Channelized reservoir estimation using a low-dimensional parameterization based on high-order singular value decomposition

Prior to the estimation process of channelized reservoirs, in the context of any Assisted History Matching method, the parameterization of facies field is a necessary task. The parameterization of the facies field consists of defining a numerical field (parameter field) on the reservoir domain so that, using a projection function, we are able to recover the facies field from the values of parameter field. One of the most important issues encountered is the loss of the multipoint geostatistical properties in the updates (channel continuity). In this study, we start from an initial (global) parameterization of the channelized field and infer from it a low-dimensional parameterization obtained after a high-order singular value decomposition of a tensor built with the parameter fields. We decompose the parameter field as a linear combination of some basis functions with coefficients. The decomposition is followed by a truncation so that we keep the relevant information from the channel continuity perspective, but with a small number of coefficients. The coefficients will represent the low-dimensional parameterization and are further introduced in the estimation process of facies field, using the Ensemble Smoother with Multiple Data Assimilations (ES-MDA). For a fair assessment of the parameterization, we perform a comparison of the results with those obtained by applying the traditional truncated singular value decomposition and the global parameterization. In addition, we compare the parameterization with a low-dimensional parameterization defined with the PCA decomposition. The comparison is done from the perspective of multipoint geostatistical characteristics of the updates and predictions. We show that the new parameterization is able to better keep the multipoint geostatistical structure in the updates than the other parameterizations, while the prediction capabilities are the same.