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

Prior to any estimation process of channelized reservoirs, in the context of an Assisted History Matching method, the parameterization of facies fields is a necessary task. The parameterization of channelized reservoirs consists of defining a numerical field (parameter field) so that a projection function recovers the facies field from the parameter field. Mostly, the dimension of parameter field is equal to the dimension of reservoir domain. The issue of dimensionality is becoming relevant when the history matching method is applied, especially due to the tremendous number of parameters involved in the estimation process of the channelized reservoirs. In addition, one of the most important issue encountered is the loss of the multi-point geostatistical properties in the updates (channel continuity). In this study, we start from an initial parameterization of the channelized fields 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 show how the facies fields are fully characterized by a linear combination of a small number of coefficients with "basis functions". The decomposition is followed by a truncation so that we keep the relevant information from the channel continuity perspective. This new parameterization is further introduced in the estimation process of facies fields, using the ensemble smoother with multiple data assimilation (ES-MDA), updating the coefficients of decomposition. For a fair assessment of the parameterization, we perform a comparison of the results with those obtained by applying the traditional singular value decomposition and the original parameterization. The comparison is done from the perspective of multipoint geostatistical characteristics of the updates and predictions (oil and water rates). We show that the new parameterization is able to better keep the multipoint geostatistical structure in the updates than the other two parameterizations, while the prediction capabilities are the same.