Rapid Updating of Stochastic Models by Use of an Ensemble-Filter Approach

Applying an ensemble Kalman filter (EnKF) is an effective method for reservoir history matching. The underlying principle is that an initial ensemble of stochastic models can be progressively updated to reflect measured values as they become available. The EnKF performance is only optimal, however, if the prior-state vector is linearly related to the predicted data and if the joint distribution of the prior-state vector is multivariate Gaussian. Therefore, it is challenging to implement the filtering scheme for non-Gaussian random fields, such as channelized reservoirs, in which the continuity of permeability extremes is well-preserved. In this paper, we develop a methodology by combining model classification with multidimensional scaling (MDS) and the EnKF to create rapidly updating models of a channelized reservoir. A dissimilarity matrix is computed by use of the dynamic responses of ensemble members. This dissimilarity matrix is transformed into a lower-dimensional space by use of MDS. Responses mapped in the lower-dimension space are clustered, and on the basis of the distances between the models in a cluster and the actual observed response, the closest models to the observed response are retrieved. Model updates within the closest cluster are performed with EnKF equations. The results of an update are used to resample new models for the next step. Two-dimensional, waterflooding examples of channelized reservoirs are provided to demonstrate the applicability of the proposed method. The obtained results demonstrate that the proposed algorithm is viable both for sequentially updating reservoir models and for preserving channel features after the data-assimilation process.