Parameterization method of reservoir properties for ensemble-based data assimilation using intermediate latent space of StyleGAN

Ensemble smoothers are 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 (non-Gaussian). In this way, for these methods, we need to apply efficient parameterization techniques. Currently, the most efficient methods for performing parameterization are deep learning models. However, given the variety of existing deep learning models, studies have not identified which is most suitable for use with ensemble-based methods, although some important models had already been evaluated. Based on a recent literature review, the most promising models selected were VAE-GAN, Latent Diffusion, and StyleGAN models. As a novel aspect of this work, data assimilation with the second generation of StyleGAN (StyleGAN2) model was performed using the latent z-space and intermediate w-space, separately. They were applied in two 2D case studies: one categorical (three facies) and the other continuous. The results demonstrated that all three models are highly efficient, with the StyleGAN2 model standing out for generating samples with geological realism and achieving excellent data matching in the cases studied. Our findings show that performing data assimilation with StyleGAN2 using the intermediate space (w-space) yielded better results than the traditional application in the latent space (z-space). This is due to the fact that ESMDA uses linear updates and the w-space is much more linear and disentangled than the highly entangled z-space, thereby ensuring that the updated vectors remain close to realistic geological patterns. These results were validated using main geostatistical and history matching metrics.