Mathematical modeling and artificial intelligence methods for oil filtration processes in multilayer porous media: An analytical review

Аннотация

Oil filtration in porous media is a complex multiphase and nonstationary process that plays an important role in petroleum production, reservoir engineering, and environmental protection. Accurate prediction of filtration behavior requires advanced mathematical models capable of describing fluid transport, phase interactions, and heterogeneity of porous structures. Classical approaches based on Darcy’s law, transport equations, multiphase flow models, and computational fluid dynamics (CFD) provide reliable physical descriptions; however, their application is limited by computational complexity and dependence on empirical parameters. This review analyzes modern mathematical and computational approaches for modeling oil filtration in multilayer porous media, including continuum-scale models, pore-scale simulations, digital rock physics, and numerical methods such as finite difference, finite element, and CFD approaches. Particular attention is given to artificial intelligence methods, including machine learning, deep learning, and physics-informed neural networks (PINNs), applied for permeability prediction, pressure field estimation, filtration performance analysis, and process optimization. The analysis shows that hybrid physics–AI approaches provide promising opportunities to overcome the limitations of traditional models by combining physical laws with data-driven learning. Such frameworks can improve prediction accuracy, reduce computational costs, and support the development of intelligent models for nonstationary oil filtration processes in heterogeneous multilayer porous media.