Recursive update of channel information for reliable history matching of channel reservoirs using EnKF with DCT

Abstract

Ensemble Kalman filter (EnKF) is one of the promising reservoir characterization schemes for history matching. It has been widely researched due to its excellence in recursive data processing and dependable uncertainty quantification. However, EnKF has critical limitations for applying to non-Gaussian distribution fields such as channel reservoirs.In this study, we propose a novel scheme to characterize channel reservoirs reliably. The scheme, recursive update of channel information (RUCI), updates key channel information such as facies ratio and permeabilities of each rock facies as components of the state vector. Since permeabilities assimilated by EnKF follow a Gaussian distribution, EnKF itself is not adequate to preserve channel structure. To overcome this limitation, we use cumulative distribution function mapping to maintain its bimodal distribution. In addition to RUCI, discrete cosine transform (DCT) is utilized to preserve clear channel continuities by figuring out essential channel trend.The proposed method, RUCI in EnKF with DCT, is applied to three different channel reservoir cases and is compared with typical three methods: EnKF, EnKF with DCT, and EnKF with normal score transform (NST). Both of conventional EnKF and EnKF with DCT show overshooting and fail to present channel details. Furthermore, their permeability distributions have a tendency to follow a Gaussian, not a typical bimodal distribution of sand and shale. Even if EnKF with NST maintains a bimodal distribution after updates, it cannot figure out overall channel trend. The proposed method not only prevents overshooting but also preserves a bimodal distribution of permeability. It can clearly characterize true channel trend even though initial reservoir models are poorly made. In addition, it gives better estimation of future oil and water productions than the other 3 methods by reducing uncertainties and matching true performances.