History matching geological facies models based on ensemble smoother and deep generative models

The current research trend in history matching is to consider more realistic reservoir models with complex geology. Hence, it is important to be able to update facies models during the solution. Although Kalman filter-based methods have been applied with success in several real-life history-matching problems, their performance is severely degraded when the prior geology is described in terms of complex facies distributions, since these methods rely on Gaussian assumptions. This paper investigates a novel parameterization based on deep learning techniques for proper history matching of facies models with methods based on the Kalman filter. The proposed method consists on a parameterization of geological facies by means of a deep generative model, with a deep belief network used as an autoencoder. To perform the history matching, we use the ensemble smoother with multiple data assimilation (ES-MDA) that iteratively updates the model to account the observed production data. The proposed method is compared to the standard ES-MDA and ES-MDA combined with optimization-based principal component analysis (OPCA). The results showed clear improvements over the standard ES-MDA in terms of preserving channelized features in the realizations and a performance comparable to the parameterization with OPCA.