Enhancing the parameterization of reservoir properties for data assimilation using deep VAE-GAN

Currently, the methods called Iterative Ensemble Smoothers, especially the method called Ensemble Smoother with Multiple Data Assimilation (ESMDA) can be considered state-of-the-art for history matching in petroleum reservoir simulation. However, this approach has two important limitations: the use of an ensemble with finite size to represent the distributions and the Gaussian assumption in parameter and data uncertainties. This latter is particularly important because many reservoir properties have non-Gaussian distributions. Parameterization involves mapping non-Gaussian parameters to a Gaussian field before the update and then mapping them back to the original domain to forward the ensemble through the reservoir simulator. A promising approach to perform parameterization is through deep learning models. Recent studies have shown that Generative Adversarial Networks (GAN) performed poorly concerning data assimilation, but generated more geologically plausible realizations of the reservoir, while the Variational Autoencoder (VAE) performed better than the GAN in data assimilation, but generated less geologically realistic models. This work is innovative in combining the strengths of both to implement a deep learning model called Variational Autoencoder Generative Adversarial Network (VAE-GAN) integrated with ESMDA. The methodology was applied in two case studies, one case being categorical and the other with continuous values of permeability. Our findings demonstrate that by applying the VAE-GAN model we can obtain high quality reservoir descriptions (just like GANs) and a good history matching on the production curves (just like VAEs) simultaneously. • The VAE-GAN model can generate higher-quality geologically realistic realizations than VAE and better data match than GANs. • The hybrid model can transform a non-Gaussian distribution to a Gaussian one spending less computational time. • Successfully applied in categorical and continuous cases. • Integration between VAE-GAN and ESMDA to map a non-Gaussian parameter (permeability) into a Gaussian distribution. • Training time can be reduced depending on the case and parameters used, showing feasibility for larger 3D cases.