Stochastic simulation of fan deltas using parallel multi-stage generative adversarial networks

Abstract

The stochastic simulation of fan deltas has always been one of the significant problems in the numerical simulation of reservoirs. As one of the important numerical simulation methods of fan deltas, multiple-point statistics (MPS) obtains the statistical characteristics through the patterns in the training image (TI) to perform simulation. However, due to the non-stationarity of the TI of fan deltas, the traditional MPS cannot extract the non-stationary characteristics of the TI smoothly. Besides, traditional MPS mainly relies on CPU-based simulation, and the extracted probability information cannot be reused during simulation since the information only stored in memory instead of files on the storage medium, 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 fan delta simulation possibly will be largely improved. The generative adversarial network (GAN) is an important deep learning method for image generation, but it suffers from the lengthy simulation time and needs large-quantity training samples. Some variants of GAN, such as the single-image GAN (SinGAN), were proposed to reduce the amount of training data when realizing GAN. Based on SinGAN, a stochastic simulation method of fan deltas using parallel multi-stage GAN is proposed in this paper, through which the structural characteristics of fan deltas are learned from a single image of TI, and the stochastic simulation process can be parallelized for acceleration without lowering the simulation quality.