Efficient integration of production and seismic data into reservoir models exhibiting complex connectivity using an iterative ensemble smoother

Ensemble-based algorithms have been successfully implemented for history matching of geological models. However, their performance is optimal only 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. Moreover, the number of degrees of freedom is as large as the ensemble size, so the assimilation of large amounts of production or seismic data might lead to the ensemble collapse which results in inaccurate predictions of future performance. In this paper, we introduce a methodology that combines model classification with multidimensional scaling (MDS) and the ensemble smoother algorithm to efficiently history match fluvial and channelized reservoir models. The dynamic responses (production and seismic data) of the different ensemble members are used to compute a dissimilarity matrix. This dissimilarity matrix is then transformed into a lower-dimensional space by the use of MDS. Then, model classification is performed based on the distances between the mapped responses in the lower dimensional space and the actual observed response. In the proposed method. the transformed lower-dimensional data are used instead of original observations in the update equation to update the cluster of ensemble members that are closest to the observed response. In this manner, a limited number of ensemble members are enough to assimilate large amount of observed data without triggering the ensemble collapse problem. The updated subset of models (cluster) are used to infer a probability map and/or new hard conditioning data to re-sample new conditional members for the next iteration or next data-assimilation step. The proposed algorithm is tested by assimilating production and time-lapse seismic data into channelized reservoir models. The presented computational results show significant improvements in terms of preserving channelized features and in terms of reliability of predictions compared to the standard implementation of ensemble-based algorithms.