Rapid updating of stochastic models using an ensemble filter approach

Ensemble Kalman filtering (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 the measured values as they become available. However, the ensemble Kalman filter updating scheme restricts the method to multivariate Gaussian random fields. Therefore, it is challenging to implement the filtering scheme for non-Gaussian random fields such as reservoirs where there is a strong contrast in permeability between different geological facies. In this paper, we develop a methodology to combine multidimensional scaling and the ensemble Kalman filter for rapidly updating models for a channelized reservoir. A dissimilarity matrix is computed using the dynamic responses of ensemble members. This dissimilarity matrix is transformed to a lower dimensional space using multidimensional scaling. The responses mapped in the lower dimension space are clustered and based on distances between the models in a cluster and the actual observed response, the closest models to the observed response are retrieved. Updating of models within the closest cluster are performed using EnKF equations. The results of the update are used to re-sample new models for the next step. A two dimensional water flooding example of a channelized reservoir is set up to demonstrate the applicability of the proposed method. The obtained results demonstrate that the proposed algorithm is viable for sequentially updating reservoir models and for preserving the channel features after the data assimilation process.