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

TL;DR

Ensemble-based history matching often fails for non-Gaussian facies. This work combines deep generative networks (VAEs, GANs, WGANs, alpha-GANs, Cycle-GANs, and style-transfer variants) with ES-MDA to parameterize facies in a latent space and perform hydraulic data assimilation on synthetic channelized models. It benchmarks seven formulations and introduces two localization strategies to enable distance-based updates, demonstrating improved data fits and preserved geological plausibility, with VAE-Local and PCA-Cycle-GAN-Local showing robust performance in larger problems. The study highlights training cost and 3D extension as key future challenges, and provides open-source code for reproducibility and further development.

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 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.

Figures (26)

• Figure 1: Schematic of a generative model
• Figure 2: Schematic architecture of a variational autoencoder network
• Figure 3: Schematic architecture of a generative adversarial network
• Figure 4: Schematic architecture of an $\alpha$-GAN
• Figure 5: Schematic architecture of a Cycle-GAN