Mitigating loss of variance in ensemble data assimilation: machine learning-based and distance-free localizations for better covariance estimation

We propose two new methods based/inspired by machine learning for tabular data and distance-free localization to enhance the covariance estimations in an ensemble data assimilation. The main goal is to enhance the data assimilation results by mitigating loss of variance due to sampling errors. We also analyze the suitability of several machine learning models and the balance between accuracy and computational cost of the covariance estimations. We introduce two distance-free localization techniques leveraging machine learning methods specifically tailored for tabular data. The methods are integrated into the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) framework. The results show that the proposed localizations improve covariance accuracy and enhance data assimilation and uncertainty quantification results. We observe reduced variance loss for the input variables using the proposed methods. Furthermore, we compare several machine learning models, assessing their suitability for the problem in terms of computational cost, and quality of the covariance estimation and data match. The influence of ensemble size is also investigated, providing insights into balancing accuracy and computational efficiency. Our findings demonstrate that certain machine learning models are more suitable for this problem. This study introduces two novel methods that mitigate variance loss for model parameters in ensemble-based data assimilation, offering practical solutions that are easy to implement and do not require any additional numerical simulation or hyperparameter tuning.

Recent Developments Combining Ensemble Smoother and Deep Generative Networks for Facies History Matching

Ensemble smoothers are among the most successful and efficient techniques currently available for history matching. However, because these methods rely on Gaussian assumptions, their performance is severely degraded when the prior geology is described in terms of complex facies distributions. Inspired by the impressive results obtained by deep generative networks in areas such as image and video generation, we started an investigation focused on the use of autoencoders networks to construct a continuous parameterization for facies models. In our previous publication, we combined a convolutional variational autoencoder (VAE) with the ensemble smoother with multiple data assimilation (ES-MDA) for history matching production data in models generated with multiple-point geostatistics. Despite the good results reported in our previous publication, a major limitation of the designed parameterization is the fact that it does not allow applying distance-based localization during the ensemble smoother update, which limits its application in large-scale problems. The present work is a continuation of this research project focusing in two aspects: firstly, we benchmark seven different formulations, including VAE, generative adversarial network (GAN), Wasserstein GAN, variational auto-encoding GAN, principal component analysis (PCA) with cycle GAN, PCA with transfer style network and VAE with style loss. These formulations are tested in a synthetic history matching problem with channelized facies. Secondly, we propose two strategies to allow the use of distance-based localization with the deep learning parameterizations.

Towards a Robust Parameterization for Conditioning Facies Models Using Deep Variational Autoencoders and Ensemble Smoother

The literature about history matching is vast and despite the impressive number of methods proposed and the significant progresses reported in the last decade, conditioning reservoir models to dynamic data is still a challenging task. Ensemble-based methods are among the most successful and efficient techniques currently available for history matching. These methods are usually able to achieve reasonable data matches, especially if an iterative formulation is employed. However, they sometimes fail to preserve the geological realism of the model, which is particularly evident in reservoir with complex facies distributions. This occurs mainly because of the Gaussian assumptions inherent in these methods. This fact has encouraged an intense research activity to develop parameterizations for facies history matching. Despite the large number of publications, the development of robust parameterizations for facies remains an open problem. Deep learning techniques have been delivering impressive results in a number of different areas and the first applications in data assimilation in geoscience have started to appear in literature. The present paper reports the current results of our investigations on the use of deep neural networks towards the construction of a continuous parameterization of facies which can be used for data assimilation with ensemble methods. Specifically, we use a convolutional variational autoencoder and the ensemble smoother with multiple data assimilation. We tested the parameterization in three synthetic history-matching problems with channelized facies. We focus on this type of facies because they are among the most challenging to preserve after the assimilation of data. The parameterization showed promising results outperforming previous methods and generating well-defined channelized facies.