Recent developments combining ensemble smoother and deep generative networks for facies history matching
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ORIGINAL PAPER
Recent developments combining ensemble smoother and deep generative networks for facies history matching ´ Potratz1 · Alexandre A. Emerick2 Smith W. A. Canchumuni1 · Jose D. B. Castro1 · Julia
´ C. Pacheco1 · Marco Aurelio
Received: 8 May 2020 / Accepted: 22 October 2020 © Springer Nature Switzerland AG 2020
Abstract 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 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 on two aspects: firstly, we benchmark nine different formulations, including VAE, generative adversarial network (GAN), Wasserstein GAN (WGAN), WGAN with gradient penalty, WGAN with spectral normalization, 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. Keywords Deep learning · Data assimilation · Facies models · Ensemble smoother
Alexandre A. Emerick
1 Introduction
[email protected] Smith W. A. Canchumuni [email protected] Jose D. B. Castro [email protected] J´ulia Potratz [email protected] Marco Aur´elio C. Pacheco [email protected] 1
Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil
2
Petrobras Research and Development Center (CENPES), Av. Hor´acio de Macedo 950, Cidade Universit´aria, Rio de Janeiro, RJ, 21941-915, Brazil
Ensemble smoother with multiple data assimilation (ESMDA) [21] has been used as a robust history-matching technique due to its ability to condition multiple realizations of reservoir models with a balanced computational cost. However, similarly to other ensemble-based methods, ESMDA relies on Gaussian assumptions which degrades its performance when the prior geology is described in terms of complex facies distributions. In these cases, the posterior models do not present the expected geological f
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