Stochastic simulation of deltas based on a concurrent multi-stage VAE-GAN model

Abstract

The stochastic simulation of deltas has always been one of the significant problems in the numerical simulation of reservoirs. Three problems of deltaic simulations are non-stationary geological characteristics in training images (TIs), insufficient quantity of TIs in certain regions and unavailable reuse of training parameters and models even after the first training, which have caused big challenges for the stochastic simulation of deltas especially in the circumstances of only heterogeneous TIs are available and the simulation quantity is quite large. As one of the important numerical methods for the simulation of deltas, multiple-point statistics (MPS) obtains the statistical characteristics through the patterns in TIs to perform simulation. However, due to the non-stationarity of deltaic TIs, the traditional MPS cannot extract the non-stationary characteristics of TIs smoothly and is incapable of reusing the extracted probability information, making the simulation process quite time-consuming if multiple simulations are performed successively. Thanks to the powerful feature extraction capability brought by deep learning, the delta simulation possibly will be largely improved. The generative adversarial network (GAN) is an important deep learning method for image generation, but it needs large-quantity training samples and its training process is unstable, but another famous neural network variational auto-encoder (VAE) is more stable. On the other hand, VAE-generated images are often a little blurred but GAN-generated images are clearer. Therefore, based on VAE, GAN and a multi-stage idea, a concurrent multi-stage VAE-GAN model is proposed for the stochastic simulation of deltas to hopefully address the three problems in deltaic simulation by concurrently performing multi-stage simulation based on GAN and VAE. The comparison of our method with some typical MPS methods and deep learning methods has shown its good performance in deltaic simulation.