Efficient Surrogate Modeling Based on Improved Vision Transformer Neural Network for History Matching

Abstract

Summary For history-matching problems, simulations of reservoir models usually involve high computational costs. Surrogate modeling based on deep learning has proved to be an efficient method to accelerate simulation and decrease computational costs. In this paper, we design a deep-learning-based surrogate model, improved from the vision transformer neural network (ViT-NN), for solving history matching problems. The proposed surrogate model named improved vision transformer neural network (IViT-NN) has three main fundamental parts, which are feature extraction (FE), flattened linear projection (FLP), and multistep dimension-reduction (MSDR). Specifically, realizations of permeability field of the reservoirs can be entered into the IViT-NN surrogate model to obtain the corresponding production data quickly. Case studies are performed to investigate the performance and generalization of this surrogate model. The results indicate that the proposed surrogate model based on IViT-NN can be used for obtaining production data accurately and efficiently. Further, the trained surrogate model is used for history matching as well as production forecasting without using additional reservoir simulations, as compared with the method using full reservoir simulations. The posterior results of the estimated permeability field or corresponding productions obtained by reservoir simulation and the surrogate model are approximate, which demonstrates that the IViT-NN surrogate model is applicable for history matching.