PHYSICS-INFORMED NEURAL NETWORKS FOR PREDICTING PRESSURE DISTRIBUTION IN POROUS MEDIA

Abstract

In recent years, the integration of modern information technologies has become pervasive across various industries, and the oil sector is no exception. The utilization of high-performance computing technologies, artificial intelligence algorithms, and advanced methods for data collection, processing, and storage has been instrumental in addressing challenges related to enhancing oil recovery. While deep learning has demonstrated significant advancements in diverse applications, its application to solving partial differential equations has recently gained prominence. A noteworthy strategy entails substituting conventional numerical techniques with neural networks that approximate solutions to partial differential equations. Physics-informed neural networks (PINNs) represent a significant development in this domain by incorporating partial differential equations directly within the loss function of neural network through automatic differentiation. This study presents a numerical algorithm and a PINNs to solve the one-dimensional equation describing the distribution of water and oil pressure within the context of the Buckley-Leverett mathematical model. The obtained results include the numerical solution and predictions derived from the PINN neural network to solve the pressure distribution. The insights gained from the comparative analysis underscore the promising role of PINNs as a robust and competitive tool for addressing intricate problems within the realm of complex fluid dynamics.