKF algorithm. To meet the assumption, normal score transformation can be applied to ensemble parameters. Even though this preserves initial permeability distribution of ensembles, it cannot provide reliable results when initial reservoir models are quite different from the reference one. In this study, an ensemble-based history matching scheme is suggested for channel reservoirs using EnKF with continuous update of channel information. We define channel information which consists of the facies ratio and the mean permeability of each rock face. These are added to the ensemble state vector of EnKF and updated recursively with other model parameters. Using the updated channel information, ensemble parameters are retransformed after each assimilation step. The proposed method gives better characterization results in case of using even poorly designed initial ensemble members. The method also alleviates overshooting problem of EnKF without further modifications of EnKF algorithm. The methodology is applied to channel reservoirs with extreme non-Gaussian permeability distribution. The result shows that the updated models can find channel pattern successfully and the uncertainty range is decreased properly to make a reasonable decision. Although initial channel information of the ensemble members shows big difference with the real one, it can be updated to follow the reference. Keywords Uncertainty quantification, channel field characterization, ensemble Kalman filter (EnKF), normalscore ensemble Kalman filter (NS-EnKF), characterizing channel information

Efficient Assessment of Reservoir Uncertainty Using Distance-Based Clustering: A Review

“…DCT is also used to extract the main information of a static model in a history matching area [27][28][29][30][31][32][33][34][35]. After original data are transformed to coefficients of discrete cosine functions, the coefficients are arranged in descending order of frequencies of cosine functions.…”

“…The selection of a subset of DCT coefficients depends on the objective of the research. For example, to characterize channel reservoirs, several papers applied DCT to permeability data to extract only the main channel trends in the ensemble models with low frequencies' coefficients [27][28][29][30][31][32]34,35]. The channel trends in reservoirs can be described with only a small number of coefficients.…”

Integration of an Iterative Update of Sparse Geologic Dictionaries with ES-MDA for History Matching of Channelized Reservoirs

“…The coefficients are sorted in descending order from the top left, capturing the overall trend of channel patterns, to bottom right, delineating details in channel patterns. Previous studies have shown that non-Gaussian channel patterns can be reproduced sufficiently via inverse transform of essential DCT coefficients [18,28,35]. Updating the truncated DCT coefficients can yield a calibrated model set.…”

Ensemble-Based Data Assimilation in Reservoir Characterization: A Review

“…The empirical cumulative distribution function (CDF) of model parameter was transformed into the corresponding quantile in CDF of standard normal distribution. This approach is useful, because any distribution could be converted to a standard normal distribution, which satisfies the Gaussian assumption in ensemble-based methods [33,34]. DCT is a method of representing audio or image information as a sum of cosine functions of different frequencies.…”

“…A lot of equiprobable models could make this matter worse, by increasing computing time. Some works calibrated the grid properties, e.g., grid permeability, facies ratio, or mean value of permeability allocated to each facies [33,34]. However, it was hard to directly modify parameters for geostatistics from dynamic data, due to high nonlinearity.…”