Characterization of Channelized Reservoir Using Ensemble Kalman Filter with Clustered Covariance

Abstract

Ensemble Kalman filter (EnKF) has the limitation of applications for multipoint geostatistics because it assumes Gaussian random field. It also uses all ensembles to get covariance matrix, even though they have different permeability field each other, resulting in filter divergence. The proposed method suggests the concept of clustered covariance by grouping initial ensembles using a distance-based method. Hausdorff distance is used for calculating similarity between permeability fields and they are separated by kmeans clustering. When EnKF is applied to a 2D channel field, it shows overshooting problem and mismatches the true production data. The proposed method gives better history matching and future performance prediction without overshooting problems. Furthermore, it shows stable results for sensitivity analyses over the number of total ensembles. The more accurate covariance is calculated by clustering, the better results are obtained.

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

“…It is highly correlated with future production because it is an important parameter that affects flow rate in Darcy's law. Facies for each grid also have been applied for the criterion in many previous researches [8][9][10][11]. Facies can substantially affect the reservoir responses because parameters for a reservoir simulation, such as the relative permeability function and saturation function, are assigned according to the facies.…”

“…For this reason, some researchers applied other distance calculation methods for effective pattern recognition. One of these methods is the Hausdorff distance, which measures the distance between two datasets and enables many-to-many correspondence [3,[8][9][10][11][12]. Given the two point sets A and B, the Hausdorff distance calculates the distance H(A, B) using Equations (1) and (2).…”

“…If more than three datasets exist, an exact solution in 2D space does not exist but we numerically approximate the position. Since MDS is a simple but very powerful algorithm to manage the data, many studies used MDS to reduce the data dimension [2][3][4][6][7][8][9]14,15,18,20,21,26,[36][37][38][39][40][43][44][45]51,53]. MDS can maintain the distance information while reducing the dimension in a lower space.…”

“…Each cluster has a centroid, and the algorithm minimizes the defined distance between centroids and data points. A mathematics expression of the algorithm can be presented by Equation (8).…”

Characterization of three-dimensional channel reservoirs using ensemble Kalman filter assisted by principal component analysis

“…Arroyo-Negrete et al (2008) utilized streamlines and Jeong et al (2010) added a gradual deformation method to EnKF so that they calculated Kalman gain with better reliability. Lee et al (2013) used clustering analysis and they made several clusters by considering permeability distributions. In each cluster, the reservoir models are updated using different Kalman gains.…”